{"1": {"fulltext": "", "height": "4308", "width": "2500", "jp2-path": "introductionto00olm_0001.jp2"}, "2": {"fulltext": "T yT\\\\", "height": "4303", "width": "2577", "jp2-path": "introductionto00olm_0002.jp2"}, "3": {"fulltext": "", "height": "4303", "width": "2577", "jp2-path": "introductionto00olm_0003.jp2"}, "4": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0004.jp2"}, "5": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0005.jp2"}, "6": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0006.jp2"}, "7": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0007.jp2"}, "8": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0008.jp2"}, "9": {"fulltext": "//o", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0009.jp2"}, "10": {"fulltext": "Mv\\nT uiir/asni\\n1. IeLsscopic view cf\u00c2\u00a3 the \u00c2\u00b1uU Moon. 3.TeLescopic ram of Saium .v tas rings.\\nLo do of a. ^p art of the Hooii tlp;it quadrature 4. do r,f Jimitrr v ins Minnie.", "height": "4225", "width": "2498", "jp2-path": "introductionto00olm_0010.jp2"}, "11": {"fulltext": "A2\u00c2\u00bb*\\nINTRODUCTION\\nASTRONOMY\\nDESIGNED AS A\\nTEXT BOOK\\nSTUDENTS OF YALE COLLEGE\\nEE VISED EDITION,\\nWITLT NUMEROUS ALTERATIONS AND ADDITIONS, INCLUDING THE LATEST\\nDISCOVERIES.\\nBY DEKOT OUISTP, LL.D.\\nPROFESSOR OF NATURAL PHILOSOPBT AND ASTRONOMY,\\nNEW YORK:\\nROBERT B.COLLINS, 254 PEARL-STREET.\\n1854.", "height": "3995", "width": "2482", "jp2-path": "introductionto00olm_0011.jp2"}, "12": {"fulltext": "$3 4$\\nEntered, according to Act of Congress, in the year 1854,\\nBy Denison Olmsted,\\nIn the Clerk s Office of the District Court of Connecticut.\\nStereotyped by\\nRICHARD C. VALENTINE,\\n17 Dutch-st., cor. of Fulton.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0012.jp2"}, "13": {"fulltext": "REVISED EDITION\\nThe great progress of astronomical discovery, during the last few years, has\\ninduced the author of this work to prepare, with much labor and expense, a\\nnew edition, which should fully exhibit the features of the science in their\\nlatest physiognomy. Since the stereotype edition was first published, in\\n1844, numerous and important discoveries have been made, both in the solar\\nsystem and among the fixed stars. The dimensions of the planetary system\\nhave been nearly doubled by the addition of the planet Neptune the number\\nof the Asteroids has been increased from four to twenty-seven; interesting\\ndiscoveries have been made in the Rings of Saturn, and an eighth member has\\nbeen added to his retinue of satellites and the subject of Comets has received\\na new impulse by the appearance of the remarkable comet of 1848.\\nMeanwhile, the introduction into practical astronomy of Telescopes greatly\\nexceeding in light and power those previously directed to the heavens, has dis-\\nclosed new wonders among the fixed stars, and especially among the Nebulao\\na problem, which had eluded the eager pursuit of astronomers, that of find-\\ning the distances of the fixed stars, has been solved stellar astronomy has\\nbeen greatly enriched by the observations of Sir John Herschel in the southern\\nhemisphere our knowledge of the proper motions of the stars has been en-\\nlarged, and crowned with several most interesting results some progress has\\nbeen made towards determining the magnitudes of the stars, the nature of\\ntheir orbits, the velocities of their motions, and the periods of their revolu-\\ntions and recent investigations inspire the hope, that the mechanism of the\\nuniverse will shortly be understood as perfectly as is that of the solar system.\\nBesides a notice of these important results, there will also be found, in the\\npresent edition, a concise statement of the phenomena and causes of Meteoric\\nShowers. a topic which, for peculiar reasons, the author has forborne to in-\\ntroduce into the text of previous editions, but it is now inserted in conformity\\nwith the example of Sir John Herschel, Humboldt, and other distinguished\\nwriters of astronomical works, who have not scrupled to assign to the period-\\nical meteors a distinct place in the solar system. The Numerical Relations of\\nthe sun and planets a subject which has heretofore appeared only in the\\nAddenda is now incorporated with the text and, illustrated as it is by a\\nvariety of curious and interesting problems, it will lead the pupil to form just\\nand accurate ideas of those relations, and of the laws that govern them.\\nThe part of astronomy which relates to the Earth, the Sun, and the Moon,\\nhas undergone, of late, but few changes but that which relates to the Planets\\nand Fixed Stars has been enriched by so many new discoveries, that it has\\nbeen necessary to re-write it, and to cast it anew. With these improvements,\\nit is believed the present work will be found to be as well suited to initiate\\nthe student of astronomy into the mysteries of this noble science, and to in-\\nspire a taste for its pursuits, as can reasonably be expected of any work com-\\nprised within such narrow limits.\\nYale College, January, 1854.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0013.jp2"}, "14": {"fulltext": "PREFACE.\\nNeably all who have written Treatises on Astronomy, designed for young\\nlearners, appear to have erred in one of two ways they have either disre-\\ngarded demonstrative evidence, and relied on mere popular illustration, or they\\nhave exhibited the elements of the science in naked mathematical formulae.\\nThe former are usually diffuse and superficial the latter, technical and ab-\\nstruse.\\nIn the following Treatise, we have endeavored to unite the advantages of\\nboth methods. We have sought, first, to establish the great principles of\\nastronomy on a mathematical basis and, secondly, to render the study inter-\\nesting and intelligible to the learner, by easy and familiar illustrations. We\\nwould not encourage any one to believe that he can enjoy a full view of the\\ngrand edifice of astronomy, while its noble foundations are hidden from his\\nsight; nor would we assure him that he can contemplate the structure in its\\ntrue magnificence, while its basement alone is within his field of vision. We\\nwould, therefore, that the student of astronomy should confine his attention\\nneither to the exterior of the building, nor to the mere analytic investigation\\nof its structure. We would desire that he should not only study it in models\\nand diagrams, and mathematical formula?, but should at the same time acquire\\na love of nature herself, and cultivate the habit of raising his views to the\\ngrand originals. Nor is the effort to form a clear conception of the motions and\\ndimensions of the heavenly bodies, less favorable to the improvement of the\\nintellectual powers, than the study of pure geometry.\\nBut it is evidently possible to follow out all the intricacies of an analytical\\nprocess, and to arrive at a full conviction of the great truths of astronomy, and\\nyet know very little of nature. According to our experience, however, but few\\nstudents in the course of a liberal education will feel satisfied with this. They\\ndo not need so much to be convinced that the assertions of astronomers are\\ntrue, as 1hey desire to know what the truths are, and how they were ascer-\\ntained and they will derive from the study of astronomy little of that moral\\nand intellectual elevation which they had anticipated, unless they learn to look\\nupon the heavens with new views, and a clear comprehension of their won-\\nderful mechanism.\\nMuch of the difficulty that usually attends the early progress of the astro-\\nnomical student, arises from his being too soon introduced to the most perplex-\\ning part of the whole subject, the planetary motions. In this work, the con-\\nsideration of these is for the most part postponed until the learner has become\\nfamiliar with the artificial circles of the sphere, and conversant with the celes-\\ntial bodies. We then first take the most simple view possible of the planetary\\nmotions by contemplating them as they really are in nature,, and afterwards\\nproceed to the more difficult inquiry, why they appear as they do. Probably\\nno science derives such signal advantage from a happy arrangement, as as-\\ntronomy an order, which brings out every fact or doctrine of the science just\\nin the place where the mind of the learner is prepared to receive it.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0014.jp2"}, "15": {"fulltext": "ANALYSIS.\\nDESIGNED AS A BASIS FOR REVIEW AND EXAMINATION.\\nPRELIMINARY OBSERVATIONS.\\nAstronomy defined,\\nDescriptive Astronomy,\\nPhysical do. 1\\nPractical do. 1\\nHistory. Ancient nations who cultiva-\\nted astronomy,\\nPythagoras his age and country,\\nHis views of the celestial motions, 1\\nAlexandrian School when founded\\nby whom introduction of astronomi-\\ncal instruments, 2\\nHipparchus his character, 2\\nPtolemy the Almagest, 2\\nCopernicus, Tycho Brahe, Kepler and\\nGalileo respective labors of each,....\\nSir Isaac Newton his great discovery.\\nLa Place Mecanique Celeste, 2\\nAstrology Natural and Judicial ob-\\nject of each, 2\\nAccuracy aimed at by astronomers, 3\\nCopernican System its leading doc-\\ntrines, 3\\nPlan of this work, 3\\nPart I.\u00e2\u0080\u0094 OF THE EARTH.\\nChapter 1. of the figure and dimensions\\nOF THE EARTH, AND THE DOCTRINE OF THE\\nSPHERE.\\nFigure of the earth, 4\\nProofs, 4\\nDip of the horizon, 4\\nHow found, 5\\nTable of the dip its use, 6\\nExact figure of the earth, 6\\nIts circumference, 6\\nSmall inequalities of the earth s surface, 6\\nDiameter of the earth how determined, 7\\nHow to divest the mind of preconceived\\nerroneous notions, 8\\nDoctrine of the Sphere, defined, 9\\nGreat and small circles defined, 9\\nAxis of a circle pole, 9\\nSituation of the poles of two great cir-\\ncles which cut each other at right an-\\ngles, 9\\nPoints of intersection of two great cir-\\ncles how many degrees apart, 10\\nPage.\\nPage. When a great circle passes through the\\npole of another, how does it cut it 10\\nSecondary defined, 10\\nAngle made by two great circles how\\nmeasured, 10\\nTerrestrial and Celestial spheres distin-\\nguished, 10\\nHorizon defined, 1\\nSensible horizon, 1\\nRational do 1\\nZenith and Nadir, 1\\nVertical circles, 1\\nMeridian, 1\\nPrime Vertical, 1\\nHow the place of a celestial body is de-\\ntermined, 11\\nAltitude azimuth amplitude, 12\\nZenith Distance how measured, 12\\nAxis of the earth axis of the celestial\\nsphere, 12\\nPoles of the earth poles of the heav-\\nens, 12\\nEquator terrestrial and celestial, 12\\nHour circles, 13\\nLatitude, 13\\nPolar Distance, how related to latitude, 13\\nLongitude, 13\\nStandard Meridians, 13\\nEcliptic, 13\\nInclination of the ecliptic to the equa-\\ntor, 13\\nEquinoctial points, 13\\nEquinoxes Vernal and autumnal, 13\\nSolstitial points, 14\\nSolstices, 14\\nSigns of the ecliptic enumerated, 14\\nColures Equinoctial and Solstitial,... 14\\nRight ascension, 15\\nDeclination, 15\\nCelestial Longitude, 15\\nCelestial Latitude, 15\\nNorth Polar Distances, how related tc\\nlatitude, 15\\nParallels of Latitude, 15\\nTropics, 16\\nPolar circles, 16\\nZones, 16\\nZodiac, 16", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0015.jp2"}, "16": {"fulltext": "VI\\nANALYSIS.\\nPage.\\nElevation of the pole to what is it\\nequal? 16\\nElevation of the equator, 16\\nDistance of a place from the pole, to\\nwhat equal 16\\nChapter II. diurnal revolution arti-\\nficial GLOBES ASTRONOMICAL PROBLEMS.\\nCircles of Diurnal Revolution, 17\\nSidereal day defined, 17\\nAppearance of the circles of diurnal\\nrevolution at the equator, 17\\nA Right Sphere defined, 18\\nA Parallel Sphere, 19\\nAn Oblique Sphere, 19\\nCircle of Perpetual Apparition, 20\\nCircle of Perpetual Occupation, 20\\nHow are the circles of daily motion cut\\nby the horizon in the different\\nspheres? 20\\nExplanation of the peculiar appearan-\\nces of each sphere, from the revolu-\\ntion of the earth on its axis, 21\\nArtificial Globes terrestrial and celes-\\ntial, 22\\nTheir use, 23\\nMeridian how represented how gra-\\nduated, 23\\nHorizon how represented how gra-\\nduated, 23\\nHour Circles, how represented, 23\\nHour Index described, 23\\nQuadrant of Altitude, 24\\nIts use described, 24\\nTo rectify the globe for anyplace, 24\\nProblems on the terrestrial Globe\\nTo find. t)\\\\e latitude and longitude\\nof a place, 24\\nTo find a -place, its latitude and longi-\\ngitude being given, 25\\nTo find the bearing and distance of\\ntwo places, 25\\nTo determine the difference of time of\\ntwo places, 25\\nThe hour being given at any place, to\\ntell what hour it is in any other part\\nof the world, 25\\nTo find the antosci, periceci, and antipo-\\ndes, 25\\nTo rectify the globe for the sun s place, 26\\nThe latitude of the place being given,\\nto find the time of the sun s rising\\nand setting,\\nProblems on the celestial Globe.\\nTo find the right ascension and decli-\\nnation, 26\\nTo represent the appearance of the\\nheavens at any time,\\nTo find the altitude and azimuth of a\\nstar,\\nPage\\nTo find the angular distance of two\\nstars from each other, 27\\nTo find the su/i s meridian altitude,\\nthe latitude and day of the month\\nbeing given,. 28\\nChapter III. Parallax Refraction\\nTwilight.\\nParallax defined, 23\\nHorizontal Parallax, 29\\nRelation of parallax to the zenith dis-\\ntance, and distance from the center\\nof the earth, 29\\nTo find the horizontal parallax from\\nthe parallax at any altitude, 29\\nAmount of parallax in the zenith and\\nin the horizon, 30\\nEffect of parallax upon the altitude of\\na body, 30\\nMode of determining the horizontal\\nparallax of a body,.. 30\\nAmount of the sun s hor. par 31\\nUse ofy parallax, 31\\nRefraction. Its effect upon the alti-\\ntude of a body, 32\\nIts nature illustrated, 32\\nIts amount at different angles of eleva-\\ntion, 32\\nHow the amount is ascertained, 33\\nSources of inaccuracy in estimating the\\nrefraction 35\\nEffect of refraction upon the sun and\\nmoon when near thehoi*izon, 35\\nOval figure of these bodies explained,. 35\\nApparent enlargement of the sun and\\nmoon near the horizon, 36\\nTwilight. Its cause explained, 37\\nLength of twilight in different latitudes, 37\\nHow the atmosphere contributes to dif-\\nfuse the sun s light, 37\\nChapter IV.\u00e2\u0080\u0094 Time.\\nTime defined, 38\\nWhat period is a sidereal day, 38\\nUniformity of sidereal days, 38\\nSolar time, how reckoned, 39\\nWhv solar days are longer than side-\\nreal, 39\\nApparent time defined, 39\\nMean time, 40\\nAn astronomical day, 40\\nEquation of time defined, 40\\nWhen do apparent time and mean\\ntime differ most? 40\\nWhen do they come together? 40\\nEffect of a change in the place of the\\nearth s perihelion, 40\\nCauses of the inequality of the solar\\ndays, 41\\nExplain the first cause, depending on\\nthe unequal velocities of the sun,... 4l", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0016.jp2"}, "17": {"fulltext": "ANALYSIS.\\nVll\\nPage\\nExplain the second cause, depending\\non the obliquity of the ecliptic, 42\\nWhen does the sidereal day com-\\nmence 44\\nThe Calendar. Astronomical year de-\\nfined, 45\\nHow the most ancient nations deter.\\nmined the number of days in the year, 45\\nJulius Caesar s reformation of the calen.\\ndar explained, 45\\nErrors of this calendar, 45\\nReformation by Pope Gregory......... 46\\nRule for the Gregorian calendar, 46\\nNew style, when adopted in England, 46\\nWhat nations still adhere to the old\\nstyle? 46\\nWhat number of days is now allowed\\nbetween old and new style 47\\nHow the common year begins and ends, 47\\nHow leap year begins and ends, 47\\nDoes the confusion of different calen-\\ndars affect astronomical observations 47\\nChapter V. Astronomical Instruments\\nand Problems Figure and Density of\\nthe earth.\\nHow the most ancient nations acquired\\ntheir knowledge of Astronomy, 48\\nUse of instruments in the Alexandrian\\nSchool, 48\\nDitto, by Tycho Brahe, 48\\nDitto, by the Astronomers Royal, 48\\nSpace occupied by 1 on the limb of an\\ninstrument, 48\\nExtent of actual divisions on the limb, 49\\nVernier, defined, 49\\nIts use illustrated, 49\\nChief astronomical instruments enu-\\nmerated, 50\\nObservations taken on the meridian.. 50\\nReasons of this, 50\\nTransit Instrument defined, 51\\nDitto described, 51\\nMethod of placing it in the meridian. 51\\nLine of collimation defined, 52\\nSystem of wires in the focus, 52\\nIts use for arcs of right ascension, 52\\nAstronomical Clock, how regulated, 52\\nWhat does it show 52\\nHow to test its accuracy, 53\\nHow corrected, 53\\nMural Circle, its object, 54\\nDescribe it, 54\\nHow the different parts contribute to\\nthe object, 54\\nMural Quadrant, 55\\nUse of the Mural Circle for arcs of de-\\nclination, 56\\nAltitude and Azimuth Instrument de-\\nfined, 56\\nPage.\\nIts use, 56\\nDescribe it, 57\\nSextant described, 58\\nHow to measure the angular distance\\nof the moon from the sun, 59\\nHow to take the altitude of a heavenly\\nbody 59\\nUse of the artificial horizon, 59\\nIn what consists the peculiar value of\\ntheSextant? 60\\nAstronomical Problems. Given the\\nthe sun s right ascension and decli-\\nnation, to find his longitude and the\\nobliquity of the ecliptic, 61\\nNapier s Rule of circular parts, 62\\nGiven the sun s declination to find his\\nrising and setting at any place whose\\nlatitude is known, 63\\nGiven the latitude of a place and the\\ndeclination of a heavenly body, to\\ndetermine its altitude and azimuth\\nwhen on the six o clock hour circle, 64\\nThe latitudes and longitudes of two\\ncelestial objects being given, to find\\ntheir distance apart, 6b\\nFigure and Density of the Earth\\nreason for ascertaining it with great\\nprecision, 66\\nHow found from the centrifugal force, 66\\nFrom measuring an arc of the meridian, 67\\nFrom observations with the pendulum, 68\\nFrom the motions of -the moon, 68\\nDensity of the earth compared with\\nwater, 68\\nHow ascertained by Dr. Maskelyne, 69\\nWhy an important element, 69\\nPart II.\u00e2\u0080\u0094 OF THE SOLAR SYSTEM\\nChapter 1. The Sun Solar Spots Zo\\n1 diacal Light.\\nFigureof the sun, 70\\nAngle subtended by a line of 400 miles, 70\\nDistance from the earth, 70\\nIllustrated by motion on a railway car, 70\\nApparent diameter of the sun how\\nfound, 72\\nHow to find the linear diameter, 71\\nHow much larger is the sun than the\\nearth, 71\\nIts density and mass compared with\\nthe earth s, 71\\nWeight at the surface of the sun, 72\\nVelocity of falling bodies at the sun 72\\nSolar Spots. Their number, 72\\nSize...... 72\\nDescription, 72\\nWhat region of the sun do they oc-\\ncupy, 73\\nProof that they are on the sun, 73", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0017.jp2"}, "18": {"fulltext": "V1U\\nANALYSIS.\\nPage.\\nHow we learn the revolution of the sun\\non his axis, 73\\nTime of the revolution, 73\\nApparent paths of the spots, 74\\nInclination of the solar axis, 74\\nSun s Nodes when does the sun pass\\nthem? 75\\nCause of the solar spots, 76\\nFaculae, 76\\nZodiacal Light. Where seen, 76\\nIts form, 76\\nAspects at different seasons, 76\\nIts motions, 77\\nIts nature, 77\\nChapter II. Apparent Annual Motion\\nof the Sun Seasons Figure of the\\nEarth s Orbit.\\nApparent motion of the sun, 78\\nHow both the sun and earth are said to\\nmove from west to east, 79\\nNature and position of the sun s orbit,\\nhow determined, 79\\nChanges in declination how found, 79\\nDitto, in right ascension, 80\\nInferences from a table of the sun s de-\\nclinations,... 80\\nDitto, of right ascensions, 81\\nPath of the sun, how proved to be a\\ngreat circle, 81\\nObliquity of the ecliptic, how found, 81\\nHow it varies, 81\\nGreat dimensions of the earth s orbit, 81\\nEarth s daily motion in miles, 82\\nDitto,hourly ditto, 82\\nDiurnal motion at the equator per\\nhour, 82\\nSeasons. Causes of the change of sea-\\nsons, 82\\nHow each cause operates,. 82\\nIllustrated by a diagram, 83\\nChange of seasons had the equator been\\nperpendicular to the ecliptic, 84\\nFigure of the Earth s Orbit. Proof\\nthat the earth s orbit is not circular, 85\\nRadius vector defined, 85\\nFigure of the earth s orbit how ob-\\ntained, 86\\nRelative distances of the earth from the\\nsun, how found, 86\\nPerihelion and Aphelion denned, 87\\nVariations in the sun s apparent diame-\\nter, 87\\nAngular velocities of the sun at the pe-\\nrihelion and aphelion, 87\\nRatio of these velocities to the dis-\\ntances, 87\\nHow to calculate the relative distances\\nof the earth from the sun s daily mo-\\ntions,\\nPago\\nProduct of the angle described in any\\ngiven time by the square of the dis-\\ntance, 88\\nSpace described by the radius vector of\\nthe solar orbit in equal times, 83\\nHow to represent the sun s orbit by a\\ndiagram, 89\\nChapter III. Universal Gravitation.\\nUniversal Gravitation defined, 90\\nWhy is it called attraction, 90\\nHistory of its discovery, 90\\nHow was the gravitation of the moon\\nto the earth first inferred 91\\nLaws of Gravitation. If a body re-\\nvolves about an immovable center\\nof force, and is constantly attracted\\nto it, how will itmove 92\\nIf a body describes a curve around a\\ncenter towards which it tends by any\\nforce, how is its angular velocity re-\\nlated to the distance, 93\\nIn the same curve, the velocity at any\\npoint of the curve varies as what 93\\nIf equal areas be described about a cen-\\nter in equal times, to what must the\\nforce tend? 94\\nHow is the distance of any planet from\\nthe sun at any point in its orbit, to\\nits distance from the superior focus 94\\nCase of two bodies gravitating to the\\nsame center where one descends in a\\nstraight line, and the other revolves\\nin a curve, 95\\nVelocity of a body at any point when\\nfalling directly to the sun, 97\\nRelation between the distances and pe-\\nriodic times, 99\\nKepler s three great laws, 99\\nMotion in an Elliptical Orbit, 100\\nIdea of a projectile force, 100\\nNature of the impulse originally given\\nto the earth, 100\\nTwo forces under which a body re-\\nvolves, 100\\nIllustrated by the motion of a cannon\\nball, 101\\nWhy a planet returns to the sun, 102\\nIllustration by a suspended ball, 103\\nChapter IV. Precession of the Equi-\\nnoxes Nutation Aberration Mean\\nand True Places of the sun.\\nPrecession of the Equinoxes defined, 104\\nWhy so called, 104\\nAmount of Precession annually, 104\\nRevolution of the equinoxes, 104\\nRevolution of the pole of the equator\\naround the pole of the ecliptic, 105", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0018.jp2"}, "19": {"fulltext": "ANALYSIS.\\nIX\\nPage.\\nChanges among the stars caused by\\nprecession, 105\\nThe present pole star not always such, 105\\nWhat will be the pole star 13,000\\nyears hence 105\\nCause of the precession of the equi-\\nnoxes, 105\\nExplain how the cause operates, 106\\nProportionate effect of the sun and\\nmoon in producing precession, 107\\nTropical year defined, 107\\nHow much shorter than the sidereal\\nyear, 107\\nUse of the precession of the equinoxes\\nin chronology, 107\\nNotation, defined, 108\\nExplain its operation, 108\\nCause of Nutation, 108\\nAberration, defined,.. 108\\nIllustrated by a diagram, 109\\nAmount of aberration, 109\\nEffect on the places of the stars, 109\\nMotion of the Apsides, the fact sta-\\nted, 109\\nDirection of this motion, 110\\nTime of revolution of the line of Ap-\\nsides, 110\\nPresent longitude of the perihelion,. 110\\nWhen was it nothing? 110\\nMean and True Places of the Sun, 1 11\\nMean Motion defined, Ill\\nIllustrated by surveying a field, Ill\\nMean and true longitude distinguish-\\ned, Ill\\nEquations defined, Ill\\nTheir object, Ill\\nMean and True anomaly defined,.... 112\\nEquation of the Center, 112\\nExplain from the figure, 112\\nChapter V. The Moon Lunar Geogra-\\nphy Phases of the Moon Her Revo-\\nlutions.\\nDistance of the moon from the earth, 113\\nHer mean horizontal parallax, 113\\nHer diameter, 113\\nVolume, density, and mass, 113\\nShines by reflected light, 113\\nAppearance in the telescope, 113\\nTerminator defined, 113\\nIts appearance, 113\\nProofs of Valleys, 114\\nForm of these, 114\\nBest time for observing the lunar\\nmountains and valleys, 114\\nNames of places on the moon double, 115\\nDusky regions how named, 115\\nPoint out remarkable places on the\\nmap of the moon, 115\\nExplain the method of estimating the\\nheight of lunar mountains, 115\\nPage.\\nSpecify the heights of particular\\nmountains, 117\\nVolcanoes, proof of their existence, 117\\nHas the moon an atmosphere? 117\\nImprobability of identifying artificial\\nstructures in the moon, 117\\nPhases of the Moon, their cause,.... 118\\nSuccessive appearances of the moon\\nfrom one new moon to another, 118\\nSyzygies defined, 118\\nExplain the phases of the moon from\\nfigure 46, 119\\nRevolutions of the moon. Period\\nof her revolutions about the earth, 119\\nHer apparent orbit a great circle, 120\\nA sidereal month defined, 120\\nA synodical do. 120\\nLength of each, 120\\nWhy the synodical is longer, 120\\nHow each is obtained, 120\\nInclination of the lunar orbit, 121\\nNodes defined, 121\\nWhy the moon sometimes runs high\\nand sometimes low, 121\\nHarvest moon defined, 122\\nDitto explained, 122\\nExplain why the moon is nearer to us\\nwhen on the meridian than when\\nnear the horizon, 122\\nTime of the moon s revolution on its\\naxis, 123\\nHow known, 123\\nLibrations explained, 123\\nDiurnal Libration, 124\\nLength of the Lunar days, 124\\nEarth never seen on the opposite side\\nof the moon, 124\\nAppearances of the earth to a specta-\\ntoron the moon, 124\\nWhy the earth would appear to re-\\nmain fixed, 125\\nAscending and descending nodes dis-\\ntinguished, 125\\nWhether the earth carries the moon\\naround the sun, 126\\nHow much more is the moon attract-\\ned towards the sun than towards\\nthe earth, 126\\nWhen does the sun act as a disturbing\\nforce upon the moon 126\\nWhy does not the moon abandon the\\nearth at the conjunction? 126\\nThe moon s orbit concave towards the\\n127\\nHow the elliptical motion of the moon\\nabout the earth is to be conceived\\nof, 127\\nIllustrations, 127\\nChapter VI. Lunar Irregularities.\\nSpecify their general cause, 127", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0019.jp2"}, "20": {"fulltext": "ANALYSIS.\\nPage.\\nUnequal action of the sun upon the\\nearth andmoon, 128\\nOblique action of earth and sun, 128\\nGravity of the moon towards the\\nearth at the syzygies, 129\\nGravity at the quadratures, 129\\nExplain the disturbances in the\\nmoon s motions from figure 48, 130\\nFigure of the moon s orbit, 132\\nHow its figure is ascertained, 132\\nMoon s greatest and least apparent di-\\name ters, 132\\nHer greatest and least distances from 132\\nthe earth, 132\\nPerigee and Apogee defined, 132\\nEccentricities of the solar and lunar\\norbits compared, 133\\nMoon s nodes, their change of place,. 133\\nRate of this change per annum, 133\\nPeriod of their revolution, 133\\nIrregular curve described by the\\nmoon, 133\\nCause of the retrograde motion of\\nnodes, 133\\nExplain from figure 50, 134\\nSynodical revolution of the node de-\\nfined, 135\\nIts period, 135\\nThe Saros explained, 1 35\\nThe Metonic Cycle, 135\\nGolden Number, 136\\nRevolution of the line of apsides, 136\\nIts period, 136\\nHow the places of the perigee may be\\nfound, 136\\nMoon s anomaly denned, 136\\nCause of the revolution of the apsides, 136\\nAmount of the equation of the Center, 137\\nEvection denned, 137\\nIts cause explained, 138\\nVariation defined,.. 140\\nIts cause, 140\\nAnnual Equation explained, 140\\nHow these irregularities were first\\ndiscovered, 141\\nHow many equations are applied to\\nthe moon s motions 141\\nMethod of proceeding in finding the\\nmoon s place, 141\\nSuccessive degrees of accuracy at-\\ntained, 141\\nPeriodic and secular irregularities dis-\\ntinguished, 141\\nAcceleration of the moon s mean mo-\\ntion explained, 141\\nIts consequences, 142\\nLunar inequalities of latitude and\\nparallax, 142\\nChapter VII. Eclipses.\\nEclipse of the moon, when it happens, 143\\nPage.\\nEclipse of the sun, when it happens, 143\\nWhen only can each occur, 143\\nWhy an eclipse does not occur at\\nevery new and full moon 144\\nWhy eclipses happen at two opposite\\nmonths, 144\\nCircumstances which affect the length\\nof the earth s shadow, 144\\nSemi-angle of the cone of the earth s\\nshadow, to what equal,...: 145\\nLength of the earth s shadow, 145\\nIts breadth where it eclipses the\\nmoon, 146\\nLunar ecliptic limit defined, 146\\nSolar, ditto 146\\nAmount of the lunar ecliptic limit,.... 146\\nAppulse defined, 147\\nPartial, total, central, eclipse, each\\ndefined, 147\\nPenumbra defined, 147\\nSemi-angle of the moon s penumbra,\\nto what equal, 148\\nSemi-angle of a section of the penum-\\nbra where the moon crosses it, 148\\nMoon s horizontal parallax increased\\neV 148\\nWhy the moon is visible in a total\\neclipse, 148\\nCalculation of eclipses, general mode\\nof proceeding, 149\\nTo find the exact time of the begin-\\nning, end, duration, and magnitude\\nof a lunar eclipse, by figures 53, 54, 150\\nElements of an eclipse defined, 151\\nDigits defined, 153\\nHow the shadow of the moon travels\\nover the earth in a solar eclipse,.... 153\\nWhy the calculation of a solar eclipse\\nis more complicated than a lunar,. 154\\nVelocity of the moon s shadow, 154\\nDifferent ways in which the shadow\\ntraverses the earth, according as\\nthe conjunction is near the node or\\nnear the limit, 155\\nWhen do the greatest eclipses hap-\\npen\\n15^\\nCase in which the moon s shadow\\nnearly reaches the earth,\\nHow far may the shadow reach be-\\nyond the center of the earth\\nGreatest diameter of the moon s sha-\\ndow where it traverses the earth,..\\nGreatest portion of the earth s surface\\never covered by the moon s penum-\\nbra,\\nMoon s apparent diameter compared\\nwith the sun s,\\nAnnular eclipse, its cause,\\nDirection in which the eclipse passes\\non the sun s disk, 159\\n156\\n157\\n157\\n157\\n158\\n158", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0020.jp2"}, "21": {"fulltext": "ANALYSIS.\\nXI\\nPace.\\n159\\nGreatest duration of total darkness,...\\nEclipses of the sun more frequent\\nthan of the moon, why\\nLunar eclipses oftener visible, why\\nRadiation of light in a total eclipse of\\nthe sun,\\nInteresting phenomena of a total\\neclipse of the sun,\\nPhenomena of the eclipse of 1806, de-\\nscribed, 160\\nWhen does ihe next total eclipse of\\nthe sun. visible in the United\\n159\\n159\\n160\\n160\\nStates, occur\\n161\\n161\\n162\\nChapter VIII. Longitude. Tides.\\nObjects of the ancients in studying\\nastronomy, 161\\nDitto of the moderns, 161\\nLongitude. How to find the differ-\\nence of longitude between two\\nplaces,\\nMethod bv the Chronometer explain-\\ned,\\nHow to set the chronometer to Green-\\nwich time, 162\\nAccuracy of some chronometers, 162\\nObjections to them, 162\\nLongitude, by eclipses explained, 163\\nLunar method of finding the longi-\\ntude, 163\\nCircumstances which render this\\nmethod somewhat, difficult, 164\\nDisadvantages of this method, 164\\nDegree of accuracy attainable, 165\\nTides. defined, 165\\nHigh, Low. Spring, Neap, Flood, and\\nEbb Tide, severally defined, 165\\nSimilar tides on opposite sides of the\\nearth, 165\\nInterval between two successive high\\ntides, 165\\nAverage height for the whole globe, 166\\nExtreme height, 166\\nCause of the tides, 166\\nExplain by figure 56, 166\\nTide-wave defined, 167\\nComparative effects of the sun and\\nmoon in raising the tide, 167\\nWhy the moon raises a higher tide\\nthan the sun,\\nSpring tides accounted for,\\nNeap tides, ditto\\nPower of the sun or moon to raise\\nthe tide, in what ratio to its dis-\\ntance,\\nInfluence of the declinations of the\\nsun and moon on the tides, 169\\nExplain from figures 57 and 58, 169\\nMotion of the tide-wave not progres-\\nsive, 170\\nT:des of rivers, narrow bays, how\\nproduced, 170\\nPage\\nCotidal Lines defined, 170\\nDerivative and Primitive tides distin-\\nguished, 170\\nVelocity of the tide-wave, circum-\\nstances which affect it, 171\\nExplain by figure 59, 171\\nExamples of very high tides, 172\\nUnit of altitude defined, 172\\nUnit of altitude for different places, 172\\nTides on the coast of N. America,\\nwhence derived, 173\\nWhy no tides in lakes and seas, 173\\nIntricacy of the problem of the tides, 173\\nAtmospheric tide, 173\\n16\\n168\\n168\\n168\\nChapter IX. The Planets Inferior\\nPlanets Mercury and Venus.\\nSignification of the term planet 174\\nPlanets known from antiquity 174\\nPlanets added in 1781 and in 1846 174\\nAsteroids, their number and names 174\\nPrimary and Secondary Planets dis-\\ntinguished 174\\nNumber of each 175\\nInclination of the planetary orbits\\nto the ecliptic 175\\nInferior and Superior Planets dis-\\ntinguished 175\\nHow the planets differ among them-\\nselves 175\\nDistances from the sun in miles 175\\nGreat dimensions of the planetary\\nsystem 176\\nIllustrated by the motion of a rail-\\nway car 176\\nOrder by which the distances of the\\nplanets increase 176\\nBode s law of distances 177\\nMean distances, bow determined... 177\\nDiameters in miles 177\\nGreat diversity in respect to mag-\\nnitude 178\\nHow the real diameters are found\\nfrom the apparent 178\\nPeriodic Times in months aud years 17S\\nWhich of the planets move rapidly\\nand which slowly 179\\nInferior Planets. Proximity to\\nthe sun 179\\nIllustration by Fig. 60 ISO\\nConjunction defined inferior and\\nsuperior ISO\\nSy nodical revolution defined ISO\\nHow to find the synodical from the\\nsidereal 1S1\\nMotion of an inferior planet, when\\ndirect and when retrograde 181\\nHow these motions are affected by\\nthe earth s motions 182\\nWhen the inferior planets are sta-\\ntionary 182", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0021.jp2"}, "22": {"fulltext": "ANALYSIS.\\nElongation of the stationary points\\nfor Mercury and Venus 183\\nPhases of the inferior planets 183\\nRelative distances from the sun 183\\nEccentricity of their orbits 1 84\\nMost favorable time for determining\\nthe sidereal period 184\\nWhen is an inferior planet bright-\\nest 185\\nDiurnal revolutions of Mercury and\\nVenus 185\\nVenus as the morning and evening\\nstar 185\\nPhenomena every eight years 186\\nTransits of the Inferior Planets\\ndefined 186\\nWhen they occur why not at ev-\\nery inferior conjunction 186\\nWhy those of Mercury in May and\\nNovember 186\\nWhy those of Venus in June and\\nDecember 186\\nIntervals between the transits of\\nMercury 187\\nIntervals between the transits of\\nVenus 187\\nHow found 188\\nWhy so great an interest is attached\\nto the transits of Venus 188\\nWhy the sun s horizontal parallax\\ncannot be found like the moon s 189\\nWhy distant places of observation\\nare taken 189\\nProcess for the sun s hor. par. ex-\\nplained from Fig. 63 189\\nCircumstances favorable to the ac-\\ncuracy of the result 190\\nSun s hor. par. in seconds 191\\nTo find the hor. par. of Venus and\\nof Mars 191\\nAtmosphere of Venus 191\\nSatellites of Mercury and of Venus 191\\nChapter X. Superior Planets Aster-\\noids Motions of the Planets.\\nSuperior Planets, how distinguished\\nfrom the Inferior 192\\nMars size distance from the sun 192\\nChanges in apparent magnitude and\\nbrightness 193\\nPhases of Mars, Fig. 64 193\\nTelescopic appearances 194\\nSatellite ellipticity 194\\nTo find the hor. par. of Mars 194\\nJupiter magnitude figure diur-\\nnal revolution 195\\nInclination of the axis to the orbit,\\nand change of seasons 195\\nTelescopic appearances 195\\nBelts described and explained 196\\nSatellites how seen names 197\\nPage.\\nMagnitudes distances periods 198\\nOrbits form inclination 198\\nEclipses their various phenomena,\\nFig. 65 198\\nShadows cast by the satellites on\\nthe Primary 200\\nLongitudes from the eclipses of Ju-\\npiter s satellites 201\\nVelocity of light, how discovered.. 202\\nSaturn size ring telescopic\\nview 202\\nRing described 203\\nDimensions of the system 203\\nPosition of the axis of rotation 2 04\\nRapid diurnal revolution 204\\nRevolution of the ring around the\\nsun 204\\nIts changes and disappearances ex-\\nplained 205\\nRevolution of the ring in its own\\nplane, how discovered 205\\nThickness of the ring new ring 208\\nSatellites of Saturn number and\\nnames 209\\nEclipses 209\\nUranus its discovery 210\\nSize periodic time inclination 210\\nSatellites number peculiarities.. 210\\nNeptune distance diameter\\nperiod 211\\nHistory of its discovery 211\\nAgreement of observation with\\ntheory 212\\nSimultaneous discovery 213\\nResults obtained by Walker 214\\nAsteroids history of the first four 215\\nDistance from the sun size orbits 216\\nWhole number 216\\nPlanetary Motions two methods\\nof studying them 216\\nAppearances viewed from the sun 217\\nMotions of Mercury explained 217\\nThree things to be regarded in the\\nplanetary orbits 219\\nWhy diagrams and orreries repre-\\nsent them erroneously 219\\nApparent motions of the planets... 220\\nTwo causes make them unlike the\\nreal 220\\nApparent motions illustrated by\\nFig. 69 221\\nApparent motions of the Superior\\nPlanets 222\\nIllustrated by Fig. 70 222\\nChapter XL Determination of the\\nPlanetary Orbits Kepler s Discov-\\neries Elements of the Orbits of the\\nPlanets Masses.\\nFigure of the planetary orbits an-\\ncient ideas 224", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0022.jp2"}, "23": {"fulltext": "ANALYSIS.\\nPage.\\nNotions of Ptolemy and Hipparcbus 224\\nKepler Investigation of the mo-\\ntions of Mars 225\\nDiscovery of the first law the\\nsecond the third 225\\nModification of the third law 227\\nElements of the Planetary Orb-\\nits enumerated 227\\nWhy not found like the lunar and\\nsolar orbits 227\\nFirst steps of the process for finding\\nthe elements 22S\\nTo convert geocentric longitudes\\nand latitudes into heliocentric,\\nFig. 71 228\\nTo determine the position of the\\nnodes 229\\nTo determine the inclination 230\\nTo find the periodic time 230\\nThe position of a planet which is\\nmost favorable for finding the\\nelements 231\\nExemplified in finding the period-\\nic time of Saturn 231\\nTo determine the distance from the\\nsun 232\\nHow the mean distance is found 232\\nHow the distance at any point in\\nthe orbit 232\\nMethod for the Inferior Planets 232\\nMethod for the Superior, Fig. 73 232\\nTo determine the place of the peri-\\nhelion 233\\nTo determine the epoch of pausing\\nthe perihelion 235\\nTo find the eccentricity 235\\nQuantity of Matter in the Sun\\nand Planets 236\\nHow found in terms of the distances\\nand periodic times 236\\nHow found by the spaces fallen\\nthrough. Fig. 75 237\\nHow found in planets which have\\nno satellites 238\\nDensities, how found 238\\nSpecific gravities of the sun and\\nplanets respectively 239\\nComparative densities 239\\nChapter XII. Perturbations of the\\nPlanets Stability of the System\\nNumerical Plelations Problems.\\nPerturbations Numerous causes 240\\nCase where the only bodies are a\\ncentral and a revolving body 240\\nHow these irregularities have been\\ndiscovered 241\\nPeriodical and secular perturba-\\ntions distinguished 241\\nExample Changes of eccentricity\\nof the earth s orbit 242\\nPage.\\nWhether the perturbations accumu-\\nlate indefinitely 242\\nStability of the system how main-\\ntained 242\\nNature of the evidence to prove\\nthe stability 243\\nInvariability of the grand axes 243\\nLimits to the variation of the ec-\\ncentricity 243\\nAlso to that of the inclination 244\\nWhat kind of perturbations are cu-\\nmulative and what are oscilla-\\ntory 244\\nConditions essential to this stabil-\\nity 244\\nLong inequality of Jupiter and\\nSaturn 244\\nAlso of the earth and Ven us 245\\nNumerical Relations of the Plan-\\netary System 245\\nChange of velocity necessary on in-\\ncreasing the mass 245\\nAlso on increasing the distance 245\\nMembers of the solar system, how\\nadjusted 246\\nRelatiou between the rate of mo-\\ntion, distance, periodic time, and\\nforce of gravity 246\\nDemonstration of the rules. 246\\nThe rules stated 247\\nGiven, the rate of motion, to find\\nthe other terms 247\\nGiven, the distance 247\\nGiven, the periodic time 247\\nGiven, the force of gravitation 248\\nRequired, the rate of motion, dis-\\ntance, period, and force of gravi-\\ntation respectively 248\\nProblems 249\\nChapter XIII. Comets Meteoric\\nShowers.\\nComets their several parts 252\\nNumber belonging to the System.. 253\\nThe six most remarkable 253\\nVariations in magnitude and bright-\\nness 254\\nTo what owing 255\\nPeriods of revolution 255\\nDistances from the sun 256\\nFigure of the orbit of Halley s com-\\net 256\\nSource of the light 256\\nDirection of the trains 257\\nQuantity of matter in comets 257\\nHow the orbit of a comet may be\\nchanged 258\\nExample in the comet of 1770 258\\nOrbits and Motions of Comets 260\\nHow they differ from those of plan-\\nets 260", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0023.jp2"}, "24": {"fulltext": "XIV\\nANALYSIS.\\nPage.\\nElements enumerated 260\\nTheir investigation, why difficult... 260\\nHow the return of a comet is pre-\\ndicted 262\\nExemplified in Halley s comet 263\\nIts return in 1759 and 1835 264\\nWhy an astronomical event of great\\ninterest 264\\nEncke s comet its period 265\\nQuestion of a resisting medium 265\\nComet of 1843 its remarkable pe-\\nculiarities 266\\nPhysical nature of comets 267\\nPossibility of their striking the\\nearth 268\\nMeteoric Showers great shower\\nof Nov. 1833 270\\nPoint of apparent radiation 270\\nExtent and duration 270\\nPeriods of its recurrence 271\\nWhy an astronomical or cosmical\\nphenomenon 271\\nOf the periods of meteoric showers 271\\nConclusions respecting the meteors,\\nas to their origin, nature, veloci-\\nty, size, light, and heat 271\\nReasons for these conclusions 272\\nPart III.\u00e2\u0080\u0094 OF THE FIXED STARS\\nAND SYSTEM OF THE WORLD.\\nChapter I. Fixed Stars Constella-\\ntions.\\nWhy called fixed stars 274\\nClassification 274\\nNumber in each class 274\\nAntiquity of the constellations 275\\nTheir names how individual stars\\nare denoted 275\\nCatalogues of the stars 275\\nNumber in the catalogue of Hip-\\nparchus 276\\nNumber in Lalande s 276\\nUtility of learning the constella-\\ntions 276\\nConstellations of the Zodiac Aries,\\nTaurus 277\\nSeven stars in Pleiades 278\\nGemini, Cancer 278\\nPrassepe, or the Bee-hive 279\\nLeo, Virgo, Libra 279\\nScorpio, Sagittarius, Capricornus,\\nAquarius, Pisces 280\\nNorthern Constellations 281\\nUrsa Minor, Ursa Major 281\\nDraco 282\\nCepheus, Cassiopeia, Camelopard,\\nAndromeda 283\\nPerseus, Auriga, Leo Minor, Canes\\nVenatici, Coma Berenices, Bootes, 284\\nPage.\\nCorona Borealis, Hercules, Lyra,\\nCygnus 285\\nVulpecula, Aquila, Antinous, Del-\\nphinus, Pegasus, Ophiuchus 286\\nSouthern Constellations 286\\nOrion, Lepus, Canis Major 287\\nCanis Minor, Menoceros, Hydra 288\\nLesson for the middle of September 288\\nLesson for the middle of December. 289\\nLesson for the middle of March 290\\nLesson for the middle of June 290\\nChapter II. Double Stars Temporary\\nStars Variable Stars Clusters\\nand Nebulas.\\nUse of great telescopes in studying\\nthe stars 291\\nHerschel s 40-feet telescope 291\\nRosse telescope 292\\nPulkova and Cambridge telescopes 292\\nDouble Stars denned 293\\nBy whom discovered 293\\nExamples number 293\\nWhen merely optically double 294\\nWhen physically double 294\\nSystem of double, triple, and mul-\\ntiple stars 294\\nColors of the components 294\\nTemporary Stars defined 294\\nExamples 295\\nVariable Stars defined 295\\nExamples.\\nEvidence of activity among the\\nstars 295\\nClusters examples 296\\nNebdlje defined 297\\nExamples nebulas of Andromeda 297\\nNebula of Hercules 297\\nMagellanic clouds 297\\nNebula of Orion 298\\nUse of great telescopes for these\\nobjects 29S\\nSingular forms of nebulas 298\\nResolvable and irresolvable dis-\\ntinguished 298\\nSigns of beauty and symmetry\\namong the nebulas 299\\nNebulous Stars defined 299\\nAnnular Nebulce defined 299\\nExample in Lyra 299\\nPlanetary Nebulce 299\\nResemblance to planets great ex-\\ntent 299\\nExample in Andromeda 300\\nMilky Way cause of its peculiar\\nlight 300\\nNumber of its component stars 300\\nChapter III. Motions of the Fixed\\nStars Distan ces Nature.\\nBinary Stars defined 301", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0024.jp2"}, "25": {"fulltext": "ANALYSIS.\\nXV\\nPage.\\nNumber of these 801\\nPeriodic times examples 301\\nLaw of gravitation among the stars 302\\nProper Motions of the stars 302\\nResult on comparing the places of\\ncertain stars in ancient and mod-\\nern catalogues 30-3\\nMotion of the solar system in space 303\\nPoint toward which it is moving 304\\nRate of motion per annum 304\\nExamples of great annual proper\\nmotions -305\\nDistances of the Stars how found 305\\nWhat is the base. line for parallax. 306\\nWhy it was supposed impossible to\\ndetermine a parallax of less than\\n1 306\\nDistance implied by a par. of l 306\\nBessel s determination of the par.\\nof 61 Cygni 307\\nHis method of investigation 307\\nDistance measured by the progress\\nof light and by a railway car,\\nrespectively 807\\nActual period of revolution of the\\ncomponents of 61 Cygni 307\\nSpace described by the star annu-\\nally 307\\nReliance to be placed on Bessel s\\ndetermination 308\\nNature of the Stars 308\\nSize of Sirius compared with the 308\\nsun 308\\nProof that the fixed stars are\\nsuns 309\\nEnd for which they were made 809\\nArguments for a plurality of worlds 309\\nChapter IV. System of the World.\\nPage.\\nSystem of the world denned 310\\nComplex character of early sys-\\ntems 310\\nThings known to Pythagoras 310\\nHis visionary notions 311\\nRejection of his system 311\\nCrystalline spheres of Eudoxus 312\\nHow the two motions were ac-\\ncounted for 312\\nHipparchus truths discovered by\\nhim 312\\nAlmagest of Ptolemy 312\\nPtolemaic System explained 313\\nIllustrated by Fig. 81 314\\nDefects of this system 315\\nObjections to it 315\\nTychonic System explained 315\\nObjections to it 316\\nCopernican System explained 316\\nArguments on which it rests 816\\nProofs that the planets revolve\\nabout the sun 317\\nProofs of systems among the stars. 317\\nExemplified in the Pleiades, Nebu-\\nla of Hercules, Binary Stars, and\\nNebulas 318\\nUniformity of plan in natural struc-\\ntures 318\\nAscending orders of systems de-\\nscribed 318\\nSupposed centre of the universe 318\\nCentral sun where placed 319\\nReasons for believing that all the\\nheavenly bodies are united in one\\ngrand system 319", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0025.jp2"}, "26": {"fulltext": "DC/ 3 Diagrams for public recitations.\\nAs many of the figures of this work are too complicated to be\\ndrawn on the black-board at each recitation, we have found it\\nvery convenient to provide a set of permanent cards of paste-\\nboard, on which the diagrams are inscribed on so large a scale, as\\nto be distinctly visible in all parts of the lecture room. The let-\\nters may be either made with a pen, or better procured of the\\nprinter, and pasted on.\\nThe cards are made by the bookbinder, and consist of a thick\\npaper board about 18 by 14 inches, on each side of which a white\\nsheet is pasted, w T ith a neat finish around the edges. A loop at-\\ntached to the top is convenient for hanging the card on a nail.\\nCards of this description, containing diagrams for the whole\\ncourse of mathematical and philosophical recitations, have been\\nprovided in Yale College, and are found a valuable part of our ap-\\nparatus of instruction.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0026.jp2"}, "27": {"fulltext": "INTRODUCTION TO ASTRONOMY.\\nPRELIMINARY OBSERVATIONS.\\n1 Astronomy is that science which treats of the heavenly bodies.\\nMore particularly, its object is to teach what is known respect-\\ning the Sun, Moon, Planets, Comets, and Fixed Stars and also to\\nexplain the methods by which this knowledge is acquired. Astron-\\nomy is sometimes divided into Descriptive, Physical, and Practi-\\ncal. Descriptive Astronomy respects facts Physical Astronomy\\ncauses; Practical Astronomy, the means of investigating the facts,\\nwhether by instruments, or by calculation. It is the province of\\nDescriptive Astronomy to observe, classify, and record, all the\\nphenomena of the heavenly bodies, whether pertaining to those\\nbodies individually, or resulting from their motions and mutual\\nrelations. It is the part of Physical Astronomy to explain the\\ncauses of these phenomena, by investigating and applying the\\ngeneral laws on which they depend especially by tracing out all\\nthe consequences of the law of universal gravitation. Practical\\nAstronomy lends its aid to both the other departments.\\n2. Astronomy is the most ancient of all the sciences. At a\\nperiod of very high antiquity, it was cultivated in Egypt, in Chal-\\ndea, in China, and in India. Such knowledge of the heavenly\\nbodies as could be acquired by close and long continued observa-\\ntion, without the aid of instruments, was diligently amassed and\\ntables of the celestial motions were constructed, which could be\\nused in predicting eclipses, and other astronomical phenomena.\\nAbout 500 years before the Christian era, Pythagoras, of\\nGreece, taught astronomy at the celebrated school at Crotona, and\\nexhibited more correct views of the nature of the celestial mo-\\ntions, than were entertained by any other astronomer of the an-\\ncient world. His views, however, were not generally adopted\\n1", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0027.jp2"}, "28": {"fulltext": "2 PRELIMINARY OBSERVATIONS.\\nbut lay neglected for nearly 2000 years, when they were revived\\nand established by Copernicus and Galileo. The most celebrated\\nastronomical school of antiquity was at Alexandria, in Egypt,\\nwhich was established and sustained by the Ptolemies, (Egyptian\\nprinces,) about 300 years before the Christian era. The employ-\\nment of instruments for measuring angles, and the introduction of\\ntrigonometrical calculations to aid the naked powers of observa-\\ntion, gave to the Alexandrian astronomers great advantages over\\nall their predecessors. The most able astronomer of the Alexan-\\ndrian school was Hipparchus, who was distinguished above all the\\nancients for the accuracy of his astronomical measurements and\\ndeterminations. The knowledge of astronomy possessed by the\\nAlexandrian school, and recorded in the Almagest, or great work\\nof Ptolemy, constituted the chief of what was known of our\\nscience during the middle ages, until the fifteenth and sixteenth\\ncenturies, when the labors of Copernicus of Prussia, Tycho Brake\\nof Denmark, Kepler of Germany, and Galileo of Italy, laid the\\nsolid foundations of modern astronomy. Copernicus expounded\\nthe true theory of the celestial motions Tycho Brahe carried\\nthe use of instruments and the art of astronomical observation to\\na far higher degree of accuracy than had ever been done before\\nKepler discovered the great laws of the planetary motions and\\nGalileo, having first enjoyed the aid of the telescope, made innu-\\nmerable discoveries in the solar system. Near the beginning of\\nthe eighteenth century, Sir Isaac Newton discovered, in the law\\nof universal gravitation, the great principle that governs the ce-\\nlestial motions and recently, La Place has more fully completed\\nwhat Newton began, having followed out all the consequences of\\nthe law of universal gravitation, in his great work, the Mecan-\\nique Celeste.\\n3. Among the ancients, astronomy was studied chiefly as sub-\\nsidiary to astrology. Astrology was the art of divining future\\nevents by the stars. It was of two kinds, natural and judicial.\\nNatural Astrology, aimed at predicting remarkable occurrences in\\nthe natural world, as earthquakes, volcanoes, tempests, and pesti-\\nlential diseases. Judicial Astrology, aimed at foretelling the fates\\nof individuals, or of empires.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0028.jp2"}, "29": {"fulltext": "PRELIMINARY OBSERVATIONS. 3\\n4. Astronomers of every age, have been distinguished for their\\npersevering industry, and their great love of accuracy. They\\nhave uniformly aspired to an exactness in their inquiries, far be-\\nyond what is aimed at in most geographical investigations, satis-\\nfied with nothing short of numerical accuracy, wherever this is\\nattainable and years of toilsome observation, or laborious calcu-\\nlation, have been spent with the hope of attaining a few seconds\\nnearer to the truth. Moreover, a severe but delightful labor is\\nimposed on all who would arrive at a clear and satisfactory knowl-\\nedge of the subject of astronomy. Diagrams, artificial globes,\\norreries, and familiar comparisons and illustrations, proposed by\\nthe author or the instructor, may afford essential aid to the learner,\\nbut nothing can convey to him a perfect comprehension of the\\ncelestial motions, without much diligent study and reflection.\\n5. In expounding the doctrines of astronomy, we do not, as in\\ngeometry, claim that every thing shall be proved as soon as as-\\nserted. We may first put the learner in possession of the leading\\nfacts of the science, and afterwards explain to him the methods\\nby which those facts were discovered, and by which they may\\nbe verified; we may assume the principles of the true system of\\nthe world, and employ those principles in the explanation of manv\\nsubordinate phenomena, while we reserve the discussion of the\\nmerits of the system itself, until the learner is extensively ac-\\nquainted with astronomical facts, and therefore better able to ap-\\npreciate the evidence by which the system is established.\\n6. The Coper nican System is that which is held to be the true\\nsystem of the world. It maintains (1,) That the apparent diur-\\nnal revolution of the heavenly bodies, from east to west, is owing\\nto the real revolution of the earth on its own axis from west to\\neast, in the same time and (2,) That the sun is the center around\\nwhich the earth and planets all revolve from west to east, con-\\ntrary to the opinion that the earth is the center of motion of the\\nsun and planets.\\n7. We shall treat, first, of the Earth in its astronomical rela-\\ntions secondly, of the Solar System and, thirdly, of the Fixed\\nStars.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0029.jp2"}, "30": {"fulltext": "PART I. OF THE EARTH.\\nCHAPTER I.\\nOF THE FIGURE AND DIMENSIONS OF THE EARTH, AND THE DOCTRINE\\nOF THE SPHERE.\\n8. The figure of the earth is nearly globular. This fact is\\nknown, first, by the circular form of its shadow cast upon the\\nmoon in a lunar eclipse secondly, from analogy, each of the\\nother planets being seen to be spherical thirdly, by our seeing\\nthe tops of distant objects while the other parts are invisible, as\\nthe topmast of a ship, while either leaving or approaching the\\nshore, or the lantern of a light-house, which, when first descried\\nat a distance at sea, appears to glimmer upon the very surface of\\nthe water fourthly, by the depression or dip of the horizon when\\nthe spectator is on an eminence and, finally, by actual observa-\\ntions and measurements, made for the express purpose of ascer-\\ntaining the figure of the earth, by means of which astronomers are\\nenabled to compute the distances from\\nthe center of the earth of various places Fl 1#\\non its surface, which distances are found\\nto be nearly equal.\\n9. The Dip of the Horizon, is the ap-\\nparent angular depression of the hori-\\nzon, to a spectator elevated above the\\ngeneral level of the earth. The eye\\nthus situated, takes in more than a ce-\\nlestial hemisphere, the excess being the\\nmeasure of the dip.\\nThus, in Fig. 1, let AO represent the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0030.jp2"}, "31": {"fulltext": "FIGURE AND DIMENSIONS.\\nheight of a mountain, ZO the direction of the plumb line, HOR a\\nline touching the earth at the point O, and at right angles to the\\nplumb line, C the center of the earth, DAE the portion of the\\nearth s surface seen from O; OD, OE, lines drawn from the\\nplace of the spectator to the most distant parts of the horizon,\\nand CD a radius of the earth. The dip of the horizon is the an-\\ngle HOD or ROE. Now the angle made between the direction\\nof the plumb line and that of the extreme line of the horizon or\\nthe surface of the sea, namely, the angle ZOD, can be easily-\\nmeasured and subtracting the right angle ZOH from ZOD, the\\nremainder is the dip of the horizon, from which the length of the\\nline OD may be calculated, (see Art. 10,) the height of the spec-\\ntator, that is, the line OA, being known. This length, to whatever\\npoint of the horizon the line is drawn, is always found to be the\\nsame and hence it is inferred, that the boundary which limits\\nthe view on all sides, is a circle. Moreover, at whatever elevation\\nthe dip of the horizon is taken, in any part of the earth, the\\nspace seen by the spectator is always circular. Hence the. sur-\\nface of the earth is spherical.\\n10. The earth being a sphere, the dip of the horizon HOD=\\nOCD. Therefore, to find the dip of the horizon corresponding\\nto any given height AO (the diameter of the earth being known,)\\nwe have in the triangle OCD, the right angle at D, and the two\\nsides CD, CO, to find the angle OCD. Therefore,\\nCO rad. CD cos. OCD. Learning the dip corresponding\\nto different altitudes, by giving to the line AO different values,\\nwe may arrange the results in a table.\\nThe learner will remark that the line AO, as drawn in the figure, is much larger\\nin proportion to CA than is actually the case, and that the angle HOD is much too\\ngreat for the reality. Such disproportions are very frequent in astronomical diagrams,\\nespecially when some of the parts are exceedingly small compared with others and\\nhence the diagrams employed in astronomy are not to be regarded as true pictures of\\nthe magnitudes concerned, but merely as representing their abstract geometrical re-\\nlations.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0031.jp2"}, "32": {"fulltext": "THE EARTH.\\nTable showing the Dip of the Horizon at different elevations, from\\nI foot to 100 feet*\\nFeet.\\nFeet.\\nFeet.\\nu\\n1\\n0.59\\n13\\n3.33\\n26\\n5.01\\n2\\n1.24\\n14\\n3.41\\n28\\n5.13\\n3\\n1.42\\n15\\n3.49\\n30\\n5.23\\n4\\n1.58\\n16\\n3.56\\n35\\n5.49\\n5\\n2.12\\n17\\n4.03\\n40\\n6.14\\n6\\n2.25\\n18\\n4.11\\n45\\n6.36\\n7\\n2.36\\n19\\n4.17\\n50\\n6.58\\n8\\n2.47\\n20\\n4.24\\n60\\n7.37\\n9\\n2.57\\n21\\n4.31\\n70\\n8.14\\n10\\n3.07\\n22\\n4.37\\n80\\n8.48\\n11\\n3.16\\n23\\n4.43\\n90\\n9.20\\n12\\n3.25\\n24\\n4.49\\n100\\n9.51\\nSuch a table is of use in estimating the altitude of a body\\nabove the horizon, when the instrument (as usually happens) is\\nmore or less elevated above the general level of the earth. For\\nif it is a star whose altitude above the horizon is required, the\\ninstrument being situated at O, (Fig. 1,) the inquiry is how far\\nthe star is elevated above the level HOR, but the angle taken is\\nthat above the visible horizon OD. The dip, therefore, or the\\nangle HOD, corresponding to the height of the point O, must be\\nsubtracted, to obtain the true altitude. On the Peak of Tene-\\nrifFe, a mountain 13,000 feet high, Humboldt observed the surface\\nof the sea to be depressed on all sides nearly 2 degrees. The\\nsun arose to him 12 minutes sooner than to an inhabitant of the\\nplain and from the plain, the top of the mountain appeared en-\\nlightened 12 minutes before the rising or after the setting of\\nthe sun.\\n11. The foregoing considerations show that the form of the\\nearth is spherical but more exact determinations prove, that the\\nearth, though nearly globular, is not exactly so its diameter from\\nthe north to the south pole is about 26 miles less than through\\nthe equator, giving to the earth the form of an oblate spheroid,f\\nThis table includes the allowance for refraction.\\nt An oblate spheroid is the solid described by the revolution of an ellipse about ita\\nshorter axis.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0032.jp2"}, "33": {"fulltext": "FIGURE AND DIMENSIONS. 7\\nor a flattened sphere resembling an orange. We shall reserve the\\nexplanations of the methods by which this fact is established,\\nuntil the learner is better prepared than at present to understand\\nthem.\\n12. The mean or average diameter of the earth, is 7912.4 miles,\\na measure which the learner should fix in his memory as a stand-\\nard of comparison in astronomy, and of which he should endeavor\\nto form the most adequate conception in his power. The circum-\\nference of the earth is about 25,000 miles (24857.5).* Although\\nthe surface of the earth is uneven, sometimes rising in high moun-\\ntains, and sometimes descending in deep valleys, yet these eleva-\\ntions and depressions are so small in comparison with the immense\\nvolume of the globe, as hardly to occasion any sensible deviation\\nfrom a surface uniformly curvilinear. The irregularities of the\\nearth s surface in this view, are no greater than the rough points\\non the rind of an orange, which do not perceptibly interrupt its\\ncontinuity for the highest mountain on the globe is only about\\nfive miles above the general level and the deepest mine hitherto\\n5 1\\nopened is only about half a mile.f Now wt^^tt^s or about\\none sixteen hundredth part of the whole diameter, an inequality\\nwhich, in an artificial globe of eighteen inches diameter, amounts\\nto only the eighty-eighth part of an inch.\\n13. The diameter of the earth, con-\\nsidered as a perfect sphere, may be de-\\ntermined by means of observations on\\na mountain of known elevation, seen\\nin the horizon from the sea. Let BD\\n(Fig. 2,) be a mountain of known\\nheight a, whose top is seen in the hori-\\nzon by a spectator at A, b miles from it.\\nLet x denote the radius of the earth.\\nThen x* b 2 (x+df x 2 2ax a\\\\\\nIt will generally be sufficient to treasure up in the memory the round number,\\nbut sometimes, in astronomical calculations, the more exact number may be required,\\nand it is therefore inserted.\\nt Sir John Herschel.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0033.jp2"}, "34": {"fulltext": "8 THE EARTH.\\nb 2 a 2\\nHence, 2ax=b 2 --a\\\\ and x~\u00e2\u0080\u0094 For example, suppose the\\nheight of the mountain is just one mile then it will be found,\\nby observation, to be visible on the horizon at the distance of\\no\u00e2\u0080\u009e -i i tt 2 2 (89) 2 -l 7921-1 A\\n89 miles=6. Hence, =3960=radius\\n2a 2 2\\nof the earth, and 7920=the earth s diameter.\\n14. Another method, and the most ancient, is to ascertain the\\ndistance on the surface of the earth, corresponding to a degree of\\nlatitude. Let us select two convenient places, one lying directly\\nnorth of the other, whose difference of latitude is known. Sup-\\npose this difference to be 1\u00c2\u00b0 30 and the distance between the\\ntwo places, as measured by a chain, to be 104 miles. Then,\\nsince there are 360 degrees of latitude in the entire circumference,\\n24Q60\\n1\u00c2\u00b0 30 104 360\u00c2\u00b0 24960. And =7944.\\n3.1416\\nThe foregoing approximations are sufficient to show that the\\nearth is about 8,000 miles in diameter.\\n15. The greatest difficulty in the way of acquiring correct\\nviews in astronomy, arises from the erroneous notions that pre-\\noccupy the mind. To divest himself of these, the learner should\\nconceive of the earth as a huge globe occupying a small portion\\nFig. 3.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0034.jp2"}, "35": {"fulltext": "DOCTRINE OF THE SPHERE. 9\\nof space, and encircled on all sides with the starry sphere. He\\nshould free his mind from its habitual proneness to consider one\\npart of space as naturally up and another down, and view him-\\nself as subject to a force which binds him to the earth as truly as\\nthough he were fastened to it by some invisible cords or wires, as\\nthe needle attaches itself to all sides of a spherical loadstone. He\\nshould dwell on this point until it appears to him as truly up in\\nthe direction of BB CC DD (Fig. 3,) when he is at B, C, and\\nD, respectively, as in the direction of AA when he is at A.\\nDOCTRINE OF THE SPHERE.\\n16. The definitions of the different lines, points, and circles,\\nwhich are used in astronomy, and the propositions founded upon\\nthem, compose the Doctrine of the Sphere.*\\n17. A section of a sphere by a plane cutting it in any manner,\\nis a circle. Great circles are those which pass through the center\\nof the sphere, and divide it into two equal hemispheres Small\\ncircles, are such as do not pass through the center, but divide the\\nsphere into two unequal parts. Every circle, whether great or\\nsmall, is divided into 360 equal parts called degrees. A degree,\\ntherefore, is not any fixed or definite quantity, but only a certain\\naliquot part of any circle.\\n18. The Axis of a circle, is a straight line passing through its\\ncenter at right angles to its plane.\\n19. The Pole of a great circle, is the point on the sphere where\\nits axis cuts through the sphere. Every great circle has two\\npoles, each of which is every where 90\u00c2\u00b0 from the great circle.\\nFor, the measure of an angle at the center of a sphere, is the\\narc of a great circle intercepted between the two lines that con-\\ntain the angle and, since the angle made by the axis and any\\nradius of the circle is a right angle, consequently its measure on\\nthe sphere, namely, the distance from the pole to the circumfer-\\nIt is presumed that many of those who read this work, will have studied Spherical\\nGeometry but it is so important to the student of astronomy to have a clear idea of\\nthe circles of the sphere, that it is thought best to introduce them here.\\n2", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0035.jp2"}, "36": {"fulltext": "10 THE EARTH.\\nence of the circle, must be 90\u00c2\u00b0. If two great circles cut each\\nother at right angles, the poles of each circle lie in the circum-\\nference of the other circle. For each circle passes through the\\naxis of the other.\\n20. All great circles of the sphere cut each other in two points\\ndiametrically opposite, and consequently, their points of section\\nare 180\u00c2\u00b0 apart. For the line of common section, is a diameter\\nin both circles, and therefore bisects both.\\n21. A great circle which passes through the pole of another\\ngreat circle, cuts the latter at right angles. For, since it passes\\nthrough the pole and the center of the circle, it must pass through\\nthe axis which being at right angles to the plane of the circle,\\nevery plane which passes through it is at right angles to the same\\nplane.\\nThe great circle which passes through the pole of another great\\ncircle and is at right angles to it, is called a secondary to that circle.\\n22. The angle made by two great circles on the surface of the\\nsphere, is measured by the arc of another great circle, of which\\nthe angular point is the pole, being the arc of that great circle\\nintercepted between those two circles. For this arc is the meas-\\nure of the angle formed at the center of the sphere by two radii,\\ndrawn at right angles to the line of common section of the two\\ncircles, one in one plane and the other in the other, which angle\\nis therefore that of the inclination of those planes.\\n23. In order to fix the position of any plane, either on the sur-\\nface of the earth or in the heavens, both the earth and the heav-\\nens are conceived to be divided into separate portions by circles,\\nwhich are imagined to cut through them in various ways. The\\nearth thus intersected is called the terrestrial, and the heavens the\\ncelestial sphere. The learner will remark, that these circles have\\nno existence in nature, but are mere landmarks, artificially con-\\ntrived for convenience of reference. On account of the immense\\ndistance of the heavenly bodies, they appear to us, wherever we\\nare placed, to be fixed in the same concave surface, or celestial", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0036.jp2"}, "37": {"fulltext": "DOCTRINE OF THE SPHERE. 11\\nvault. The great circles of the globe, extended every way to\\nmeet the concave surface of the heavens, become circles of the\\ncelestial sphere.\\n24. The Horizon is the great circle which divides the earth\\ninto upper and lower hemispheres, and separates the visible heav-\\nens from the invisible. This is the rational horizon. The sen-\\nsible horizon, is a circle touching the earth at the place of the\\nspectator, and is bounded by*the line in which the earth and skies\\nseem to meet. The sensible horizon is parallel to the rational,\\nbut is distant from it by the semi-diameter of the earth, or nearly\\n4,000 miles. Still, so vast is the distance of the starry sphere,\\nthat both these planes appear to cut that sphere in the same line\\nso that we see the same hemisphere of stars that we should see if\\nthe upper half of the earth were removed, and we stood on the\\nrational horizon.\\n25. The poles of the horizon are the zenith and nadir. The\\nZenith is the point directly over our head, and the Nadir that di-\\nrectly under our feet. The plumb line is in the axis of the hori-\\nzon, and consequently directed towards its poles.\\nEvery place on the surface of the earth has its own horizon\\nand the traveller has a new horizon at every step, always extend-\\ning 90 degrees from his zenith in all directions.\\n26. Vertical circles are those which pass through the poles of\\nthe horizon, perpendicular to it.\\nThe Meridian is that vertical circle which passes through the\\nnorth and south points.\\nThe Prime Vertical, is that vertical circle which passes through\\nthe east and west points.\\n27. As in geometry, we determine the position of any point by\\nmeans of rectangular coordinates, or perpendiculars drawn from\\nthe point to planes at right angles to each other, so in astron-\\nomy we ascertain the place of a body, as a fixed star, by taking\\nits angular distance from two great circles, one of which is per-\\npendicular to the other. Thus the horizon and the meridian, or the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0037.jp2"}, "38": {"fulltext": "12 THE EARTH.\\nhorizon and the prime vertical, are coordinate circles used for such\\nmeasurements.\\nThe Altitude of a body, is its elevation above the horizon meas-\\nured on a vertical circle.\\nThe Azimuth of a body, is its distance measured on the hori-\\nzon from the meridian to a vertical circle passing through the body.\\nThe Amplitude of a body, is its distance on the horizon, from\\nthe prime vertical, to a vertical circle passing through the body.\\nAzimuth is reckoned 90\u00c2\u00b0 from either the north or south point\\nand amplitude 90\u00c2\u00b0 from either the east or west point. Azimuth\\nand amplitude are mutually complements of each other. When a\\npoint is on the horizon, it is only necessary to count the number\\nof degrees of the horizon between that point and the meridian,\\nm order to find its azimuth but if the point is above the horizon,\\nthen its azimuth is estimated by passing a vertical circle through\\nit, and reckoning the azimuth from the point where this circle cuts\\nthe horizon.\\nThe Zenith Distance of a body is measured on a vertical cir-\\ncle, passing through that body. It is the complement of the alti-\\ntude.\\n28. The Axis of the Earth is the diameter, on which the earth\\nis conceived to turn in its diurnal revolution. The same line con-\\ntinued until it meets the starry concave, constitutes the axis of the\\ncelestial sphere.\\nThe Poles of the Earth are the extremities of the earth s axis\\nthe Poles of the Heavens, the extremities of the celestial axis.\\n29. The Equator is a great circle cutting the axis of the earth\\nat right angles. Hence the axis of the earth is the axis of the\\nequator, and its poles are the poles of the equator. The intersec-\\ntion of the plane of the equator with the surface of the earth,\\nconstitutes the terrestrial, and with the concave sphere of the\\nheavens, the celestial equator. The latter, by way of distinction,\\nis sometimes denominated the equinoctial.\\n30. The secondaries to the equator, that is, the great circles\\npassing through the poles of the equator, are called Meridians,", "height": "4209", "width": "2302", "jp2-path": "introductionto00olm_0038.jp2"}, "39": {"fulltext": "DOCTRINE OF THE SPHERE. 13\\nbecause that secondary which passes through the zenith of any\\nplace is the meridian of that place, and is at right angles both to\\nthe equator and the horizon, passing as it does through the poles\\nof both. (Art. 21.) These secondaries are also called Hour Circles,\\nbecause the arcs of the equator intercepted between them are used\\nas measures of time.\\n31. The Latitude of a place on the earth, is its distance from\\nthe equator north or south. The Polar Distance, or angular dis-\\ntance from the nearest pole, is the complement of the latitude.\\n32. The Longitude of a place is its distance from some stand-\\nard meridian, either east or west, measured on the equator. The\\nmeridian usually taken as the standard, is that of the Observatory\\nof Greenwich, near London. If a place is directly on the equator,\\nwe have only to inquire how many degrees of the equator there\\nare between that place and the point where the meridian of Green-\\nwich cuts the equator. If the place is north or south of the equa-\\ntor, then its longitude is the arc of the equator intercepted between\\nthe meridian which passes through the place, and the meridian of\\nGreenwich.\\n33. The Ecliptic is a great circle in which the earth performs\\nits annual revolution around the sun. It passes through the center\\nof the earth and the center of the sun. It is found by observa-\\ntion that the earth does not lie with its axis at right angles to the\\nplane of the ecliptic, but that it is turned about 23\u00c2\u00a3 degrees out of\\na perpendicular direction, making an angle with the plane itself of\\n66^\u00c2\u00b0. The equator, therefore, must be turned the same distance\\nout of a coincidence with the ecliptic, the two circles making\\nan angle with each other of 23^\u00c2\u00b0, (23\u00c2\u00b0 27 40 It is particu-\\nlarly important for the learner to form correct ideas of the eclip-\\ntic, and of its relations to the equator, since to these two circles a\\ngreat number of astronomical measurements and phenomena are\\nreferred.\\n34. The Equinoctial Points, or Equinoxes,* are the intersec-\\nThe term Equinoxes strictly denotes the times when the sun arrives at the equi-\\nnoctial points, but it is also frequently used to denote those points themselves.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0039.jp2"}, "40": {"fulltext": "14 THE EARTH.\\ntions of the ecliptic and equator. The time when the sun crosses\\nthe equator in returning northward is called the vernal, and in\\ngoing southward, the autumnal equinox. The vernal equinox\\noccurs about the 21st of March, and the autumnal the 22d of\\nSeptember.\\n35. The Solstitial Points are the two points of the ecliptic\\nmost distant from the equator. The times when the sun comes\\nto them are called solstices. The summer solstice occurs about\\nthe 22d of June, and the winter solstice about the 22d of De-\\ncember.\\nThe ecliptic is divided into twelve equal parts of 30\u00c2\u00b0 each,\\ncalled signs, which, beginning at the vernal equinox, succeed each\\nother in the following order\\nNorthern.\\nSouthern.\\n1. Aries T\\n7. Libra\\n2. Taurus 8\\n8. Scorpio fli\\n3. Gemini II\\n9. Sagittarius\\n4. Cancer 3d\\n10. Capricornus VS\\n5. Leo SI\\n11. Aquarius\\n6. Virgo T$\\n12. Pisces x\\nThe mode of reckoning on the ecliptic, is by signs, degrees,\\nminutes, and seconds. The sign is denoted either by its name\\nor its number. Thus 100\u00c2\u00b0 may be expressed either as the 10th\\ndegree of Cancer, or as 3 s 10\u00c2\u00b0\\n36. Of the various meridians, two are distinguished by the\\nname of Colures. The Equinoctial Colure, is the meridian which\\npasses through the equinoctial points. The Solstitial Colure, is\\nthe meridian which passes through the solstitial points. As the\\nsolstitial points are 90\u00c2\u00b0 from the equinoctial points, so the sol-\\nstitial colure is 90\u00c2\u00b0 from the equinoctial colure. It is also at right\\nangles, or a secondary to both the ecliptic and equator. For like\\nevery other meridian, it is of course perpendicular to the equator,\\npassing through its poles. Moreover, the equinox, being a point\\nboth in the equator and in the ecliptic, is 90\u00c2\u00b0 from the solstice,\\nfrom the pole of the equator, and from the pole of the ecliptic.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0040.jp2"}, "41": {"fulltext": "DOCTRINE OF THE SPHERE.\\n15\\nHence the solstitial colure, which passes through the solstice and\\nthe pole of the equator, passes also through the pole of the ecliptic,\\nbeing the great circle of which the equinox itself is the pole.\\nConsequently, the solstitial colure is a secondary to both the equa-\\ntor and the ecliptic. (See Arts. 19, 20, 21.)\\n37. The position of a celestial body is referred to the equator\\nby its right ascension and declination. (See Art. 27.) Right\\nAscension, is the angular distance from the vernal equinox, meas-\\nured on the equator. If a star is situated on the equator, then its\\nright ascension is the number of degrees of the equator between\\nthe star and the vernal equinox. But if the star is north or south\\nof the equator, then its right ascension is the arc of the equator\\nintercepted between the vernal equinox and that secondary to the\\nequator which passes through the star. Declination is the dis-\\ntance of a body from the equator, measured on a secondary to the\\nlatter. Therefore, right ascension and declination correspond to\\nterrestrial longitude and latitude, right ascension being reckoned\\nfrom the equinoctial colure, in the same manner as longitude is\\nreckoned from the meridian of Greenwich. On the other hand,\\ncelestial longitude and latitude are referred, not to the equator,\\nbut to the ecliptic. Celestial Longitude, is the distance of a body\\nfrom the vernal equinox reckoned on the ecliptic. Celestial Lati-\\ntude, is distance from the ecliptic measured on a secondary to the\\nlatter. Or, more briefly, Longitude is distance on the ecliptic\\nLatitude, distance from the ecliptic. The North Polar Distance\\nof a star, is the complement of its declination.\\n38. Parallels of Latitude are small\\ncircles parallel to the equator. They\\nconstantly diminish in size as we go\\nfrom the equator to the pole, the ra-\\ndius being always equal to the cosine\\nof the latitude. In fig. 4, let HO be\\nthe horizon, EQ the equator, PP the\\naxis of the earth, ZN the prime ver-\\ntical, and ZL a parallel of latitude of\\nany place Z. Then ZE is the lati-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0041.jp2"}, "42": {"fulltext": "16 THE EARTH.\\ntude, (Art. 31,) and ZP the complement of the latitude but Zw\\nthe radius of the parallel of latitude ZL, is the sine of ZP, and\\ntherefore the cosine of the latitude.\\n39. The Tropics are the parallels of latitude that pass through\\nthe solstices. The northern tropic is called the tropic of Cancer\\nthe southern, the tropic of Capricorn.\\n40. The Polar Circles are the parallels of latitude that pass\\nthrough the poles of the ecliptic, at the distance of 23| degrees\\nfrom the pole of the earth. (Art. 33.)\\n41. The earth is divided into five zones. That portion of the\\nearth which lies between the tropics, is called the Torrid Zone\\nthat between the tropics and polar circles, the Temperate Zones\\nand that between the polar circles and the poles, the Frigid\\nZones.\\n42. The Zodiac is the part of the celestial sphere which lies\\nabout 8 degrees on each side of the ecliptic. This portion of the\\nheavens is thus marked off by itself, because the planets are never\\nseen further from the ecliptic than this limit.\\n43. The elevation of the pole is equal to the latitude of the place.\\nThe arc PE (Fig. 4.)=ZO.\\\\PO=ZE which equals the lati-\\ntude.\\n44. The elevation of the equator is equal to the complement of\\nthe latitude.\\nZH=90\u00c2\u00b0. But ZE=Lat. EH=90\u00e2\u0080\u0094 Lat.=colatitude.\\n45. The distance of any place from the pole (or the polar dis-\\ntance) equals the complement of the latitude,\\nEP=90\u00c2\u00b0. But EZ=Lat. ZP=90-Lat.=colatitude.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0042.jp2"}, "43": {"fulltext": "DIURNAL REVOLUTION. 17\\nCHAPTER II.\\nDIURNAL REVOLUTION ARTIFICIAL GLOBES ASTRONOMICAL\\nPROBLEMS.\\n46. The apparent diurnal revolution of the heavenly bodies\\nfrom east to west, is owing to the actual revolution of the earth\\non its own axis from west to east. If we conceive of a radius of\\nthe earth s equator extended until it meets the concave sphere of\\nthe heavens, then as the earth revolves, the extremity of this line\\nwould trace out a curve on the face of the sky, namely, the celes-\\ntial equator. In curves parallel to this, called the circles of diurnal\\nrevolution, the heavenly bodies actually appear to move, every star\\nhaving its own peculiar circle. After the learner has first rendered\\nfamiliar the real motions of the earth from west to east, he may then,\\nwithout danger of misconception, adopt the common language,\\nthat all the heavenly bodies revolve around the earth once a day\\nfrom east to west, in circles parallel to the equator and to each other.\\n47. The time occupied by a star in passing from any point in\\nthe meridian until it comes round to the same point again, is called\\na sidereal day, and measures the period of the earth s revolution\\non its axis. If we watch the returns of the same star from day to\\nday, we shall find the intervals exactly equal to one another;\\nthat is, the sidereal days are all equal.* Whatever star we select\\nfor the observation, the same result will be obtained. The stars,\\ntherefore, always keep the same relative position, and have a\\ncommon movement round the earth, a consequence that natu-\\nrally flows from the hypothesis, that their apparent motion is all\\nproduced by a single real motion, namely, that of the earth. The\\nsun, moon, and planets, revolve in like manner, but their returns to\\nthe meridian are not, like those of the fixed stars, at exactly equal\\nintervals.\\n48. The appearances of the diurnal motions of the heavenly\\nAllowance is here supposed to be made for the effects of precession, c.\\n3", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0043.jp2"}, "44": {"fulltext": "18 THE EARTH.\\nbodies are different in different parts of the earth, since every\\nplace has its own horizon, (Art. 15,) and different horizons are\\nvariously inclined to each other. Let us suppose the spectator\\nviewing the diurnal revolutions, successively, from several different\\npositions on the earth.\\n49. If he is on the equator, his horizon passes through both poles\\nfor the horizon cuts the celestial vault at 90 degrees in every di-\\nrection from the zenith of the spectator but the pole is likewise\\n90 degrees from his zenith, and consequently, the pole must be\\nin his horizon. The celestial equator coincides with his Prime\\nVertical, being a great circle passing through the east and\\nwest points. Since all the diurnal circles are parallel to the equa-\\ntor, they are all, like the equator, perpendicular to his horizon.\\nSuch a view of the heavenly bodies, is called a right sphere or,\\nA Right Sphere is one in which all the daily revolutions of\\nthe heavenly bodies are in circles perpendicular to the horizon.\\nA right sphere is seen only at the equator. Any star situated\\nin the celestial equator, would appear to rise directly in the east, at\\nnoon to pass through the zenith of the spectator, and to set directly in\\nthe west in proportion as stars are at a greater distance from the\\nequator towards the pole, they describe smaller and smaller circles,\\nuntil, near the pole, their motion is hardly perceptible. In a right\\nsphere every star remains an equal time above and below the hori-\\nzon and since the times of their revolutions are equal, the veloci-\\nties are as the lengths of the circles they describe. Consequently,\\nas the stars are more remote from the equator towards the pole,\\ntheir motions become slower, until, at the pole, the north star ap-\\npears stationary.\\n50. If the spectator advances one degree towards the north\\npole, his horizon reaches one degree beyond the pole of the earth,\\nand cuts the starry sphere one degree below the pole of the heav-\\nens, or below the north star, if that be taken as the place of the\\npole. As he moves onward towards the pole, his horizon contin-\\nually reaches further and further beyond it, until when he comes\\nto the pole of the earth, and under the pole of the heavens, his\\nhorizon reaches on all sides to the equator and coincides with it.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0044.jp2"}, "45": {"fulltext": "DIURNAL REVOLUTION. 19\\nMoreover, since all the circles of daily motion are parallel to the\\nequator, they become, to the spectator at the pole, parallel to the\\nhorizon. This is what constitutes a parallel sphere. Or,\\nA Parallel Sphere is that in which all the circles of daily\\nmotion are parallel to the horizon,\\n51. To render this view of the heavens familiar, the learner\\nshould follow round in his mind a number of separate stars, one\\nnear the horizon, one a few degrees above it, and a third near the\\nzenith. To one who stood upon the north pole, the stars of the\\nnorthern hemisphere would all be perpetually in view when not\\nobscured by clouds or lost in the sun s light, and none of those of\\nthe southern hemisphere would ever be seen. The sun would\\nbe constantly above the horizon for six months in the year, and\\nthe remaining six constantly out of sight. That is, at the pole\\nthe days and nights are each six months long. The phenomena\\nat the south pole are similar to those at the north.\\n52. A perfect parallel sphere can never be seen except at one\\nof the poles,- a point which has never been actually reached by\\nman; yet the British discovery ships penetrated within a few\\ndegrees of the north pole, and of course enjoyed the view of a\\nsphere nearly parallel.\\n53. As the circles of daily motion are parallel to the horizon of\\nthe pole, and perpendicular to that of the equator, so at all places\\nbetween the two, the diurnal motions are oblique to the horizon.\\nThis aspect of the heavens constitutes an oblique sphere, which is\\nthus defined\\nAn Oblique Sphere is that in which the circles of daily mo-\\ntion are oblique to the horizon.\\nSuppose for example the spectator is at the latitude of fifty de-\\ngrees. His horizon reaches 50\u00c2\u00b0 beyond the pole of the earth, and\\ngives the same apparent elevation to the pole of the heavens. It\\ncuts the equator, and all the circles of daily motion, at an angle\\nof 40\u00c2\u00b0, being always equal to the co-altitude of the pole. Thus,\\nlet HO (Fig. 5,) represent the horizon, EQ the equator, and\\nPP the axis of the earth. Also, lh mm, c. parallels of latitude.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0045.jp2"}, "46": {"fulltext": "THE EARTH.\\nThen the horizon of a spectator Fig. 5.\\nat Z, in latitude 50\u00c2\u00b0 reaches to\\n50\u00c2\u00b0 beyond the pole (Art. 50)\\nand the angle ECH, is 40\u00c2\u00b0. As\\nwe advance still further north,\\nthe elevation of the diurnal cir-\\ncles grows less and less, and\\nconsequently the motions of the\\nheavenly bodies more and more\\noblique, until finally, at the pole,\\nwhere the latitude is 90\u00c2\u00b0, the\\nangle of elevation of the equator\\nvanishes, and the horizon and equator coincide with each other,\\nas before stated.\\n54. The circle of perpetual apparition, is the boundary of\\nthat space around the elevated pole, where the stars never set.\\nIts distance from the pole is equal to the latitude of the place.\\nFor, since the altitude of the pole is equal to the latitude, a star\\nwhose polar distance is just equal to the latitude, will when at its\\nlowest point only just reach the horizon and all the stars nearer\\nthe pole than this will evidently not descend so far as the horizon.\\nThus, mm (Fig. 5,) is the circle of perpetual apparition, be-\\ntween which and the north pole, the stars never set, and its dis-\\ntance from the pole OP is evidently equal to the elevation of the\\npole, and of course to the latitude.\\n55. In the opposite hemisphere, a similar part of the sphere\\nadjacent to the depressed pole never rises. Hence,\\nThe circle of perpetual occultation, is the boundary of that\\nspace around the depressed pole, within which the stars never rise.\\nThus, m m (Fig. 5,) is the circle of perpetual occultation, be-\\ntween which and the south pole, the stars never rise.\\n56. In an oblique sphere, the horizon cuts the circles of daily\\nmotion unequally. Towards the elevated pole, more than half\\nthe circle is above the horizon, and a greater and greater portion\\nas the distance from the equator is increased, until finally, within", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0046.jp2"}, "47": {"fulltext": "DIURNAL REVOLUTION. 21\\nthe circle of perpetual apparition, the whole circle is above the\\nhorizon. Just the opposite takes place in the hemisphere next\\nthe depressed pole. Accordingly, when the sun is in the equator,\\nas the equator and horizon, like all other great circles of the\\nsphere, bisect each other, the days and nights are equal all over\\nthe globe. But when the sun is north of the equator, our days\\nbecome longer than our nights, but shorter when the sun is\\nsouth of the equator. Moreover, the higher the latitude, the\\ngreater is the inequality in the lengths of the days and nights.\\nAll these points will be readily understood by inspecting figure 5\\n57. Most of the phenomena of the diurnal revolution can be\\nexplained, either on the supposition that the celestial sphere actu-\\nally all turns around the earth once in 24 hours, or that this mo-\\ntion of the heavens is merely apparent, arising from the revolu-\\ntion of the earth on its axis in the opposite direction, a motion\\nof which we are insensible, as we sometimes lose the conscious-\\nness of our own motion in a ship or a steamboat, and observe all\\nexternal objects to be receding from us with a common motion.\\nProofs entirely conclusive and satisfactory, establish the fact, that\\nit is the earth and not the celestial sphere that turns but these\\nproofs are drawn from various sources, and the student is not pre-\\npared to appreciate their value, or even to understand some of\\nthem, until he has made considerable proficiency in the study of\\nastronomy, and become familiar with a great variety of astronom-\\nical phenomena. To such a period of our course of instruction,\\nwe therefore postpone the discussion of the hypothesis of the\\nearth s rotation on its axis.\\n58. While we retain the same place on the earth, the diurnal\\nrevolution occasions no change in our horizon, but our horizon\\ngoes round as well as ourselves. Let us first take our station on\\nthe equator at sunrise our horizon now passes through both the\\npoles, and through the sun, which we are to conceive of as at a\\ngreat distance from the earth, and therefore as cut, not by the\\nterrestrial but by the celestial horizon. As the earth turns, the\\nhorizon dips more and more below the sun, at the rate of 15 de-\\ngrees for every hour, and, as in the case of the polar star, (Art. 50,)", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0047.jp2"}, "48": {"fulltext": "22 THE liAkTH.\\nthe sun appears to rise at the same rate. In six hours, therefore,\\nit is depressed 90 degrees below the sun, which brings us directly\\nunder the sun, which, for our present purpose, we may consider as\\nhaving all the while maintained the same fixed position in space.\\nThe earth continues to turn, and in six hours more, it completely\\nreverses the position of our horizon, so that the western part of\\nthe horizon which at sunrise was diametrically opposite to the\\nsun now cuts the sun, and soon afterwards it rises above the level\\nof the sun, and the sun sets. During the next twelve hours, the\\nsun continues on the invisible side of the sphere, until the hori-\\nzon returns to the position from which it started, and a new day\\nbegins.\\n59. Let us next contemplate the similar phenomena at the poles.\\nHere the horizon, coinciding as it does with the equator, would\\ncut the sun through its center, and the sun would appear to re-\\nvolve along the surface of the sea, one half above and the other\\nhalf below the horizon. This supposes the sun in its annual\\nrevolution to be at one of the equinoxes. When the sun is north\\nof the equator, it revolves continually round in a path which,\\nduring a single revolution, appears parallel to the equator, and it\\nis constantly day and when the sun is south of the equator, it is,\\nfor the same reason, continual night.\\n60. We have endeavored to conceive of the manner in which\\nthe apparent diurnal movements of the sun are really produced at\\ntwo stations, namely, in the right sphere, and in the parallel sphere.\\nThese two cases being clearly understood, there will be little dif-\\nficulty in applying a similar explanation to an oblique sphere\\nARTIFICIAL GLOBES.\\n61. Artificial globes are of two kinds, terrestrial and celestial.\\nThe first exhibits a miniature representation of the earth the\\nsecond, of the visible heavens and both show the various circles\\nby which the two spheres are respectively traversed. Since all\\nglobes are similar solid figures, a small globe, imagined to be sit-\\nuated at the center of the earth or of the celestial vault, may rep-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0048.jp2"}, "49": {"fulltext": "ARTIFICIAL GLOBES. 23\\nresent all the visible objects and artificial divisions of either sphere,\\nand with great accuracy and just proportions, though on a scale\\ngreatly reduced. The study of artificial globes, therefore, cannot\\nbe too strongly recommended to the student of astronomy.*\\n62. An artificial globe is encompassed from north to south by\\na strong brass ring to represent the meridian of the place. This\\nring is made fast to the two poles and thus supports the globe,\\nwhile it is itself supported in a vertical position by means of a\\nframe, the ring being usually let into a socket in which it may be\\neasily slid, so as to give any required elevation to the pole. The\\nbrass meridian is graduated each way from the equator to the\\npole 90\u00c2\u00b0, to measure degrees of latitude or declination, according\\nas the distance from the equator refers to a point on the earth or\\nin the heavens. The horizon is represented by a broad zone, made\\nbroad for the convenience of carrying on it a circle of azimuth, an-\\nother of amplitude, and a wide space on which are delineated the\\nsigns of the ecliptic, and the sun s place for every day in the year\\nnot because these points have any special connexion with the hori-\\nzon, but because this broad surface furnishes a convenient place\\nfor recording them.\\n63. Hour Circles are represented on the terrestrial globe by\\ngreat circles drawn through the pole of the equator but, on the\\ncelestial globe, corresponding circles pass through the poles of the\\necliptic, constituting circles of celestial latitude, (Art. 37,) while the\\nbrass meridian, being a secondary to the equinoctial, becomes an\\nhour circle of any star which, by turning the globe, is brought un-\\nder it.\\n64. The Hour Index is a small circle described around the pole\\nof the equator, on which are marked the hours of the day. As\\nthis circle turns along with the globe, it makes a complete revo-\\nlution in the same time with the equator or, for any less period,\\nIt were desirable, indeed, that every student of the science should have the ce/es-\\ntial globe at least, constantly before him. One of a small size, as eight or nine inches,\\nwill answer the purpose, although globes of these dimensions cannot usually be relied\\non for nice measurements.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0049.jp2"}, "50": {"fulltext": "24 THE EARTH.\\nthe same number of degrees of this circle and of the equator\\nunder the meridian. Hence the hour index measures arcs of\\nright ascension. (Art. 37.)\\n65. The Quadrant of Altitude is a flexible strip of brass, gradu-\\nated into ninety equal parts, corresponding in length to degrees\\non the globe, so that when applied to the globe and bent so as\\nclosely to fit its surface, it measures the angular distance between\\nany two points. When the zero, or the point where the gradua-\\ntion begins, is laid on the pole of any great circle, the 90th degree\\nwill reach to the circumference of that circle, and being therefore\\na great circle passing through the pole of another great circle, it\\nbecomes a secondary to the latter. (Art. 21 Thus the quadrant\\nof altitude may be used as a secondary to any great circle on the\\nsphere but it is used chiefly as a secondary to the horizon, the\\npoint marked 90\u00c2\u00b0 being screwed fast to the pole of the horizon,\\nthat is, the zenith, and the other end, marked 0, being slid along\\nbetween the surface of the sphere and the wooden horizon. It\\nthus becomes a vertical circle, on which to measure the altitude\\nof any star through which it passes, or from which to measure\\nthe azimuth of the star, which is the arc of the horizon intercept-\\ned between the meridian and the quadrant of altitude passing\\nthrough the star, (Art. 27.)\\n66. To rectify the globe for any place, the north pole must be\\nelevated to the latitude of the place (Art. 43) then the equator\\nand all the diurnal circles will have their due inclination in respect\\nto the horizon and, on turning the globe, (the celestial globe west,\\nand the terrestrial east.) every point on either globe will revolve as\\nthe same point does in nature and the relative situations of all\\nplaces will be the same as on the respective native spheres.\\nPROBLEMS ON THE TERRESTRIAL GLOBE.\\n67. To find the Latitude and Longitude of a place Turn the\\nglobe so as to bring the place to the brass meridian then the de-\\ngree and minute on the meridian directly over the place will indi-\\ncate its latitude, and the point of the equator under the meridian,\\nwill show its longitude.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0050.jp2"}, "51": {"fulltext": "PROBLEMS ON THE TERRESTRIAL GLOBE. 25\\nEx. What are the Latitude and Longitude of the city of New\\nYork?\\n68. To find a place having its latitude and longitude given Bring\\nto the brass meridian the point of the equator corresponding to\\nthe longitude, and then at the degree of the meridian denoting the\\nlatitude, the place will be found.\\nEx. What place on the globe is in Latitude 39 N. and Longi-\\ntude 77 W.\\n69. To find the hearing and distance of two places: Rectify the\\nglobe for one of the places (Art. 66) screw the quadrant of alti-\\ntude to the zenith,* and let it pass through the other place. Then\\nthe azimuth will give the bearing of the second place from the\\nfirst, and the number of degrees on the quadrant of altitude, mul-\\ntiplied by 69|, (the number of miles in a degree,) will give the\\ndistance between the two places.\\nEx. What is the bearing of New Orleans from New York, and\\nwhat is the distance between these places\\n70. To determine the difference of time in different places\\nBring the place that lies eastward of the other to the meridian,\\nand set the hour index at XII. Turn the globe eastward until\\nthe other place comes to the meridian, then the index will point\\nto the hour required.\\nEx. When it is noon at New York, what time is it at London\\n71. The hour being given at any place, to tell what hour it is in\\nany other part of the world Find the difference of time between\\nthe two places, (Art. 70,) and, if the place whose time is required\\nis eastward of the other, add this difference to the given time, but\\nif westward, subtract it.\\nEx. What time is it at Canton, in China, when it is 9 o clock\\nA. M. at New York\\n72. To find the antceci,-\\\\ the periceci,% and the antipodes^ of any\\nThe zenith will of course be the point of the meridian over the place,\\nt avrt oikos. X tpt oikos. am *\u00c2\u00bbf.\\n4", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0051.jp2"}, "52": {"fulltext": "26 THE EARTH.\\n\u00e2\u0096\u00a0place Bring the given place to the meridian then, under the\\nmeridian, in the opposite hemisphere, in the same degree of lati-\\ntude, will be found the antceci. The same place remaining under\\nthe meridian, set the index to XII, and turn the globe until the\\nother XII is under the index then the perioeci will be on the me-\\nridian, under the same degree of latitude with the given place,\\nand the antipodes will be under the meridian, in the same latitude,\\nin the opposite hemisphere.\\nEx. Find the antoeci, the perioeci, and the antipodes of the citi-\\nzens of New York.\\nThe antoeci have the same hour of the day, but different seasons\\nof the year the perioeci have the same seasons, but opposite hours\\nand the antipodes have both opposite hours and opposite seasons.\\n73. To rectify the globe for the suris place On the wooden\\nhorizon, find the day of the month, and against it is given the sun s\\nplace in the ecliptic, expressed by signs and degrees.* Look for\\nthe same sign and degree on the ecliptic, bring that point to the\\nmeridian and set the hour index to XII. To all places under the\\nmeridian it will then be noon.\\nEx. Rectify the globe for the sun s place on the 1st of September.\\n74. The latitude of the place being given, to find the time of the\\nsun s rising and setting on any given day at that place Having\\nrectified the globe for the latitude, (Art. 66,) bring the sun s place\\nin the ecliptic to the graduated edge of the meridian, and set the\\nhour index to XII then turn the globe so as to bring the sun to\\nthe eastern and then to the western horizon, and the hour index\\nwill show the times of rising and setting respectively.-\\nEx. At what time will the sun rise and set at New Haven,\\nLat. 41\u00c2\u00b0 18 on the 10th of July?\\nPROBLEMS ON THE CELESTIAL GLOBE.\\n75. To find the Declination and Right Ascension of a heavenly\\nbody Bring the place of the body (whether the sun or a star) to\\nthe meridian. Then the degree and minute standing over it will\\nThe larger globes have the day of the month marked against the corresponding\\nsign on the ecliptic itself.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0052.jp2"}, "53": {"fulltext": "PROBLEMS ON THE CELESTIAL GLOBE. 27\\nshow its declination, and the point of the equinoctial under the\\nmeridian will give its right ascension. It will be remarked, that\\nthe declination and right ascension are found in the same manner\\nas latitude and longitude on the terrestrial globe. Right ascen-\\nsion is expressed either in degrees or in hours both being reck-\\noned from the vernal equinox, (Art. 37.)\\nEx. What is the declination and right ascension of the bright\\nstar Lyra also of the sun on the 5th of June\\n76. v To represent the appearance of the heavens at any time\\nRectify the globe for the latitude, bring the sun s place in the\\necliptic to the meridian, and set the hour index to XII then turn\\nthe globe westward until the index points to the given hour, and\\nthe constellations would then have the same appearance to an eye\\nsituated at the center of the globe, as they have at that moment\\nin the sky.\\nEx. Required the aspect of the stars at New Haven, Lat. 41\u00c2\u00b0\\n18 at 10 o clock, on the evening of December 5th.\\n77. To find the altitude and azimuth of any star Rectify the\\nglobe for the latitude and the sun s place, and let the quadrant\\nof altitude be screwed to the zenith, and be made to pass through\\nthe star. The arc on the quadrant, from the horizon to the star,\\nwill denote its altitude, and the arc of the horizon from the\\nmeridian to the quadrant, will be its azimuth.\\nEx. What are the altitude and azimuth of Sirius (the brightest\\nof the fixed stars) on the 25th of December at 10 o clock in the\\nevening, in Lat. 41\u00c2\u00b0\\n78. To find the angular distance of two stars from each other\\nApply the zero mark of the quadrant of altitude to one of the\\nstars, and the point of the quadrant which falls on the other star,\\nwill show the angular distance between the two.\\nEx. What is the distance between the two largest stars of the\\nGreat Bear?*\\nThese two stars are sometimes called the Pointers, from the line which passes\\nthrough them being always nearly in the direction of the north star. The angular\\ndistance between them is about 5\u00c2\u00b0, and may be learned as a standard for reference m\\nestimating, by the eye, the distance between any two points on the celestial vault.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0053.jp2"}, "54": {"fulltext": "28 PARALLAX.\\n79. To find the surfs meridian altitude, the latitude and day\\nof the month being given: Having rectified the globe for the\\nlatitude, (Art. 66,) bring the sun s place in the ecliptic to the me-\\nridian, and count the number of degrees and minutes between\\nthat point of the meridian and the zenith. The complement of\\nthis arc will be the sun s meridian altitude.\\nEx. What is the sun s meridian altitude at noon on the 1st of\\nAugust, in Lat. 41\u00c2\u00b0 18\\nCHAPTER III.\\nOF PARALLAX, REFRACTION, AND TWILIGHT.\\n80. Parallax is the apparent change of place which bodies\\nundergo by being viewed from different points. Thus in figure\\n6. let A represent the earth, CH the horizon, H Z a quadrant of\\na great circle of the heavens, extending from the horizon to the\\nzenith and let E, F, G, H, be successive positions of the moon\\nat different elevations, from the horizon to the meridian. Now a\\nspectator on the surface of the earth at A, would refer the place\\nof E to h, whereas, if seen from the center of the earth, it would", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0054.jp2"}, "55": {"fulltext": "PARALLAX. 29\\nappear at H The arc K h is called the parallactic arc, and the\\nangle H E/\u00c2\u00ab, or its equal AEC, is the angle of parallax. The\\nsame is true of the angles at F, G, and H, respectively.\\n81. Since then a heavenly body is liable to be referred to dif-\\nferent points on the celestial vault, when seen from different parts\\nof the earth, and thus some confusion occasioned in the deter-\\nmination of points on the celestial sphere, astronomers have agreed\\nto consider the true place of a celestial object to be that where it\\nwould appear if seen from the center of the earth. The doctrine\\nof parallax teaches how to reduce observations made at any place\\non the surface of the earth, to such as they would be if made\\nfrom the center.\\n82. The angle AEC is called the horizontal parallax, which\\nmay be thus defined. Horizontal Parallax, is the change of po-\\nsition which a celestial body, appearing in the horizon as seen\\nfrom the surface of the earth, would assume if viewed from the\\nearth s center. It is the angle subtended by the semi-diameter\\nof the earth, as viewed from the body itself. If we consider any\\none of the triangles represented in the figure, ACG for example,\\nSin. AGC Sin. GAZ AC CG\\nc -p Sin. GAZ x AC Sin. GAZ\\nSin. rarailax= oo\\nCG CG\\nHence the sine of the angle of parallax, or (since the angle of\\nparallax is always very small*) the parallax itself varies as the\\nsine of the zenith distance of the body directly, and the distance\\nof the body from the center of the earth inversely. Parallax, there-\\nfore, increases as a body approaches the horizon, (but increasing\\nwith the sines, it increases much slower than in the simple ratio\\nof the distance from the zenith,) and diminishes, as the distance\\nfrom the spectator increases* Again, since the parallax AGC is as\\nthe sine of the zenith distance, let P represent the horizontal par-\\nallax, and P the parallax at any altitude then,\\nThe moon, on account of its nearness to the earth, has the greatest horizontal\\nparallax of any of the heavenly bodies yet this is less than 1\u00c2\u00b0 (being 570 while the\\ngreatest parallax of any of the planets does not exceed 30 The difference in an\\narc of 1\u00c2\u00b0, between the length of the arc and the sine, is only 0. 18.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0055.jp2"}, "56": {"fulltext": "30 THE EARTH.\\nP\\nP P sin. zenith dist. sin. 90\u00c2\u00b0.\\\\P=\u00e2\u0080\u0094 -jrr-\\nsm. zen. dist.\\nHence, the horizontal parallax of a body equals its parallax at\\nany altitude, divided by the sine of its distance from the zenith.\\n83. From observations, therefore, on the parallax of a body at\\nany elevation, we are enabled to find the angle subtended by the\\nsemi-diameter of the earth as seen from the body. Or if the\\nhorizontal parallax is given, the parallax at any altitude may be\\nfound, for\\np/=Pxsin. zenith distance.\\nHence, in the zenith the parallax is nothing, and is at its max-\\nimum in the horizon.\\n84. It is evident from the figure, that the effect of parallax\\nupon the place of a celestial body is to depress it. Thus, in con-\\nsequence of parallax, E is depressed by the arc H h F by the\\narc Vp G by the arc Rr while H sustains no change. Hence,\\nin all calculations respecting the altitude of the sun, moon, or plan-\\nets, the amount of parallax is to be added the stars, as we shall\\nsee hereafter, have no sensible parallax. As the depression which\\narises from parallax is in the direction of a vertical circle, a body,\\nwhen on the meridian, has only a parallax in declination but\\nin other situations, there is at the same time a parallax in\\ndeclination and right ascension for its direction being oblique\\nto the equinoctial, it can be resolved into two parts, one of which\\n(the declination) is perpendicular, and the other (the right ascen-\\nsion) is parallel to the equinoctial.\\n85. The mode of determining the horizontal parallax, is as\\nfollows\\nLet O, O (Fig. 7,) be two places n the earth, situated under\\nthe same meridian, at a great distance from each other one place,\\nfor example, at the Cape of Good Hope, and the other in the north\\nof Europe. The latitude of each place being known, the arc of\\nthe meridian 00 is known, and the angle OCO also is known.\\nLet the celestial body M, (the moon for example,) he observed\\nsimultaneously at O and O and its zenith distance at each place", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0056.jp2"}, "57": {"fulltext": "PARALLAX.\\n31\\naccurately taken, namely, ZY and Flff\\nZ Y then the angles ZOM and\\nZOM, and of course their sup-\\nplements COM,CO M are found.\\nThen in the quadrilateral figure\\nCOMO we have all the angles\\nand the two radii, CO, CO\\nwhence by joining 00 the side\\nOM may be easily found. Hav-\\ning- CO and OM, we may find\\nCMO=sine of the angle of par-\\nallax; or (since the arc is very\\nsmall) equals the parallax P\\nBut when M as seen from O is in the horizon, ZOM becomes a\\nright angle, and its sine equal to radius. Then, CM being found,\\nCM CO 1 P=horizontal parallax=^.\\nOn this principle, the horizontal parallax of the moon was de-\\ntermined by La Caille and La Lande, two French astronomers,\\none stationed at the Cape of Good Hope, the other at Berlin and\\nin a similar way the parallax of Mars was ascertained, by ob-\\nservations made simultaneously at the Cape of Good Hope and\\nat Stockholm.\\n86. On account of the great distance of the sun, his horizontal\\nparallax, which is only 8 .6, cannot be accurately ascertained by\\nthis method. It can, however, be determined by means of the\\ntransits of Venus, a process to be described hereafter.\\n87. The determination of the horizontal parallax of a celestial\\nbody is an element of great importance, since it furnishes the\\nmeans of estimating the distance of the body from the center of\\nthe earth. Thus, if the angle AEC (Fig. 6,) be found, the radius\\nof the earth AC being known, we have in the triangle AEC,\\nright angled at A, the side AC and all the angles, to find the hypo-\\nthenuse CE, which is the distance of the moon from the center\\nof the earth.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0057.jp2"}, "58": {"fulltext": "32 THE EARTH.\\nREFRACTION.\\n88. While parallax depresses the celestial bodies subject to it,\\nrefraction elevates them; and it affects alike the most distant\\nas well as nearer bodies, being occasioned by the change of di-\\nrection which light undergoes in passing through the atmos-\\nphere. Let us conceive of the atmosphere as made up of a great\\nnumber of concentric strata, as A A, BB, CC, and DD, (Fig. 8,)\\nFig. 8.\\nincreasing rapidly in density (as is known to be the fact) in ap-\\nproaching near to the surface of the earth. Let S be a star, from\\nwhich a ray of light Sa enters the atmosphere at a, where, being\\nturned towards the radius of the convex surface, it would change\\nits direction into the line ab, and again into be, and cO, reach-\\ning the eye at O. Now, since an object always appears in the\\ndirection in which the light finally strikes the eye, the star would\\nbe seen in the direction of the last ray cO, and the star would\\napparently change its place, in consequence of refraction, from\\nS to S being elevated out of its true position. Moreover,\\nsince on account of the constant increase of density in descend-\\ning through the atmosphere, the light would be continually turned\\nout of its course more and more, it would therefore move, not\\nin the polygon represented in the figure, but in a corresponding\\ncurve, whose curvature is rapidly increased near the surface of\\nthe earth.\\n89. When a body is in the zenith, since a ray of light from it\\nenters the atmosphere at right angles to the refracting medium, it\\nsuffers no refraction. Consequently, the position of the heavenly", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0058.jp2"}, "59": {"fulltext": "REFRACTION.\\n33\\nbodies, when in the zenith, is not changed by refraction, while,\\nnear the horizon, where a ray of light strikes the medium very\\nobliquely, and traverses the atmosphere through its densest part,\\nthe refraction is greatest. The following numbers, taken at dif-\\nferent altitudes, will show how rapidly refraction diminishes from\\nthe horizon upwards. The amount of refraction at the horizon\\nis 34- 00 At different elevations it is as follows.\\nElevation.\\nRefraction.\\nElevation.\\nRefraction.\\nC 10\\n32 00\\n30\u00c2\u00b0\\nV 40\\n20\\n30 00\\n40\\n1 09\\n1 00\\n24 25\\n45\\n58\\n5 00\\n10 00\\n60\\n33\\n10 00\\n5 20\\n80\\n10\\n20 00\\n2 39\\n90\\n00\\nFrom this table it appears, that while refraction at the horizon\\nis 34 minutes, at so small an elevation as only 10 minutes above\\nthe horizon it loses 2 minutes, more than the entire change from\\nthe elevation of 30\u00c2\u00b0 to the zenith. From the horizon to 1\u00c2\u00b0 above,\\nthe refraction is diminished nearly 10 minutes. The amount at\\nthe horizon, at 45\u00c2\u00b0, and at 90\u00c2\u00b0, respectively, is 34 58 and 0. In\\nfinding the altitude of a heavenly body, the effect of parallax must\\nbe added, but that of refraction subtracted.\\n90. Let us now learn the method, by which the amount of re-\\nfraction at different elevations is ascertained. To take the sim-\\nplest case, we will suppose ourselves in a high latitude, where\\nsome of the stars within the circle of perpetual apparition pass\\nthrough the zenith of the place. We measure the distance of\\nsuch a star from the pole when on the meridian above the pole,\\nthat is, in the zenith, where it is not at all affected by refraction,\\nand again its distance from the pole in its lower culmination.\\nWere it not for refraction, these two polar distances would be\\nequal, since, in the diurnal revolution of a star, it is in fact always\\nat the same distance from the pole but, on account of refraction,\\nthe lower distance will be less than the upper, and the difference\\nbetween the two will show the amount of refraction at the lower\\nculmination, the latitude of the place being known.\\nExample. At Paris, latitude 48\u00c2\u00b0 50 a star was observed to", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0059.jp2"}, "60": {"fulltext": "34\\nTHE EARTH.\\npass the meridian 6 north of the zenith, and consequently, 41\u00c2\u00b0 4\\nfrom the pole.* It should have passed the meridian at the same\\ndistance below the pole, but the distance was found to be only\\n40\u00c2\u00b0 57 35 Hence, 41\u00c2\u00b0 4 -40\u00c2\u00b0 57 35 =6 25 is the refraction\\ndue to that altitude, that is, at the altitude of 7\u00c2\u00b0 46 =(48\u00c2\u00b0 50\\n41\u00c2\u00b0 4 By taking similar observations in various places situated\\nin high latitudes, the amount of refraction might be ascertained\\nfor a number of different altitudes, and thus the law of increase\\nin refraction as we proceed from the zenith towards the horizon,\\nmight be ascertained.\\n91. Another method of finding the refraction at different alti-\\ntudes, is as follows. Take the altitude of the sun or a star, whose\\nright ascension and declination are known, and note the time by\\nthe clock. Observe also when it crosses the meridian, and the\\ndifference of time between the two observations will give the hour\\nangle ZPa:, (Fig. 9.) In this triangle ZPa: we also know PZ the\\nFig. 9.\\nco-latitude and Pa? the co-declination. Hence we can find the co-\\naltitude Za?, and of course the true altitude. Compare the alti-\\ntude thus found with that before determined by observation, and\\nthe difference will be the refraction due to the apparent altitude.\\n*For the polar distance of the plaee=90-48\u00c2\u00b0 50 =41\u00c2\u00b0 10 and 41\u00c2\u00b0 10 -6\\n41\u00c2\u00b0 4.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0060.jp2"}, "61": {"fulltext": "REFRACTION. 35\\nEx. On May 1, 1738, at 5h. 20m. in the morning, Cassini ob-\\nserved the altitude of the sun s center at Paris to be 5\u00c2\u00b0 0 14 The\\nlatitude of Paris being 48\u00c2\u00b0 50 10 and the sun s declination at\\nthat time being 15\u00c2\u00b0 0 25 Required the refraction.\\nBy spherical trigonometry, Zx will be found equal to 85\u00c2\u00b0 10\\n8 consequently, the true altitude was 4\u00c2\u00b0 49 52 Now to 5\u00c2\u00b0\\n0 14 the apparent altitude, 9 must be added for parallax,\\nand we have 5\u00c2\u00b0 0 23 the apparent altitude corrected for parallax\\nHence, 5\u00c2\u00b0 0 23 -4\u00c2\u00b0 49 52 =10 31 the refraction at the ap-\\nparent altitude 5\u00c2\u00b0 0 14\\n92. By these and similar methods, we could easily determine\\nthe refraction due to any elevation above the horizon, provided\\nthe refracting medium (the atmosphere) were always uniform.\\nBut this is not the fact the refracting power of the atmosphere\\nis altered by changes in density and temperature. f Hence in\\ndelicate observations, it is necessary to take into the account the\\nstate of the barometer and of the thermometer, the influence of\\nthe variations of each having been very carefully investigated,\\nand rules having been given accordingly. With every precaution\\nto insure accuracy, on account of the variable character of the\\nrefracting medium, the tables are not considered as entirely accu-\\nrate to a greater distance from the zenith than 74\u00c2\u00b0 but almost all\\nastronomical observations are made at a greater altitude than this.\\n93. Since the whole amount of refraction near the horizon ex-\\nceeds 33 and the diameters of the sun and moon are severally\\nless than this, these luminaries are in view both before they have\\nactually risen and after they have set.\\n94. The rapid increase of refraction near the horizon, is strik-\\ningly evinced by the oval figure which the sun assumes when\\nnear the horizon, and which is seen to the greatest advantage\\nwhen light clouds enable us to view the solar disk. Were all\\nGregory s Ast. p. 65.\\nt It is said that the effects of humidity are insensible for the most accurate\\nexperiments seem to prove that watery vapor diminishes the density of air in the\\nsame ratio as its own refractive power is greater than that of air. (New Encyc.\\nBrit. Ill, 762.)", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0061.jp2"}, "62": {"fulltext": "36 THE EARTH.\\nparts of the sun equally raised by refraction, there would be no\\nchange of figure but since the lower side is more refracted than\\nthe upper, the effect is to shorten the vertical diameter and thus\\nto give the disk an oval form. This effect is particularly remark-\\nable when the sun, at his rising or setting, is observed from the\\ntop of a mountain, or at an elevation near the sea shore for in\\nsuch situations the rays of light make a greater angle than or-\\ndinary with a perpendicular to the refracting medium, and the\\namount of refraction is proportionally greater. In some cases of\\nthis kind, the shortening of the vertical diameter of the sun has\\nbeen observed to amount to 6 or about one fifth of the whole.*\\n95. The apparent enlargement of the sun and moon in the hori-\\nzon, arises from an optical illusion. These bodies in fact are\\nnot seen under so great an angle when in the horizon, as when on\\nthe meridian, for they are nearer to us in the latter case than in\\nthe former. The distance of the sun is indeed so great that it\\nmakes very little difference in his apparent diameter, whether he\\nis viewed in the horizon or on the meridian but with the moon\\nthe case is otherwise its angular diameter, when measured with\\ninstruments, is perceptibly larger at the time of its culmination.\\nWhy then do the sun and moon appear so much larger when near\\nthe horizon 1 It is owing to that general law, explained in optics,\\nby which we judge of the magnitudes of distant objects, not\\nmerely by the angle they subtend at the eye, but also by our im-\\npressions respecting their distance, allowing, under a given angle,\\na greater magnitude as we imagine the distance of a body to be\\ngreater. Now, on account of the numerous objects usually in\\nsight between us and the sun, when on the horizon, he appears\\nmuch further removed from us than when on the meridian, and\\nwe assign to him a proportionally greater magnitude. If we view\\nthe sun, in the two positions, through smoked glass, no such dif-\\nference of size is observed, for here no objects are seen but the\\nsun himself.\\nIn extreme cold weather, this shortening of the sun s vertical diameter sometimes\\nexceeds this amount.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0062.jp2"}, "63": {"fulltext": "TWILIGHT. 37\\nTWILIGHT.\\n96. Twilight also is another phenomenon depending upon the\\nagency of the earth s atmosphere. It is due partly to refraction\\nand partly to reflexion, but mostly the latter. While the sun\\nis within 18\u00c2\u00b0 of the horizon, before it rises or after it sets, some\\nportion of its light is conveyed to us by means of numerous re-\\nflections from the atmosphere. Let AB (Fig. 10,) be the horizon\\nFig. 10.\\nof the spectator at A, and let SS be a ray of light from the sun\\nwhen it is two or three degrees below the horizon. Then to\\nthe observer at A, the segment of the atmosphere ABS would be\\nilluminated. To a spectator at C, whose horizon was CD, the\\nsmall segment SDx would be the twilight while, at E, the twi-\\nlight would disappear altogether.\\n97. At the equator, where the circles of daily motion are per-\\npendicular to the horizon, the sun descends through 18\u00c2\u00b0 in an\\nhour and twelve minutes (}f =l}h.), and the light of day there-\\nfore declines rapidly, and as rapidly advances after daybreak in the\\nmorning. At the pole, a constant twilight is enjoyed while the sun\\nis .within 13\u00c2\u00b0 of the .horizon, occupying nearly two thirds of the\\nhalf year when the direct light of the sun is withdrawn, so that\\nthe progress from continual day to constant night is exceedingly\\ngradual. To the inhabitants of an oblique sphere, the twilight\\nis longer in proportion as the place is nearer the elevated pole.\\n98. Were it not for the power the atmosphere has of dispersing", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0063.jp2"}, "64": {"fulltext": "38 THE EARTH.\\nthe solar light, and scattering it in various directions, no objects\\nwould be visible to us out of direct sunshine every shadow of a\\npassing cloud would be pitchy darkness the stars would be visi-\\nble all day, and every apartment into which the sun had not di-\\nrect admission, would be involved in the obscurity of night. This\\nscattering action of the atmosphere on the solar light, is greatly\\nincreased by the irregularity of temperature caused by the sun,\\nwhich throws the atmosphere into a constant state of undulation,\\nand by thus bringing together masses of air of different tempera-\\ntures, produces partial reflections and refractions at their common\\nboundaries, by which means much light is turned aside from the\\ndirect course, and diverted to the purposes of general illumination.*\\nIn the upper regions of the atmosphere, as on the tops of very\\nhigh mountains, where the air is too much rarefied to reflect much\\nlight, the sky assumes a black appearance, and stars become visi-\\nble in the day time.\\nCHAPTER IV.\\nOF TIME.\\n99. Time is a measured portion of indefinite duration.\\nAny event may be taken as a measure of time, which divides\\na portion of duration into equal parts as the pulsations of the\\nwrist, the vibrations of a pendulum, or the passage of sand from\\none vessel into another, as in the hour-glass.\\n100. The great standard of time is the period of the revolution\\nof the earth on its axis, which, by the most exact observations, is\\nfound to be always the same. The time of the earth s revolution\\non its axis is called a sidereal day, and is determined by the revo-\\nlution of a star from the instant it crosses the meridian, until it\\ncomes round to the meridian again. This interval being called a\\nHerschel.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0064.jp2"}, "65": {"fulltext": "TIME.\\n39\\nsidereal day, it is divided into 24 sidereal hours. Observations\\ntaken upon numerous stars, in different ages of the world, show\\nthat they all perform their diurnal revolutions in the same time,\\nand that their motion during any part of the revolution is per-\\nfectly uniform.\\n101. Solar time is reckoned by the apparent revolution of the\\nsun, from the meridian round to the same meridian again. Were\\nthe sun stationary in the heavens, like a fixed star, the time of its\\napparent revolution would be equal to the revolution of the earth\\non its axis, and the solar and the sidereal days would be equal.\\nBut since the sun passes from west to east, through 360\u00c2\u00b0 in 365\u00c2\u00a3\\ndays, it moves eastward nearly 1\u00c2\u00b0 a day, (59 8 .3). While,\\ntherefore, the earth is turning round on its axis, the sun is moving\\nin the same direction, so that when we have come round under\\nthe same celestial meridian from which we started, we do not\\nfind the sun there, but he has moved eastward nearly a degree,\\nand the earth must perform so much more than one complete\\nrevolution, in order to come under the sun again. Now since a\\nplace on the earth gains 359\u00c2\u00b0 in 24 hours, how long will it take\\nto gain 1\u00c2\u00b0\\n94\\n359 24 1 \u00e2\u0080\u0094=4 m nearly.\\n359 J\\nHence the solar day is about 4 minutes longer than the sidereal\\nand if we were to reckon the sidereal day 24 hours, we should\\nreckon the solar day 24h. 4m. To suit the purposes of society at\\nlarge, however, it is found most convenient to reckon the solar day\\n24 hours, and to throw the fraction into the sidereal day. Then,\\n24h. 4m. 24 24 23h. 56m. (23h. 56 m 4 S .09) the length\\nof a sidereal day.\\n102. The solar days, however, do not always differ from the\\nsidereal by precisely the same fraction, since the increments of\\nright ascension, (Art. 37,) which measure the difference between\\na sidereal and a solar day, are not equal to each other. Apparent\\ntime, is time reckoned by the revolutions of the sun from the\\nmeridian to the meridian again. These intervals being unequal,\\nof course the apparent solar days are unequal to each other.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0065.jp2"}, "66": {"fulltext": "40 THE EARTH.\\n103. Mean time, is time reckoned by the average length of all\\nthe solar days throughout the year. This is the period which con-\\nstitutes the civil day of 24 hours, beginning when the sun is on\\nthe lower meridian, namely, at 12 o clock at night, and counted\\nby 12 hours from the lower to the upper culmination, and from\\nthe upper to the lower. The astronomical day is the apparent\\nsolar day counted through the whole 24 hours, instead of by pe-\\nriods of 12 hours each, and begins at noon. Thus 10 days and\\n14 hours of astronomical time, would be 1 1 days and 2 hours of\\ncivil time.\\n104. Clocks are usually regulated so as to indicate mean solar\\ntime yet as this is an artificial period, not marked off, like the\\nsidereal day, by any natural event, it is necessary to know how\\nmuch is to be added to or subtracted from the apparent solar\\ntime, in order to give the corresponding mean time. The inter-\\nval by which apparent time differs from mean time, is called the\\nequation of time. If a clock were constructed (as it may be) so\\nas to keep exactly with the sun, going faster or slower according\\nas the increments of right ascension were greater or smaller, and\\nanother clock were regulated to mean time, then the difference\\nof the two clocks, at any period, would be the equation of time\\nfor that moment. If the apparent clock were faster than the\\nmean, then the equation of time must be subtracted but if the\\napparent clock were slower than the mean, then the equation of\\ntime must be added, to give the mean time. The two clocks\\nwould differ most about the 3d of November, when the apparent\\ntime is 16\u00c2\u00a3 m greater than the mean (16 ra 17 B But, since appa-\\nrent time is sometimes greater and sometimes less than mean\\ntime, the two must obviously be sometimes equal to each other.\\nThis is in fact the case four times a year, namely, April 15th,\\nJune 15th, September 1st, and December 22d. These epochs,\\nhowever, do not remain constant for, on account of the change\\nin the position of the perihelion, or the point where the earth is\\nnearest the sun, (which shifts its place from west to east about\\n12 a year,) the period when the sun s motions are most rapid, as\\nwell as that when they are slowest, will occur at different parts of\\nthe year. The change is indeed exceedingly small in a single", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0066.jp2"}, "67": {"fulltext": "TIME.\\n41\\nyear but in the progress of ages, the time of year when the sun s\\nmotion in its orbit is most accelerated, will not be, as at present, on\\nthe first of January, but may fall on the first of March, June, or\\nany other day of the year, and the amount of the equation of\\ntime is obviously affected by the sun s distance from its perihelion,\\nsince the sun moves most rapidly when nearest the perihelion, and\\nslowest when furthest from that point.\\n105. The inequality of the solar days depends on two causes, the\\nunequal motion of the earth in its orbit, and the inclination of the\\nequator to the ecliptic.\\nFirst, on account of the eccentricity* of the earth s orbit, the\\nearth actually moves faster from the autumnal to the vernal equi-\\nnox, than from the vernal to the autumnal, the difference of the\\ntwo periods being about eight days (7d. 17h. 17m.) Thus, let\\nFig. n.\\nAEB (Fig. 11,) represent the earth s orbit, S being the place of\\nThe exact figure of the earth s orbit will be more particularly shown hereafter.\\nAll that the student requires to know, in order to understand the present subject,\\n6", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0067.jp2"}, "68": {"fulltext": "42 THE EARTH.\\nthe sun, A the perihelion, or nearest distance of the earth from\\nthe sun, B the aphelion, or greatest distance, and E, E E posi-\\ntions of the earth in different points of its orbit. The place of\\nthe earth among the signs is the part of the heavens to which it\\nwould be referred if seen from the sun and the place of the sun\\nis the part of the heavens to which it is referred as seen from the\\nearth. Thus, when the earth is at E, it is said to be in Aries\\nand as it moves from E through E to A, its path in the heavens\\nis through Aries, Taurus, Gemini, c. Meanwhile the sun takes\\nits place successively in Libra, Scorpio, Sagittarius, c. Now,\\nas will be shown more fully hereafter, the earth moves faster\\nwhen proceeding from Aries through its perihelion to Libra, than\\nfrom Libra through its aphelion to Aries, and, consequently, de-\\nscribes the half of its apparent orbit in the heavens, T, S\\nsooner than the half VS, T. The line of the apsides, that is,\\nthe major axis of the ellipse, is so situated at present, that the\\nperihelion is in the sign Cancer, nearly 100\u00c2\u00b0 (99\u00c2\u00b0 30 5 from the\\nvernal equinox. The earth passes through it about the first of\\nJanuary, and then its velocity is the greatest in the whole year,\\nbeing always greater as the distance is less, the angular velocity\\nbeing inversely as the square of the distance, as will be shown by\\nand by.\\n106. But differences of time are not reckoned on the eclip-\\ntic, but on the equinoctial for the ecliptic being oblique to the\\nmeridian in the diurnal motion, and cutting it at different angles at\\ndifferent times, equal portions will not pass under the meridian in\\nequal times, and therefore such portions could not be employed, as\\nthey are in the equinoctial, as measures of time. If therefore the\\nsun moved uniformly in his orbit, so as to make the daily incre-\\nments of longitude equal, still the corresponding arcs of right as-\\ncension, which determine the lengths of the solar day, would be\\nunequal. Let us start from the equinox, from which both longi-\\ntude and right ascension are reckoned, the former on the ecliptic,\\nis that the earth s orbit is an ellipse, and that the earth s real motion, and conse-\\nquently the sun s apparent motion, is greater in proportion as the earth is nearer\\n(he sun.", "height": "3995", "width": "2473", "jp2-path": "introductionto00olm_0068.jp2"}, "69": {"fulltext": "TIME.\\n43\\nthe latter on the equinoctial. Suppose the sun has described 70\u00c2\u00b0\\nof longitude then to ascertain the corresponding arc of right as-\\ncension, we let a meridian pass through the sun the point where\\nit cuts the equator gives the sun s right ascension. Now since the\\necliptic makes an acute angle with the meridian, while the equi-\\nnoctial makes a right angle with it, consequently the arc of longi-\\ntude is greater than the arc of right ascension. The difference,\\nhowever, grows constantly less and less as we approach the tropic,\\nas the angle made between the ecliptic and the meridian constantly\\nincreases, until, when we reach the tropic, the meridian is at right\\nangles to both circles, and the longitude and right ascension each\\nequals 90\u00c2\u00b0, and they are of course equal to each other. Beyond\\nthis, from the tropic to the other equinox, the arc of the ecliptic\\nintercepted between the meridian and the autumnal equinox being\\ngreater than the corresponding arc of the equinoctial, of course\\nits supplement, which measures the longitude, is less than the sup-\\nplement of the corresponding arc of the equator which measures\\nthe right ascension. At the autumnal equinox again, the right\\nascension and longitude become equal. In a similar manner we\\nmight show that the daily increments of longitude and right as-\\ncension are unequal.\\nIn order to illustrate the foregoing points, let T (Fig. 12,\\nFig. 12.\\nrepresent the equator, T T the ecliptic, and PSE, PSE two\\nmeridians meeting the sun in S and S Then in the triangle TES,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0069.jp2"}, "70": {"fulltext": "44 THE EARTH.\\nthe arc of longitude TS, is greater than TE, the corresponding\\narc of right ascension but towards the tropic the difference\\nbetween the two arcs evidently grows less and less, until at T\\nthe arcs become equal, being each 90\u00c2\u00b0. But, beyond the tropic,\\nsince TE TS /=2 are equal to each other, each being equal\\nto 180\u00c2\u00b0, and since S is greater than E =a=, therefore TS must\\nbe less than TE\\n1 07. As the whole arc of right ascension reckoned from the\\nfirst of Aries, does not keep uniform pace with the corresponding\\narc of longitude, so the daily increments of right ascension differ\\nfrom those of longitude. If we suppose in the quadrant TT,\\npoints taken to mark the progress of the sun from day to day, and\\nlet meridians like PSE pass through these points, the arc of the\\necliptic embraced between the meridians will be the daily incre-\\nments of longitude, while the corresponding parts of the equinoc-\\ntial will be the daily increments of right ascension. Near T, the\\noblique direction in which the ecliptic cuts the meridian, will make\\nthe daily increments of longitude exceed those of right ascension\\nbut this advantage is diminished as we approach the tropic, where\\n.he ecliptic becomes less oblique, and finally parallel to the equi-\\nloctial while the convergence of the meridians contributes still\\nfarther to lessen the ratios of the daily increments of longitude to\\nthose of right ascension. Hence, at first, the diurnal arcs of\\nright ascension are less than those of longitude, but afterwards\\ngreater and they continue greater for a similar distance beyond\\nthe tropic.\\n108. From the foregoing considerations it appears, that the\\ndiurnal arcs of right ascension, by which the difference between\\nthe sidereal and the solar days is measured, are unequal, on ac-\\ncount both of the unequal motion of the sun in his orbit, and of\\nthe inclination of his orbit to the equinoctial.\\n109. As astronomical time commences when the sun is on the\\nmeridian, so sidereal time commences when the vernal equinox\\nis on the meridian, and is also counted from to 24 hours. By\\n3 o clock, for instance, of sidereal time, we mean that it is three", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0070.jp2"}, "71": {"fulltext": "THE CALENDAR. 45\\nhours since the vernal equinox crossed the meridian as we say it\\nis 3 o clock of astronomical or of civil time, when it is three hours\\nsince the sun crossed the meridian.\\nTHE CALENDAR.\\n1 1 0. The astronomical year is the time in which the sun makes\\none revolution in the ecliptic, and consists of 365d. 5h. 48m. 5P.60.\\nThe civil year consists of 365 days. The difference is nearly 6\\nhours, making one day in four years.\\n111. The most ancient nations determined the number of days\\nin the year by means of the stylus, a perpendicular rod which\\ncast its shadow on a smooth plane, bearing a meridian line. The\\ntime when the shadow was shortest, would indicate the day of\\nthe summer solstice and the number of days which elapsed until\\nthe shadow returned to the same length again, would show the\\nnumber of days in the year. This was found to be 365 whole\\ndays, and accordingly this period was adopted for the civil year.\\nSuch a difference, however, between the civil and astronomical\\nyears, at length threw all dates into confusion. For, if at first\\nthe summer solstice happened on the 21st of June, at the end of\\nfour years, the sun would not have reached the solstice until the\\n22d of June, that is, it would have been behind its time. At the\\nend of the next four years the solstice would fall on the 23d\\nand in process of time it would fall successively on every day of\\nthe year. The same would be true of any other fixed date.\\nJulius Caesar made the first correction of the calendar, by intro-\\nducing an intercalary day every fourth year, making February\\nto consist of 29 instead of 28 days, and of course the whole year\\nto consist of 366 days. This fourth year was denominated Bis-\\nsextile.* It is also called Leap Year.\\n112. But the true correction was not 6 hours, but 5h. 49m.;\\nhence the intercalation was too great by 1 1 minutes. This small\\nfraction would amount in 100 years to of a day, and in 1000\\nThe sextus dies ante Kalendas being reckoned twice, (Bis).", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0071.jp2"}, "72": {"fulltext": "46 THE EARTH.\\nyears to more than 7 days. From the year 325 to 1582, it had\\nin fact amounted to about 10 days; for it was known that in 325,\\nthe vernal equinox fell on the 21st of March, whereas, in 1582 it\\nfell on the 11th. In order to restore the equinox to the same date,\\nPope Gregory XIII decreed, that the year should be brought for-\\nward ten days, by reckoning the 5th of October the 15th. In or-\\nder to prevent the calendar from falling into confusion afterwards,\\nthe following rule was adopted\\nEvery year whose number is not divisible by 4 without a re-\\nmainder, consists of 365 days every year which is so divisible, but\\nis not divisible by 100, of 366; every year divisible by 100 but not\\nby 400, again of 365 and every year divisible by 400, of 366.\\nThus the year 1838, not being divisible by four, contains 365 days,\\nwhile 1836 and 1840 are leap years. Yet to make every fourth\\nyear consist of 366 days would increase it too much by about\\nof a day in 100 years; therefore every hundredth year has only\\n365 days. Thus 1800, although divisible by 4, was not a leap\\nyear, but a common year. But we have allowed a whole day\\nin a hundred years, whereas we ought to have allowed only three\\nfourths of a day. Hence, in 400 years we should allow a day too\\nmuch, and therefore we let the 400th year remain a leap year.\\nThis rule involves an error of less than a day in 4237 years.* If\\nthe rule were extended by making every year divisible by 4,000\\n(which would now consist of 366 days) to consist of 365 days, the\\nerror would not be more than one day in 100,000 years. f\\n113. This reformation of the calendar was not adopted in Eng-\\nland until 1752, by which time the error in the Julian calendar\\namounted to about 11 days. The year was brought forward, by\\nreckoning the 3d of September the 14th. Previous to that time\\nthe year began the 25th of March but it was now made to be-\\ngin on the 1st of January, thus shortening the preceding year,\\n1751, one quarter. J\\nWoodhouse, p. 874. t Herschel s Ast. p. 384.\\nRussia, and the Greek Church generally, adhere to the old style. In order to make\\nthe Russian dates correspond to ours, we must add to them 12 days. France and other\\nCatholic countries, adopted the Gregorian calendar soon after it was promulgated.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0072.jp2"}, "73": {"fulltext": "THE CALENDAR. 47\\n114. As in the year 1582, the error in the Julian calendar\\namounted to 10 days, and increased by of a day in a century,\\nat present the correction is 12 days and the number of the year\\nwill differ by one with respect to dates between the 1st of Janu-\\nary and the 25th of March.\\nExamples. General Washington was born Feb. 11, 1731, old\\nstyle to what date does this correspond in new style\\nAs the date is the earlier part of the 18th century, the correc-\\ntion is 1 1 days, which makes the birth day fall on the 22d of\\nFebruary; and since the year 1731 closed the 25th of March,\\nwhile according to new style 1732 would have commenced on\\nthe preceding 1st of January therefore, the time required is Feb.\\n22, 1732. It is usual, in such cases, to write both years, thus:\\nFeb. 11, 1731-2, O. S.\\n2. A great eclipse of the sun happened May 15th, 1836 to\\nwhat date would this time correspond in old style\\nAns. May. 3d.\\n115. The common year begins and ends on the same day of\\nthe week but leap year ends one day later in the iveeh than it began.\\nFor 52x7=364 days; if therefore the year begins on Tues-\\nday, for example, 364 days would complete 52 weeks, and one\\nday would be left to begin another week, and the following year\\nwould begin on Wednesday. Hence, any day of the month is one\\nday later in the week than the corresponding day of the preceding\\nyear. Thus, if the 16th of November, 1838, falls on Friday,\\nthe 16th of November, 1837, fell on Thursday, and will fall in\\n1839 on Saturday. But if leap year begins on Sunday, it ends\\non Monday, and the following year begins on Tuesday while\\nany given day of the month is two days later in the week than\\nthe corresponding date of the preceding year.\\n116. Fortunately for astronomy, the confusion of dates involved\\nin different calendars affects recorded observations but little. Re-\\nmarkable eclipses, for example, can be calculated back for several\\nthousand years, without any danger of mistaking the day of their\\noccurrence and whenever any such eclipse is so interwoven with\\nthe account given by an ancient author of some historical event,", "height": "4117", "width": "2302", "jp2-path": "introductionto00olm_0073.jp2"}, "74": {"fulltext": "48 THE EARTH.\\nas to indicate precisely the interval of time between the eclipse\\nand the event, and at the same time completely to identify the\\neclipse, that date is recovered and fixed forever.*\\nCHAPTER V.\\nOP ASTRONOMICAL INSTRUMENTS AND PROBLEMS FIGURE AND DEN-\\nSITY OP THE EARTH.\\n117. The most ancient astronomers employed no instruments\\nfor measuring angles, but acquired their knowledge of the heav-\\nenly bodies by long continued and most attentive inspection with\\nthe naked eye. In the Alexandrian school, about 300 years before\\nthe Christian era, instruments began to be freely used, and thence-\\nforward trigonometry lent a powerful aid to the science of astron-\\nomy. Tycho Brahe, in the 16th century, formed a new era in\\npractical astronomy, and carried the measurement of angles to\\n10 a degree of accuracy truly wonderful, considering that he\\nhad not the advantage of the telescope. By the application of\\nthe telescope to astronomical instruments, a far better defined view\\nof objects was acquired, and a far greater degree of refinement\\nwas attainable. The astronomers royal of Great Britain perfected\\nthe art of observation, bringing the measurement of angles to 1\\nand the estimation of differences of time to T V of a second. Be-\\nyond this degree of refinement it is supposed that we cannot\\nadvance, since unavoidable errors arising from the uncertainties\\nof refraction, and the necessary imperfection of instruments, for-\\nbid us to hope for a more accurate determination than this. But\\na little reflection will show us, that 1 on the limb of an astro-\\nnomical instrument, must be a space exceedingly small. Suppose\\nthe circle, on which the angle is measured, be one foot in diameter.\\nAn elaborate view of the Calendar may be found in Delambre s Astronomy, t. III.\\nA useful table for finding the day of the week of any given date, is inserted in the\\nAmerican Almanac for 1832, p. 72.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0074.jp2"}, "75": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 49\\n12x3.14159 10\\nThen T V inch space occupied by 1\u00c2\u00b0. Hence\\n=space of and =space of 1 Such minute\\n10X60 600 i 36000 v\\nangles can be measured only by large circles. If. for example,\\na circle is 20 feet in diameter, a degree on its periphery would\\noccupy a space 20 times as large as a degree on a circle of 1 foot.\\nA degree therefore of the limb of such an instrument would\\noccupy a space of 2 inches one minute, of an inch and one\\nsecond, TJ 7 of an inch.\\n118. But the actual divisions on the limb of an astronomical\\ninstrument never extend to seconds in the smaller instruments\\nthey reach only to 10 and on the largest rarely lower than 1\\nThe subdivision of these spaces is carried on by means of the\\nVernier, which may be thus defined\\nA Vernier is a contrivancce attached to the graduated limb of\\nan instrument, for the purpose of measuring aliquot parts of the\\nsmallest spaces, into which the instrument is divided.\\nThe vernier is usually a narrow zone of metal, which is made\\nto slide on the graduated limb. Its divisions correspond to those\\non the limb, except that they are a little larger,* one tenth, for\\nexample, so that ten divisions on the vernier w T ould equal eleven\\non the limb. Suppose now that our instrument is graduated to\\ndegrees only, but the altitude of a certain star is found to be 40\u00c2\u00b0\\nand a fraction, or 40\u00c2\u00b0+ff. In order to estimate the amount of this\\nfraction, we bring the zero point of the vernier to coincide with\\nthe point which indicates the exact altitude, or 40\u00c2\u00b0 +x. We then\\nlook along the vernier until we find where one of its divisions\\ncoincides with one of the divisions of the limb. Let this be at the\\nfourth division of the vernier. In four divisions, therefore, the ver-\\nnier has gained upon the divisions of the limb, a space equal to x\\nand since, in the case supposed, it gains T V of a degree, or 6 at each\\ndivision, the entire gain is 24 and the arc in question is 40\u00c2\u00b0 24\\n119. As the vernier is used in the barometer, where its applica-\\nIn the more modern instruments the divisions of the vernier are smaller than those\\nof the limb.\\n7", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0075.jp2"}, "76": {"fulltext": "D0\\nTHE EARTH.\\ntion is more easily seen than in astronomical instruments, while the\\nprinciple is the same in both cases, let us Fig. 13.\\nsee how it is applied to measure the ex-\\nact height of a column of mercury. Let\\nAB (Fig. 13,) represent the upper part\\nof a barometer, the level of the mercury\\nbeing at C, namely, at 30.3 inches, and\\nnearly another tenth. The vernier being\\nbrought (by a screw which is usually at-\\ntached to it) to coincide with the surface\\nof the mercury, we look along down the\\nscale, until we find that the coincidence\\nis at the 8th division of the vernier.\\nNow as the vernier gains T of r T i t\\nof an inch at each division upward, it of\\ncourse gains T in eight divisions. The fractional quantity, there-\\nfore, is .08 of an inch, and the height of the mercury is 30.38. If\\nthe divisions of the vernier were such, that each gained jg (when\\n60 on the vernier would equal 61 on the limb) on a limb divided\\ninto degrees, we could at once take off minutes and were the limb\\ngraduated to minutes, we could in a similar way read off seconds.\\n120. The instruments most used for astronomical observations,\\nare the Transit Instrument, the Astronomical Clock, the Mural\\nCircle, and the Sextant. A large portion of all the observations,\\nmade in an astronomical observatory, are taken on the meridian.\\nWhen a heavenly body is on the meridian, being at its highest\\npoint above the horizon, it is then least affected by refraction and\\nparallax its zenith distance (from which its altitude and decli-\\nnation are easily derived) is readily estimated and its right as-\\ncension may be very conveniently and accurately determined by\\nmeans of the astronomical clock. Having the right ascension\\nand declination of a heavenly body, various other particulars re-\\nspecting its position may be found, as we shall see hereafter, by\\nthe aid of spherical trigonometry. Let us then first turn our at-\\ntention to the instruments employed for determining the right\\nascension and declination. They are the Transit Instrument, the\\nAstronomical Clock, and the Mural Circle.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0076.jp2"}, "77": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n51\\n121. The Transit Instrument is a telescope, which is fixed\\npermanently in the meridian, and moves only in that plane. It\\nrests on a horizontal axis, which consists of two hollow cones\\napplied base to base, a form uniting lightness and strength. The\\ntwo ends of the axis rest on two firm supports, as pillars of stone,\\nfor example, usually built up from the ground, and so related to\\nthe building as to be as free as possible from all agitation. In\\nfigure 14, AD represents the telescope, E, W, massive stone pillars\\nsupporting the horizontal axis, beneath which is seen a spirit level,\\n(which is used to bring the axis to a horizontal position,) and n a\\nvertical circle graduated into degrees and minutes. This circle\\nserves the purpose of placing the instrument at any required alti-\\ntude or distance from the zenith, and of course for determining\\naltitudes and zenith distances.\\nFig. 14.\\n122. Various methods are described in works on practical as-\\ntronomy, for placing the Transit Instrument accurately in the\\nmeridian. The following method by observations on the pole\\nstar, may serve as an example. If the instrument be directed", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0077.jp2"}, "78": {"fulltext": "52\\nTHE EARTH.\\ntowards the north star, and so adjusted that the star Alioth (the\\nfirst in the tail of the Great Bear) and the pole star are both in\\nthe same vertical circle, the former below the pole and the latter\\nabove it, the instrument will be nearly in the plane of the meridian.\\nTo adjust it more exactly, compare the time occupied by the pole\\nstar in passing from its upper to its lower culmination, with the\\ntime of passing from its lower to its upper culmination. These\\ntwo intervals ought to be precisely equal; and if they are so, the\\nlustrument is truly placed in the meridian but if they are not\\nequal, the position of the instrument must be shifted until they\\nbecome exactly equal.\\n123. The line of collimation of a telescope, is a line joining the\\ncenter of the object glass with the center of the eye glass. When\\nthe transit instrument is properly adjusted, this line, as the instru-\\nment is turned on its axis, moves in the plane of the meridian.\\nHaving, by means of the vertical circle n, set the instrument at\\nthe known altitude or zenith distance of any star, upon which we\\nwish to make observations, we wait until the star enters the field\\nof the telescope, and note the exact instant when it crosses the\\nvertical wire in the center of the field, which wire marks the true\\nplane of the meridian. Usually, however, there are placed in the\\nfocus of the eye glass five parallel wires or threads, two on each\\nside of the central wire, and all\\nat equal distances from each\\nother, as is represented in the\\nfollowing diagram. The time\\nof arriving at each of the wires\\nbeing noted, and all the times\\nadded together and divided by\\nthe number of observations, the\\nresult gives the instant of cross-\\ning the central wire.\\n124. The Astronomical Clock\\nis the constant companion of the\\nTransit Instrument. This clock is so regulated as to keep exact\\npace with the stars, and of course with the revolution of the earth", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0078.jp2"}, "79": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 53\\non its axis that is, it is regulated to sidereal time. It measures\\nthe progress of a star, indicating an hour for every 15\u00c2\u00b0, and 24\\nhours for the whole period of the revolution of the star. Sidereal\\ntime, it will be recollected, commences when the vernal equinox\\nis on the meridian, just as solar time commences when the sun is\\non the meridian. Hence, the hour by the sidereal clock has no\\ncorrespondence with the hour of the day, but simply indicates\\nhow long it is since the equinoctial point crossed the meridian.\\nFor example, the clock of an observatory points to 3h. 20m. this\\nmay be in the morning, at noon, or any other time of the day, since\\nit merely shows that it is 3h. 20m. since the equinox was on the\\nmeridian. Hence, when a star is on the meridian, the clock\\nitself shows its right ascension and the interval of time between\\nthe arrival of an} 7 two stars upon the meridian, is the measure of\\ntheir difference of right ascension.\\n125. Astronomical clocks are made of the best workmanship,\\nwith a compensation pendulum, and every other advantage which\\ncan promote their regularity. The Transit Instrument itself,\\nwhen once accurately placed in the meridian, affords the means\\nof testing the correctness of the clock, since one revolution of a\\nstar from the meridian to the meridian again, ought to correspond\\nto exactly 24 hours by the clock, and to continue the same from\\nday to day and the right ascension of various stars, as they cross\\nthe meridian, ought to be such by the clock as they are given in\\nthe tables, where they are stated according to the most accurate\\ndeterminations of astronomers. Or by taking the difference of\\nright ascension of any two stars on successive days, it will be seen\\nwhether the going of the clock is uniform for that part of the\\nday and by taking the right ascension of different pairs of stars,\\nwe may learn the rate of the clock at various parts of the day.\\nWe thus learn, not only whether the clock accurately measures\\nthe length of the sidereal day, but also whether it goes uniformly\\nfrom hour to hour.\\nAlthough astronomical clocks have been brought to a great de-\\ngree of perfection, so as to vary hardly a second for many months,\\nyet none are absolutely perfect, and most are so far from it as to\\nrequire to be corrected by means of the Transit Instrument every", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0079.jp2"}, "80": {"fulltext": "54 THE EARTH.\\nfew days. Indeed, for the nicest observations, it is usual not to\\nattempt to bring the clock to an absolute state of correctness, but\\nafter bringing it as near to such a state as can conveniently be\\ndone, to ascertain how much it gains or loses in a day that is, to\\nascertain its rate of going, and to make allowance accordingly.\\n126. The vertical circle (n, Fig. 14,) usually connected with\\nthe Transit Instrument, affords the means of measuring arcs on\\nthe meridian, as meridian altitudes, zenith distances, and decli-\\nnations but as the circle must necessarily be small, and there-\\nfore incapable of measuring very minute angles, the Mural Cir-\\ncle is usually employed for measuring arcs of the meridian. The\\nMural Circle is a graduated circle, usually of very large size, fixed\\npermanently in the plane of the meridian, and attached firmly to\\na perpendicular wall. It is made of large size, sometimes 1 1 feet\\nin diameter, in order that very small angles may be measured on\\nits limb and it is attached to a massive wall of solid masonry in\\norder to insure perfect steadiness, a point the more difficult to\\nattain in proportion as the instrument is heavier. The annexed\\ndiagram represents a Mural Circle fixed to its wall and ready for\\nobservations. It will be seen that every expedient is employed\\nto give the instrument firmness of parts and steadiness of position.\\nIts radii are composed of hollow cones, uniting lightness and\\nstrength, and its telescope revolves on a large horizontal axis,\\nfixed as firmly as possible in a solid wall. The graduations are\\nmade on the outer rim of the instrument, and are read off by six\\nmicroscopes (called reading microscopes) attached to the wall, one\\nof which is represented at A, and the places of the five others\\nare marked by the letters B, C, D, E, F. Six are used, in order\\nthat by taking the mean of such a number of readings, a higher\\ndegree of accuracy may be insured, than could be obtained by a\\nsingle reading. In a circle of six feet diameter, like that repre-\\nsented in the figure, the divisions may be easily carried to five\\nminutes each. The microscope (which is of the variety called\\ncompound microscope) forms an enlarged image of each of these\\ndivisions in the focus of the eye glass. With it is combined the\\nprinciple of the micrometer. This is effected by placing in the\\nfocus a delicate wire, which may be moved by means of a screw", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0080.jp2"}, "81": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\nFig. 16.\\n55\\nin a direction parallel to the divisions of the limb, and which is sc\\nadjusted to the screw as to move over the whole magnified space\\nof five minutes by five revolutions of the screw. Of course one\\nrevolution of the screw measures one minute. Moreover, if the\\nscrew itself is made to carry an index attached to its axis and re-\\nvolving with it over a disk graduated into sixty equal parts, then\\nthe space measured by moving the index over one of these parts,\\nwill be one second.\\nWe have been thus minute in the description of this instrument,\\nin order to give the learner some idea of the vast labor and grea\\npatience demanded of practical astronomers, in order to obtain\\nmeasurements of such extreme accuracy as those to which they\\naspire.\\nOn account of the great dimensions of this circle, and the ex-\\npense attending it, as well as the difficulty of supporting it firmly,\\nsometimes only one fourth of it is employed, constituting the Mu-\\nral Quadrant. This instrument has the disadvantage, however.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0081.jp2"}, "82": {"fulltext": "56\\nTHE EARTH.\\nof being applicable to only one hemisphere at a time, either the\\nnorthern or the southern, according as it is fixed to the eastern\\nor the western side of the wall.\\n127. We have before shown (Art. 124,) the method of finding\\nthe right ascension of a star by means of the Transit Instrument\\nand the clock. The declination may be obtained by means of the\\nmural circle in several different ways, our object being always -to\\nfind the distance of the star, when on the meridian, from the equa-\\ntor (Art. 37.) First, the declination may be found from the me-\\nridian altitude. Let S (Fig. 17,) be the place of a star when\\non the meridian. Then its meridian altitude will be SH, which\\nwill best be found by taking its ze-\\nnith distance ZS, of which it is the\\ncomplement. From SH, subtract EH,\\nthe elevation of the equator, which\\nequals the co-latitude of the place of\\nobservation, (Art. 44,) and the remain-\\nder SE is the declination. Or if the\\nstar is nearer the horizon than the\\nequator is, as at S subtract its me-\\nridian altitude from the co-latitude, for\\nthe declination. Secondly, the declination may be found from\\nthe north polar distance, of which it is the complement. Thus\\nfrom P to E is 90\u00c2\u00b0. Therefore, PE-PS=90\u00c2\u00b0-PS=SE=the\\ndeclination. The height of the pole P is always known when the\\nlatitude of the place is known, being equal to the latitude.\\n128. The astronomical instruments already described are adapt-\\ned to taking observations on the meridian only but we some-\\ntimes require to know the altitude of a celestial body when it is\\nnot on the meridian, and its azimuth, or distance from the meridian\\nmeasured on the horizon and also the angular distance between\\ntwo points on any part of the celestial sphere. An instrument\\nespecially designed to measure altitudes and azimuths, is called an\\nAltitude and Azimuth Instrument, whatever may be its particular\\nform. When a point is on the horizon its distance from the me-\\nridian, or its azimuth, may be taken by the common surveyor s", "height": "4018", "width": "2314", "jp2-path": "introductionto00olm_0082.jp2"}, "83": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n57\\ncompass, the direction of the meridian being determined by the\\nneedle but when the object, as a star, is not on the horizon, its\\nazimuth, it must be remembered, is the arc of the horizon from\\nthe meridian to a vertical circle passing through the star (Art. 27)\\nat whatever different altitudes, therefore, two stars may be, and\\nhowever the plane which passes through them may be inclined to\\nthe horizon, still it is their angular distance measured on the hori-\\nzon which determines their difference of azimuth. Figure 18 rep-\\nresents an Altitude and Azimuth Instrument, several of the usual\\nappendages and subordinate contrivances being omitted for the\\nsake of distinctness and simplicity. Here abc is the vertical or\\naltitude circle, and EFG the horizontal or azimuth circle AB is a\\nFig. 18.\\ntelescope mounted on a horizontal axis and capable of two mo-\\ntions, one in altitude parallel to the circle abc, and the other in\\nazimuth parallel to EFG. Hence it can be easily brought to bear\\nupon any object. At m, under the eye glass of the telescope, is a\\nsmall mirror placed at an angle of 45\u00c2\u00b0 with the axis of the tele-\\nscope, by means of which the image of the object is reflected up-\\nwards, so as to be conveniently presented to the eye of the ob-\\n8", "height": "4018", "width": "2314", "jp2-path": "introductionto00olm_0083.jp2"}, "84": {"fulltext": "58 THE EARTH.\\nserver. At d is represented a tangent screw, by which a slow\\nmotion is given to the telescope at c. At h and g are seen two\\nspirit levels at right angles to each other, which show when the\\nazimuth circle is truly horizontal. The instrument is supported\\non a tripod, for the sake of greater steadiness, each foot being\\nfurnished with a screw for leveling.\\n129. The sextant is one of the most useful instruments, both\\nto the astronomer and the navigator, and will therefore merit\\nparticular attention. In figure 19. 1 and H are two small mirrors,\\nand T a small telescope. I D represents a movable arm, or\\nradius, which carries an index at D. The radius turns on a pivot\\nat I, and the index moves on a graduated arc EF. I is called\\nFig. 19.\\n*s\\nthe Index Glass and H the Horizon Glass. The finder part only\\nof the horizon glass is coated with quicksilver, the upper part\\nbeing left transparent so that while one object is seen through\\nthe upper part by direct vision, another may be seen through\\nthe lower part by reflexion from the two mirrors. The instru-\\nment is so contrived, that when the index is moved up to F,\\nwhere the zero point is placed, or the graduation begins, the two", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0084.jp2"}, "85": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 59\\nreflectors I and II are exactly parallel to each other. If we\\nnow look through the telescope, T, so pointed as to see the star\\nS through the transparent part of the horizon glass, we shall\\nsee the same star, in the same place, reflected from the silvered\\npart for the star (or any similar object) is at. such a distance\\nthat the rays of light which strike upon the index glass I, are\\nparallel to those which enter the eye directly, and will exhibit:\\nthe object at the same place. Now, suppose we wish to meas-\\nure the angular distance between two bodies, as the moon and a\\nstar, and let the star be at S and the moon at M. The telescope\\nbeing still directed to S, turn the index arm ID from F towards\\nE until the image of the moon is brought down to S. its lower\\nlimb just touching S. By a principle in optics, the angular dis-\\ntance which the image of the moon passes over, is twice that of\\nthe mirror I. But the mirror has passed over the graduated arc\\nFD therefore double that arc is the angular distance between\\nthe star and the moon s lower limb. If we then bring the upper\\nlimb into contact with the star, the sum of both observations,\\ndivided by 2, will give the angular distance between the star\\nand the moon s center. As each degree on the limb EF meas-\\nures two degrees of angular distance, hence the divisions for sin-\\ngle degrees are in fact only half a degree asunder and a sextant,\\nor the sixth part of the circle, measures an angular distance of\\n120\u00c2\u00b0. The upper and lower points in the disk of the sun or of\\nthe moon, may be considered as two separate objects, whose\\ndistance from each other may be taken in a similar manner,\\nand thus their apparent diameters at any time be determined.\\nWe may select our points of observation either in a vertical, or\\nin a horizontal direction.\\n130. If we make a star, or the limb of the sun or moon, one of\\nthe objects, and the point in the horizon directly beneath, the oth-\\ner, we thus obtain the altitude of the object. In this observation,\\nthe horizon is viewed through the transparent part of the hori-\\nzon glass. At sea, where the horizon is usually well defined, the\\nhorizon itself may be used for taking altitudes but on land, in-\\nequalities of the earth s surface, oblige us to have recourse to an\\nartificial horizon. This, in its simple state, is a basin of either", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0085.jp2"}, "86": {"fulltext": "60 THE EARTH.\\nwater or quicksilver. By this means we see the image of the\\nsun (or other body) just as far below the horizon as it is in reality\\nabove it. Hence, if we turn the index glass until the limb of the\\nsun, as reflected from it, is brought into contact with the image\\nseen in the artificial horizon, we obtain double the altitude.*\\nThe sextant must be held in such a manner, that its plane shall\\npass through the plane of the two objects. It must be held\\ntherefore in a vertical plane in taking altitudes, and in a horizontal\\nplane in taking the horizontal diameters of the sun and moon.\\nHolding the instrument in the true plane of the two bodies, whose\\nangular distance is measured, is indeed the most difficult part of\\nthe operation.\\nThe peculiar value of the sextant consists in this, that the ob-\\nservations taken with it are not affected by any motion in the\\nobserver hence it is the chief instrument used for angular meas-\\nurements at sea.\\n131. Examples illustrating the use of the Sextant.\\nEx. 1. Alt. O s lower limb, 49\u00c2\u00b0 10 00\\n0 s semi-diameter, 15 51\\nSubtract Refraction,\\nAdd Parallax,\\nTrue altitude O s center, 49\u00c2\u00b0 25 08\\nEx. 2. With the Artificial Horizon.\\nAltitude of 0 s upper limb above the image in the artificial ho-\\nrizon, 100\u00c2\u00b0 2 47\\nTrue altitude, 50\u00c2\u00b0 01 23. 5\\nO s semi-diameter, 00 15 50.\\n49\u00c2\u00b0\\n25\\n51\\n00\\n00\\n49\\n49\u00c2\u00b0\\n25\\n02\\n00\\n00\\n06\\n49\u00c2\u00b0 45 33. 5\\nRefraction 00 00 48.\\n49\u00c2\u00b0 44 45. 5\\nParallax, 00 00 05.\\nTrue altitude of O s center, 49\u00c2\u00b0 44 50. 5\\nWoodhouse s Ast. p. 774.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0086.jp2"}, "87": {"fulltext": "ASTRONOMICAL PROBLEMS.\\n61\\nASTRONOMICAL PROBLE.MS.*\\n132. Given the sun s Right Ascension and Declination, to find\\nhis Longitude and the Obliquity of the Ecliptic.\\nLet PCP (Fig. 20,) represent the celestial meridian that passes\\nthrough the first of Cancer and Capricorn, (the solstitial colure,)\\nPP the axis of the sphere, EQ the equator, E C the ecliptic, and\\nPSP the declination circle (Art. Fig. 20.\\n37,) passing through the sun S\\nthen ARS is a right angle, and in\\nthe right angled spherical triangle\\nARS, are given the right ascension\\nAR (Art. 37,) and the declination\\nRS, to find the longitude AS and\\nthe obliquity SAR.\\nAs longitude and right ascension\\nare measured from A, the first point\\nof Aries, in the direction AS of the signs, quite round the globe,\\nwhen, of the four quantities mentioned in the problem, the obliquity\\nand the declination are given to find the others, we must know\\nwhether the sun is north, or whether it is south of the equator, the\\nlongitude being in the one case AS, and in the other, instead of\\nAS it is 360\u00e2\u0080\u0094 AS that is, the supplement of AS We must\\nalso know on which side of the tropic the sun is, for the sun in\\npassing from one of the tropics to the equinox, passes through the\\nsame degrees of declination as it had gone through in ascending\\nfrom the other equinox to the tropic, although its longitude and\\nright ascension go on continually increasing. From the 21st of\\nMarch to the 21st of June, wdiile describing the first quadrant\\nfrom the vernal equinox, the declination is north and increasing\\nnorth but decreasing, in the second quadrant, until the 23d of\\nSeptember south and increasing in the third quadrant, until the\\n21st of December; and finally, in the fourth quadrant, south but\\ndecreasing until the 21st of March.\\nEx. 1. On the 17th of May, the sun s Right Ascension was\\n53\u00c2\u00b0 38 and his Declination 19\u00c2\u00b0 15 57 required his Longitude\\nand the Obliquity of the Ecliptic.\\nYoung s Spherical Trigonometry, p. 136. Vince s Complete System, Vol. I.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0087.jp2"}, "88": {"fulltext": "62 THE EARTH.\\nApplying Napier s rule* to the right angled triangle, ARS, we\\nhave\\n1. Rad. cos. AS=cos. AR cos. RS.\\n2. Rad. sin. AR=tan. RS cot. A.*. cot. A=\\ntan. RS\\nHence the computation for AS and A is as follows\\nFor the Longitude AS. For the Obliquity A.\\ncos.AR 53\u00c2\u00b0 38 00 9.7730185 sin AR 9.9059247\\ncos.RSl9 15 57 9.9749710 tan. RS, ar. com. 0.4565209\\ncos.AS 55 57 43 9.7479895 cot. A 23\u00c2\u00b0 27 50| 10.3624456\\nEx. 2. On the 31st of March, 1816, the sun s Declination was\\nobserved at Greenwich to be 4\u00c2\u00b0 13 31i required his Right\\nAscension, the obliquity of the ecliptic being 23\u00c2\u00b0 27 51\\nAns. 9\u00c2\u00b0 47 59\\nEx. 3. What was the sun s Longitude on the 28th of Novem-\\nThe student ,s supposed to be acquainted with Spherical Trigonometry but to re-\\nfresh his memory, we may insert a remark or two.\\nIt will be recollected that in Napier s rule for the solution of a right angled spherical\\ntriangle, by means of the Five Circular Parts, we proceed as follows.\\nIn a right angled spherical triangle we are to recognize but five parts, viz. the three\\nsides and the two oblique angles. If we take any one of these as a middle part, the\\ntwo which lie next to it on each side will be adjacent parts. Thus, (in Fig. 21,) taking\\nA for a middle part, b and c will be the adjacent parts if we take c for the middle part,\\nA and B will be the adjacent parts if we jtj^ 21.\\ntake B for the middle part, c and a will be\\nthe adjacent parts but if we take a for\\nthe middle part, then as the angle C is\\nnot considered as one of the circular parts,\\nB and b are the adjacent parts and, last-\\nly, if b is the middle part, then the adja-\\ncent parts are A and a. The two parts immediately beyond the adjacent parts on each\\nside, still disregarding the right angle, are called the opposite parts; thus if A is the\\nmiddle part, the opposite parts are a and B. Napier s rule is as follows\\nRadius into the sine of the middle part, equals the product of the tangents of the\\nadjacent extremes, or of the cosines of the opposite extremes.\\n(The corresponding vowels are marked to aid the memory.) This rule is modified\\nby using the complements of the two angles and the hypothenuse instead of the parts\\nthemselves. Thus instead of rad.Xsin. A, we say rad.Xcos. A, when A is the middle\\npart and rad.Xcos. AB, when the hypothenuse is the middle part.\\nExamples. 1. In the right angled triangle ABC, are given the two perpendicular\\nsides, viz. \u00c2\u00ab=48\u00c2\u00b0 24 10 6=59\u00c2\u00b0 38 27 to find the hypothenuse c. The hypothenuse\\nbeing made the middle part, the other sides become the opposite parts, being separated", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0088.jp2"}, "89": {"fulltext": "ASTRONOMICAL PROBLEMS.\\n63\\nber, 1810, when his Declination was 21\u00c2\u00b0 16 4 and his Right\\nAscension, in time, 16h. 14m. 58.4s.?\\nAns. 245\u00c2\u00b0 39 10\\nEx. 4. The sun s Longitude being 8s. 7\u00c2\u00b0 40 56 and the Ob-\\nliquity 23\u00c2\u00b0 27 42\u00c2\u00a3 what was the Right Ascension in time?\\nAns. 16h. 23m. 34s.\\n133. Given the sun s Declination to find the time of his Rising\\nand Setting at any place whose latitude is known.\\nLet PEP (Fig. 22.) represent the meridian of the place, Z\\nbeing the zenith, and HO the horizon and let LL be the appa-\\nrent path of the sun on the proposed\\nday, cutting the horizon in S. Then\\nthe arc EZ will be the latitude of the\\nplace, and consequently EH, or its\\nequal QO, will be the co-latitude, and\\nthis measures the angle OAQ also\\nRS will be the sun s declination, and\\nAR expressed in time will be the timf\\nof risincr before 6 o clock. For it is\\nevident that it will be sunrise when\\nthe sun arrives at -the horizon at S but PP being an hour circle\\nw r hose plane is perpendicular to the meridian, (and of course pro-\\njected into a straight line on the plane of projection.) the time the\\nsun is passing from S to S taken from the time of describing S L,\\nwhich is six hours, must be the time from midnight to sunrise.\\nBut the time of describing SS is measured on the corresponding\\narc of the equinoctial AR.\\nIn the right angled triangle ARS, we have the declination RS,\\nand the angle A to find AR. Therefore,\\nRad. xsin. AR=cot. A xtan. RS.\\nfrom the middle part by the angles A and B. Hence, rad. cos. c=cos. a cos. b cos. c=\\ncos. a cos. h\\n70\u00c2\u00b023 40\\nrad.\\n2. In the spherical triangle, right angled at C, are given two perpendicular sides,\\nviz. a=116\u00c2\u00b0 30 43 6=29\u00c2\u00b0 41 32 to find the angle A.\\nHere, the required angle is adjacent to one of the given parts, viz. 6, which make\\nthe middle part. Then,\\nRad.Xsin. =cot. A tan, a cot. A=\\nrad. Xsin. b\\ntan. a.\\n=76\u00c2\u00b07 13", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0089.jp2"}, "90": {"fulltext": "64\\nTHE EARTH.\\nEx. 1. Required the time of sunrise at latitude 52\u00c2\u00b0 13 N.\\nwhen the sun s declination is 23\u00c2\u00b0 28\\nRad\\nCot. A or tan. 52\u00c2\u00b0 13\\nTan.RS= 23\u00c2\u00b0 28\\nSin. 34\u00c2\u00b0 03 211\\n2h. 16 13 25\\n6\\n10.\\n10.1105786\\n9.6376106\\n9.7481892\\n3h. 43 46 35 the time after midnight, and of\\ncourse the time of rising.\\nEx. 2. Required the time of sunrise at latitude 57\u00c2\u00b0 2 54 N.\\nwhen the sun s declination is 23\u00c2\u00b0 28 N.\\nAns. 3h. 11m. 49s.\\nEx. 3. How long is the sun above the horizon in latitude 58\\n12 N. when his declination is 18\u00c2\u00b0 40 S.\\nAns. 7h. 35m. 52s.\\n134. Given the Latitude of the place, and the Declination of a\\nheavenly body, to determine its Altitude and Azimuth when on the\\nsix o clock hour circle.\\nLet HZO (Fig. 23.) be the meridian of the place, Z the zenith.\\nHO the horizon, S the place of no\\n1 Fig. 23.\\nthe object on the 6 o clock hour\\ncircle PSP which of course cuts\\nthe equator in the east and west\\npoints, and ZSB the vertical cir-\\ncle passing through the body.\\nThen in the right angled triangle\\nSBA, the given quantities are\\nAS, which is the declination,\\nand the arc OP or angle SAB,\\nthe latitude of the place, to find\\nthe altitude BS, and the azimuth\\nBO, or the amplitude AB, which is its complement.\\nEx. 1. What were the altitude and azimuth of Arcturus, when\\nDegrees are converted into hours by multiplying by 4 and dividing by 60.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0090.jp2"}, "91": {"fulltext": "ASTRONOMICAL PROBLEMS. 65\\nupon the six o clock hour circle of Greenwich, lat. 51\u00c2\u00b0 28 40 N.\\non the first of April, 1822 its declination being 20\u00c2\u00b0 6 50 N.?\\nFor the Altitude. For the Azimuth.\\nRad. sin. BS=sin. AS sin. A\\nRad. 10.\\nSin. 20\u00c2\u00b0 06 50 9.5364162\\nSin. 51 28 40 9.8934103\\nSin. 15 36 27 9.4298265\\nRad. cos. A=cot. BO cot. AS\\nCot. 20\u00c2\u00b0 06 50 10.4362545\\nCos. 51 28 40 9.7943612\\nRad. 10.\\nCot. 77\u00c2\u00b0 09 04 9.3581067\\nEx. 2. At latitude 62\u00c2\u00b0 12 N. the altitude of the sun at 6 o clock\\nin the morning was found to be 18\u00c2\u00b0 20 23 required his declina-\\ntion and azimuth.\\nAns. Dec. 20\u00c2\u00b0 50 12 N. Az. 79\u00c2\u00b0 56 4\\n135. The Latitudes and Longitudes of two celestial objects be-\\ning given, to find their Distance apart.\\nLet P (Fig. 24,) represent the pole of the ecliptic, and PS, PS\\ntwo arcs of celestial latitude (Art. 37,) drawn to the two objects\\nSS then will these arcs represent the Fig. 24\\nco-latitudes, the angle P will be the\\ndifference of longitude, and the arc SS\\nwill be the distance sought. Here we\\nhave the two sides and the included\\nangle given to find the third side. By\\nNapier s Rules for the solution of oblique angled spherical triangles,\\n(see Spherical Trigonometry,) the sum and difference of the two\\nangles opposite the given sides may be found, and thence the an-\\ngles themselves. The required side may then be found by the theo-\\nrem, that the sines of the sides are as the sines of their opposite\\nangles.* The computation is omitted here on account of its great\\nlength. If P be the pole of the equator instead of the ecliptic,\\nthen PS and PS will represent arcs of co-declination, and the\\nangle P will denote difference of right ascension. From these\\ndata, also, we may therefore derive the distance between any two\\nstars. Or, finally, if P be the pole of the horizon, the angle at P\\nMore concise formulae for the solution of this case may be found in Young s Tri-\\ngonometry, p. 99. Francoeur s Uranography, Art. 330. Dr. Bowditch s Practical\\nNavigator, p. 436.\\n9", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0091.jp2"}, "92": {"fulltext": "66 THE EARTH.\\nwill denote difference of azimuth, and the sides PS, PS zenith\\ndistances, from which the side SS may likewise be determined.\\nFIGURE AND DENSITY OF THE EARTH.\\n136. We have already shown, (Art. 8,) that the figure of the\\nearth is nearly globular but since the semi-diameter of the earth\\nis taken as the base line in determining the parallax of the heav-\\nenly bodies, and lies therefore at the foundation of all astronomi-\\ncal measurements, it is very important that it should be ascertained\\nwith the greatest possible exactness. Having now learned the\\nuse of astronomical instruments, and the method of measuring\\narcs on the celestial sphere, we are prepared to understand the\\nmethods employed to determine the exact figure of the earth.\\nThis element is indeed ascertained in four different ways, each\\nof which is independent of all the rest, namely, by investigating\\nthe effects of the centrifugal force arising from the revolution of\\nthe earth on its axis by measuring arcs of the meridian by\\nexperiments with the pendulum and by the unequal action of the\\nearth on the moon, arising from the redundance of matter about\\nthe equatorial regions. We will briefly consider each of these\\nmethods.\\n137. First, the known effects of the centrifugal force, would give\\nto the earth a spheroidal figure, elevated in the equatorial, and flat-\\ntened in the polar regions.\\nHad the earth been originally constituted (as geologists sup-\\npose) of yielding materials, either fluid or semi-fluid, so that\\nits particles could obey their mutual attraction, while the body\\nremained at rest it would spontaneously assume the figure of a\\nperfect sphere as soon, however, as it began to revolve on its\\naxis, the greater velocity of the equatorial regions would give to\\nthem a greater centrifugal force, and cause the body to swell out-\\ninto the form of an oblate spheroid.* Even had the solid part of\\nthe earth consisted of unyielding materials and been created a\\nperfect sphere, still the waters that covered it would have receded\\nfrom the polar and have been accumulated in the equatorial re-\\nSee a good explanation of this subject in the Edinburgh Encyclopaedia, II. 665.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0092.jp2"}, "93": {"fulltext": "FIGURE OF THE EARTH.\\n67\\ngions, leaving bare extensive regions on the one side, and ascend-\\ning to a mountainous elevation on the other.\\nOn estimating from the known dimensions of the earth and\\nthe velocity of its rotation, the amount of the centrifugal force in\\ndifferent latitudes, and the figure of equilibrium which would\\nresult, Newton inferred that the earth must have the form of an\\noblate spheroid before the fact had been established by observa-\\ntion and he assigned nearly the true ratio of the polar and equa-\\ntorial diameters.\\n138. Secondly, the spheroidal figure of the earth is proved, by\\nactually measuring the length of a degree on the meridian in differ-\\nent latitudes.\\nWere the earth a perfect sphere, the section of it made by a\\nplane passing through its center in any direction would be a per-\\nfect circle, whose curvature would be equal in all parts but if\\nwe find by actual observation, that the curvature of the section is\\nnot uniform, we infer a corresponding departure in the earth from\\nthe figure of a perfect sphere. This task of measuring portions of\\nthe meridian, has been executed in different countries by means\\nof a system of triangles with astonishing accuracy.* The result\\nis, that the length of a degree increases as we proceed from the\\nequator towards the pole, as may be seen from the following table\\nPlaces of observation.\\nLatitude.\\nLength of a degree in miles.\\nPeru,\\n00\u00c2\u00b0 00 00\\n68.732\\nPennsylvania,\\n39 12 00\\n68.896\\nItaly,\\n43 01 00\\n68.998\\nFrance,\\n46 12 00\\n69.054\\nEngland,\\n51 29 54\u00c2\u00a3\\n69.146\\nSweden,\\n66 20 10\\n69.292\\nCombining the results of various measurements, the dimensions\\nof the terrestrial spheroid are found to be as follows f\\nEquatorial diameter, 7925.308\\nPolar diameter, 7898.952\\nMean diameter, 7912.130\\nThe difference between the greatest and least, is 26.356\\n30 1\\nSee Day s Trigonometry.\\nt Bessel.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0093.jp2"}, "94": {"fulltext": "68 THE EARTH.\\nof the greatest. This fraction T is denominated the elliplicity\\nof the earth, being the excess of the transverse over the conjugate\\naxis, on the supposition that the section of the earth coinciding\\nwith the meridian, is an ellipse and that such is the case, is\\nproved by the fact that calculations on this hypothesis, of the\\nlengths of arcs of the meridian in different latitudes, agree nearly\\nwith the lengths obtained by actual measurement.\\n139. Thirdly, the figure of the earth is shown to be spheroidal, by\\nobservations with the pendulum.\\nThe use of the pendulum in determining the figure of the\\nearth, is founded upon the principle that the number of vibra-\\ntions performed by the same pendulum, when acted on by differ-\\nent forces, varies as the square root of the forces.* Hence, by\\ncarrying a pendulum to different parts of the earth, and counting\\nthe number of vibrations it performs in a given time, we obtain\\nthe relative forces of gravity at those places, and this leads to a\\nknowledge of the relative distance of each place from the center\\nof the earth, and finally, to the ratio between the equatorial and\\nthe polar diameters.\\n140. Fourthly, that the earth is of a spheroidal figure, is infer-\\nred from the motions of the moon.\\nThese are found to be affected by the excess of matter about\\nthe equatorial regions, producing certain irregularities in the lunar\\nmotions, the amount of which becomes a measure of the excess\\nitself, and hence affords the means of determining the earth s\\nellipticity. This calculation has been made by the most profound\\nmathematicians, and the figure deduced from this source corres-\\nponds very nearly to that derived from the several other indepen-\\ndent methods.\\nWe thus have the shape of the earth established upon the most\\nsatisfactory evidence, and are furnished with a starting point from\\nwhich to determine various measurements among the heavenly\\nbodies.\\n141. The density of the earth compared with water, that is, its\\nMechanics, Art. 183.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0094.jp2"}, "95": {"fulltext": "DENSITY OF THE EARTII.\\n69\\nspecific gravity, is 5?.* The density was first estimated by Dr.\\nHutton, from observations made by Dr. Maskelyne, Astronomer\\nRoyal, on Schehallien, a mountain of Scotland, in the year 1774.\\nFig. 25.\\nG G\\nE E-\\nThus, let M (Fig. 25,) represent\\nthe mountain, D, B, two stations\\non opposite sides of the moun-\\ntain, and I a star; and let IE\\nand IG be the zenith distances as\\ndetermined by the differences of\\nlatitudes of the two stations. But\\nthe apparent zenith distances as\\ndetermined by the plumb line\\nare IE and IG The deviation\\ntowards the mountain on each\\nside exceeded 7 .f The attrac-\\ntion of the mountain being ob-\\nserved on both sides of it, and\\nits mass being computed from a number of sections taken in all\\ndirections, these data, when compared with the known attraction\\nand magnitude of the earth, led to a knowledge of its mean den-\\nsity. According to Dr. Hutton, this is to that of water as 9 to 2\\nbut later and more accurate estimates have made the specific\\ngravity of the earth as stated above. But this density is nearly\\ndouble the average density of the materials that compose the ex-\\nterior crust of the earth, showing a great increase of density\\ntowards the center.\\nThe density of the earth is an important element, as we shall\\nfind that it helps us to a knowledge of the density of each of the\\nother members of the solar system.\\nBaily, Ast. Tables, p. 21,\\nt Robison s Phys. Ast.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0095.jp2"}, "96": {"fulltext": "PART II. OF THE SOLAR SYSTEM.\\n142. Having considered the Earth, in its astronomical relations,\\nand the Doctrine of the Sphere, we proceed now to a survey of\\nthe Solar System, and shall treat successively of the Sun, Moon,\\nPlanets, and Comets.\\nCHAPTER I.\\nOP THE SUN SOLAR SPOTS ZODIACAL LIGHT.\\n143. The figure which the sun presents to us is that of a per-\\nfect circle, whereas most of the planets exhibit a disk more or less\\nelliptical, indicating that the true shape of the body is an oblate\\nspheroid. So great, however, is the distance of the sun, that a\\nline 400 miles long would subtend an angle of only 1 at the eye,\\nand would therefore be the least space that could be measured.\\nHence, were the difference between two conjugate diameters of\\nthe sun any quantity less than this, we could not determine by\\nactual measurement that it existed at all. Still we learn from\\ntheoretical considerations, founded upon the known effects of cen-\\ntrifugal force, arising from the sun s revolution on his axis, that\\nhis figure is not a perfect sphere, but is slightly spheroidal.*\\n144. The distance of the sun from the earth, is nearly 95,000,000\\nmiles. For, its horizontal parallax being 8. 6, (Art. 86,) and the\\nsemi-diameter of the earth 3956 miles,\\nSin. 8. 6 3956 Rad. 95,000,000 nearly. In order to form\\nsome faint conception at least of this vast distance, let us reflect\\nthat a railway car, moving at the rate of 20 miles per hour, would\\nrequire more than 500 years to reach the sun.\\nSee Mecanique Celeste, III, 165. Delambre, 1. 1, p. 48a", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0096.jp2"}, "97": {"fulltext": "SOLAR SPOTS. 71\\n145. The apparent diameter of the sun may be found either by\\nthe Sextant, (Art. 129,) by an instrument called the Heliometer,\\nspecially designed for measuring its angular breadth, or by the time\\nit occupies in crossing the meridian. If, for example, it occupied\\n4 m its angular diameter would be 1\u00c2\u00b0. It in fact occupies a little\\nmore than 2 m and hence its apparent diameter is a little more than\\nhalf a degree, (32 3 Having the distance and angular diameter,\\nwe can easily find its linear diameter. Let E (Fig. 26,) be the\\nearth, S the sun, ES a line drawn to the Fig. 26.\\ncenter of the disk, and EC a line drawn\\ntouching the disk at C. Join SC then\\nRad. ES (95,000,000) sin. 16 l. 5\\n442840=semi-diameter, and S85680=diam-\\n,885680 ___ V\\neter. And =112 nearly; that is, it\\n7912 J\\nwould require one hundred and twelve bo-\\ndies like the earth, if laid side by side, to\\nreach across the diameter of the sun and a\\nship sailing at the rate of ten knots an hour,\\nwould require more than ten years to sail\\nacross the solar disk. Since spheres are to\\neach other as the cubes of their diameters,\\nI 3 112 3 1 1,400,000 nearly; that is, the sun is about\\n1,400,000 times as large as the earth. The distance of the moon\\nfrom the earth being 237,000 miles, were the center of the sun\\nmade to coincide with the center of the earth, the sun would ex-\\ntend every way from the earth nearly twice as far as the moon.\\n146. In density, the sun is only one fourth that of the earth,\\nbeing but a little heavier than water (Art. 141) and since the\\nquantity of matter, or mass of a body, is proportioned to its mag-\\nnitude and density, hence, 1,400,000 x\u00c2\u00b1 350,000, that is, the\\nquantity of matter in the sun is three hundred and fifty thousand\\n(or, more accurately, 354,936) times as great as in the earth. Now\\nthe weight of bodies (which is a measure of the force of gravity)\\nvaries directly as the quantity of matter, and inversely as the\\nsquare of the distance. A body, therefore, would weigh 350,000\\ntimes as much on the surface of the sun as on the earth, if the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0097.jp2"}, "98": {"fulltext": "72 THE SUN.\\ndistance of the center of force were the same in both cases but\\nsince the attraction of a sphere is the same as though all the mat-\\nter were collected in the center, consequently, the weight of a\\nbody, so far as it depends on its distance from the center of force,\\nwould be the square of 112 times less at the sun than at the earth.\\nOr, putting W for the weight at the earth, and W for the weight\\nat the sun, then\\n_\u00e2\u0080\u009e _\u00e2\u0080\u009e, 1 350000 n\\nW W th-=27.9 lbs.\\nI 2 (112) 2\\nHence a body would weigh nearly 28 times as much at the sun\\nas at the earth. A man weighing 200 lbs. would, if transported\\nto the surface of the sun, weigh 5,580 lbs., or nearly 2i tons. To\\nlift one s limbs, would, in such a case, be beyond the ordinary\\npower of the muscles. At the surface of the earth, a body falls\\nthrough 16 T T 2 feet in a second and since the spaces are as the\\nvelocities, the times being equal, and the velocities as the forces,\\ntherefore a body would fall at the sun in one second, through\\n16 T V x 27 T 448.7 feet.\\nSOLAR SPOTS.\\n147. The surface of the sun, when viewed with a telescope,\\nusually exhibits dark spots, which vary much, at different times,\\nin number, figure, and extent. One hundred or more, assembled\\nin several distinct groups, are sometimes visible at once on the\\nsolar disk. The solar spots are commonly very small, but\\noccasionally a spot of enormous size is seen occupying an extent\\nof 50,000 miles or more in diameter. They are sometimes\\neven visible to the naked eye, when the sun is viewed through\\ncolored glass, or when near the horizon, it is seen through light\\nclouds or vapors. When it is recollected that 1 of the solar\\ndisk implies an extent of 400 miles, (Art. 143,) it is evident that a\\nspace large enough to be seen by the naked eye, must cover a very\\nlarge extent.\\nA solar spot usually consists of two parts, the nucleus and the\\numbra, (Fig. 27.) The nucleus is black, of a very irregular shape,\\nand is subject to great and sudden changes, both in form and size.\\nSpots have sometimes seemed to burst asunder, and to project frag-\\nments in different directions. The umbra is a wide margin of lighter", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0098.jp2"}, "99": {"fulltext": "SOLAR SPOTS.\\n73\\nshade, and is commonly of greater Fi g* 27\\nextent than the nucleus. The spots\\nare usually confined to a zone ex-\\ntending across the central regions\\nof the sun, not exceeding G0\u00c2\u00b0 in\\nbreadth. When the spots are ob-\\nserved from day to day, they are\\nseen to move across the disk of the\\nsun, occupying about two weeks in\\npassing from one limb to the other.\\nAfter an absence of about the same\\nperiod, the spot returns, having taken 27d. 7h. 37m. in the entire\\nrevolution.\\n148. The spots must be nearly or quite in contact with the body\\nof the sun. Were they at any considerable distance from it, the\\ntime during which they would be seen on the solar disk, would\\nbe less than that occupied in the remainder of the revolution.\\nThus, let S (Fig. 28,) be the sun, E the earth, and abc the path\\nof the body, revolving about the sun.\\nUnless the spot were nearly or quite\\nin contact with the body of the sun,\\nbeing projected upon his disk only\\nwhile passing from b to c, and being\\ninvisible while describing the arc cab,\\nit would of course be out of sight lon-\\nger, than in sight, whereas the two pe-\\nriods are found to be equal. Moreover,\\nthe lines which all the solar spots de-\\nscribe on the disk of the sun, are found\\nto be parallel to each other, like the\\ncircles of diurnal revolution around the\\nearth and hence it is inferred that\\nthey arise from a similar cause, namely,\\nthe revolution of the sun on his axis,\\na fact which is thus made known to\\nus.\\nBut although the spots occupy about 27| days in passing from\\n10", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0099.jp2"}, "100": {"fulltext": "74\\nTHE SUN.\\none limb of the sun around to the same limb again, yet this is not\\nthe period of the sun s revolution on his axis, but exceeds it by\\nnearly two days. For, let AA B (Fig. 29,) represent the sun, and\\nEE M the orbit of the earth. When the earth is at E, the\\nvisible disk of the sun will be AA B\\nand if the earth remained stationary at\\nE, the time occupied by a spot after\\nleaving A until it returned to A, would\\nbe just equal to the time of the sun s\\nrevolution on his axis. But during the\\n27|- days in which the spot has been\\nperforming its apparent revolution, the\\nearth has been advancing in his orbit\\nfrom E to E where the visble disk of\\nthe sun is A B Consequently, before\\nthe spot can appear again on the limb from which it set out, it\\nmust describe so much more than an entire revolution as equals\\nthe arc A A which equals the arc EE Hence,\\n365d. 5h. 48m.+27d. 7h. 37m. 365d. 5h. 48m. 27d. 7h. 37m.\\n25d. 9h. 59m.=the time of the sun s revolution on his axis.\\n149. If the path which the spots appear to describe by the re-\\nvolution of the sun on his axis left each a visible trace on his sur-\\nface, they would form, like the circles of diurnal revolution on the\\nearth, so many parallel rings, of which that which passed through\\nthe center would constitute the solar equator, while those on each\\nside of this great circle would be small circles, corresponding to\\nparallels of latitude on the earth. Let us conceive of an artifi-\\ncial sphere to represent the sun, having such rings plainly marked\\non its surface. Let this sphere be placed at some distance from\\nthe eye, with its axis perpendicular to the axis of vision, in which\\ncase the equator would coincide with the line of vision, and its\\nedge be presented to the eye. It would therefore be projected in-\\nto a straight line. The same would be the case with all the small-\\ner rings, the distance being supposed such that the rays of light\\ncome from them all to the eye nearly parallel. Now let the axis,\\ninstead of being perpendicular to the line of vision, be inclined to\\nthat line, then all the rings being seen obliquely would be projected", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0100.jp2"}, "101": {"fulltext": "SOLAR SPOTS. 75\\ninto ellipses. If, however, while the sphere remained in a fixed\\nposition, the eye were carried around it, (being always in the same\\nplane,) twice during the circuit it would be in the plane of the\\nequator, and project this and all the smaller circles into straight\\nlines and twice, at points 90\u00c2\u00b0 distant from the foregoing posi-\\ntions, the eye would be at a distance from the planes of the rings\\nequal to the inclination of the equator of the sphere to the line of\\nvision. Here it would project the rings into wider ellipses than\\nat other points and the ellipses would become more and more\\nacute as the eye departed from either of these points, until they\\nvanished again into straight lines.\\n150. It is in a similar manner that the eye views the paths de-\\nscribed by the spots on the sun. If the sun revolved on an axis\\nperpendicular to the plane of the earth s orbit, the eye being situ-\\nated in the plane of revolution, and at such a distance from the\\nsun that the light comes to the eye from all parts of the solar\\ndisk nearly parallel, the paths described by the spots would be\\nprojected into straight lines, and each would describe a straight\\nline across the solar disk, parallel to the plane of revolution. But\\nthe axis of the sun is inclined to the ecliptic about 7^\u00c2\u00b0 from a per-\\npendicular, so that usually all the circles described by the spots are\\nprojected into ellipses. The breadth of these, however, will vary\\nas the eye, in the annual revolution, is carried around the sun, and\\nwhen the eye comes into the plane of the rings, as it does twice a\\nyear, they are projected into straight lines, and for a short time a\\nspot seems moving in a straight line inclined to the plane of the\\necliptic 7j\u00c2\u00b0. The two points where the sun s equator cuts the\\necliptic are called the sun s nodes. The longitudes of the nodes\\nare 80\u00c2\u00b0 7 and 260\u00c2\u00b0 7 and the earth passes through them about\\nthe 12th of December, and the 11th of June. It is at these times\\nthat the spots appear to describe straight lines. We have men-\\ntioned the various changes in the apparent paths of the solar spots,\\nwhich arise from the inclination of the sun s axis to the plane of\\nthe ecliptic but it was in fact by first observing these changes,\\nand proceeding in the reverse order from that which we have pur-\\nsued, that astronomers ascertained that the sun revolves on his\\naxis, and that this axis is inclined to the ecliptic 82\u00c2\u00a3\u00c2\u00b0.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0101.jp2"}, "102": {"fulltext": "76\\nTHE SUN.\\n151. With regard to the cause of the solar spots, various hypo-\\ntheses have been proposed, none of which is entirely satisfactory.\\nThat which ascribes their origin to volcanic action, appears to us\\nthe most reasonable.*\\nBesides the dark spots on the sun, there are also seen, in dif-\\nferent parts, places that are brighter than the neighboring por-\\ntions of the disk. These are called faculce. Other inequalities\\nare observable in powerful telescopes, all indicating that the sur-\\nface of the sun is in a state of constant and powerful agitation.\\nZODIACAL LIGHT.\\n152. The Zodiacal Light is a faint light resembling the tail of\\na comet, and is seen at certain seasons of the year following the\\ncourse of the sun after evening twilight, or preceding his approach\\nin the morning sky. Figure 30 represents its appearance as seen\\nin the evening in March, 1836. The following are the leading\\nfacts respecting it.\\n1. Its form is that of a luminous Fig. 30.\\npyramid, having its base towards\\nthe sun. It reaches to an immense\\ndistance from the sun, sometimes\\neven beyond the orbit of the earth.\\nIt is brighter in the parts nearer the\\nsun than in those that are more\\nremote, and terminates in an ob-\\ntuse apex, its light fading away by\\ninsensible gradations, until it be-\\ncomes too feeble for distinct vision.\\nHence its limits are, at the same\\ntime, fixed at different distances!\\nfrom the sun by different observers,\\naccording to their respective powers\\nof vision.\\n2. Its aspects vary very much with the different seasons of the\\nyear. About the first of October, in our climate, (Lat. 41\u00c2\u00b0 18\\nIn the system of instruction in Yale College, subjects of this kind are discussed\\nin a course of astronomical lectures, addressed to the class after they have finished the\\nperusal of the text-book.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0102.jp2"}, "103": {"fulltext": "ZODIACAL LIGHT. 77\\nit becomes visible before the dawn of day, rising along north of\\nthe ecliptic, and terminating above the nebula of Cancer. About\\nthe middle of November, its vertex is in the constellation Leo.\\nAt this time no traces of it are seen in the west after sunset, but\\nabout the first of December it becomes faintly visible in the west,\\ncrossing the Milky Way near the horizon, and reaching from the\\nsun to the head of Capricornus, forming, as its brightness increases,\\na counterpart to the Milky Way, between which on the right,\\nand the Zodiacal Light on the left, lies a triangular space embra-\\ncing the Dolphin. Through the month of December, the Zodi-\\nacal Light is seen on both sides of the sun, namely, before the\\nmorning and after the evening twilight, sometimes extending \u00c2\u00a30\u00c2\u00b0\\nwestward, and 70\u00c2\u00b0 eastward of the sun at the same time. After\\nit begins to appear in the western sky, it increases rapidly from\\nnight to night, both in length and brightness, and withdraws itself\\nfrom the morning sky, where it is scarcely seen after the month\\nof December, until the next October.\\n3. The Zodiacal Light moves through the heavens in the order of\\nthe signs. It moves with unequal velocity, being sometimes sta-\\ntionary and sometimes retrograde, while at other times it ad-\\nvances much faster than the sun. In February and March, it is\\nvery conspicuous in the west, reaching to the Pleiades and be-\\nyond but in April it becomes more faint, and nearly or quite dis-\\nappears during the month of May. It is scarcely seen in this lat-\\nitude during the summer months.\\n4. It is remarkably conspicuous at certain periods of a few\\nyears, and then for a long interval almost disappears.\\n5. The Zodiacal Light was formerly held to be the atmosphere of\\nthe sun* But La Place has shown that the solar atmosphere\\ncould never reach so far from the sun as this light is seen to ex-\\ntend. *f It has been supposed by others to be a nebulous body\\nrevolving around the sun. The idea has been suggested, that the\\nextraordinary Meteoric Showers, which at different periods visit\\nthe earth, especially in the month of November, may be derived\\nfrom this body.J\\nMairan, Memoirs French Academy, for 1733. t Mec. Celeste, III, 525.\\n1 See note on Meteoric Showers, at the end of the volume.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0103.jp2"}, "104": {"fulltext": "CHAPTER II.\\nOF THE APPARENT ANNUAL MOTION OF THE SUN SEASONS\u00e2\u0080\u0094 FIGURE\\nOF THE EARTH S ORBIT.\\n153. The revolution of the earth around the sun once a year,\\nproduces an apparent motion of the sun around the earth in the\\nsame period. When bodies are at such a distance from each\\nother as the earth and the sun, a spectator on either would pro-\\nject the other body upon the concave sphere of the heavens, al-\\nways seeing it on the opposite side of a great circle, 180\u00c2\u00b0 from\\nhimself. Thus when the earth arrives at Libra (Fig. 11,) we see\\nthe sun in the opposite sign Aries. When the earth moves from\\nLibra to Scorpio, as we are unconscious of om* own motion, the\\nsun it is that appears to move from Aries to Taurus, being always\\nseen in the heavens, where a line drawn from the eye of the spec-\\ntator through the body meets the concave sphere of the heavens.\\nHence the v line of projection carries the sun forward on one side\\nof the ecliptic, at the same rate as the earth moves on the oppo-\\nsite side and therefore, although we are unconscious of our own\\nmotion, we can read it from day to day in the motions of the sun.\\nIf we could see the stars at the same time with the sun, we could\\nactually observe from day to day the sun s progress through them,\\nas we observe the progress of the moon at night only the sun s\\nrate of motion would be nearly fourteen times slower than that\\nof the moon. Although we do not see the stars when the sun is\\npresent, yet after the sun is set, we can observe that it makes daily\\nprogress eastward, as is apparent from the constellations of the\\nZodiac occupying, successively, the western sky after sunset,\\nproving that either all the stars have a common motion westward\\nindependent of their diurnal motion, or that the sun has a motion\\npast them, from west to east. We shall see hereafter abundant\\nevidence to prove, that this change in the relative position of the\\nsun and stars, is owing to a change in the apparent place of the\\nsun, and not to any change in the stars.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0104.jp2"}, "105": {"fulltext": "ANNUAL MOTION. 79\\n154. Although the apparent revolution of the sun is in a direc-\\ntion opposite to the real motion of the earth, as regards absolute\\nspace, yet both are nevertheless from west to east, since these\\nterms do not refer to any directions in absolute space, but to the\\norder in which certain constellations (the constellations of the\\nZodiac) succeed one another. The earth itself, on opposite sides\\nof its orbit, does in fact move towards directly opposite points of\\nspace but it is all the while pursuing its course in the order of\\nthe signs. In the same manner, although the earth turns on its\\naxis from west to east, yet any place on the surface of the earth\\nis moving in a direction in space exactly opposite to its direction\\ntwelve hours before. If the sun left a visible trace on the face\\nof the sky, the ecliptic would of course be distinctly marked on\\nthe celestial sphere as it is on an artificial globe and were the\\nequator delineated in a similar manner, (by any method like that\\nsupposed in Art. 46,) we should then see at a glance the relative\\nposition of these two circles, the points where they intersect one\\nanother constituting the equinoxes, the points where they are at\\nthe greatest distance asunder, or the solstices, and various other\\nparticulars, which, for want of such visible traces, we are now\\nobliged to search for by indirect and circuitous methods. It will\\neven aid the learner to have constantly before his mental vision,\\nan imaginary delineation of these two important circles on the\\nface of the sky.\\n155. The method of ascertaining the nature and position of the\\nearth s orbit, is by observations on the sun s Declination and Right\\nAscension.\\nThe exact declination of the sun at any time is determined\\nfrom his meridian altitude or zenith distance, the latitude of the\\nplace of observation being known, (Art. 37.) The instant the\\ncenter of the sun is on the meridian, (which instant is given by\\nthe transit instrument,) we take the distance of his upper and\\nthat of his lower limb from the zenith half the sum of the two\\nobservations corrected for refraction, gives the zenith distance of\\nthe center. This result is diminished for parallax, (Art. 84,) and\\nwe obtain the zenith distance as it would be if seen from the\\ncenter of the earth. The zenith distance being known, the de-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0105.jp2"}, "106": {"fulltext": "80 THE SUN.\\nciination is readily found, by subtracting that distance from the\\nlatitude. By thus taking the sun s declination for every day of\\nthe year at noon, and comparing the results, we learn its motion\\nto and from the equator.\\n156. To obtain the motion in right ascension, we observe, with\\na transit instrument, the instant when the center of the sun is on\\nthe meridian. Our sidereal clock gives us the right ascension in\\ntime (Art. 124,) which we may easily, if we choose, convert into\\ndegrees and minutes, although it is more common to express right\\nascension by hours, minutes, and seconds. The differences of\\nright ascension from day to day throughout the year, give us the\\nsun s annual motion parallel to the equator. From the daily re-\\ncords of these two motions, at right angles to each other, arran-\\nged in a table,* it is easy to trace out the path of the sun on the\\nartificial globe or to calculate it with the greatest precision by\\nmeans of spherical triangles, since the declination and right ascen-\\nsion constitute two sides of a right angled spherical triangle, the\\ncorresponding arc of the ecliptic, that is, the longitude, being the\\nthird side, (Art. 132.) By inspecting a table of observations,\\nwe shall find that the declination attains its greatest value on\\nthe 22d of December, when it is 23\u00c2\u00b0 21 54 south; that from\\nthis period it diminishes daily and becomes nothing on the 21st\\nof March that it then increases towards the north, and reaches\\na similar maximum at the northern tropic about the 22d of June\\nand, finally, that it returns again to the southern tropic by gra-\\ndations similar to those which marked its northward progress. A\\ntable of observations also would show us, that the daily differences\\nof declination are very unequal that, for several days, when the\\nsun is near either tropic, its declination scarcely varies at all\\nwhile near the equator, the variations from day to day are very\\nrapid, a fact which is easily understood, when we reflect, that\\nat the solstices the equator and the ecliptic are parallel to each\\nother,f both being at right angles to the meridian while at the\\nSuch a table may be found in Biot s Astronomy, in Delarnbre, and in most collec-\\ntions of Astronomical Tables.\\nt Or, more properly, the tangents of the two circles (which denote the directions of\\nthe curves at those points) are parallel.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0106.jp2"}, "107": {"fulltext": "ANNUAL MOTION. 81\\nequinoxes, the ecliptic departs most rapidly from the direction of\\nthe equator.\\nOn examining, in like manner, a table of observations of the\\nright ascension, we find that the daily differences of right ascen-\\nsion are likewise unequal that the mean of them all is 3 m 56*,\\nor 236 s but that they have varied between 215 s and 266 s On\\nexamining, moreover, the right ascension at each of the equi-\\nnoxes, we find that the two records differ by 180\u00c2\u00b0; which proves\\nthat the path of the sun is a great circle, since no other would\\nbisect the equinoctial as this does.\\n157. The obliquity of the ecliptic is equal to the sun s greatest\\ndeclination. For, by article 22, the inclination of any two great\\ncircles is equal to their greatest distance asunder, as measured on\\nthe sphere. The obliquity of the ecliptic may be determined\\nfrom the sun s meridian altitude, or zenith distance, on the day\\nof the solstice. The exact instant of the solstice, however, will\\nnot of course occur when the sun is on the meridian, but may\\nhappen at some other meridian still, the changes of declination\\nnear the solstice are so exceedingly small, that but a slight error\\ncan result from this source. The obliquity may also be found,\\nwithout knowing the latitude, by observing the greatest and least\\nmeridian altitudes of the sun, and taking half the difference.\\nThis is the method practiced in ancient times by Hipparchus.\\n(Art. 2.) On comparing observations made at different periods\\nfor more than two thousand years, it is found, that the obliquity\\nof the ecliptic is not constant, but that it undergoes a slight dimi-\\nnution from age to age, amounting to 52 in a century, or about\\nhalf a second annually. We might apprehend that by successive\\napproaches to each other the equator and ecliptic would finally\\ncoincide but astronomers have ascertained by an investigation,\\nfounded on the principles of universal gravitation, that this varia-\\ntion is confined within certain narrow limits, and that the obli-\\nquity, after diminishing for some thousands of years, will then\\nincrease for a similar period, and will thus vibrate for ever about\\na mean value.\\n158. The dimensions of the earth! s orbit, when compared with its\\nown magnitude, are immense.\\n11", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0107.jp2"}, "108": {"fulltext": "52 THE SUN.\\nSince the distance of the earth from the sun is 95,000,000\\nmiles, and the length of the entire orbit nearly 600,000,000 miles,\\nit will be found, on calculation, that the earth moves 1,640,000\\nmiles per day, 68,000 miles per hour, 1,100 miles per minute, and\\nnearly 19 miles every second, a velocity nearly fifty times as great\\nas the maximum velocity of a cannon ball. A place on the earth s\\nequator turns, in the diurnal revolution, at the rate of about 1,000\\nmiles an hour and T 5 T of a mile per second. The motion around\\nthe sun, therefore, is nearly 70 times as swift as the greatest mo-\\ntion around the axis.\\nTHE SEASONS.\\n159. The change of seasons depends on two causes, (1) the ob-\\nliquity of the ecliptic, and (2) the earth! s axis always remaining\\nparallel to itself Had the earth s axis been perpendicular to the\\nplane of its orbit, the equator would have coincided with the\\necliptic, and the sun would have constantly appeared in the equa-\\ntor. To the inhabitants of the equatorial regions, the sun would\\nalways have appeared to move in the prime vertical and to the\\ninhabitants of either pole, he would always have been in the ho-\\nrizon. But the axis being turned out of a perpendicular direc-\\ntion 23\u00c2\u00b0 28 the equator is turned the same distance out of the\\necliptic and since the equator and ecliptic are two great circles\\nwhich cut each other in two opposite points, the sun, while per-\\nforming his circuit in the ecliptic, must evidently be once a year\\nin each of those points, and must depart from the equator of the\\nheavens to a distance on either side equal to the inclination of the\\ntwo circles, that is, 23\u00c2\u00b0 28 (Art. 22.)\\n160. The earth being a globe, the sun constantly enlightens\\nthe half next to him,* while the other half is in darkness. The\\nboundary between the enlightened and the unenlightened part, is\\ncalled the circle of illumination. When the earth is at one of\\nthe equinoxes, the sun is at the other, and the circle of illumina-\\nIn fact, the sun enlightens a little more than half the earth, since on account of\\nhis vast magnitude the tangents drawn from opposite sides of the sun to opposite sides\\nof the earth, converge to a point behind the earth, as will be seen by and by in the\\nrepresentation of eclipses. The amount of illumination also is increased by refraction.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0108.jp2"}, "109": {"fulltext": "THE SEASONS.\\n83\\ntion passes through both the poles. When the earth reaches one\\nof the tropics, the sun being at the other, the circle of illumina-\\ntion cuts the earth so as to pass 23\u00c2\u00b0 28 beyond the nearer, and\\nthe same distance short of the remoter pole. These results would\\nnot be uniform, were not the earth s axis always to remain parallel\\nto itself. The following figure will illustrate the foregoing state-\\nments.\\nFig. 31.\\nLet ABCD represent the earth s place in different parts of its\\norbit, having the sun in the center. Let A, C, be the position of\\nthe earth at the equinoxes, and B, D, its positions at the tropics,\\nthe axis ns being always parallel to itself.* At A and C the sun\\nshines on both n and s and now let the globe be turned round\\non its axis, and the learner will easily conceive that the sun will\\nappear to describe the equator, which being bisected by the hori-\\nThe learner will remark that the hemisphere towards n is above, and that towards\\nis below the plane of the paper. It is important to form a just conception of the\\nposition of the axis with respect to the plane of its orbit.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0109.jp2"}, "110": {"fulltext": "84\\nTHE SUN.\\nzon of every place, of course the day and night will be equal in all\\nparts of the globe.* Again, at B when the earth is at the south-\\nern tropic, the sun shines 23|\u00c2\u00b0 beyond the north pole n, and falls\\nthe same distance short of the south pole s. The case is exactly\\nreversed when the earth is at the northern tropic and the sun at\\nthe southern. While the earth is at one of the tropics, at B for\\nexample, let us conceive of it as turning on its axis, and we shall\\nreadily see that all that part of the earth which lies within the\\nnorth polar circle will enjoy continual day, while that within the\\nsouth polar circle will have continual night, and that all other\\nplaces will have their days longer as they are nearer to the en-\\nlightened pole, and shorter as they are nearer to the unenlightened\\npole. This figure likewise shows the successive positions of the\\nearth at different periods of the year, with respect to the signs,\\nand what months correspond to particular signs. Thus the earth\\nenters Libra and the sun Aries on the 21st of March, and on the\\n21st of June the earth is just entering Capricorn and the sun Can-\\ncer.\\n161. Had the axis of the earth been perpendicular to the plane\\nof the ecliptic, then the sun would always have appeared to move\\nin the equator, the days would every where have been equal to the\\nnights, and there could have been no change of seasons. On the\\nother hand, had the inclination of the ecliptic to the equator been\\nmuch greater than it is, the vicissitudes of the seasons would have\\nbeen proportionally greater than at present. Suppose, for instance,\\nthe equator had been at right angles to the ecliptic, in which case,\\nthe poles of the earth would have been situated in the ecliptic\\nitself; then in different parts of the earth the appearances would\\nhave been as follows. To a spectator on the equator, the sun as\\nhe left the vernal equinox would every day perform his diurnal\\nrevolution in a smaller and smaller circle, until he reached the\\nnorth pole, when he would halt for a moment and then wheel\\nabout and return to the equator in the reverse order. The pro-\\ngress of the sun through the southern signs, to the south pole,\\nwould be similar to that already described. Such would be the\\nAt the pole, the solar disk, at the time of the equinox, appears bisected by the ho-\\nrizon.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0110.jp2"}, "111": {"fulltext": "85\\nappearances to an inhabitant of the equatorial regions. To a\\nspectator living in an oblique sphere, in our own latitude for ex-\\nample, the sun while north of the equator would advance continu-\\nally northward, making his diurnal circuits in parallels further and\\nfurther distant from the equator, until he reached the circle of per-\\npetual apparition, after which he would climb by a spiral course\\nto the north star, and then as rapidly return to the equator. By a\\nsimilar progress southward, the sun would at length pass the circle\\nof perpetual occultation, and for some time (which would be\\nlonger or shorter according to the latitude of the place of obser-\\nvation) there would be continual night.\\nThe great vicissitudes of heat and cold which would attend\\nsuch a motion of the sun, would be wholly incompatible with the\\nexistence of either the animal or the vegetable kingdoms, and all\\nterrestrial nature would be doomed to perpetual sterility and deso-\\nlation. The happy provision which the Creator has made against\\nsuch extreme vicissitudes, by confining the changes of the seasons\\nwithin such narrow bounds, conspires with many other express\\narrangements in the economy of nature to secure the safety and\\ncomfort of the human race.\\n162. Thus far we have taken the earth s orbit as a great circle,\\nsuch being the projection of it on the celestial sphere but we now\\nproceed to investigate its actual figure.\\nWere the earth s path a circle, having the sun in the center, the\\nsun would always appear to be at the same distance from us that\\nis, the radius of its orbit, or radius vector, the name given to a line\\ndrawn from the center of the sun to the orbit of any planet,\\nwould always be of the same length. But the earth s distance\\nfrom the sun is constantly varying, which shows that its orbit is\\nnot a circle. We learn the true figure of the orbit, by ascertain-\\ning the relative distances of the earth from the sun at various pe-\\nriods of the year. These all being laid down in a diagram, accord-\\ning to their respective lengths, the extremities, on being connected,\\ngive us our first idea of the shape of the orbit, which appears of\\nan oval form, and at least resembles an ellipse and, on further", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0111.jp2"}, "112": {"fulltext": "86\\nTHE SUN.\\ntrial, we find that it has the properties of an ellipse. Thus, let E\\n(Fig. 32,) be the place of the earth, and a, b, c, c. successive po-\\nsitions of the sun the relative lengths of the lines Ea, E6, c. be-\\ning known on connecting the points, a, b, c, c. the resulting\\nfigure indicates the true shape of the earth s orbit.\\nFig. 32.\\n163. These relative distances are found in two different ways\\nfirst, by changes in the surfs apparent diameter, and, secondly, by\\nvariations in his angular velocity. Were the variations in the\\nsun s horizontal parallax considerable, as is the case with the\\nmoon s, this might be made the measure of the relative distances,\\nfor the parallax varies inversely as the distance, (Art. 82) but the\\nwhole horizontal parallax of the sun is only 9 and its variations\\nare too slight and delicate, and too difficult to be found, to serve\\nas a criterion of the changes in the sun s distance from the earth.\\nBut the changes in the sun y s apparent diameter, are much more\\nsensible, and furnish a better method of measuring the relative\\ndistances of the earth from the sun. By a principle in optics, the\\napparent diameter of an object, at different distances from the\\nspectator, is inversely as the distance.* Hence, the apparent\\ndiameters of the sun, taken at different periods of the year, be-\\ncome measures of the different lengths of the radius vector.\\nMore exactly, the tangent of the apparent diameter is inversely as the distance\\nbut in small angles like those concerned in the present inquiry, the angle itself may be\\ntaken for the tangent.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0112.jp2"}, "113": {"fulltext": "87\\n164. The point where the earth, or any planet, in its revolution,\\nis nearest the sun, is called its perihelion the point where it is\\nfurthest from the sun, its aphelion. The place of the earth s peri-\\nhelion is known, since there the apparent magnitude of the sun is\\ngreatest and when the sun s magnitude is least, the earth is\\nknown to be at its aphelion. The sun s apparent diameter when\\ngreatest is 32 35. 6 and when least, 31 31 hence the radius\\nvector at the aphelion rad. vector at the perihelion 32.5933\\n31.5167 1.034 1. Half of the difference of the two is equal\\nto the distance of the focus of the ellipse from the center, a quan-\\ntity which is always taken as the measure of the eccentricity of a\\nplanetary orbit.\\n165. The differences of angular velocity in the sun in the dif-\\nferent parts of his apparent revolution, are still more remarkable.\\nAt the perihelion, the sun moves in twenty-four hours over an arc\\nof 61 while at the aphelion he describes in the same time an arc\\nof only 57 these being the daily increments of longitude in those\\ntwo points respectively. If the apparent motions of the sun de-\\npended alone on our different distances from him, the angular ve-\\nlocity would vary inversely as the distance, and the ratio expressed\\nby these two numbers would be the same as that of the two num-\\nbers which denote the differences of apparent diameter in these\\ntwo points. That is, (=1.07) would equal (=1.034)\\nbut the first fraction is equal to the square of the second, for 1.07=\\n1 .034 2 Hence, the sun s angular velocities are to each other inversely\\nas the squares of the distances at the perihelion and the aphelion and\\nby a similar method, the same is found to be true in all points of\\nthe revolution.\\nThe angular velocities, therefore, which can be measured very\\naccurately by the daily differences of right ascension and declina-\\ntion (Art. 132,) converted into corresponding longitudes, enable\\nus to determine the different distances of the earth from the sun\\nat various points in the orbit.\\n166. Since the arcs described by the earth in any small times,\\nas in single days, are inversely as the squares of the distances, con-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0113.jp2"}, "114": {"fulltext": "88\\nTHE SUN.\\nsequently, the distances are inversely as the square roots of the arcs.\\nUpon this principle, the relative distances of the earth from the\\nsun, in every point of its revolution, may be easily calculated.\\nThus, we have seen that the arcs described by the sun in one day\\nat the perihelion and aphelion are as 61 to 57. Hence the distances\\nof the earth from the sun at those two points are as /57 to \\\\/6i,\\nor as 1 to 1.034. From twenty-four observations made with the\\ngreatest care by Dr. Maskelyne at the Royal Observatory of\\nGreenwich, the following distances of the earth from the sun are\\ndetermined for each month in the year.\\nTime of Observation.\\nDistances.\\nTime of Observation.\\nDistances.\\nJanuary\\n12-13,\\n0.98448\\nJuly\\n18-19,\\n1.01658\\nFebruary\\n17-18,\\n0.98950\\nAugust\\n26-27,\\n1.01042\\nMarch\\n14-15,\\n0.99622\\nSeptember\\n22-23,\\n1.00283\\nApril\\n28-29,\\n1.00800\\nOctober\\n24-25,\\n0.99303\\nMay\\n15-16,\\n1.01234\\nNovember\\n18-20,\\n0.98746\\nJune\\n17-18,\\n1.01654\\nDecember\\n17-18,\\n0.98415\\n167. The angular velocity being Fi 33\\ninversely as the square of the distance\\nin all parts of the solar orbit, it follows\\nthat the product of the angle described By\\nin any given time, by the square of the\\ndistance, is always the same constant\\nquantity. For if of two factors, A x\\nB, A is increased as B is diminished,\\nthe product of A and B is always the\\nsame. If, therefore, from the sun S\\n(Fig. 33,) two radii be drawn to T,\\nB, the extremities of the arc described in one day. then ST 2 xTB\\ngives the same product in all parts of the orbit.*\\n168. The radius vector of the solar orbit describes equal spaces\\nin equal times, and in unequal times, spaces proportional to the times,\\nLet TB (Fig. 33,) be the arc described by the sun in one day\\nthen, Sector TSB-4SB xTB.\\nTB, as seen from the earth, would be projected into a circular arc, equal to the\\nmeasure of the angle at S.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0114.jp2"}, "115": {"fulltext": "89\\nTaking Sb as any radius, describe the circular arc ab, which is\\nthe measure of the angle at S. Now,\\nSbiab:: SB: BT=SBx?| and substituting this value of BT\\nin the above equation, we have TSB=|SBxSBx ^=-iSB 2 x^.\\nkb feo\\nBut S6 is constant, and the product of 8B 2 x\u00c2\u00ab is likewise constant\\ntherefore the sector is always equal to a constant quantity, and\\ntherefore the radius vector passes over equal spaces in equal\\ntimes.*\\nThe sun s orbit may be accurately represented by taking some\\npoint as the perihelion, drawing the radius vector to that point,\\nand, considering this line as unity, drawing other radii making\\nangles with each other such that the included areas shall be pro-\\nportional to the times, and of a length required by the distance of\\neach point as given in the table (Art. 166.) On connecting these\\nradii, we shall thus see at once how little the earth s orbit departs\\nfrom a perfect circle. Small as the difference appears between\\nthe greatest and least distances, yet it amounts to nearly of the\\nperihelion distance, a quantity no less than 3,000,000 of miles.\\n169. The foregoing method of determining the figure of the\\nearth s orbit is founded on observation but this figure is subject\\nto numerous irregularities, the nature of which cannot be clearly\\nunderstood without a knowledge of the leading principles of Uni-\\nversal Gravitation. An acquaintance with these will also be in-\\ndispensable to our understanding the causes of the numerous ir-\\nregularities, which (as will hereafter appear) attend the motions\\nof the moon and planets. To the laws of universal gravitation,\\ntherefore, let us next apply our attention.\\nFrancoeur, Uran., p. 62.\\n12", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0115.jp2"}, "116": {"fulltext": "CHAPTER III.\\nOF UNIVERSAL GRAVITATION.\\n170. Universal Gravitation, is that influence by which every\\nbody in the universe, whether great or small, tends towards every\\nother, with a force which is directly as the quantity of matter, and\\ninversely as the square of the distance.\\nAs this force acts as though bodies were drawn towards each\\nother by a mutual attraction, the force is denominated attraction\\nbut it must be borne in mind, that this term is figurative, and im-\\nplies nothing respecting the nature of the force.\\nThe existence of such a force in nature was distinctly asserted\\nby several astronomers previous to the time of Sir Isaac Newton,\\nbut its laws were first promulgated by this wonderful man in his\\nPrincipia, in the year 1687. It is related, that while sitting in a\\ngarden, and musing on the cause of the falling of an apple, he\\nreasoned thus that, since bodies far removed from the earth fall\\ntowards it, as from the tops of towers, and the highest mountains,\\nwhy may not the same influence extend even to the moon and\\nif so, may not this be the reason why the moon is made to revolve\\naround the earth, as would be the case with a cannon ball were\\nit projected horizontally near the earth with a certain velocity.\\nAccording to the first law of motion, the moon, if not continually\\ndrawn or impelled towards the earth by some force, would not\\nrevolve around it, but would proceed on in a straight line. But\\ngoing around the earth as she does, in an orbit that is nearly cir-\\ncular, she must be urged towards the earth by some force, which,\\nin a given time, may be represented by the versed sine of the arc\\ndescribed in that time. For let the earth (Fig. 34,) be at E, and\\nlet the arc described by the moon in one second of time be Ab.\\nWere the moon influenced by no extraneous force, to turn her\\naside, she would have described, not the arc Ab, but the straight\\nline AB, and would have been found at the end of the given time\\nPemberton s View of Newton s Philosophy.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0116.jp2"}, "117": {"fulltext": "UNIVERSAL GRAVITATION.\\n91\\nat B instead of b. She therefore departs from the line in which\\nshe tends naturally to move, by the line Bb, which in small angles\\nmay be taken as equal to the versed sine A#. This deviation\\nfrom the tangent must be owing to\\nsome extraneous force. Does this force\\ncorrespond to what the force of gravi-\\nty exerted by the earth, would be at the\\ndistance of the moon? Now we know the\\ndistance of the moon from the earth, and\\nof course the circumference of her orbit.\\nWe also know the time of her revolu-\\ntion around the earth. Hence we may\\nestimate the length of the arc Ab de-\\nscribed in one second and knowing\\nthe arc, we can calculate its versed sine.\\nFor the moon being 60 times as far from the center of the earth,\\nas the surface of the earth is from the center, consequently, since\\nthe force of gravity decreases as the square of the distance in-\\ncreases,* the space through which the moon would fall by the\\nforce of the earth s attraction alone, would be\\n16 T y\\n60^\\n.05 inches.\\nOn calculating the value of the versed sine of the arc described in\\none second, it proves to be the same. Hence gravity, and no other\\nforce than gravity, causes the moon to circulate around the earth.\\n171. By this process it was discovered that the law of gravita-\\ntion extends to the moon. By subsequent inquiries it was found\\nto extend in like manner to all the planets, and to every member\\nof the solar system and, finally, recent investigations have shown\\nthat it extends to the fixed stars. The law of gravitation, there-\\nfore, is now established as the grand principle which governs all\\nthe motions of the heavenly bodies. Hence, nothing can be more\\ndeserving of the attention of the student, than the development of\\nthe results of this universal law. A few of them only are all that\\ncan be exhibited in a work like the present their full develop-\\nNatural Philosophy, Art. 7. That gravity follows the ratio of the inverse square\\nof the distance was, however, inferred by Newton from one of Kepler s Laws, to be\\nmentioned hereafter.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0117.jp2"}, "118": {"fulltext": "92 UNIVERSAL GRAVITATION.\\nment must be sought for in such great works as the Mecanique\\nCeleste of La Place.\\n172. If a body revolves about an immovable center of force, and\\nis constantly attracted to it, it will always move in the same plane,\\nand describe areas about the center proportional to the times.*\\nLet S (Fig. 35,) be the center of force, and suppose a body to\\nbe projected at P in the direction of PQR, and take PQ=QR;\\nthen, by the first law of motion, the body would move uniformly\\nin the direction PQR, and describe PQ, QR, in the same time, if\\nno other force acted upon it. But when the body comes to Q,\\nFiff. 35.\\nlet a single impulse act at S, sufficient to draw the body through\\nQV, in the time it would have described QR and complete the\\nparallelogram VQRC, and the body in the same time will describe\\nQC therefore, PQ, QC, are described in the same time. But\\nthe triangle SCQ=SRQ=SPQ that is, equal areas are described\\nin equal times. For the same reason, if a single impulse act at\\nC, D, E, c. at equal intervals of time, the several areas SPQ,\\nSQC, SCD, SDE, c. will all be equal to each other. Now this\\nThe learner will remark that what has been before proved (Art. 168,) respecting\\nthe radius vector of the earth, is here shown to hold good with respect to every body\\nwhich revolves around a center of force and the same is true of several other propo-\\nsitions demonstrated in this chapter.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0118.jp2"}, "119": {"fulltext": "UNIVERSAL GRAVITATION.\\ndemonstration is independent of any particular dimensions in the\\nseveral triangles, and consequently holds good when they are\\ntaken indefinitely small, in which case we may consider the force\\nas acting, not by separate impulses, but constantly, causing the\\nbody to describe a curve around S. And as no force acts out of\\nthe plane SPQ, the whole curve must lie in that plane that is,\\nthe body moves always in the same plane.\\n173. If a body describes a curve around a center towards which it\\ntends by any force, the angular velocity of the body around that center\\nis reciprocally as the square of the distance from it.*\\nLet ABE (Fig. 36,) be any curve de- Fig. 36.\\nscribed about the center S draw SA, SB,\\nto any two points of the curve A and B\\nand let AD, BE, be described in indefi-\\nnitely small equal times. Join SD and\\nSE, and with the center S and distance\\nSD, describe a circle meeting SA, SB, SE,\\nin F, G, II and with the center S and\\ndistance SE describe a circle meeting SB\\nin K.\\nBecause AD and BE are described in\\nequal times, the triangl )s ASD, BSE, are\\nequal. Hence, (Euc. 15. 6.)\\nDF EK BS ASf BS 2 BSxAS (1)\\nGH EK SH SE SF SE SA SB SA 2 BSxAS (2)\\nHence, (1) DF BS 2 EK BS x AS\\n(2) GH: AS 2 EK: BSxAS\\nDF:GH::BS 2 AS 2\\nBut DF and GH measure the respective angular velocities at\\nA and B, while AS and BS represent the distance at the same\\npoints. Therefore the angular velocities are reciprocally as the\\nsquares of the distances. J\\n174. In the same curve, the velocity, at any point of the curve,\\nIt will be remarked that this is a general proposition, of which article 165 affords\\na. particular example.\\nt DF and EK are considered as the alttudes of the triangles respectively.\\nT Stewart s Phys. and Math. Essays.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0119.jp2"}, "120": {"fulltext": "94 UNIVERSAL GRAVITATION.\\nvaries inversely as the perpendicular drawn from the center of\\nforce to the tangent at that point.\\nDraw SY (Fig. 35,) perpendicular to QP produced then the\\narea SPQ=\u00c2\u00a3PQ x SY, which varies as PQ x SY PQ x\\narea SPQ n T area SPQ\\ngy But P Q a V the velocity at P V a gy^ W\\nin the curve described from P, with a constant force, SY becomes\\na perpendicular to the tangent to the curve. But by article\\n72, the area described in a given time is constant. Therefore\\nSPQ is constant, and V a that is, the velocity varies inverse-\\nSY\\nly as the perpendicular upon the tangent. Hence, the velocity of\\na revolving body increases as it approaches the center of force.\\n175. If equal areas be described about a center in equal times*\\nthe force must tend towards that center.\\nLet SPQ (Fig. 35,)=SQC now SPQ=SQR SQC-SQR/.\\nCR is parallel to QS. Complete the parallelogram QRCV, and\\nby the supposition the body describes QC, in consequence of the\\nimpulse at Q, and it would have described QR if no such impulse\\nhad acted therefore QV must represent that motion impressed\\nat Q, which, in conjunction with the motion QR, can make a body\\ndescribe QC, and QV is directed to S.\\n176. Now it appears from article 168, that it is a fact, derived\\nfrom observation, that the earth s radius vector describes equal\\nareas in equal times and by similar observations the same is\\nfound to be true of each of the primary planets about the sun,\\nand of each of the satellites about its primary. Hence, it is in-\\nferred, that the primary planets all gravitate towards the sun, and\\nthat the secondary planets all gravitate towards their respective\\nprimaries.\\nIt has further been established by observation, (Art. 162,) that\\nthe planetary orbits are ellipses and hence the application of the\\nprinciples of gravitation, so far as respects the sun and planets,\\nmay be confined to the consideration of the motion of a body in\\nan elliptical orbit.\\n177. The distance of any planet from the sun at any point in its", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0120.jp2"}, "121": {"fulltext": "UNIVERSAL GRAVITATION.\\n95\\norbit, is to its distance from the superior focus, as the square of its\\nvelocity at its mean distance from the sun, is to the square of its ve-\\nlocity at the given point.\\nLet ADBE (Fig. 37,) be the orbit of a planet, S the focus in\\nwhich the sun is placed, AB the transverse and DE the conjugate\\naxis, C the center, and F the superior focus. Let the planet be\\nany where at P and draw a tangent to the orbit at P, on which\\nfrom the foci let fall the perpendiculars SG, FH. Draw also DK\\ntouching the orbit in D, and let SK be perpendicular to it. Let\\nFig. 37.\\nN\\nthe velocity of the planet when at the mean distance at D=C, and\\nwhen at P=V. Join SP, FP. Then (Art. 174,) the velocity at\\nD is to the velocity at P, as SG to SK that is,\\nC:V::SG:DC.\\nC 2 V 2 SG 2 DC 2\\nBut because the triangles SGP, FHP, are equiangular, having\\nright angles at G and H, and also, from the nature of the ellipse,\\nthe angles SPG, FPH, equal,\\nSP PF SG FH SG 2 CD 2 =FHxSG\\nSP:PF::C 2 :V 2\\n178. If of two bodies gravitating to the same center, one descends\\nin a straight line, and the other revolves in a curve then, if the ve~\\ninMpg of the up. hnrfips are eoual in ami one case, when they are", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0121.jp2"}, "122": {"fulltext": "96\\nUNIVERSAL GRAVITATON.\\nequally distant from the center, they will always be equal when they\\nare equally distant from it.\\nLet ABC (Fig. 38,) be a curve which a body\\ndescribes about a center S to which it gravi-\\ntates, while another body descends in a\\nstraight line AS to that center. Let BC be\\nany arc of the curve ABC, and let BD, CH,\\nbe arcs of circles described from the center\\nS, intersecting the line AS in D and H.\\nFrom the center S describe the arc bd, in-\\ndefinitely near to BD, and draw E/ perpen-\\ndicular to Bb. Then, because the distances\\nSD and SB are equal, the forces of gravity\\nat D and B are also equal. Let these forces\\nbe expressed by the equal lines Dd and BE\\nand let the force BE be resolved into the\\nforces ~Ef and Bf The force E/ acting at\\nright angles to the path of the body, will not affect its velocity in\\nthat path, but will only draw it aside from a rectilinear course and\\nmake it proceed in the curve BbC. But the other force Bf acting\\nin the direction of the course of the body, will be wholly employed\\nin accelerating it. And because B and b are indefinitely near to\\neach other, and likewise D and d, the accelerating force from B to\\nb and from D to d, may be considered as acting uniformly.\\nTherefore, the accelerations of the bodies in D and B, produced\\nin equal times, are as the lines Dd, Bf; and hence, putting d for\\nthe increment of velocity at d, and/ for the increment of velocity\\nat/,\\n^:/::D^orBE:B/. (1)\\nAnd because the angle at E is a right angle,\\nBE 2 =B6xB/.-.BE=v/B6x^/B/.-.BExv/B/=VB6xB/.\\nHence, BE Bf: VBb VBf (2)\\nAnd, (1) and (2), d VBb VBf (3)\\nBut, putting b for the velocity at b, and observing that, in falling\\nbodies, the velocities are as the square roots of the spaces,\\nb:f::VBb:VBf(4)\\nTherefore, (3) and (4), b:f::d b=d that is, the velocity at\\nb equals the velocity at d. And, since the same reasoning holds", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0122.jp2"}, "123": {"fulltext": "UNIVERSAL GRAVITATION. 97\\ntor successive points that may be taken at equal distances from B\\nand D, therefore, if of two bodies, c.\\n179. The law according to which the planets gravitate is such, that\\nany body under the influence of the same force, and falling direct to\\nthe sun, will have its velocity at any point equal to a constant velocity\\nmultiplied into the square root of the distance it has fallen through,\\ndivided by the square root of the distance between the body and the\\nstill s center.\\nSuppose a planet to revolve in the elliptical orbit APB (Fig. 37);\\n(AFX 1\\nJ 2 (Art. 177) or\\nif AN, in the axis produced=AF, Y=C(^-- 2 Let a body at\\nA begin to descend towards S with this velocity, then if SL=SP,\\nthe velocity of the planet at P will be the same as that of the fall-\\ning body at L, (Art. 178.) But the velocity of the planet at P is\\n(pp\\\\i /NL\\\\-\\nJ 2 =C I But this velocity is equal to the constant ve-\\nlocity expressed by C, multiplied into the square root of NL, the\\ndistance fallen through,^ divided by the square root of LS, the\\ndistance between the body and the sun s center.\\n180. The force with which any planet gravitates to the sun, is in-\\nversely as the square of its distance from the sun s center.\\nLet C (Fig. 39,) be the center to which the falling body gravi-\\ntates, A the point from which it begins to fall, and its velocity at\\nany point B, is to its velocity in the point G, which bisects AC, as\\n/ABU\\n\\\\bc;\\nor a perpendicular to AC, meeting the curve in D, and BE any other\\n1.11 Let DEF be a curve such that if AD be an ordinate\\nPrincipia, Lib. i, Pr. 40. Stewart s Math, and Phys. Essays, Pr. 13.\\nI For SN=AB=SP-f-PF=SP-f-NL PF=NL.\\nThat NL (=PF) is the distance fallen through to acquire the velocity at P, is de-\\nmonstrated by writers on Central Forces. (See Vince, Syst. Ast., Art. 823.)\\nPlayfair, Phys. Ast.\\nFor, denoting the velocity at B by V, and the velocity at G by V,\\n^)*.o(^)*..(^)*.(^,.(a\u00c2\u00bb.L\\n13", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0123.jp2"}, "124": {"fulltext": "Af 1\u00c2\u00bb\\nt)S UNIVERSAL GRAVITATION.\\nordinate, AD is to BE as the force at A to the force at B, then\\nwill twice the area ABED be equal to the Fi g- 39\\nsquare of the velocity which the body has\\nacquired in B. If therefore the velocity B j_\\nat B be V, that at the middle point G being c,\\nl AT?\\n2 and therefore 2ABED=c 2\\nand since AB AC BC, 2ABED c 2\\nAC-BC\\nCr\\nMS)\\n\\\\BC\\nFor the same reason,\\nBC\\nif be be drawn indefinitely near to BE, 2AbeD\\n=c 2 1 and therefore the difference of\\nthese areas, or 2B5eE, that is, 2EBxB =c 2\\n/AC AC\\\\ oAC(BC-5C) ACxBZ _ e\\n(iC Bc) =C BCxftC ^TSgT Wherefore d dm b\\nB ,2EB=c 2 f r 7 orEB^c 2 now c 2 and AG are constant\\nquantities, therefore EB varies inversely as BC 2 But EB repre-\\nsents the force of gravity at B, and BC the distance from the\\nsun. Therefore, the force of gravity of a planet in different parts\\nof its orbit, is inversely as the square of its distance from the sun,\\n181. The line CG is the same with the mean distance of the\\nplanet in an orbit of which AC is the length of the transverse axis\\nand if the gravitation at that distance =F, and the mean distance\\nLtself=a, then since EB=c 2 ==-j F=c 2 x or aF=c i\\nBC 5 cr a\\nThis principle is demonstrated by the aid of Fluxions as follows\\nBy construction, BE is proportional to the force at B=y-, v being the velocity\\nwhich the moving body has acquired at B, and t the time of the descent from A to B.\\nNow Bb is the momentary increment of B A the space, and therefore=ucZif therefore\\nBExBb=vdv. And 2BExBb=2vdv. But BE xBb is the momentary increment of\\nthe area ABED, and 2vdv is the momentary increment of v 2 therefore the square of\\nthe velocity of the moving body, and twice the area of ABED, increase at the same\\nrate, and begin to exist at the same time therefore they are equal. (See Play fair s\\nOutlines, Mechanics, Art. 96.)\\nt JC being ultimately equal to BC.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0124.jp2"}, "125": {"fulltext": "UNIVERSAL GRAVITATION. 9$\\n182. The squares of the times of revolution of any two planets,\\nare as the cubes of their mean distances from the sun.\\nIf a be the mean distance, or the semi-transverse axis, b the\\nsemi-conjugate, then ra =area of the orbit.* But as c is the ve-\\nlocity at the mean distance, or the elliptic arch which the planet\\nmoves over in a second when it is at D, (Fig. 37.) the vertex of the\\nconjugate axis, therefore \\\\bc is the area described in that second\\nby the radius vector and since the area is the same for every\\nsecond of the planet s revolution (Art. 172,) therefore the area of\\nthe orbit divided by \\\\bc will give the number of seconds in\\nwhich the revolution is completed, which=\u00e2\u0080\u0094 or, since\\n\\\\bc c\\nc 3 a\u00c2\u00a5, (Art. 181,) the time of a revolution ==2rf\\\\/ fr-\\nVaF v 1*\\nHence, let t, t be the times of revolutions for two different plan-\\nets, of which the mean distances are a, a and the force of gravity\\nat those distances F, P. Then t V 2* \\\\/\u00c2\u00a3r 2 Vt^ Vp\\nf: t^i .^S. But (Art. 180,) F F tf 2 tf 2 t?\\na\\n-y, or t~ :t 2 ::a 3 1 a 3 That is, the squares of the times are as the\\ncubes of the mean distances or, since the major axes of the or-\\nbits are double the mean distances, the squares of the times are as\\nthe cubes of the major axes.\\n183. This is one of Kepler s three great Laws, which, taken in\\nconnexion, are as follows\\n1. The orbits of all the planets are ellipses, the sun occupying the\\ncommon focus. (Art. 178.)\\n2. The radius vector of any planet describes areas proportional\\nto the times. (Art. 172.)\\n3. The squares of the periodical times are as the cubes of the ma-\\njor axes of the orbits. (Art. 182.)\\nThese great and fundamental principles of the planetary mo-\\ntions, were discovered by the illustrious Kepler by long and as-\\nsiduous study of the observations made by Tycho Brahe, and\\nDay s Mensuration.\\ns/", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0125.jp2"}, "126": {"fulltext": "100 UNIVERSAL GRAVITATION.\\nhence he has been called the legislator of the skies. They, there-\\nfore, became known as facts, before they were demonstrated\\nmathematically. The glory of this achievement was reserved\\nfor Newton, who proved that they were necessary results of the\\nlaw of universal gravitation.\\n3IOTION IN AN ELLIPTICAL ORBIT.\\n184. Having now acquired some knowledge of the law of uni-\\nversal gravitation, let us next endeavor to gain a just conception\\nof the forces by which the planets are made to revolve in their\\norbits about the sun. In obedience to the first law of motion,\\nevery moving body tends to move in a straight line and were not\\nthe planets deflected continually towards the sun by the force of\\nattraction, these bodies as well as others would move forward in\\na rectilineal direction. We call the force by which they tend to\\nsuch a direction the projectile force, because its effects are the\\nsame as though the body were originally projected from a certain\\npoint in a certain direction. It is an interesting problem for me-\\nchanics to solve, what was the nature of the impulse originally\\ngiven to the earth, in order to impress upon it its two motions, the\\none around its own axis, the other around the sun If struck in\\nthe direction of its center of gravity it might receive a forward\\nmotion, but no rotation on its axis. It must, therefore, have been\\nimpelled by a force, whose direction did not pass through its cen-\\nter of gravity. Bernouilli, a celebrated mathematician, has calcu-\\nlated that the impulse must have been given very nearly in the\\ndirection of the center, the point of projection being only the 165th\\npart of the earth s radius from the center.* This impulse alone\\nwould cause the earth to move in a right line gravitation towards\\nthe sun causes it to describe an orbit. Thus a top spinning on a\\nsmooth plane, as that of glass or ice, if impelled in a direc-\\ntion not passing through the center of gravity, may be made to\\nimitate the two motions of the earth, especially if the experiment\\nis tried in a concave surface like that of a large bowl. The re-\\nsistance occasioned by the surface on which the top moves, and\\nFrancceur, Uran. p. 49", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0126.jp2"}, "127": {"fulltext": "UNIVERSAL GRAVITATION.\\n101\\nthat of the air, will generally destroy the force of projection and\\ncause the top to revolve in a smaller and smaller orbit but the\\nearth meets with no such resistance, and therefore makes both her\\ndays and years of the same length from age to age. A body,\\ntherefore, revolving in an orbit about a center of attraction, is\\nconstantly under the influence of two forces, the projectile force,\\nwhich tends to carry it forward in a straight line which is a tan-\\ngent to its orbit, and the centripetal force, by which it tends to-\\nwards the center.\\n185. The most simple example we have of the combined action\\nof these two forces is the motion of a missile thrown from the\\nhand, or of a ball fired from a cannon. It is well known that the\\nparticular form of the curve described by the projectile, in either\\ncase, will depend upon the velocity with which it is thrown. In\\neach case the body will begin to move in the line of direction in\\nwhich it is projected, but it will soon be deflected from that line\\ntowards the earth. It will however continue nearer to the line of\\nprojection as the velocity of projection is greater. Thus let AB\\nFig. 40.\\nB\\n(Fig. 40,) perpendicular to AC represent the line of projection.\\nThe body will, in every case, commence its motion in the line AB,\\nwhich will therefore be the tangent to the curve it describes but\\nif it be thrown with a small velocity, it will soon depart from the\\ntangent, describing the line AD with a greater velocity it will\\ndescribe a curve nearer to the tangent, as AE and with a still\\ngreater velocity it will describe the curve AF.\\nAs an example of a body revolving in an orbit under the influ-\\nence of two forces, suppose a body placed at any point P (Fig. 40\\nabove the surface of the earth, and let PA be the direction of the\\nearth s center that is, a line perpendicular to the horizon. If the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0127.jp2"}, "128": {"fulltext": "102\\nUNIVERSAL GRAVITATION.\\nbody were allowed to move without receiving any impulse, it\\nwould descend to the earth in the direction PA with an accelerated\\nmotion. But suppose that, at the moment of its departure from\\nP, it receives a blow in the direction PB, which would carry it to\\nB in the time the body would fall from P to A then, under the in-\\nfluence of both forces, it would descend along the curve PD. If\\na stronger blow were given to it in the direction PB, it would de-\\nscribe a larger curve, PE or, finally, if the impulse were suffi-\\nciently strong, it would circulate quite around the earth, and re-\\nturn again to P, describing the circle PFG. With a velocity of\\nprojection still greater, it would describe an ellipse, PIK and if\\nthe velocity were increased to a certain degree, the figure would\\nbecome a parabola or hyperbola LMP, and never return into\\nitself.\\n186. In figure 41, suppose the planet to have passed the point C\\nwith so small a velocity, that the attraction of the sun bends its\\npath very much, and causes it immediately to begin to approach\\ntowards the sun the sun s attraction will increase its velocity as\\nit moves through D, E, and F. For the sun s attractive force on\\nthe planet, when at D, is acting in the direction DS, and, on account\\nof the small inclination of DE to DS, the force acting in the line\\nDS helps the planet forward in the path DE, and thus increases\\nits velocity. In like manner the velocity of the planet will be con-\\ntinually increasing as it passes through D, E, and F and though\\nthe attractive force, on account of the planet s nearness, is so much\\nincreased, and tends, therefore, to make the orbit more curved,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0128.jp2"}, "129": {"fulltext": "UNIVERSAL GRAVITATION.\\n103\\nyet the velocity is also so much increased, that the orbit is not\\nmore curved than before. The same increase of velocity occa-\\nsioned by the planet s approach to the sun, produces a greater in-\\ncrease of centrifugal force which carries it off again. We may\\nsee also why, when the planet has\\nreached the most distant parts of its\\norbit, it does not entirely fly off, and\\nnever return to the sun. For when\\nthe planet passes along H, K, A, the\\nsun s attraction retards the planet,\\njust as gravity retards a ball rolled up\\nhill and when it has reached C, its\\nvelocity is very small, and the attrac-\\ntion at the center of force causes a\\na great deflection from the tangent,\\nsufficient to give its orbit a great cur-\\nvature, and the planet turns about, returns to the sun, and goes\\nover the same orbit again.* As the planet recedes from the sun,\\nits centrifugal force diminishes faster than the force of gravity, so\\nthat the latter finally preponderates.f\\n187. We may imitate the two motions of the earth, the diurnal\\nand the annual, in the following manner. Suspend from the ceiling\\nof a room, by a string long enough to reach to the level of the\\neye, a ball (of wood for example) four or five inches in diameter, to\\nrepresent the earth. In the point occupied by the ball when at\\nrest, let a small globe be supported to represent the sun. The sus-\\npended ball being drawn out of its place of rest, which is directly\\nunder the point of suspension, it will tend constantly towards the\\nsame point, by a force which corresponds to the force of attraction\\nof a central body. If, when thus drawn out, it be impelled by a\\nblow in the direction of the center of gravity, it will revolve with-\\nout turning on its axis but if struck out of the center of gravity\\nit will, at the same time, revolve on its axis and in its orbit.\\nAiry.\\nt The centrifugal force varies inversely as the cube of the distance, while the force\\nof gravity is inversely as the square. The centrifugal force, therefore, increases faster\\nthan the force of gravity as a body is approaching the sun, and decreases faster as the\\nbody recedes from the sun. (See M. Stewart s Phys. and Math. Tracts, Prop. 8.)", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0129.jp2"}, "130": {"fulltext": "CHAPTER IV.\\nPRECESSION OF THE EQUINOXES NUTATION ABERRATION MOTION\\nOF THE APSIDES MEAN AND TRUE PLACES OF THE SUN.\\n188. The Precession of the Equinoxes, is a slow hut continual\\nshifting of the equinoctial points from east to west.\\nSuppose that we mark the exact place in the heavens, where,\\nduring the present year, the sun crosses the equator, and that this\\npoint is close to a certain star next year the sun will cross the\\nequator a fittle way westward of that star, and so every year a\\nlittle further westward, until, in a long course of ages, the place\\nof the equinox will occupy successively every part of the ecliptic,\\nuntil we come round to the same star again. As, therefore, the\\nsun, revolving from west to east in his apparent orbit, comes\\nround towards the point where it left the equinox, it meets the\\nequinox before it reaches that point. The appearance is as though\\nthe equinox goes forward to meet the sun, and hence the phenom-\\nenon is called the Precession of the Equinoxes, and the fact is\\nexpressed by saying that the equinoxes retrograde on the ecliptic,\\nuntil the line of the equinoxes makes a complete revolution from\\neast to west. The equator is conceived as sliding westward on\\nthe ecliptic, always preserving the same inclination to it, as a ring\\nplaced at a small angle with another of nearly the same size,\\nwhich remains fixed, may be slid quite around it, giving a cor-\\nresponding motion to the two points of intersection. It must be\\nobserved, however, that this mode of conceiving of the precession\\nof the equinoxes is purely imaginary, and is employed merely for\\nthe convenience of representation.\\n189. The amount of precession annually is 50. 1 whence,\\nsince there are 3600 in a degree, and 360\u00c2\u00b0 in the whole circum-\\nference, and consequently, 1296000 this sum divided by 50.1\\ngives 25868 years for the period of a complete revolution of the\\nequinoxes.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0130.jp2"}, "131": {"fulltext": "PRECESSION OF THE EQUINOXES. 105\\n190. Suppose now we fix to the center of each of the two\\nrings (Art. 188) a wire representing its axis, one corresponding to\\nthe axis of the ecliptic, the other to that of the equator, the ex-\\ntremity of each being the pole of its circle. As the ring deno-\\nting the equator turns round on the ecliptic, which with its axis\\nremains fixed, it is easy to conceive that the axis of the equator\\nrevolves around that of the ecliptic, and the pole of the equator\\naround the pole of the ecliptic, and constantly at a distance equal\\nto the inclination of the two circles. To transfer our conceptions\\nto the celestial sphere, we may easily see that the axis of the diur-\\nnal sphere, (that of the earth produced, Art. 28,) would not have\\nits pole constantly in the same place among the stars, but that this\\npole would perform a slow revolution around the pole of the\\necliptic from east to west, completing the circuit in about 26,000\\nyears. Hence the star which we now call the pole star, has not\\nalways enjoyed that distinction, nor will it always enjoy it here-\\nafter. When the earliest catalogues of the stars were made, this\\nstar was 12\u00c2\u00b0 from the pole. It is now 1\u00c2\u00b0 24 and will approach\\nstill nearer or, to speak more accurately, the pole will come still\\nnearer to this star, after which it will leave it, and successively\\npass by others. In about 13,000 years, the bright star Lyra,\\nwhich lies on the circle of revolution opposite to the present pole\\nstar, will be within 5\u00c2\u00b0 of the pole, and will constitute the Pole\\nStar. As Lyra now passes near our zenith, the learner might\\nsuppose that the change of position of the pole among the stars,\\nwould be attended with a change of altitude of the north pole\\nabove the horizon. This mistaken idea is one of the many mis-\\napprehensions which result from the habit of considering the\\nhorizon as a fixed circle in space. However the pole might shift\\nits position in space, we should still be at the same distance from\\nit, and our horizon would always reach the same distance be-\\nyond it.\\n191. The precession of the equinoxes is an effect of the spheroidal\\nfigure of the earth, and arises from the attraction of the sun and\\nmoon upon the excess of matter about the eartKs equator.\\nWere the earth a perfect sphere the attractions of the sun and\\nmoon upon the earth would be in equilibrium among themselves.\\n14", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0131.jp2"}, "132": {"fulltext": "106\\nTHE SUN.\\nBut if a globe were cut out of the earth, (taking half the polar\\ndiameter for radius,) it would leave a protuberant mass of matter\\nin the equatorial regions, which may be considered as all collected\\ninto a ring resting on the earth. The sun being in the ecliptic,\\nwhile the plane of this ring is inclined to the ecliptic 23\u00c2\u00b0 28 of\\ncourse the action of the sun is oblique to the ring, and may be\\nresolved into two forces, one in the plane of the equator, and the\\nother perpendicular to it. The latter only can act as a disturbing\\nforce, and tending as it does to draw down the ring to the ecliptic,\\nthe ring would turn upon the line of the equinoxes as upon a\\nhinge, and dragging the earth along with it, the equator would\\nultimately coincide with the ecliptic were it not for the revolution\\nof the earth upon its axis. This may be better understood by the\\naid of a diagram. Let TAB (Fig. 42,) represent the equator,\\nFisr. 42.\\nTED the ecliptic, and AD the solstitial colure. Let AB be the\\nmovement of rotation for a very short time, being of course in the\\norder of the signs and in the direction of the equator. Let BC be\\nthe movement produced by the disturbing force of the sun in the\\nsame time. The point A will describe the diagonal AC, the equa-\\ntor will take the inclined situation CAT the equinoctial point\\nwill retrograde from T to T the colure AD will take the posi-\\ntion AE, while the inclination of the two planes, that is, the ob-\\nliquity of the ecliptic, will remain nearly the same.*\\n192. The moon conspires with the sun in producing the pre-\\ncession of the equinoxes, its effect, on account of its nearness to\\nthe earth, being more than double that of the sun, or as 7 to 3.\\nThe planets likewise, by their attraction, produce a small effect\\nDelambre, t. 3, p. 145. Playfair s Outlines, 2, 308.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0132.jp2"}, "133": {"fulltext": "PRECESSION OP THE EQUINOXES. 10*7\\nupon the equatorial ring, but the result is slightly to diminish the\\namount of precession. The whole effect of the sun and moon\\nbeing 50. 41, that of the planets is 0.31, leaving the actual amount\\nof precession 50. 1.*\\nThis effect is not to be imagined as taking place merely at the\\ntime of the equinoxes, but as resulting constantly from the action\\nof the sun and moon on the equatorial ring, and at every revolu-\\ntion of this ring along with the earth on its axis. Conceive of\\nany point in the ring, and follow it round in the diurnal revolution,\\nand it will be seen that that point, in consequence of the attrac-\\ntion of the sun and moon, will be made to cross the ecliptic a little\\nfurther westward than on the preceding day.\\n193. The time occupied by the sun in passing from the equinoc-\\ntial point round to the same point again, is called the tropical year.\\nAs the sun does not perform a complete revolution in this inter-\\nval, but falls short of it 50. 1, the tropical year is shorter than the\\nsidereal by 20m. 20s. in mean solar time, this being the time of\\ndescribing an arc of 50. 1 in the annual revolution.^ The\\nchanges produced by the precession of the equinoxes in the ap-\\nparent places of the circumpolar stars, have led to some interest-\\ning results in chronology. In consequence of the retrograde mo-\\ntion of the equinoctial points, the signs of the ecliptic (Art. 35,)\\ndo not correspond at present to the constellations which bear the\\nsame names, but lie about one whole sign or 30\u00c2\u00b0 westward of\\nthem. Thus, that division of the ecliptic which is called the sign\\nTaurus, lies in the constellation Aries, and the sign Gemini in the\\nconstellation Taurus. Undoubtedly, however, when the ecliptic\\nwas thus first divided, and the divisions named, the several con-\\nstellations lay in the respective divisions which bear their names.\\nHow long is it, then, since our zodiac was formed\\n50. 1 1 year 30\u00c2\u00b0(=108000 2155.6 years.\\nThe result indicates that the present divisions of the zodiac\\nwere made soon after the establishment of the Alexandrian school\\nof astronomy. (Art 2.)\\nFrancoeur, Uran. 162. t 59 8. 3 24h. 50. 1 20m. 20s.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0133.jp2"}, "134": {"fulltext": "108 THE SUN.\\nNUTATION.\\n194. Nutation is a vibratory motion of the earth! s axis, arising\\nfrom periodical fluctuations in the obliquity of the ecliptic.\\nIf the sun and moon moved in the plane of the equator, there\\nwould be no precession, and the effect of their action in producing\\nit varies with their distance from that plane. Twice a year, there-\\nfore, namely, at the equinoxes, the effect of the sun is nothing\\nwhile at the solstices the effect of the sun is a maximum. On\\nthis account, the obliquity of the ecliptic is subject to a semi-an-\\nnual variation, since the sun s force which tends to produce a\\nchange in the obliquity is variable, while the diurnal motion of\\nthe earth which prevents the change from taking place, is con-\\nstant. Hence the plane of the equator is subject to an irregular\\nmotion which is called the Solar Nutation. The name is derived\\nfrom the oscillatory motion communicated by it to the earth s axis,\\nwhile the pole of the equator is performing its revolution around\\nthe pole of the ecliptic (Art. 190.) The effect of the sun however\\nis less than that of the moon, in the ratio of 2 to 5. By the nuta-\\ntion alone the pole of the earth would perform a revolution in a\\nvery small ellipse, only 18 in diameter, the center being in the\\ncircle which the pole describes around the pole of the ecliptic\\nbut the combined effects of precession and nutation convert the\\ncircumference of this circle into a wavy line. The motion of the\\nequator occasioned by nutation, causes it alternately to approach\\nto and recede from the stars, and thus to change their declinations.\\nThe solar nutation, depending on the position of the sun with re-\\nspect to the equinoxes, passes through all its variations annually\\nbut the lunar nutation depending on the position of the moon with\\nrespect to her nodes, varies through a period of about 18| years.\\nABERRATION.\\n195. Aberration is an apparent change of place in the stars,\\noccasioned by the joint effects of the motion of the earth in its orbit,\\nand the progressive motion of light.\\nLet EE (Fig. 43,) represent a part of the earth s orbit, and SE\\na ray of light from the star S. Take EC and EA proportional", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0134.jp2"}, "135": {"fulltext": "MOTION OF THE APSIDES.\\n109\\nto the velocity of each respectively com-\\nplete the parallelogram, and draw the diagonal\\nEB. Since an object always appears in the\\ndirection in which a ray of light coming from\\nit, meets the eye, the combination of the two\\nmotions produces an impression on the eye\\nexactly similar to that which would have been\\nproduced if the eye had remained at rest in\\nthe point E, and the particle of light had come\\ndown to it in the direction S E the star,\\ntherefore, whose place is at S, will appear to\\nthe spectator at E to be situated at S The\\ndifference between its true and its apparent place, that is, the\\nangle SES is the aberration, the magnitude of which is obtained\\nfrom the known ratio of EA to EC, or the velocity of light to that\\nof the earth in its orbit.\\nThe velocity of light is 192,000 miles per second, while that of\\nthe earth in its orbit is about 19 miles per second. Represent-\\ning the velocity of light by the line EA, and that of the earth by\\nAB, then,\\n192,000 19: Rad. tan. 20. 5=the angle at E, which is the\\namount of aberration when the direction of the ray of light is per-\\npendicular to the earth s motion.\\nThe effect of aberration upon the places of the fixed stars is to\\ncarry their apparent places a little forward of their real places in\\nthe direction of the earth s motion. The effect upon each particu-\\nlar star will be to make it describe a small ellipse in the heavens,\\nhaving for its center the point in which the star would be seen if\\nthe earth were at rest.\\nMOTION OF THE APSIDES.\\n196. The two points of the ecliptic where the earth is at the\\ngreatest and least distances from the sun respectively, do not\\nalways maintain the same places among the signs, but gradually\\nshift their positions from west to east. If we accurately observe\\nthe place among the stars where the earth is at the time of its\\nperihelion the present year, we shall find that it will not be pre-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0135.jp2"}, "136": {"fulltext": "110 THE SUN.\\ncisely at that point the next year when it arrives at its perihelion,\\nbut about 12 (ll. 66) to the east of it. And since the equinox\\nitself, from which longitude is reckoned, moves in the opposite\\ndirection 50. 1 annually, the longitude of the perihelion increases\\nevery year 61. 78, or a little more than one minute. This fact\\nis expressed by saying that the line of the apsides of the earth s\\norbit has a slow motion from west to east. It completes one entire\\nrevolution in its own plane in about 100,000 years (111,149.)\\nThe mean longitude of the perihelion at the commencement of\\nthe present century was 99\u00c2\u00b0 30 5 and of course in the ninth\\ndegree of Cancer, a little past the winter solstice. In the year\\n1248, the perihelion was at the place of this solstice and since the\\nincrease of longitude is 61. 76 a year, hence,\\n61. 76 1 90\u00c2\u00b0 5246=the time occupied in passing from the\\nfirst of Aries to the solstice. Hence, 5246\u00e2\u0080\u00941248=3998, which is\\nthe time before the Christian era, when the perigee was at the\\nfirst of Aries. But this differs only 6 years from the time of the\\ncreation of the world, which is fixed by chronologists at 4004\\nyears A. C. At the period of the creation, therefore, the line of\\nthe apsides of the earth s orbit, coincided with the line of the\\nequinoxes.\\n197. The angular distance of a body from its aphelion is called\\nits Anomaly and the interval between the sun s passing the point\\nof the ecliptic corresponding to the earth s aphelion, and return-\\ning to the same point again, is called the anomalistic year. This\\nperiod must be a little longer than the sidereal year, since, in order\\nto complete the anomalistic revolution, the sun must traverse an\\narc of 11. 66 in addition to 360\u00c2\u00b0.\\nNow 360\u00c2\u00b0 365.256 11. 66 4m. 44s.\\n198. Since the points of the annual orbit, where the sun is at\\nthe greatest and least distances from the earth, change their posi-\\ntion with respect to the solstices, a slow change is occasioned in\\nthe duration of the respective seasons. For, let the perihelion\\ncorrespond to the place of the winter solstice, as was the case in\\nthe year 1248 then as the sun moves more rapidly in that part\\nof his orbit, the winter months will be shorter than the summer.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0136.jp2"}, "137": {"fulltext": "MEAN AND TRUE PLACES OF THE SUN. Ill\\nBut, again, let the perihelion be at the summer solstice, as it will\\nbe in the year 6485* then the sun will move most rapidly\\nthrough the summer months, and the winters will be longer than\\nthe summers. At present the perihelion is so near the winter\\nsolstice, that, the year being divided into summer and winter by\\nthe equinoxes, the six winter months are passed over between seven\\nand eight days sooner than the summer months.\\nMEAN AND TRUE PLACES OF THE SUN.\\n199. The Mean Motion of any body revolving in an orbit, is\\nthat which it would have if, in the same time, it revolved uniformly\\nin a circle.\\nIn surveying an irregular field, it is common first to strike out\\nsome regular figure, as a square or a parallelogram, by running\\nlong lines, and disregarding many small irregularities in the boun-\\ndaries of the field. By this process, we obtain an approximation\\nto the contents of the field, although we have perhaps thrown out\\nseveral small portions which belong to it, and included a number\\nof others which do not belong to it. These being separately esti-\\nmated and added to or substracted from our first computation, we\\nobtain the true area of the field. In a similar manner, we proceed\\nin finding the place of a heavenly body, which moves in an orbit\\nmore or less irregular. Thus we estimate the sun s distance from\\nthe vernal equinox for every day of the year at noon, on the\\nsupposition that he moves uniformly in a circular orbit this is\\nthe sun s mean longitude. We then apply to this result various\\ncorrections for the irregularity of the sun s motions, and thus ob-\\ntain the true longitude.\\n200. The corrections applied to the mean motions of a heav-\\nenly body, in order to obtain its true place, are called Equations.\\nThus the elliptical form of the earth s orbit, the precession of the\\nequinoxes, and the nutation of the earth s axis, severally affect\\nthe place of the sun in his apparent orbit, for which equations are\\napplied. In a collection of Astronomical Tables, a large part of\\nBiot.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0137.jp2"}, "138": {"fulltext": "112 THE SUN.\\nthe whole are devoted to this object. They give us the amount\\nof the corrections to be applied under all the circumstances and\\nconstantly varying relations in which the sun, moon, and earth\\nare situated with respect to each other. The angular distance of\\nthe earth or any planet from its aphelion, on the supposition that\\nit moves uniformly in a circle, is called its Mean Anomaly its\\nactual distance at the same moment in its orbit is called its True\\nAnomaly.*\\nThus in figure 44, let AEB represent the orbit of the earth\\nhaving the sun in one of the foci at S. Upon AB describe the\\ncircle AMB. Let E be the place of the earth in its orbit, and M\\nthe corresponding place in the circle then the angle MCA is the\\nmean, and ESA the true anomaly. The difference between the\\nFig. 44.\\nmean and true anomaly, MCA\u00e2\u0080\u0094 ESA, is called the the Equation oj\\nthe Center, being that correction which depends on the elliptical\\nform of the orbit, or on the distance of the center of attraction\\nfrom the center of the figure, that is, on the eccentricity of the\\norbit. It is much the greatest of all the corrections used in finding\\nthe sun s true longitude, amounting, at its maximum, to nearly two\\ndegrees (1\u00c2\u00b0 55 26. 8.)\\nIn some astronomical treatises, the anomaly is reckoned from the perihelion.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0138.jp2"}, "139": {"fulltext": "CHAPTER V.\\n-PHASES OF THE MOON HER\\nREVOLUTIONS.\\n201. Next to the Sun, the Moon naturally claims our attention.\\nThe Moon is an attendant or satellite to the earth, around which\\nshe revolves at the distance of nearly 240,000 miles. Her mean\\nhorizontal parallax being 57 09 ,f consequently, sin. 57 09\\nsemi-diameter of the earth (3956.2) rad. 238,545. (Art. 87.)\\nThe moon s apparent diameter is 31 7 and her real diameter\\n2160 miles. For,\\nRad. 238,545 sin. 15 33^ 1079.8. moon s semi-diame-\\nter. (See Fig. 26, p. 71.)\\nAnd, since spheres are as the cubes of the diameters, the vol-\\nume of the moon is T V that of the earth. Her density is nearly\\n(.615) the density of the earth, and her mass x.615) is\\nabout aV\\n202. The moon shines by reflected light borrowed from the\\nsun, and when full, exhibits a disk of silvery brightness, diversi-\\nfied by extensive portions partially shaded. By the aid of the\\ntelescope, we see undoubted signs of a varied surface, composed\\nof extensive tracts of level country, and numerous mountains and\\nvalleys.\\n203. The line which separates the enlightened from the dark\\nportions of the moon s disk, is called the Terminator. (See Fig. 2.\\nFrontispiece.) As the terminator traverses the disk from new to\\nfull moon, it appears through the telescope exceedingly broken in\\nSelenography is a word more appropriate to a description of the moon, but is not\\nperhaps sufficiently familiarized by use.\\nt Baily s Astronomical Tables.\\n15", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0139.jp2"}, "140": {"fulltext": "114 THE MOON.\\nsome parts, but smooth in others, indicating that some portions of the\\nlunar surface are uneven while others are level. The broken re-\\ngions appear brighter than the smooth tracts. The latter have\\nbeen taken for seas, but it is supposed with more probability that\\nthey are extensive plains, since they are still too uneven for the\\nperfect level assumed by bodies of water. That there are moun-\\ntains in the moon, is known by several distinct indications. First,\\nwhen the moon is increasing, certain spots are illuminated sooner\\nthan the neighboring places, appearing like bright points beyond\\nthe terminator, within the dark part of the disk. (See Fig. 2.\\nFrontispiece.) Secondly, after the terminator has passed over\\nthem, they project shadows upon the illuminated part of the disk,\\nalways opposite to the sun, corresponding in shape to the form of\\nthe mountain, and undergoing changes in length from night to\\nnight, according as the sun shines upon that part of the moon\\nmore or less obliquely. Many individual mountains rise to a great\\nheight in the midst of plains, and there are several very remarka-\\nble mountainous groups, extending from a common center in long\\nchains.\\n204. That there are also valleys in the moon, is equally evident.\\nThe valleys are known to be truly such, particularly by the man-\\nner in which the light of the sun falls upon them, illuminating the\\npart opposite to the sun while the part adjacent is dark, as is the\\ncase when the light of a lamp shines obliquely into a china cup.\\nThese valleys are often remarkably regular, and some of them\\nalmost perfect circles. In several instances, a circular chain of\\nmountains surrounds an extensive valley, which appears nearly\\nlevel, except that a sharp mountain sometimes rises from the cen-\\nter. The best time for observing these appearances is near the\\nfirst quarter of the moon, when half the disk is enlightened\\nbut in studying the lunar geography, it is expedient to observe the\\nmoon every evening from new to full, or rather through her en-\\ntire series of changes.\\nIt is earnestly recommended to the student of astronomy, to examine the moon re-\\npeatedly with the best telescope he can command, using low powers at first, for the\\nsake of a better light.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0140.jp2"}, "141": {"fulltext": "LUNAR GEOGRAPHY. 115\\n205. The various places on the moon s disk have received ap-\\npropriate names. The dusky regions, being formerly supposed to\\nbe seas, were named accordingly and other remarkable places\\nhave each two names, one derived from some well known spot on\\nthe earth, and the other from some distinguished personage. Thus\\nthe same bright spGt on the surface of the moon is called Mount\\nSinai or Tucho, and another Mount Etna or Copernicus. The\\nnames of individuals, however, are more used than the others.\\nThe frontispiece exhibits the telescopic appearance of the full\\nmoon. A few of the most remarkable points have the following\\nnames, corresponding to the numbers and letters on the map. (See\\nFrontispiece.)\\n1. Tycho, A. Mare Humorum,\\n2. Kepler, B. Mare Nubium,\\n3. Copernicus, C. Mare Imbrium,\\n4. Aristarchus, D. Mare Nectaris,\\n5. Helicon, E. Mare Tranquilitatis,\\n6. Eratosthenes, F. Mare Serenitatis,\\n7. Plato, G. Mare Fecunditatis,\\n8. Archimedes, H. Mare Crisium.\\n9. Eudoxus,\\n10, Aristotle,\\n206. The method of estimating the height of lunar mountains is\\nas follows.\\nLet ABO (Fig. 45,) be the illuminated hemisphere of the moon,\\nSO a solar ray touching the moon in O, a point in the circle which\\nseparates the enlightened from the dark part of the moon. All the\\npart ODA will be in darkness but if this part contains a moun-\\ntain MF, so elevated that its summit M reaches to the solar ray\\nSOM, the point M will be enlightened. Let E be the place of the\\nobserver on the earth, the moon being at any elongation from the\\nsun, as measured by the angle EOS. Draw the lines EM, EO,\\nand CM, C being the center of the moon and let FM be the\\nheight of the mountain. Draw ON perpendicular to EM. The\\nline EO being known, and the angle OEM being measured with a\\nmicrometer, the value of ON, the projection of the lime OM, be-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0141.jp2"}, "142": {"fulltext": "116\\nTHE MOON.\\nFig. 45.\\ncomes known. Now OM\u00e2\u0080\u0094\\nON\\nkT and since OEN is a very\\ncos. MON J\\nsmall angle, EON may be considered as a right angle conse-\\nON\\nquenlly, MON=MOE-90. Therefore OM\\nON\\nON\\ncos. (MOE-90)\\nThat is, the distance between the summit\\nsin. MOE sin. EOS\\nof the mountain and the illuminated part of the moon s disk, is\\nequal to the projected distance as measured by the micrometer,\\ndivided by the sine of the moon s elongation from the sun.\\nSuppose the distance OM=?zCO, where n represents the frac\\ntion the part OM is of CO as determined by observation. Then,\\nCM 2 =C0 2 +OM 2 =C0 2 +n 2 C0 2 =C0 2 (l+n 2 CM=CO (l+n*)i\\n/.CM\\nCO or FM=CO (71+w 2 -l) =lLCO, neglecting the\\nhigher powers of n, which would be of too little value to be worth\\ntaking into the account. The value of n has been found in one\\ncase equal to T V, which gives the height of the mountain equal to\\njj 7 the semi-diameter of the moon, that is, 3} miles.\\nWhen the moon is exactly at quadrature, then EOM becomes a\\nright angle, and the value of OM is obtained directly from actual\\nmeasurement and having CO and OM, we easily obtain CM and\\nof course FM.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0142.jp2"}, "143": {"fulltext": "LUNAR GEOGRAPHY. 117\\n207. Schroeter, a German astronomer, estimated the heights of\\nthe lunar mountains by observations on their shadows. He made\\nthem in some cases as high as o} T of the semi-diameter of the\\nmoon, that is, about 5 miles. The same astronomer also estimates\\nthe depths of some of the lunar valleys at more than four miles.\\nHence it is inferred that the moon s surface is more broken and\\nirregular than that of the earth, its mountains being higher and its\\nvalleys deeper in proportion to the size of the moon than those of\\nthe earth.\\n208. Dr. Herschel is supposed also to have obtained decisive\\nevidence of the existence of volcanoes in the moon, not only\\nfrom the light afforded by their fires, but also from the formation\\nof new mountains by the accumulation of matter where fires had\\nbeen seen to exist, and which remained after the fires were extinct.\\n209. Some indications of an atmosphere about the moon have\\nbeen obtained, the most decisive of which are derived from ap-\\npearances of twilight, a phenomenon that implies the presence\\nof an atmosphere. Similar indications have been detected, it is\\nsupposed, in eclipses of the sun, denoting a transparent refracting\\nmedium encompassing the moon. The lunar atmosphere, how-\\never, if any exists, is very inconsiderable in extent and density\\ncompared with that of the earth.*\\n210. The improbability of our ever identifying artificial struc-\\ntures in the moon may be inferred from the fact that a line one\\nmile in length in the moon subtends an angle at the eye of only\\nabout one second. If, therefore, works of art were to have a suf-\\nficient horizontal extent to become visible, they can hardly be sup-\\nposed to attain the necessary elevation, when we reflect that the\\nheight of the great pyramid of Egypt is less than the sixth part of\\na mile.\\n\u00e2\u0099\u00a6See Ed. Encyc. II. 598.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0143.jp2"}, "144": {"fulltext": "118 THE MOON.\\nPHASES OF THE MOON.\\n211. The changes of the moon, commonly called her Phases,\\narise from different portions of her illuminated side being turned\\ntowards the earth at different times. When the moon is first\\nseen after the setting sun, her form is that of a bright crescent,\\non the side of the disk next to the sun, while the other portions\\nof the disk shine with a feeble light, reflected to the moon from\\nthe earth. Every night we observe the moon to be further and\\nfurther eastward of the sun, and at the same time the crescent\\nenlarges, until, when the moon has reached an elongation from\\nthe sun of 00\u00c2\u00b0, half her visible disk is enlightened, and she is\\nsaid to be in her first quarter. The terminator, or line which\\nseparates the illuminated from the dark part of the moon, is con-\\nvex towards the sun from the new moon to the first quarter, and\\nthe moon is said to be horned. The extremities of the crescent\\nare called cusps. At the first quarter, the terminator becomes a\\nstraight line, coinciding with a diameter of the disk but after\\npassing this point, the terminator becomes concave towards the\\nsun, bounding that side of the moon by an elliptical curve, when\\nthe moon is said to be gibbous. When the moon arrives at the\\ndistance of 180\u00c2\u00b0 from the sun, the entire circle is illuminated,\\nand the moon is full. She is then in opposition to the sun, rising\\nabout the time the sun sets. For a week after the full, the moon\\nappears gibbous again, until, having arrived within 90\u00c2\u00b0 of the sun,\\nshe resumes the same form as at the first quarter, being then at\\nher third quarter. From this time until new moon, she exhibits\\nagain the form of a crescent before the rising sun, until approach-\\ning her conjunction with the sun, her narrow thread of light is lost\\nin the solar blaze and finally, at the moment of passing the sun,\\nthe dark side is wholly turned towards us and for some time we\\nlose sight of the moon.\\nThe two points in the orbit corresponding to new and full moon\\nrespectively, are called by the common name of syzygies those\\nwhich are 90\u00c2\u00b0 from the sun are called quadratures; and the\\npoints half way between the syzygies and quadratures are called\\noctants. The circle which divides the enlightened from the unen-\\nlightened hemisphere of the moon, is called the circle of illumina", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0144.jp2"}, "145": {"fulltext": "PHASES.\\n119\\ntion that which divides the hemisphere that is turned towards\\nus from the hemisphere that is turned from us, is called the circle\\nof the disk.\\n212. As the moon is an opake body of a spherical figure, and\\nborrows her light from the sun, it is obvious that that half only\\nwhich is towards the sun can be illuminated. More or less of\\nthis side is turned towards the earth, according as the moon is at\\na greater or less elongation from the sun. The reason of the dif-\\nferent phases will be best understood from a diagram. Therefore\\nlet T (Fig. 46,) represent the earth, and S the sun. Let A, B, C,\\nc., be successive positions of the moon. At A the entire dark\\nEiV. 46.\\nside of the moon being turned towards the earth, the disk would\\nbe wholly invisible. At B, the circle of the disk cuts off a small\\npart of the enlightened hemisphere, which appears in the heavens\\nat b, under the form of a crescent. At C, the first quarter, the\\ncircle of the disk cuts off half the enlightened hemisphere, and the\\nmoon appears dichotomized at c. In like manner it will be seen\\nthat the appearances presented at D, E, F, c, must be those\\nrepresented at d, e,f\\nREVOLUTIONS OF THE MOON.\\n213. The moon revolves around the earth from west to east,\\nmaking the entire circuit of the heavens in about 21\\\\ days.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0145.jp2"}, "146": {"fulltext": "120 THE MOON.\\nThe precise law of the moon s motions in her revolution around\\nthe earth, is ascertained, as in the case of the sun, (Art. 155,) by\\ndaily observations on her meridian altitude and right ascension.\\nThence are deduced by calculation her latitude and longitude,\\nfrom which we find, that the moon describes on the celestial\\nsphere a great circle of which the earth is the center.\\nThe period of the moon s revolution from any point in the\\nheavens round to the same point again, is called a month. A\\nsidereal month is the time of the moon s passing from any star,\\nuntil it returns to the same star again. A synodical month* is\\nthe time from one conjunction or new moon to another. The\\nsynodical month is about 29\u00c2\u00a3 days, or more exactly, 29d. 12h.\\n44m. 2 S .8=29.53 days. The sidereal month is about two days\\nshorter, being 27d. 7h. 43m. 1 l s .5=27.32 days. As the sun and\\nmoon are both revolving in the same direction, and the sun is\\nmoving nearly a degree a day, during the 27 days of the moon s\\nrevolution, the sun must have moved 27\u00c2\u00b0. Now since the moon\\npasses over 360\u00c2\u00b0 in 27.32 days, her daily motion must be 13\u00c2\u00b0 17\\nIt must therefore evidently take about two days for the moon to\\novertake the sun. The difference between these two periods\\nmay, however, be determined with great exactness. The mid-\\ndle of an eclipse of the sun marks the exact moment of conjunc-\\ntion or new moon; and by dividing the interval between any\\ntwo solar eclipses by the number of revolutions of the moon, or\\nlunations, we obtain the precise period of the synodical month.\\nSuppose, for example, two eclipses occur at an interval of 1,000\\nlunations then the whole number of days and parts of a day\\nihat compose the interval divided by 1,000 will give the exact\\ntime of one lunation.f The time of the synodical month being\\nascertained, the exact period of the sidereal month may be derived\\nfrom it. For the arc which the moon describes in order to come\\ninto conjunction with the sun, exceeds 360\u00c2\u00b0 by the space which\\nrov and 0605, implying that the two bodies come together.\\nt It might at first view seem necessary to know the period of one lunation before\\nwe could know the number of lunations in any given interval. This period is known\\nvery nearly from the interval between one new moon and another", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0146.jp2"}, "147": {"fulltext": "REVOLUTIONS 121\\nthe sun has passed over since the preceding conjunction, that is,\\nin 29.53 days. Therefore,\\n365.24 3G0\u00c2\u00b0 29.53 29\u00c2\u00b0.l=arc which the moon must de-\\nscribe more than 360\u00c2\u00b0 in order to overtake the sun. Hence,\\n13\u00c2\u00b0 17 ld.::29\u00c2\u00b0.l 2.21d.=difference between the sidereal\\nand synodical months; and 29.53\u00e2\u0080\u0094 2.21=27.32, the time of the\\nsidereal revolution.\\n214. The moon s orbit is inclined to the ecliptic in an angle of\\nabout 5\u00c2\u00b0 (5\u00c2\u00b0 8 48 It crosses the ecliptic in two opposite points\\ncalled her nodes. The amount of inclination is ascertained by\\nobservations on the moons latitude when at a maximum, that\\nbeing of course the greatest distance from the ecliptic, and there-\\nfore equal to the inclination of the two circles.\\n215. The moon, at the same age, crosses the meridian at differ-\\nent altitudes at different seasons of the year. The full moon, for\\nexample, will appear much further in the south when on the meri-\\ndian at one period of the year than at another. This is owing, to\\nthe fact that the moon s path is differently situated with respect to\\nthe horizon, at a given time of night at different seasons o\u00c2\u00a3 the\\nyear. By taking the ecliptic on an artificial globe to represent\\nthe moon s path, (which is always near it, Art. 214,) and recollect-\\ning that the new moon is seen in the same part of the heavens\\nwith the sun, and the full moon in the opposite part of the heavens\\nfrom the sun, we shall readily see that in the winter the new\\nmoons must run low because the sun does, and for a similar rea-\\nson the full moons must run high. It is equally apparent that, in\\nsummer, when the sun runs high, the new moons must cross the\\nmeridian at a high, and the full moons at a low altitude. This\\narrangement gives us a great advantage in respect to the amount\\nof light received from the moon since the full moon is longest\\nabove the horizon during the long nights of winter, when her pre-\\nsence is most needed. This circumstance is especially favorable to\\nthe inhabitants of the polar regions, the moon, when full, travers-\\ning that part of her orbit which lies north of the equator, and of\\ncourse above the horizon of the north pole, and traversing the por-\\ntion that lies south of the equator, and below the polar horizon,\\n16", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0147.jp2"}, "148": {"fulltext": "122 THE MOON,\\nwhen new. During the polar winter, therefore, the moon, from\\nthe first to the last quarter, is commonly above the horizon, wnile\\nthe sun is absent whereas, during summer, while the sun is pre-\\nsent, the moon is above the horizon while describing her first and\\nlast quadrants.\\n216. About the time of the autumnal equinox, the moon when\\nnear the full, rises about sunset for a number of nights in succes-\\nsion and as this is, in England, the period of harvest, the phe-\\nnomenon is called the Harvest Moon, To understand the reason\\nof this, since the moon is never far from the ecliptic, we will\\nsuppose her progress to be in the ecliptic. If the moon moved\\nin the equator, then, since this great circle is at right angles to\\nthe axis of the earth, all parts of it, as the earth revolves, cut the\\nhorizon at the same constant angle. But the moon s orbit, or\\nthe ecliptic, which is here taken to represent it, being oblique\\nto the equator, cuts the horizon at different angles in different\\nparts, as will easily be seen b)^ reference to an artificial globe.\\nWhen the first of Aries, or vernal equinox, is in the eastern hori-\\nzon, it will be seen that the ecliptic, (and consequently the moon s\\norbit,) makes its least angle with the horizon. Now at the au-\\ntumnal equinox, the sun being in Libra, the moon at the full is in\\nAries, and rises when the sun sets. On the following evening,\\nalthough she has advanced in her orbit about 13\u00c2\u00b0, (Art. 213,) yet\\nher progress being oblique to the horizon, and at a small angle\\nwith it, she will be found at this time but a little way below the\\nhorizon, compared with the point where she was at sunset the\\npreceding evening. She therefore rises but little later, and so\\nfor a week only a little later each evening than she did the pre-\\nceding night.\\n217. The moon is about nearer to us when near the zenith\\nthan when in the horizon.\\nThe horizontal distance CD (Fig. 47,) is nearly equal to AD=\\nAD which is greater than CD by AC, the semi-diameter of the\\nearth =gV the distance of the moon. Accordingly, the apparent\\ndiameter of the moon, when actually measured, is about 30\\n(which equals about \u00c2\u00b0f the whole) greater when in the zenith", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0148.jp2"}, "149": {"fulltext": "REVOLUTIONS.\\n123\\nthan in the horizon. The apparent enlargement of the full moon\\n-when rising, is owing to the same causes as that of the sun, as ex-\\nplained in article 96.\\nFig. 47.\\n218. The moon turns on its axis in the same time in which it\\nrevolves around the earth.\\nThis is known by the* moon s always keeping nearly the same\\nface towards us, as is indicated by the telescope, w r hich could not\\nhappen unless her revolution on her axis kept pace w T ith her mo-\\ntion in her orbit. Thus, it will be seen by inspecting figure 31,\\nthat the earth turns different faces towards the sun at different\\ntimes and if a ball having one hemisphere white and the other\\nblack be carried around a lamp, it will easily be seen that it can-\\nnot present the same face constantly towards the lamp unless it\\nturns once on its axis while performing its revolution. The same\\nthing will be observed when a man walks aiound a tree, keeping\\nhis face constantly towards it. Since however the motion of the\\nmoon on its axis is uniform, while the motion in its orbit is une-\\nqual, the moon does in fact reveal to us a little sometimes of one\\nside and sometimes of the other. Thus when the ball above\\nmentioned is placed before the eye with its light side towards us,\\nor carrying it round, if it is moved faster than it is turned on its\\naxis, a portion of the dark hemisphere is brought into view on\\none side or if it is moved forward slower than it is turned on\\nits axis, a portion of the dark hemisphere comes into view on the\\nother side.\\n219. These appearances are called the moon s librations in lon-\\ngitude. The moon has also a libration in latitude, so called, be-\\ncause in one part of her revolution, more of the region around one", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0149.jp2"}, "150": {"fulltext": "124 THE MOON.\\nof the poles comes into view, and in another part of the revolu-\\ntion, more of the region around the other pole which gives the ap-\\npearance of a tilting motion to the moon s axis. This has nearly the\\nsame cause with that which occasions our change of seasons. The\\nmoon s axis being inclined to that of the ecliptic, about degrees,\\n(1\u00c2\u00b0 30 10 .8,) and always remaining parallel to itself, the circle\\nwhich divides the visible from the invisible part of the moon, will\\npass in such a way as to throw sometimes more of one pole into\\nview and sometimes more of the other, as would be the case with\\nthe earth if seen from the sun. (See Fig. 31.)\\nThe moon exhibits another phenomenon of this kind called\\nher diurnal libration, depending on the daily rotation of the\\nspectator. She turns the same face towards the center of the\\nearth only, whereas we view her from the surface. When she is\\non the meridian, we see her disk nearly as though we viewed it\\nfrom the center of the earth, and hence in this situation it is sub-\\nject to little change but when near the horizon, our circle of\\nvision takes in more of the upper limb than would be presented\\nto a spectator at the center of the earth. Hence, from this cause,\\nwe see a portion of one limb while the moon is rising, which is\\ngradually lost sight of, and we see a portion of the opposite limb\\nas the moon declines towards the west. It will be remarked that\\nneither of the foregoing changes implies any actual motion in the\\nmoon, but that each arises from a change of position in the spec-\\ntator relative to the moon.\\n220. An inhabitant of the moon would have but one day and\\none night during the whole lunar month of 29^ days. One of\\nits days, therefore, is equal to nearly 15 of ours. So protracted\\nan exposure to the sun s rays, especially in the equatorial regions\\nof the moon, must occasion an excessive accumulation of heat\\nand so long an absence of the sun must occasion a corresponding\\ndegree of cold. Each day would be a wearisome summer each\\nnight a severe winter.* A spectator on the side of the moon\\nwhich is opposite to us would never see the earth but one on the\\nside next to us would see the earth presenting a gradual succession\\nFrancoeur, Uranog. p. 91.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0150.jp2"}, "151": {"fulltext": "REVOLUTIONS. 125\\nof changes during his long night of 300 hours. Soon after the\\nearth s conjunction with the sun, he would have the light of the\\nearth reflected to him, presenting at first a crescent, but enlarging,\\nas the earth approaches its opposition, to a great orb, 13 times as\\nlarge as the full moon appears to us, and affording nearly 13 times\\nas much light. Our seas, our plains, our mountains, our volcanoes,\\nand our clouds, would produce very diversified appearances, as\\nwould the various parts of the earth brought successively into\\nview by its diurnal rotation. The earth while in view to an in-\\nhabitant of the moon, would remain immovably fixed in the same\\npart of the heavens. For being unconscious of his own motior\\naround the earth, as we are of our motion around the s.un^he\\nearth would seem to revolve around his own planet from west to\\neast; but, meanwhile, his rotation along with the moon on her\\naxis, would cause the earth to have an apparent motion westward\\nat the same rate. The two motions, therefore, would exactly\\nbalance each other, and the earth would appear all the while at\\nrest. The earth is full to the moon when the latter is new to us\\nand universally the two phases are complementary to each other.*\\n221. It has been observed already, (Art. 214,) that the moon s\\norbit crosses the ecliptic in two opposite points called the nodes.\\nThat which the moon crosses from south to north, is called the\\nascending node that which the moon crosses from north to south,\\nthe descending node.\\nFrom the manner in, which the figure representing the earth s\\norbit and that of the moon, is commonly drawn, the learner is\\nsometimes puzzled to see how the orbit of the moon can cut the\\necliptic in two points directly opposite to each other. But he must\\nreflect that the lunar orbit cuts the plane of the ecliptic and not\\nthe earth s path in that plane, although these respective points are\\nprojected upon that path in the heavens.\\n222. We have thus far contemplated the revolution of the moon\\naround the earth as though the earth were at rest. But, in order\\nto have just ideas respecting the moon s motions, we must recol-\\nlect that the moon likewise revolves along with the earth around\\nFrancceur, p. 92.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0151.jp2"}, "152": {"fulltext": "126 THE MOON.\\nthe sun. It is sometimes said that the earth carries the moon\\nalong with her in her annual revolution. This language may\\nconvey an erroneous idea for the moon, as well as the earth,\\nrevolves around the sun under the influence of two forces, and\\nwould continue her motion around the sun, were the earth re-\\nmoved out of the way. Indeed, the moon is attracted towards\\nthe sun 2} times more than towards the earth,* and would aban-\\ndon the earth were not the latter also carried along with her by\\nthe same forces. So far as the sun acts equally on both bodies,\\ntheir motion with respect to each other would not be disturbed.\\nBecause the gravity of the moon towards the sun is found to be\\ngreater, at the conjunction, than her gravity towards the earth,\\nsome have apprehended that, if the doctrine of universal gravi-\\ntation is true, the moon ought necessarily to abandon the earth.\\nIn order to understand the reason why it does not do thus we\\nmust reflect, that when a body is revolving in its orbit tinder the\\naction of the projectile force and gravity, whatever diminishes\\nthe force of gravity while that of projection remains the same,\\ncauses the body to recede from the center; and whatever in-\\ncreases the amount of gravity carries the body towards the center\\nNow, when the moon is in conjunction, her gravity towards the\\nearth acts in opposition to that towards the sun, while her velocity\\nremains too great to carry her, with what force remains, in a\\ncircle about the sun, and she therefore recedes from the sun, and\\ncommences her revolution around the earth. On arriving at the\\nopposition, the gravity of the earth conspires with that of the sun,\\nand the moon s projectile force being less than that required to\\nmake her revolve in a circular orbit, when attracted towards the\\nsun by the sum of these forces, she accordingly begins to approach\\nthe sun and descends again to the conjunction.!\\nIt is shown by writers on Mechanics, that the forces with which bodies revolving\\nin circular orbits tend towards their centers, are as the radii of their orbits divided\\nby the squares of their periodical times. Hence, supposing the orbits of the earth and\\nihe moon to be circular, (and their slight eccentricity will not much affect the re-\\nsult,) we have\\n400 1\\nG G (365.25)a (27.32) a: 2 2 lm\\nt M Laurin s Discoveries of Newton, B. W, ch. 5.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0152.jp2"}, "153": {"fulltext": "LUNAR IRREGULARITIES. 127\\n223. The attraction of the sun, however, being every where\\ngreater than that of the earth, the actual path of the moon around\\nthe sun is every where concave towards the latter. Still the el-\\nliptical path of the moon around the earth, is to be conceived of\\nin the same way as though both bodies were at rest with respect\\nto the sun. Thus, while a steamboat is passing swiftly around an\\nisland, and a man is walking slowly around a post in the cabin,\\nthe line which he describes in space between the forward motion\\nof the boat and his circular motion around the post, may be every\\nwhere concave towards the island, while his path around the post\\nwill stilt be the same as though both were at rest. A nail in the\\nrim of a coach wheel, will turn around the axis of the wheel, when\\nthe coach has a forward motion in the same manner as when the\\ncoach is at rest, although the line actually described by the nail\\nwill be the resultant of both motions, and very different from\\neither.\\nCHAPTER VI.\\nLUNAR IRREGULARITIES.\\n224. We have hitherto regarded the moon as describing a great\\ncircle on the face of the sky, such being the visible orbit as seen\\nby projection. But, on more exact investigation, it is found that\\nher orbit is not a circle, and that her motions are subject to very\\nnumerous irregularities. These will be best understood in con-\\nnection with the causes on which they depend. The law of uni-\\nversal gravitation has been applied with wonderful success to their\\ninvestigation, and its results have conspired with those of long\\ncontinued observation, to furnish the means of ascertaining with\\ngreat exactness the place of the moon in the heavens at any given\\ninstant of time, past or future, and thus to enable astronomers to\\ndetermine longitudes, to calculate eclipses, and to solve various\\nother problems of the highest interest. A complete understand-\\ning of all the irregularities of the moon s motions, must be sought", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0153.jp2"}, "154": {"fulltext": "128 THE MOON.\\nfor in more extensive treatises of astronomy than the present but\\nsome general acquaintance with the subject, clear and intelligible\\nas far as it goes, may be acquired by first gaining a distinct idea\\nof the mutual actions of the sun, the moon, and the earth.\\n225. The irregularities of the moon s motions, are due chiefly to\\nthe disturbing influence of the sun, which operates in two ways first,\\nby acting unequally on the earth and moon, and, secondly, by acting\\nobliquely on the moon, on account of the inclination of her orbit to\\nthe ecliptic*\\nIf the sun acted equally on the earth and moon, and always in\\nparallel lines, this action would serve only to restrain them in their\\nannual motions round the sun, and would not affect their actions\\non each other, or their motions about their common center of\\ngravity. In that case, if they were allowed to fall directly to-\\nwards the sun, they would fall equally, and their respective situa-\\ntions would not be affected by their descending equally towards\\nit. We might then conceive them as in a plane, every part of\\nwhich being equally acted on by the sun, the whole plane would\\ndescend towards the sun, but the respective motions of the earth\\nand the moon in this plane, would be the same as if it were qui-\\nescent. Supposing then this plane and all in it, to have an annual\\nmotion imprinted on it, it would move regularly round the sun.\\nwhile the earth and moon would move in it with respect to each\\nother, as if the plane were at rest, without any irregularities.\\nBut because the moon is nearer the sun in one half of her orbit\\nthan the earth is, and in the other half of her orbit is at. a greater\\ndistance than the earth from the sun, while the power of gravity\\nis always greater at a less distance it follows, that in one half of\\nher orbit the moon is more attracted than the earth towards the\\nsun, and in the other half less attracted than the earth. Thet ex-\\ncess of the attraction, in the first case, and the defect in the second,\\nconstitutes a disturbing force, to which we may add another,\\nnamely, that arising from the oblique action of the solar force,\\nsince this action is not directed in parallel lines, but in lines thai\\nmeet in the center of the sun.\\nM Laurin s Discoveries of Newton, B. iv, ch. 4. La Place s Syst. du Monde,\\nB. iv, ch. 5.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0154.jp2"}, "155": {"fulltext": "LUNAR IRREGULARITIES. 129\\n226. To see the effects of this process, let us suppose that the\\nprojectile motions of the earth and moon were destroyed, and\\nthat they were allowed to fall freely towards the sun. If the\\nmoon was in conjunction with the sun, or in that part of her orbit\\nwhich is nearest to him, the moon would be more attracted than\\nthe earth, and fall with greater velocity towards the sun so that\\nthe distance of the moon from the earth would be increased in the\\nfall. If the moon was in opposition, or in the part of her orbit\\nwhich is furthest from the sun, she would be less attracted than\\nthe earth by the sun, and would fall with a less velocity towards\\nthe sun, and would be left behind so that the distance of the\\nmoon from the earth would be increased in this case also. If the\\nmoon was in one of the quarters, then the earth and moon being\\nboth attracted towards the center of the sun, they would both de-\\nscend directly towards that center, and by approaching it, they\\nwould necessarily at the same time approach each other, and in\\nthis case their distance from each other would be diminished.\\nNow whenever the action of the sun would increase their distance,\\nif they were allowed to fall towards the sun, then the sun s action,\\nby endeavoring to separate them, diminishes their gravity to each\\nother whenever the sun s action would diminish the distance, then\\nit increases their mutual gravitation. Hence, in the conjunction\\nand opposition, that is, in the syzy ies, their gravity towards each\\nother is diminished by the action of the sun, while in the quadra-\\ntures it is increased. But it must be remembered that it is not\\nthe total action of the sun on them that disturbs their motions,\\nbut only that part of it which tends at one time to separate them,\\nand at another time to bring them nearer together. The other\\nand far greater part, has no other effect than to retain them in\\ntheir annual course around the sun.\\n227. Suppose the moon setting out from the quarter that pre-\\ncedes the conjunction with a velocity that would make her de-\\nscribe an exact circle round the earth, if the sun s action had no\\neffect on her since her gravity is increased by that action, she must\\ndescend towards the earth and move within that circle. Her or-\\nbit then would be more curved than it otherwise would have been;\\nbecause the addition to her gravity will make her fall further at\\n17", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0155.jp2"}, "156": {"fulltext": "130\\nTHE MOON.\\nthe end of an arc below the tangent drawn at the other end of it\\nHer motion will be thus accelerated, and it will continue to be\\naccelerated until she arrives at the ensuing conjunction, because\\nthe direction of the sun s action upon her, during that time, makes\\nan acute angle with the direction of her motion. (See Fig. 41.)\\nAt the conjunction, her gravity towards the earth being diminished\\nby the action of the sun, her orbit will then be less curved, and\\nshe will be carried further from the earth as she moves to the next\\nquarter and because the action of the sun makes there an obtuse\\nangle with the direction of her motion, she will be retarded in the\\nsame degree as she was accelerated before.\\n228. After this general explanation of the mode in which the\\nsun acts as a disturbing force on the motions of the moon, the\\nlearner will be prepared to understand the mathematical develop-\\nment of the same doctrine.\\nTherefore, let ADBC (Fig. 48,) be the orbit, nearly circular, in\\nwhich the moon M revolves in the direction CADB, round the\\nearth E. Let S be the sun, and let\\nSE the radius of the earth s orbit,\\nbe taken to represent the force with\\nwhich the earth gravitates to the sun.\\n1 1\\nFig. 48.\\nThen (Art. 180,) ^:^::SE:\\nSE 3\\n^-r-rjr the force by which the sun\\nSM 2 J\\ndraws the moon in the direction\\nSE 3\\nMS. Take MG=\\nSM 2\\nand let the\\nparallelogram KF be described,\\nhaving MG for its diagonal, and\\nhaving its sides parallel to EM and\\nES. The force MG may be re-\\nsolved into two, MF and MK, of\\nwhich MF, directed towards E, the\\ncenter of the earth, increases the\\ngravity of the moon to the earth, and does not hinder the areas\\ndescribed by the radius vector from being proportional to the\\nC\\n1\\nE\\n3\\nF\\nm\\\\/\\nL.\\n3\\nn\\nA\\nGf", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0156.jp2"}, "157": {"fulltext": "LUNAR IRREGULARITIES. 131\\ntimes. The other force MK draws the moon in the direction of\\nthe line joining the centers of the sun and earth. It is, however,\\nonly the excess of this force, above the force represented by SE,\\nor that which draws the earth to the sun, which disturbs the rela-\\ntive position of the moon and earth. This is evident, for if KM\\nwere just equal to ES, no disturbance of the moon relative to the\\nearth could arise from it. If then ES be taken from ME, the dif-\\nference IIK is the whole force in the direction parallel to SE, by\\nwhich the sun disturbs the relative position of the moon and earth.\\nNow, if in MK, MN be taken equal to HK, and if NO be drawn\\nperpendicular to the radius vector EM produced, the force MN\\nmay be resolved into two, MO and ON, the first lessening the\\ngravity of the moon to the earth and* the second, being parallel\\nto the tangent of the moon s orbit in M, accelerates the moon s\\nmotion from C to A, and retards it from A to D, and so alternately\\nin the other two quadrants. Thus the whole solar force directed\\nto the center of the earth, is composed of the two parts MF and\\nMO, which are sometimes opposed to one another, but which\\nnever affect the uniform description of the areas about E. Near\\nthe quadratures the force MO vanishes, and the force MF, which\\nincreases the gravity of the moon to the earth, coincides with CE\\nor DE. As the moon approaches the conjunction at A, the force\\nMO prevails over MF, and lessens the gravity of the moon to the\\nearth. In the opposite point of the orbit, when the moon is m op-\\nposition at B, the force with which the sun draws the moon is less\\nthan that with which the sun draws the earth, so that the effect of\\nthe solar force is to separate the moon and earth, or to increase\\ntheir distance that is, it is the same as if, conceiving the earth\\nnot to be acted on, the sun s force drew the moon in the direction\\nfrom E to B. This force is negative, therefore, in respect to the\\nforce at A, and the effect in both cases is to draw the moon from\\nthe earth in a direction perpendicular to the line of the quadra-\\ntures. Hence, the general result is, that by the disturbing force\\nof the sun, the gravity to the earth is increased at the quadratures,\\nand diminished at the syzygies. It is found by calculation that the\\naverage amount of this disturbing force is jf 3 of the moon s\\ngravity to the earth.*\\nPlayfair.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0157.jp2"}, "158": {"fulltext": "132 THE MOON.\\n229. With these general principles in view, we may now pro-\\nceed to investigate the figure of the moon s orbit, and the irregu-\\nlarities to which the motions of this body are subject.\\n230. The figure of the mooris orbit is an ellipse, having the earth\\nin one of the foci.\\nThe elliptical figure of the moon s orbit, is revealed to us by ob-\\nservations on her changes in apparent diameter, and in her hori-\\nzontal parallax. First, we may measure from day to day the ap-\\nparent diameter of the moon. Its variations being inversely as\\nthe distances, (Art. 163,) they give us at once the relative distance\\nof each point of observation from the focus. Secondly, the va-\\nriations on the moon s horizontal parallax, which also are inversely\\nas the distances, (Art. 82,) lead to the same results. Observations\\non the angular velocities, combined with the changes in the lengths\\nof the radius vector, afford the means of laying down a plot of the\\nlunar orbit, as in the case of the sun, represented in figure 32.\\nThe orbit is shown to be nearly an ellipse, because it is found to\\nhave the properties of an ellipse.\\nThe moon s greatest and least apparent diameters are respectively\\n33 .518 and 29 .365, while her corresponding changes of parallax\\nare 6T.4 and 53 .8. The two ratios ought to be equal, and we\\nshall find such to be the fact very nearly, as expressed by the fore-\\ngoing numbers for,\\n61.4 53.8 33.518 29.369.\\nThe greatest and least distances of the moon from the earth,\\nderived from the parallaxes, are 63.8419 and 55.9164, or nearly\\n64 and 56. the radius of the earth being taken for unity. Hence,\\ntaking the arithmetical mean, which is 59.879, we find that the\\nmean distance of the moon from the earth is very nearly 60 times\\nthe radius of the earth. The point in the moon s orbit nearest\\nthe earth, is called her perigee the point furthest from the earth,\\nher apogee.\\nThe greatest and least apparent diameters of the sun are re-\\nspectively 32.583, and 31.517, which numbers express also the ratio\\nof the greatest and least distances of the earth from the sun. By\\ncomparing this ratio with that of the distances of the moon, it will\\nbe seen that the latter vary much more than the former, and con-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0158.jp2"}, "159": {"fulltext": "LUNAR IRREGULARITIES. 133\\nsequently that the lunar orbit is much more eccentric than the so-\\nlar. The eccentricity of the moon s orbit is in fact 0.0548, (the\\nsemi-major axis being as usual taken for unity) T of its mean\\ndistance from the earth, while that of the earth is only .01685=jV\\nof its mean distance from the sun.\\n231. The moon s nodes constantly shift their positions in the eclip-\\ntic from east to west, at the rate of 19\u00c2\u00b0 35 per annum, returning to\\nthe same points in 18.6 years.\\nSuppose the great circle of the ecliptic marked out on the face\\nof the sky in a distinct line, and let us observe, at any given time,\\nthe exact point where the moon crosses this line, which we will\\nsuppose to be close to a certain star then, on its next return to\\nthat part of the heavens, we shall find that it crosses the ecliptic\\nsensibly to the westward of that star, and so on, further and fur-\\nther to the westward every time it crosses the ecliptic at eithei\\nnode. This fact is expressed by saying that the nodes retrograde\\non the ecliptic, and that the line which joins them, or the line of\\nthe nodes, revolves from east to west.\\n232. This shifting of the moon s nodes implies that the lunar\\norbit is not a curve returning into itself, but that it more resem-\\nbles a spiral like the curve represented in figure 49, where abc\\nrepresents the ecliptic, and ABC the\\nlunar orbit, having its nodes at C and\\nE, instead of A and a consequently,\\nthe nodes shift backwards through\\nthe arcs \u00c2\u00abC and AE. The manner\\nin which this effect is produced may\\nbe thus explained. That part of the\\nsolar force which is parallel to the line joining the centers of the\\nsun and earth, (See Fig. 48,) is not in the plane of the moon s\\norbit, (since this is inclined to the ecliptic about 5\u00c2\u00b0,) except when\\nthe sun itself is in that plane, or when the line of the nodes being\\nproduced, passes through the sun. In all other cases it is oblique\\nto the plane of the orbit, and may be resolved into two forces,\\none of which is at right angles to that plane, and is directed to-\\nwards the ecliptic. This force of course draws the moon continue", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0159.jp2"}, "160": {"fulltext": "134\\nTHE MOON.\\nally towards the ecliptic, or produces a continual deflection of the\\nmoon from the plane of her own orbit towards that of the earth.\\nHence the moon meets the plane of the ecliptic sooner than it\\nwould have done if that force had not acted. At every half revo-\\nlution, therefore, the point in which the moon meets the ecliptic,\\nshifts in a direction contrary to that of the moon s motion, or con-\\ntrary to the order of the signs, If the earth and sun were at rest,\\nthe effect of the deflecting force just described, would be to pro-\\nduce a retrograde motion of the line of the nodes till that line was\\nbrought to pass through the sun, and of consequence, the plane of\\nthe moon s orbit to do the same, after which they would both re-\\nmain in their position, there being no longer any force tending to\\nproduce change in either. But the motion of the earth carries the\\nline of the nodes out of this position, and produces, by that means,\\nits continual retrogradation. The same force produces a small\\nvariation in the inclination of the moon s orbit, giving it an alter-\\nnate increase and decrease within very narrow limits.* These\\npoints will be easily understood by the aid of a diagram. There-\\nfore, let MN (Fig. 50,) be the ecliptic, ANB the orbit of the moon,\\nthe moon being in L, and N its descending node. Let the disturb-\\ning force of the sun which tends to bring it down to the ecliptic\\nFig. 50.\\n-A\\nbe represented by U, and its velocity in its orbit by La. Under\\nthe action of these two forces, the moon will describe the diago-\\nnal Lc of the parallelogram ba, and its orbit will be changed from\\nAN to LN the node N passes to N and the exterior angle at N\\nof the triangle LNN being greater than the interior and opposite\\nPlayfair.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0160.jp2"}, "161": {"fulltext": "LUNAR IRREGULARITIES. 135\\nangle at N, the inclination of the orbit is increased at the node.\\nAfter the moon has passed the ecliptic to the south side to I, the\\ndisturbing force Id produces a new change of the orbit N7e to\\nN and the inclination is diminished as at N In general,\\nwhile the moon is receding from one of the nodes, its inclination is\\ndiminishing while it is approaching a node, the inclination is in-\\ncreasing.*\\n233. The period occupied by the sun in passing from one of\\nthe moon s nodes until it comes round to the same node again, is\\ncalled the synodical revolution of the node. This period is shorter\\nthan the sidereal year, being only about 346| days. For since\\nthe node shifts its place to the westward 19\u00c2\u00b0 35 per annum, the\\nsun, in his annual revolution, comes to it so much before he com-\\npletes his entire circuit and since the sun moves about a degree\\na day, the synodical revolution of the node is 365\u00e2\u0080\u009419=346, or\\nmore exactly, 346.619851. The time from one new moon, or\\nfrom one full moon, to another, is 29.5305887 days. Now 19\\nsynodical revolutions of the nodes contain very nearly 223 of\\nthese periods.\\nFor 346.619851x19=6585.78,\\nAnd 29.5305887X223=6585.32.\\nHence, if the sun and moon were to leave the moon s node toge-\\nther, after the sun had been round to the same node 19 times, the\\nmoon would have performed very nearly 223 synodical revolu-\\ntions, and would, therefore, at the end of this period meet at the\\nsame node, to repeat the same circuit. And since eclipses of the\\nsun and moon depend upon the relative position of the sun, the\\nmoon, and node, these phenomena are repeated in nearly the same\\norder, in each of those periods. Hence, this period, consisting of\\nabout 18 years and 10 days, under the name of the Saros, was\\nused by the Chaldeans and other ancient nations in predicting\\neclipses.\\n234. The Metonic Cycle is not the same with the Saros, but\\nconsists of 19 tropical years. During this period the moon makes\\nFrancoeur, Uranog. p. 158. Robison s Phys. Astronomy, Art. 264.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0161.jp2"}, "162": {"fulltext": "136 THE MOON.\\nvery nearly 235 synodical revolutions, and hence the new and full\\nmoons, if reckoned by periods of 19 years, recur at the same\\ndates. If, for example, a new moon fell on the fiftieth day of one\\ncycle, it would also fall on the fiftieth day of each succeeding cycle\\nand, since the regulation of games, feasts, and fasts, has been\\nmade very extensively according to new or full moons, hence this\\nlunar cycle lias been much used both in ancient and modern\\ntimes. The Athenians adopted it 433 years before the Christian\\nera, for th*e regulation of their calendar, and had it inscribed in\\nletters of gold on the walls of the temple of Minerva. Hence the\\nterm Golden Number, which denotes the year of the lunar cycle.\\n235. The line of the apsides of the moon s orbit revolves from\\nwest to east through her whole orbit in about nine years.\\nIf, in any revolution of the moon, we should accurately mark\\nthe place in the heavens where the moon comes to its perigee,\\n(Art. 230,) we should find, that at the next revolution, it would\\ncome to its perigee at a point a little further eastward than before,\\nand so on at every revolution, until, after 9 years, it would come\\nto its perigee at nearly the same point as at first. This fact is\\nexpressed by saying that the perigee, and of course the apogee,\\nrevolves, and that the line which joins these two points, or the line\\nof the apsides, also revolves.\\nThe place of the perigee may be found by observing when the\\nmoon has the greatest apparent diameter. But as the magnitude\\nof the moon varies slowly at this point, a better method of ascer-\\ntaining the position of the apsides, is to take two points in the or-\\nbit where the variations in apparent diameter are most rapid, and\\nto find where they are equal on opposite sides of the orbit. The\\nmiddle point between the two will give the place of the perigee.\\nThe angular distance of the moon from her perigee in any part\\nof her revolution, is called the Moon s Anomaly.\\n236. The change of place in the apsides of the moon s orbit,\\nlike the shifting of the nodes, is caused by the disturbing influence\\nof the sun. If when the moon sets out from its perigee, it were\\nurged by no other force than that of projection, combined with its\\ngravitation towards the earth, it would describe a symmetrical", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0162.jp2"}, "163": {"fulltext": "LUNAR IRREGULARITIES. 137\\ncurve (Art. 186,) coming to its apogee at the distance of 180\u00c2\u00b0.\\nBut as the mean disturbing force in the direction of the radius\\nvector tends, on the whole, to diminish the gravitation of the\\nmoon to the earth, the portion of the path described in an instant\\nwill be less deflected from her tangent, or less curved, than if this\\nforce did not exist. Hence the path of the moon will not inter-\\nsect the radius vector at right angles, that is, she will not arrive at\\nher apogee until after passing more than 180\u00c2\u00b0 from her perigee,\\nby which means these points will constantly shift their positions\\nfrom west to east.* The motion of the apsides is found to be 3\u00c2\u00b0\\n1 20 for every sidereal revolution of the moon.\\n237. On account of the greater eccentricity of the moon s orbit\\nabove that of the sun, the Equation of the Center, or that correc-\\ntion which is applied to the moon s mean anomaly to find her true\\nanomaly (Art. 200,) is much greater than that of the sun, being\\nwhen greatest more than six degrees, (6\u00c2\u00b0 17 12 .7,) while that of\\nthe sun is less than two degrees, (1\u00c2\u00b0 55 26 8.)\\nThe irregularities in the motions of the moon may be compared\\nto those of the magnetic needle. As a first approximation, we say\\nthat the needle places itself in a north and south line. On closer\\nexamination, however, we find that, at different places, it deviates\\nmore or less from this line, and we introduce the first great cor-\\nrection under the name of the declination of the needle. But ob-\\nservation shows us that the declination alternately increases and\\ndiminishes every day, and therefore we apply to the declination\\nitself a second correction for the diurnal variation. Finally, we\\nascertain, from long continued observations, that the diurnal va-\\nriation is affected by the change of seasons, being greater in sum-\\nmer than in winter, and hence we apply to the diurnal variation a\\nthird correction for the annual variation.\\nIn like manner, we shall find the greater inequalities of the\\nmoon s motions are themselves subject to subordinate inequalities,\\nwhich give rise to smaller equations, and these to smaller still, to\\nthe last degree of refinement.\\n238. Next to the equation of the center, the greatest correction\\ni o Playfair,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0163.jp2"}, "164": {"fulltext": "138 THE MOON.\\nto be applied to the moon s longitude, is that which belongs to the\\nEvection. The evection is a change of form in the lunar orbit, by\\nwhich its eccentricity is sometimes increased, and sometimes\\ndiminished. It depends on the position of the line of the apsides\\nwith respect to the line of the syzygies.\\nThis irregularity, and its connexion with the place of the peri-\\ngee with respect to the place of conjunction or opposition, was\\nknown as a fact to the ancient astronomers, Hipparchus and\\nPtolemy but its cause was first explained by Newton in con-\\nformity with the law of universal gravitation. It was found, by\\nobservation, that the equation of the center itself was subject to a\\nperiodical variation, being greater than its mean, and greatest of\\nall when the conjunction or opposition takes place at the perigee\\nor apogee, and least of all when the conjunction or opposition\\ntakes place at a point half way between the perigee and apogee\\nor, in the more common language of astronomers, the equation of\\nthe center is increased when the line of the apsides is in syzygy,\\nand diminished when that line is in quadrature. If, for example,\\nwhen the line of the apsides is in syzygy, we compute the moon s\\nplace by deducting the equation of the center from the mean\\nanomaly (see Art. 200,) seven days after conjunction, the compu-\\nted longitude will be greater than that determined by actual obser-\\nvation, by about 80 minutes but if the same estimate is made\\nwhen the line of the apsides is in quadrature, the computed longi-\\ntude will be less than the observed, by the same quantity. These\\nresults plainly show a connexion between the velocity of the\\nmoons motions and the position of the line of the apsides with\\nrespect to the line of the syzygies.\\n239. Now any cause which, at the perigee, should have the\\neffect to increase the moon s gravitation towards the earth beyond\\nits mean, and, at the apogee, to diminish the moon s gravitation\\ntowards the earth, would augment the difference between the\\ngravitation at the perigee and at the apogee, and consequently in-\\ncrease the eccentricity of the orbit. Again, any cause which at\\nthe perigee should have the effect to lessen the moon s gravitation\\ntowards the earth, and, at the apogee, to increase it, would lessen\\nthe difference between the, two, and consequently diminish the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0164.jp2"}, "165": {"fulltext": "LUNAR IRREGULARITIES. 139\\neccentricity of the orbit, or bring it nearer to a circle. Let us\\nsee if the disturbing force of the sun produces these effects. The\\nsun s disturbing force, as we have seen in article 228, admits of\\ntwo resolutions, one in the direction of the radius vector, (OM,\\nFig. 48,) the other (ON) in the direction of a tangent to the orbit.\\nFirst, let AB be the line of the apsides in syzygy, A being the place\\nof the perigee. The sun s disturbing force OM is greatest in the\\ndirection of the line of the syzygies yet depending as it does on the\\nunequal action of the sun upon the earth and the moon, and being\\ngreater as their distance from each other is greater, it is at a mini-\\nmum when acting at the perigee, and at a maximum when acting at\\nthe apogee. Hence its effect is to draw away the moon from the\\nearth less than usual at the perigee, and of course to make her\\ngravitation towards the earth greater than usual, while at the\\napogee its effect is to diminish the tendency of the moon to the\\nearth more than usual, and thus to increase the disproportion be-\\ntween the two distances of the moon from the focus at these two\\npoints, and of course to increase the eccentricity of the orbit.\\nThe moon, therefore, if moving towards the perigee, is brought\\nto the line of the apsides in a point between its mean place and\\nthe earth or if moving towards the apogee, she reaches the line\\nof the apsides in a point more remote from the earth than its mean\\nplace.\\nSecondly, let CD be the line of the apsides, in quadrature, C\\nbeing the place of the perigee. The effect of the sun s disturb-\\ning force is to increase the tendency of the moon towards the\\nearth when in quadrature. If, however, the moon is then at her\\nperigee, such increase will be less than usual, and if at her apogee,\\nit will be more than usual hence its effect will be to lessen the\\ndisproportion between the two distances of the moon from the\\nfocus at these two points and of course to diminish the eccen-\\ntricity of the orbit. The moon, therefore, if moving towards\\nthe perigee, meets the line of the apsides in a point more remote\\nfrom the earth than the mean place of the perigee and if moving\\ntowards the apogee, in a point between the earth and the mean place\\nof the apogee.*\\nWoodhouse s Ast. p. 680.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0165.jp2"}, "166": {"fulltext": "140 THE MOON.\\n240. A third inequality in the lunar motions, is the Variation.\\nBy comparing the moon s place as computed from her mean mo-\\ntion corrected for the equation of the center and for evection,\\nwith her place as determined by observation, Tycho Brahe dis-\\ncovered that the computed and observed places did not always\\nagree. They agreed only in the syzygies and quadratures, and\\ndisagreed most at a point half way between these, that is, at the\\noctants. Here, at the maximum, it amounted to more than half\\na degree (35 41. 6.) It appeared evident from examining the\\ndaily observations while the moon is performing her revolution\\naround the earth, that this inequality is connected with the angular\\ndistance of the moon from the sun, and in every part of the orbit\\ncould be correctly expressed by multiplying the maximum value\\nas given above, into the sine of twice the angular distance between\\nthe sun and the moon. It is, therefore, at the conjunctions and\\nquadratures, and greatest at the octants. Tycho Brahe knew the\\nfact Newton investigated the cause.\\nIt appears by article 228, that the sun s disturbing force can be\\nresolved into two parts, one in the direction of the radius vector,\\nthe other at right angles to it in the direction of a tangent to the\\nmoon s orbit. The former, as already explained, produces the\\nEvection: the latter produces the Variation. This latter force\\nwill accelerate the moon s velocity, in every point of the quadrant\\nwhich the moon describes in moving from quadrature to conjunc-\\ntion, or from C to A, (Fig. 48,) but at an unequal rate, the\\nacceleration being greatest at the octant, and nothing at the quad-\\nrature and the conjunction and when the moon is past conjunction,\\nthe tangential force will change its direction and retard the moon s\\nmotion. All these points will be understood by inspection of\\nfigure 48.\\n241. A fourth lunar inequality is the Annual Equation. This\\ndepends on the distance of the earth (and of course the moon)\\nfrom the sun. Since the disturbing influence of the sun has a\\ngreater effect in proportion as the sun is nearer,* consequently all\\nthe inequalities depending on this influence must vary at different\\nVarying reciprocally as the cube of the sun s distance from the earth.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0166.jp2"}, "167": {"fulltext": "LUNAR IRREGULARITIES. 141\\nseasons of the year. Hence, the amount of this effect due to any-\\nparticular time of the year is called the Annual Equation.\\n242. The foregoing are the largest of the inequalities of the\\nmoon s motions, and may serve as specimens of the corrections that\\nare to be applied to the mean place of the moon in order to find\\nher true place. These were first discovered by actual observa-\\ntion but a far greater number, though most of them are exceed-\\ningly minute, have been made known by the investigations of Phys-\\nical Astronomy, in following out all the consequences of universal\\ngravitation. In the best tables, about 30 equations are applied to\\nthe mean motions of the moon. That is, we first compute the\\nplace of the moon on the supposition that she moves uniformly\\nin a circle. This gives us her mean place. We then proceed,\\nby the aid of the Lunar Tables, to apply the different corrections,\\nsuch as the equation of the center, evection, variation, the annual\\nequation, and so on, to the number of 28. Numerous as these\\ncorrections appear, yet La Place informs us, that the whole num-\\nber belonging to the moon s longitude is no less than 60 and\\nthat to give the tables all the requisite degree of precision, addi-\\ntional investigations will be necessary, as extensive at least as\\nthose already made.* The best tables in use in the time of Tycho\\nBrahe, gave the moon s place only by a distant approximation.\\nThe tables in use in the time of Newton, (Halley s tables,) approxi-\\nmated within 7 minutes. Tables at present in use give the moon s\\nplace to 5 seconds. These additional degrees of accuracy have\\nbeen attained only by immense labor, and by the united efforts of\\nPhysical Astronomy and the most refined observations.\\n243. The inequalities of the moon s motions are divided into\\nperiodical and secular. Periodical inequalities are those which\\nare completed in comparatively short periods, like evection and\\nvariation: Secular inequalities are those which are completed\\nonly in very long periods, such as centuries or ages. Hence the\\ncorresponding terms periodical equations, and secular equations.\\nAs an example of a secular inequality, we may mention the ac-\\nSyst. du Monde, 1. iv, c. 5.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0167.jp2"}, "168": {"fulltext": "142 THE MOON.\\nceleration of the moon s mean motion. It is discovered, thai the\\nmoon actually revolves around the earth in less time now than\\nshe did in ancient times. The difference however is exceedingly\\nsmall, being only about 10 in a century, bat increases from century\\nto century as the square of the number of centuries from a given\\nepoch. This remarkable fact was discovered by Dr. H alley.* In a\\nlunar eclipse the moon s longitude differs from that of the sun, at the\\nmiddle of the eclipse, by exactly 180\u00c2\u00b0 and since the sun s lon-\\ngitude at any given time of the year is known, if we can learn\\nthe day and hour when an eclipse occurs, we shall of course know\\nthe longitude of the sun and moon. Nov/ in the year 721 before\\nthe Christian era, on a specified day and hour, Ptolemy records a\\nlunar eclipse to have happened, and to have been observed by\\nthe Chaldeans. The moon s longitude, therefore, for that time is\\nknown and as we know the mean motions of the moon at pre-\\nsent., starting from that epoch, and computing, as may easily be\\ndone, the place which the moon ought to occupy at present at any\\ngiven time, she is found to be actually nearly a degree and a half\\nin advance of that place. Moreover, the same conclusion is\\nderived from a comparison of the Chaldean observations with those\\nmade by an Arabian astronomer of the tenth century.\\nThis phenomenon at first led astronomers to apprehend that the\\nmoon encountered a resisting medium, which, by destroying at\\nevery revolution a small portion of her projectile force, would\\nhave the effect to bring her nearer and nearer to the earth and\\nthus to augment her velocity. But in 1786, La Place demon-\\nstrated that this acceleration is one of the legitimate effects of the\\nsun s disturbing force, and is so connected with changes in the\\neccentricity of the earth s orbit, that the moon will continue to be\\naccelerated while that eccentricity diminishes, but when the eccen-\\ntricity has reached its minimum (as it will do after many ages)\\nand begins to increase, then the moon s motion will begin to be\\nretarded, and thus her mean motions will oscillate forever about a\\nmean value.\\n244. The lunar inequalities which have been considered are such\\nAstronomer Royal of Great Britain, and cotemporary with Sir Isaac ISewton.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0168.jp2"}, "169": {"fulltext": "ECLIPSES. 1 43\\nonly as affect the moon s longitude but the sun s disturbing force\\nalso causes inequalities in the moon s latitude and parallax. Those\\nof latitude alone require no less than twelve equations. Since\\nthe moon revolves in an orbit inclined to the ecliptic, it is easy to\\nsee that the oblique action of the sun must admit of a resolution\\ninto two forces, one of which being perpendicular to the moon s\\norbit, must effect changes in her latitude. Since also several of the\\ninequalities already noticed involve changes in the length of the\\nradius vector, it is obvious that the moon s parallax must be sub-\\nject to corresponding perturbations.\\nCHAPTER VII\\nECLIPSES.\\n245. An eclipse of the moon happens, when the moon in its\\nrevolution aoout the earth, falls into the earth s shadow 7 An\\neclipse of the sun happens, when the moon, coming between the\\nearth and the sun, covers either a part or the whole of the solar\\ndisk. An eclipse of the sun can occur only at the time of con-\\njunction, or new moon and an eclipse of the moon, only at the\\ntime of opposition, or full moon. Were the moon s orbit in the\\nsame plane with that of the earth, or did it coincide with the\\necliptic, then an eclipse -of the sun would take place at every\\nconjunction, and an eclipse cf the moon at every opposition for\\nas the sun and earth both lie in the ecliptic, the shadow of the\\nearth must also extend in the same plane, being of course always\\ndirectly opposite to the sun and since, as we shall soon see, the\\nlength of this shadow is much greater than the distance of the\\nmoon from the earth, the moon, if it revolved in the plane of the\\necliptic, must pass through the shadow at every full moon. For\\nsimilar reasons, the moon would occasion an eclipse of the sun,\\npartial or total, in some portions of the earth at every new moon.\\nBut the lunar orbit is inclined to the ecliptic about 5\u00c2\u00b0, so that the\\ncenter of the moon, when she is furthest from her node, is 5\u00c2\u00b0 from", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0169.jp2"}, "170": {"fulltext": "144 THE MOON.\\nthe axis of the earth s shadow (which is always in the ecliptic\\nand, as we shall show presently, the greatest distance to which the\\nshadow extends on each side of the ecliptic, that is, the greatest\\nsemi-diameter of the shadow, where the moon passes through it,\\nis only about f of a degree, while the semi-diameter of the moon s\\ndisk is only about I of a degree hence the two semi-diame-\\nters, namely, that of the moon and the earth s shadow, cannot\\noverlap one another, unless, at the time of new or full moon, the\\nsun is at or very near the moon s node. In the course of the sun s\\napparent revolution around the earth once a year, he is succes-\\nsively in every part of the ecliptic consequently, the conjunctions\\nand oppositions of the sun and moon may occur at any part of the\\necliptic, either when the sun is at the moon s node, (or when he\\nis passing that point of the celestial vault on which the moon s\\nnode is projected as seen from the earth or they may occur\\nwhen the sun is 90\u00c2\u00b0 from the moon s node, where the lunar and\\nsolar orbits are at the greatest distance from each other; or, finally,\\nthey may occur at any intermediate point. Now the sun, in his\\nannual revolution, passes each of the moon s nodes on opposite\\nsides of the ecliptic, and of course at opposite seasons of the\\nyear so that, for any given year, the eclipses commonly happen\\nin two opposite months, as January and July, February and\\nAugust, May and November. These, therefore, are called Node\\nMonths.\\n246. If the sun were of the same size with the earth, the shadow\\nof the earth would be cylindrical and infinite in length, since the\\ntangents drawn from the sun to the earth (which form the bounda-\\nries of the shadow) would be parallel to each other but as the\\nsun is a vastly larger body than the earth, the tangents converge\\nand meet in a point at some distance behind the earth, forming a\\ncone of which the earth is the base, and whose vertex (and of\\ncourse its axis) lies in the ecliptic. A little reflection will also\\nshow us, that the form and dimensions of the shadow must be\\naffected by several circumstances that the shadow must be of\\nthe greatest length and breadth when the sun is furthest from the\\nearth that its figure will be slightly modified by the spheroidal\\nfigure of the earth and that the moon, being, at the time of its", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0170.jp2"}, "171": {"fulltext": "ECLIPSES.\\n145\\nopposition, sometimes nearer to the earth, and sometimes further\\nfrom it, will accordingly traverse it at points where its breadth\\nvaries more or less.\\n247. The semi-angle of the cone of the earth s shadow, is equal\\nto the sun s apparent semi-diameter, minus his horizontal par-\\nallax.\\nLet AS (Fig. 51.) be the semi-diameter of the sun, BE that of\\nthe earth, and EC the axis of the earth s shadow. Then the\\nsemi-angle of the cone of the earth s shadow ECB=AE8-EAB,\\nFig. 51.\\nof which AES is the sun s semi-diameter and EAB his horizontal\\nparallax and as both these quantities are known, hence the angle\\nat the vertex of the shadow becomes known. Putting 5 for the\\nthe sun s semi-diameter, andp for his horizontal parallax, we have\\nthe semi-angle of the earth s shadow ECB= 6\u00e2\u0080\u0094 p.\\n248. At the mean distance of the earth from the sun, the length\\nof the earth s shadow is about 860,000 miles, or more than three times\\nthe distance of the moon from the earth.\\nIn the right angled triangle ECB, right angled at B, the angle\\nECB being known, and the side EB, we can find the side EC.\\nFor sin. (8-p) EB :R EC -r-5 This value will vary\\nsin. (8\u00e2\u0080\u0094 p)\\nwith the sun s semi-diameter, being greater as that is less. Its\\nmean value being 16 1 .5 and the sun s horizontal parallax being\\n8 .6, 5-p=15 52 .9, and EB=3956.2. Hence,\\nSin. 15 53 Rad. 3956.2 856,275.\\nSince the distance of the moon from the earth is 238,545 miles,\\nthe shadow extends about 3.6 times as far as the moon, and con-\\n19", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0171.jp2"}, "172": {"fulltext": "146 THE MOON.\\nsequently, the moon passes the shadow towards its broadest part,\\nwhere its breadth is much more than sufficient to cover the moon s\\ndisk.\\n249. The average breadth of the earth s shadow where it eclipses\\nthe moon is almost three times the moon s diameter.\\nLet mm (Fig. 51,) represent a section of the earth s shadow\\nwhere the moon passes through it, M being the center of the cir-\\ncular section. Then the angle MEm will be the angular breadth\\nof half the shadow. But,\\nMEw2=B/7iE BCE that is, since BmE is the moon s horizon-\\ntal parallax, (Art. 82,) and BCE equals the sun s semi-diameter\\nminus his horizontal parallax (5\u00e2\u0080\u0094 p,) therefore, putting P for the\\nmoon s horizontal parallax, we have\\nMEm ~P-(S-p)=\u00c2\u00a5+p\u00e2\u0080\u00948; that is, since P=57 1 and\\n5_p:=15 52 .9, therefore, 57 1 15 52 .9=41 8 .l, which is\\nnearly three times 15 33 the semi-diameter of the moon. Thus,\\nit is seen how, by the aid of geometry, we learn to estimate vari-\\nous particulars respecting the earth s shadow, by means of simple\\ndata derived from observation.\\n250. The distance of the moon from her node when she just\\ntouches the shadow of the earth, in a lunar eclipse, is called the\\nLunar Ecliptic Limit and her distance from the node in a solar\\neclipse, when the moon just touches the solar disk, is called the\\nSolar Ecliptic Limit The Limits are respectively the furthest\\npossible distances from the node at which eclipses can take place.\\n251. The Lunar Ecliptic Limit is nearly 12 degrees.\\nLet CN (Fig. 52,) be the sun s path, MN the moon s, and N the\\nnode. Let Ca be the semi-diameter of the earth s shadow, and\\nMa the semi-diameter of the moon. Since Ca and Ma are known\\nFig. 52.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0172.jp2"}, "173": {"fulltext": "ECLIPSES. 147\\nquantities, their sum CM is also known. The angle at N is\\nknown, being the inclination of the lunar orbit to the ecliptic.\\nHence, in the spherical triangle MCN, right angled at M,* by\\nNapier s theorem, (Art. 132, Note,)\\nRad.xsin. CM=sin. CNxsin. MNC.\\nThe greatest apparent semi-diameter of the earth s shadow\\nwhere the moon crosses it, computed by article 249, is 45 52\\nand the moon s greatest apparent semi-diameter, is 16 45 .5,\\nwhich together, give MC equal to 62 37 5. Taking the incli-\\nnation of the moon s orbit, or the angle MNC (what it generally\\nis in these circumstances) at 5\u00c2\u00b0 17 and we have Rad.xsin.\\n62 37 .5=sin. CNxsin. 5\u00c2\u00b0 17 or sin. CN _Rad.xsin.62 37 .5\\nsin. 5 17\\nand CN=1 1\u00c2\u00b0 25 40 This is the greatest distance of the moon from\\nher node at which an eclipse of the moon can take place. By\\nvarying the value of CM, corresponding to variations in the dis-\\ntances of the sun and moon from the earth, it is found that if NC\\nis less than 9\u00c2\u00b0, there must be an eclipse but between this and the\\nlimit, the case is doubtful\\nWhen the moon s disk only comes in contact with the earth s\\nshadow, as in figure 52 the phenomenon is called an appulse,\\nwhen only a part of the disk enters the shadow, the eclipse is\\nsaid to be partial, and total if the whole of the disk enters the\\nthe shadow. The eclipse is called central when the moon s center\\ncoincides with the axis of the shadow, which happens when the\\nmoon at the time of the eclipse is exactly at her node.\\n252. Before the moon enters the earth s shadow, the earth be-\\ngins to intercept from it portions of the sun s light, gradually in-\\ncreasing until the moon reaches the shadow. This partial light is\\ncalled the moons Penumbra. Its limits are ascertained by drawing\\nthe tangents AC B and A C B. (Fig. 51.) Throughout the space\\nincluded between these tangents more or less of the sun s light is\\nintercepted from the moon by the interposition of the earth for\\nThe line CM is to be regarded as the projection of the line which connects the\\ncenters of the moon and section of the earth s shadow, as seen from the earth.\\nt Woodhouse s Astronomy, p. 718.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0173.jp2"}, "174": {"fulltext": "148 THE MOON.\\nit is evident, that as the moon moves towards the shadow, she\\nwould gradually lose the view of the sun, until, on entering the\\nshadow, the sun would be entirely hidden from her.\\n253. The semi-angle of the Penumbra equals the sun s semi-\\ndiameter and horizontal parallax, or 5 -\\\\-p.\\nThe angle ACM (Fig. 51,)=AC S=AES+B AE. But AES is\\nthe sun s semi-diameter, and B AE is the sun s horizontal parallax,\\nboth of which quantities are known.\\n254. The semi-angle of a section of the Penumbra, where the\\nmoon crosses it, equals the moon s horizontal parallax, plus the sun s,\\nplus the sun s semi-diameter.\\nThe angle hEM (Fig. 51,) =EhC +EC h. But EftC =P, the\\nmoon s horizontal parallax, and EC h =6-{-p (Art. 253,) hEM\\n==P-fj9-H, all which are likewise known quantities.\\nHence, by means of these few elements, which are known from\\nobservation, we ascend to a complete knowledge of all the par-\\nticulars necessary to be known respecting the moon s penumbra.\\n255. In the preceding investigations, we have supposed that\\nthe cone of the earth s shadow is formed by lines drawn from the\\nsun, and touching the earth s surface. But the apparent diameter\\nof the shadow is found by observation to be somewhat greater than\\nwould result from this hypothesis. The fact is accounted for by\\nsupposing that a portion of the solar rays which graze the earth s\\nsurface are absorbed and extinguished by the lower strata of the\\natmosphere. This amounts to the same thing as though the earth\\nwere larger than it is, in which case the moon s horizontal parallax\\nwould be increased and accordingly, in order that theory and\\nobservation may coincide, it is found necessary to increase the\\nparallax by cV\\n256. In a total eclipse of the moon, its disk is still visible,\\nshining with a dull red light. This light cannot be derived di-\\nrectly from the sun, since the view of the sun is completely hid-\\nden from the moon nor by reflexion from the earth, since the\\nilluminated side of the earth is wholly turned from the moon but", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0174.jp2"}, "175": {"fulltext": "ECLIPSES. 149\\nit is owing to refraction by the earth s atmosphere, by which a few\\nscattered rays of the sun are bent round into the earth s shadow\\nand conveyed to the moon, sufficient in number to afford the feeble\\nlight in question.\\n257. In calculating an eclipse of the moon, we first learn from\\nthe tables in what month the sun, at the time of full moon in that\\nmonth, is near the moon s node, or within the lunar ecliptic limit.\\nThis it must evidently be easy to determine, since the tables ena-\\nble us to find both the longitudes of the nodes, and the longitudes\\nof the sun and moon, for every day of the year. Consequently,\\nwe can find when the sun has nearly the same longitude as one of\\nthe nodes, and also the precise moment when the longitude of the\\nmoon is 180\u00c2\u00b0 from that of the sun, for this is the time of opposition,\\nfrom which may be derived the time of the middle of the eclipse.\\nHaving the time of the middle of the eclipse, and the breadth\\nof the shadow, (Art. 249.) and knowing, from the tables, the rate\\nat which the moon moves per hour faster than the shadow, we can\\nfind how long it will take her to traverse half the breadth of the\\nshadow and this time subtracted from the time of the middle\\nof the eclipse, will give the beginning, and added to the time of\\nthe middle will give the end of the eclipse. Or if instead of the\\nbreadth of the shadow, we employ the breadth of the penumbra\\n(Art. 253,) we may find, in the same manner, when the moon\\nenters and when she leaves the penumbra. We see, therefore,\\nhow by having a few things known by observation, such as the\\nsun and moon s semi-diameters, and their horizontal parallaxes,\\nwe rise, by the aid of trigonometry, to the knowledge of various\\nparticulars respecting the length and breadth of the shadow and\\nof the penumbra. These being known, we next have recourse to\\nthe tables which contain all the necessary particulars respecting\\nthe motions of the sun and moon, together with equations or cor-\\nrections, to be applied for all their irregularities. Hence it is com-\\nparatively an easy task to calculate with great accuracy an eclipse\\nof the moon.\\n258. Let us then see how we may find the exact time of the be-\\nginning, end, duration, and magnitude, of a lunar eclipse.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0175.jp2"}, "176": {"fulltext": "150 THE MOON.\\nLet NG (Fig 53,) be the ecliptic, and ~Nag the moon s orbit, the\\nsun being in A* when the moon is in opposition at a let N be\\nthe ascending node, and Ka the moon s latitude at the instant\\nFig. 53.\\nof opposition. An hour afterwards the sun will have passed to\\nA and the moon to g, when the difference of longitude of the two\\nbodies will be GA Then gh is the moon s hourly motion in lati-\\ntude, and ah her hourly motion in longitude. As the character\\nand form of the eclipse will depend solely upon the distances\\n.between the centers of the sun and moon, that is, upon the line\\n^A instead of considering the two bodies as both in motion,\\nwe may suppose the sun at rest in A, and the moon as advancing\\nwith a motion equal to the difference between its rate and that\\nof the sun, a supposition which will simplify the calculation.\\nTherefore, draw gd parallel and equal to A A, join a A, and this\\nline being equal to gA the two bodies will be in the same relative\\nsituation as if the sun were at A and the moon at g. Join da and\\nproduce the line da both ways, cutting the ecliptic in F; then\\ndaF will be the moon s Relative Orbit Hence ai=ah~- AA =the\\ndifference of the hourly motions of the sun and moon, that is, the\\nmoon s relative ?notion in longitude, and di\u00e2\u0080\u0094 the moon s hourly\\nmotion in latitude.\\nDraw CD (Fig. 54,) to represent the ecliptic, and let A be the\\nplace of the sun. As the tables give the computation of the\\nmoon s latitude at every instant, consequently, we may take from\\nthem the latitude corresponding to the instant of opposition, and\\nto one hour later and we may take also the sun s and moon s\\nhourly motions in longitude. Take AD, AB, each equal to fhe\\nrelative motion, and A\u00c2\u00ab=the latitude in opposition, D^=the lati-\\nIt will be remarked that the point A really represents the center of the earth s\\nshadow but as the real motions of the shadow are the same with the assumed motions\\nof the sun, the latter are used in conformity with the language of the tables.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0176.jp2"}, "177": {"fulltext": "ECLIPSES.\\nFig. 54.\\n151\\n==-Sl\\ntude one hour afterwards join da and produce the line da both\\nways, and it will represent the moon s relative orbit. Draw B\\nat right angles to CD, and it will be the latitude an hour before\\nopposition. At the time of the eclipse, the apparent distance of\\nthe center of the shadow from the moon is very small conse-\\nquently, CD, cd, Dd, c. may be regarded as straight lines.\\nDuring the short interval between the beginning and end of an\\neclipse, the motion of the sun, and consequently that of the cen-\\nter of the shadow, may likewise be regarded as uniform.\\n259. The various particulars that enter into the calculation of\\nan eclipse are called its Elements and as our object is here merely\\nto explain the method of calculating an eclipse of the moon, (refer-\\nring to the Supplement for the actual computation.) we may take\\nthe elements at their mean value. Thus, we will consider cd as\\ninclined to CD 5\u00c2\u00b0 9 the moon s horizontal parallax as 58 its semi-\\ndiameter as 16 and that of the earth s shadow as 42 The line\\nAm perpendicular to cd gives the point m for the place of the\\nmoon at the middle of the eclipse, for this line bisects the chord,\\nwhich represents the path of the moon through the shadow; and\\nmM, perpendicular to CD, gives AM for the time of the middle\\nof the eclipse before opposition, the number of minutes before op-\\nposition being the same part of an hour that AM is of AB. From\\nthe center A, with a radius equal to that of the earth s shadow\\n(42 describe the semi-circle BLF, and it will represent the pro-\\njection of the shadow traversed by the moon. With a radius\\nequal to the semi-diameter of the shadow and that of the moon\\nThe situation of the moon when at m is called orbit opposition and her situation\\nwhen at a, ecliptic opposition.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0177.jp2"}, "178": {"fulltext": "152 THE MOON.\\n(=42 +16 =58 and with the center A, mark the two points c and\\non the relative orbit, and they will be the places of the center\\nof the moon at the beginning and end of the eclipse. The per-\\npendiculars cC,/F, give the times AC and AF of the commence-\\nment and the end of the eclipse, and CM, or MF gives half the\\nduration. From the centers c and f with a radius equal to the\\nsemi-diameter of the moon (16 describe circles, and they will\\neach touch the shadow, (Euc. 3.12.) indicating the position of the\\nmoon at the beginning and end of the eclipse. If the same circle\\ndescribed from m is wholly within the shadow, the eclipse will be\\ntotal if it is only partly within the shadow, the eclipse will be\\npartial. With the center A, and radius equal to the semi-diame^\\nter of the shadow minus that of the moon (42 16 =26 mark\\nthe two points c ,f, which will give the places of the center of the\\nmoon, at the beginning and end of total darkness, and MC MF\\nwill give the corresponding times before and after the middle of\\nthe eclipse. Their sum will be the duration of total darkness.\\n260. If the foregoing projection be accurately made from a scale,\\nthe required particulars of the eclipse may be ascertained by\\nmeasuring on the same scale, the lines which respectively repre-\\nsent them and we should thus obtain a near approximation to the\\nelements of the eclipse. A more accurate determination of these\\nelements may, however, be obtained by actual calculation. The\\ngeneral principles of the calculation will be readily understood.\\nFirst, knowing ai, (Fig. 53,) the moon s relative longitude, and\\ndi, her latitude, we find the angle dai, which is the inclination of\\nthe moon s relative orbit. But dai\u00e2\u0080\u0094akm and, in the triangle\\naAm, we have the angle at A, and the side A\u00c2\u00ab, being the moon s\\nlatitude at the time of opposition, which is given by the tables.\\nHence we can find the side Am. In the triangle AmM, (Fig. 54,)\\nhaving the side Am and the angle AwM (=aAm) we can find AM\\nthe arc of relative longitude described by the moon from the\\ntime of the middle of the eclipse to the time of opposition and\\nknowing the moon s hourly motion in longitude, we can convert\\nAM into time, and this subtracted from the time of opposition\\ngives us the time of the middle of the eclipse.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0178.jp2"}, "179": {"fulltext": "ECLIPSES. 153\\nSecondly, since we know the length of the line Ac* (Fig. 54)\\nand can easily find the angle cAC, we can thus obtain the side\\nAC and AC AM=MC, which arc, converted into time by com-\\nparing it with the moon s hourly motion in longitude, gives us,\\nwhen subtracted from the time of the middle of the eclipse, the\\ntime of the beginning of the eclipse, or when added to that of the\\nmiddle, the time of the end of the eclipse. The sum of the two\\nequals the whole duration.\\nThirdly, by a similar method we calculate the value of MC\\nwhich converted into time, and subtracted from the time of the\\nmiddle of the eclipse, gives the commencement of total darkness, or\\nwhen added gives the end of total darkness. Their sum is the\\nduration of total darkness.\\nFourthly, the quantity of the eclipse is determined by supposing\\nthe diameter of the moon divided into twelve equal parts called\\nDigits, and finding how many such parts lie within the shadow,\\nat the time when the centers of the moon and the shadow are\\nnearest to each other. Even when the moon lies wholly within\\nthe shadow, the quantity of the eclipse is still expressed by the num-\\nber of digits contained in that part of the line which joins the cen-\\nter of the shadow and the center of the moon, which is intercepted\\nbetween the edge of the shadow and the inner edge of the moon.\\nThus in figure 54, the number of digits eclipsed, equals\\nAo An Ao\u00e2\u0080\u0094(Am\u00e2\u0080\u0094nm) a\\n2 _ f i an expression containing only known\\nquantities.\\n261. The foregoing will serve as an explanation of the general\\nprinciples, on which proceeds the calculation of a lunar eclipse.\\nThe actual methods practiced employ many expedients to facili-\\ntate the process, and to insure the greatest possible accuracy, the\\nnature of which are explained and exemplified in Mason s Supple-\\nment to this work.\\n262. The leading particulars respecting an Eclipse of the\\nSun, are ascertained very nearly like those of a lunar eclipse. The\\nThis line is not represented in the figure, but may be easily imagined.\\n20", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0179.jp2"}, "180": {"fulltext": "154 THE MOON.\\nshadow of the moon travels over a portion of the earth, as the\\nshadow of a small cloud, seen from an eminence in a clear day,\\nrides along over hills and plains. Let us imagine ourselves stand-\\ning on the moon then we shall see the earth partially eclipsed by\\nthe shadow of the moon, in the same manner as we now see the\\nmoon eclipsed by the earth s shadow and we might proceed to\\nfind the length of the shadow, its breadth where it eclipses the\\nearth, the breadth of the penumbra, and its duration and quantity,\\nin the same way as we have ascertained these particulars for an\\neclipse of the moon.\\nBut, although the general characters of a solar eclipse might be\\ninvestigated on these principles, so far as respects the earth at\\nlarge, yet as the appearances of the same eclipse of the sun are\\nvery different at different places on the earth s surface, it is neces-\\nsary to calculate its peculiar aspects for each place separately, a\\ncircumstance which makes the calculation of a solar eclipse much\\nmore complicated and tedious than of an eclipse of the moon.\\nThe moon, when she enters the shadow of the earth, is deprived\\nof the light of the part immersed, and that part appears black\\nalike to all places where the moon is above the horizon. But it is\\nnot so with a solar eclipse. We do not see this by the shadow\\ncast on the earth, as we should do if we stood on the moon, but\\nby the interposition of the moon between us and the sun and the\\nsun may be hidden from one observer while he is in full view of\\nanother only a few miles distant. Thus, a small insulated cloud\\nsailing in a clear sky, will, for a few moments, hide the sun from\\nus, and from a certain space near us, while all the region around\\nis illuminated.\\n263. We have compared the motion of the moon s shadow over\\nthe surface of the earth to that of a cloud but its velocity is in-\\ncomparably greater. The mean motion of the moon around the\\nearth is about 33 per hour but 33 of the moon s orbit is 2280\\nmiles, and the shadow moves of course at the same rate, or 2280\\nmiles per hour, traversing the entire disk of the earth in less than\\nfour hours. This is the velocity of the shadow when it passes\\nperpendicularly over the earth when the direction of the axis of\\nthe shadow is oblique to the earth s surface, the velocity is increased", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0180.jp2"}, "181": {"fulltext": "ECLIPSES. 155\\nm proportion of radius to the sine of obliquity. Thus the shadows\\nof evening have a far more rapid motion than those of noon-day.\\nLet us endeavor to form a just conception of the manner in\\nwhich these three bodies, the sun, the earth, arid the moon, are\\nsituated with respect to each other at the time of a solar eclipse.\\nFirst, suppose the conjunction to take place at the node. Then\\nthe straight line which connects the centers of the sun and the\\nearth, also passes through the center of the moon, and coincides\\nwith the axis of its shadow and, since the earth is bisected by\\nthe plane of the ecliptic, the shadow would traverse the earth in\\nthe direction of the terrestrial ecliptic, from west to east, passing\\nover the middle regions of the earth. Here the diurnal motion of\\nthe earth being in the same direction with the shadow, but with a\\nless velocity, the shadow will appear to move with a speed equal\\nonly to the difference between the two. Secondly, suppose the\\nmoon is on the north side of the ecliptic at the time of conjunction,\\nand moving towards her descending node, and that the conjunc-\\ntion takes place just within the solar ecliptic limit, say 16\u00c2\u00b0 from the\\nnode. The shadow will now not fall in the plane of the ecliptic,\\nbut a little northward of it, so as just to graze the earth near the\\npole of the ecliptic. The nearer the conjunction comes to the\\nnode, the further the shadow will fall from the pole of the ecliptic\\ntowards the equatorial regions. In certain cases, the shadow\\nstrikes beyond the pole of the earth and then its easterly motion\\nbeing opposite to the diurnal motion of the places which it traver-\\nses, consequently its velocity is greatly increased, being equal to\\nthe sum of both.\\n264. After these general considerations, we will now examine\\nmore particularly the method of investigating the elements of a\\nsolar eclipse.\\nThe length of the moon s shadow, is the first object of inquiry.\\nThe moon, as well as the earth, is at different distances from the\\nsun at different times, and hence the length of her shadow varies,\\nbeing always greatest when she is furthest from the sun. Also,\\nsince her distance from the earth varies, the section of the moon s\\nshadow made by the earth, is greater in proportion as the moon is", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0181.jp2"}, "182": {"fulltext": "156 THE MOON.\\nnearer the earth. The greatest eclipses of the sun, therefore,\\nhappen when the sun is in apogee,* and the moon in perigee.\\n265. When the moon is at her mean distance from the earth, and\\nfrom the sun, her shadow nearly reaches the earth! s surface.\\nLet S (Fig. 55,) represent the sun, D the moon, and T the\\nearth. Then, the semi-angle of the cone of the moon s shadow,\\nDKR, will, as in the case of the earth, (Art. 247,) equal SDR\u00e2\u0080\u0094\\nDRK, of which SDR is the sun s apparent semi-diameter, as seen\\nfrom the moon, and DRK, is the sun s horizontal parallax at the\\nmoon. Since, on account of the great distance of the sun, corn-\\nFig. 55.\\nRT\\npared with that of the moon, the serni-diameter of the sun as seen\\nfrom the moon, must evidently be very nearly the same as\\nwhen seen from the earth, and since on account of the minute-\\nness of the moon s semi-diameter when seen from the sun, the\\nsun s horizontal parallax at the moon must be very small, we might,\\nwithout much error, take the sun s apparent semi-diameter from\\nthe earth, as equal to the semi-angle of the cone of the moon s\\nshadow but, for the sake of greater accuracy, let us estimate the\\nvalue of the sun s semi-diameter and horizontal parallax at the\\nmoon.\\nNow, SDR STR ST SDf 400 399 hence SDR\\nSTR=1.0025 STR and the sun s mean semi-diameter STR\\n399\\nbeing 16.025, hence SDR=1.0025x 16.025= 16.065=16 3 .9.\\nAgain, since parallax is inversely as the distance, the sun s hor-\\nizontal parallax at the moon, is on account of her being nearer the\\nsun j+f greater than at the earth but on account of her inferior\\nThe sun is said to be in apogee, when the earth is in aphelion,\\nt The apparent magnitude of an object being reciprocally as its distance from the\\neye. See Note, p. 86.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0182.jp2"}, "183": {"fulltext": "ECLIPSES. 157\\nsize it is Jfjf iess than at the earth. Hence, increasing the sun s\\nhorizontal parallax at the earth by the former fraction, and dimin-\\nishing it by the latter, we have\u00e2\u0080\u0094 X- x 9 =2 5= the sun s\\nhorizontal parallax at the moon. Therefore, the semi-angle of the\\ncone of the moon s shadow, which, as appears above, equals\\nSDR\u00e2\u0080\u0094 DRK, equals 16 3 .9-2 .5=16 1 .4, which so nearly\\nequals me sun s apparent semi-diameter, as seen from the earth,\\nthat we may adopt the latter as the value of the semi-angle of the\\nshadow. Hence, sin. 16 1 .5 1080 (BD) Rad. DK=231690.\\nBut the mean distance of the moon from the surface of the earth\\nis 238545 3956=234589, which exceeds a little the mean length\\nof the shadow as above.\\nBut when the moon is nearest the earth her distance from the\\ncenter of the earth is only 221148 miles; and when the earth is\\nfurthest from the sun, the sun s apparent semi-diameter is only\\n15 45 .5. By employing this number in the foregoing estimate,\\nwe shall find the length of the shadow 235630 miles and\\n235630-221148=14482, the distance which the moon s shadow\\nmay reach beyond the center of the earth.\\n266. The diameter of the ?noon s shadow where it traverses the\\nearth, is, at its maximum, about 170 miles*\\nIn the triangle eTK, the angle at K=15 45 .5 (Art. 265,) the\\nside Te=3956, and TK=14482.\\nOr, 3956 14482 sin. 15 45 .5 sin. 57 41 .5.\\nAnd 57 41 .5+15 45 .5=1\u00c2\u00b0 13 21 =dTe, or the arc de.\\nAnd 2Je=2\u00c2\u00b0 26 54 =erc.\\nHence 360 2.45 (=2\u00c2\u00b0 26 54 24899f 170 (nearly).\\na\\n267. The greatest portion of the earth s surface ever covered by\\nthe moon s penumbra, is about 4393 miles.\\nThe semi-angle of the penumbra B1D=BSD SBR. of which\\nBSD the sun s horizontal parallax at the moon =2 .5, and SBR\\nthe sun s apparent semi-diameter =16 3 .9, and hence BID is\\nThis supposes the conjunction to take place at the node, and the shadow to strike\\nthe earth perpendicularly to its surface where it strikes obliquely, the section may be\\ngTeater than this.\\nt The equatorial circumference.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0183.jp2"}, "184": {"fulltext": "158\\nTHE MOON.\\nknown. The moon s apparent semi-diameter BGD=16 45 .5.\\nTherefore GDT is known, as likewise DT and TG. Hence the\\nangle GTd mav be found, and the arc dQ and its double GH,\\nwhich equals the angular breadth of the penumbra. It may be\\nconverted into miles by stating a proportion as in article 266.\\nOn making the calculation it will be found to be 4393 miles.\\n268. The apparent diameter of the moon is sometimes larger\\nthan that of the sun, sometimes smaller, and sometimes exactly\\nequal to it. Suppose an observer placed on the right line which\\njoins the centers of the sun and moon if the apparent diameter of\\nthe moon is greater than that of the sun, the eclipse will be total.\\nIf the two diameters are equal, the moon s shadow just reaches the\\nearth, and the sun is hidden but for a moment from the view of\\nspectators situated in the line which the vertex of the shadow de-\\nscribes on the surface of the earth. But if, as happens when the\\nmoon comes to her conjunction in that part of her orbit which is\\ntowards her apogee, the moon s diameter is less than the sun s,\\nthen the observer will see a ring of the sun encircle the moon,\\nconstituting an annular eclipse. (Fig. 55\\nFig. 55\\n269. Eclipses of the sun are modified by the elevation of the\\nmoon above the horizon, since its apparent diameter is augmented", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0184.jp2"}, "185": {"fulltext": "ECLIPSES. 159\\nas its altitude is increased, (Art. 217.) This effect, combined with\\nthat of parallax, may so increase or diminish the apparent distance\\nbetween the centers of the sun and moon, that from this cause\\nalone, of two observers at a distance from each other, one might\\nsee an eclipse which was not visible to the other.* If the hori-\\nzontal diameter of the moon differs but little from the apparent\\ndiameter of the sun, the case might occur where the eclipse would\\nbe annular over the places where it was observed morning and\\nevening, but total where it was observed at mid-day.\\nThe earth in its diurnal revolution and the moon s shadow both\\nmove from west to east, but the shadow moves faster than the\\nearth; hence the moon overtakes the sun on its western limb and\\ncrosses it from west to east. The excess of the apparent diame-\\nter of the moon above that of the sun in a total eclipse is so small,\\nthat total darkness seldom continues longer than four minutes, and\\ncan never continue so long as eight minutes. An annular eclipse\\nmay last 12m. 24s.\\nSince the sun s ecliptic limits are more than 17\u00c2\u00b0 and the moon s\\nless than 12\u00c2\u00b0, eclipses of the sun are more frequent than those of\\nthe moon. Yet lunar eclipses being visible to every part of the\\nterrestrial hemisphere opposite to the sun, while those of the sun\\nare visible only to the small portion of the hemisphere on which\\nthe moon s shadow falls, it happens that for any particular place\\non the earth, lunar eclipses are more frequently visible than solar.\\nIn any year, the number of eclipses of both luminaries cannot be\\nless than two nor more than seven the most usual number is four,\\nand it is very rare to have more than six. A total eclipse of the\\nmoon frequently happens at the next full moon after an eclipse of\\nthe sun. For since, in an eclipse of the sun, the sun is at or near\\none of the moon s nodes, the earth s shadow must be at or near\\nthe other node, and may not have passed so far from the node as\\nthe lunar ecliptic limits, before the moon overtakes it.\\n270. It has been observed already, that were the spectator on\\nthe moon instead of on the earth, he would see the earth eclipsed\\nby the moon, and the calculation of the eclipse would be very sim-\\nilar to that of a lunar eclipse but to an observer on the earth the\\nBiot. Ast. Phvs. p. 401.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0185.jp2"}, "186": {"fulltext": "160 THE MOON.\\neclipse does not of course begin when the earth first enters the\\nmoon s shadow, and it is necessary to determine not only what\\nportion of the earth s surface will be covered by the moon s sha-\\ndow, but likewise the path described by its center relative to va-\\nrious places on the surface of the earth. This is known when the\\nlatitude and longitude of the center of the shadow on the earth, is\\ndetermined for each instant. The latitude and longitude of the\\nmoon are found on the supposition that the spectator views it from\\nthe center of the earth, whereas his position on the surface changes,\\nin consequence of parallax, both the latitude and longitude, and\\nthe amount of these changes must be accurately estimated, before\\nthe appearance of the eclipse at any particular place can be fully\\ndetermined.\\nThe details of the method of calculating a solar eclipse cannot\\nbe understood in any way so well, as by actually performing the\\nprocess according to a given example. For such details therefore\\nthe reader is referred to the Supplement,\\n271. In total eclipses of the sun, there has sometimes been ob-\\nserved a remarkable radiation of light from the margin of the sun.\\nThis has been ascribed to an illumination of the solar atmosphere,\\nbut it is with more probability owing to the zodiacal light (Art.\\n152.) which at that time is projected around the sun, and which is\\nof such dimensions as to extend far beyond the solar orb.*\\nA total eclipse of the sun is one of the most sublime and impres-\\nsive phenomena of nature. Among barbarous tribes it is ever con-\\ntemplated with fear and astonishment, while among cultivated na-\\ntions it is recognized, from the exactness with which the time of\\noccurrence and the various appearances answer to the prediction,\\nas affording one of the proudest triumphs of astronomy. By\\nastronomers themselves it is of course viewed with the highest\\ninterest, not only as verifying their calculations, but as contribu-\\nting to establish beyond all doubt the certainty of those grand\\nlaws, the truth of which is involved in the result. During the\\neclipse of June, 1806, which was one of the most remarkable on\\nSee an excellent description and delineation of this appearance as it was exhibited\\nin the eclipse of 1806, in the Transactions of the Albany Institute, by the late Chan-\\ncellor De Witt.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0186.jp2"}, "187": {"fulltext": "LONGITUDE. 161\\nrecord, the time of total darkness, as seen by the author of this\\nwork, was about mid-day. The sky was entirely cloudless, but\\nas the period of total obscuration approached, a gloom pervaded\\nall nature. When the sun was wholly lost sight of, planets and\\nstars came into view a fearful pall hung upon the sky, unlike\\nboth to night and to twilight and, the temperature of the air rap-\\nidly declining, a sudden chill came over the earth. Even the ani-\\nmal tribes exhibited tokens of fear and agitation.\\nFrom 1831 to 1838 was a period remarkable for great eclipses\\nof the sun, in which time there were no less than five of the most\\nremarkable character. The next total eclipse of the sun, visible\\nin the United States, will occur on the 7th of August, 1869.\\nCHAPTER VIII.\\nLONGITUDE TIDES.\\n272. As eclipses of the sun afford one of the most approved\\nmethods of finding the longitudes of places, our attention is natu-\\nrally turned next towards that subject.\\nThe ancients studied astronomy in order that they might read\\ntheir destinies in the stars the moderns, that they may securely\\nnavigate the ocean. A large portion of the refined labors of\\nmodern astronomy, has been directed towards perfecting the as-\\ntronomical tables with the view of finding the longitude at sea,\\nan object manifestly worthy of the highest efforts of science, con-\\nsidering the vast amount of property and of human life involved\\nin navigation.\\n273. The difference of longitude between two places may be found\\nby any method, by which we can ascertain the difference of their local\\ntimes, at the same instant of absolute time.\\nAs the earth turns on its axis from west to east, any place that\\nlies eastward of another will come sooner under the sun, or will\\n21", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0187.jp2"}, "188": {"fulltext": "162 THE MOON.\\nhave the sun earlier on the meridian, and consequently, in respect\\nto the hour of the day, will be in advance of the other at the\\nrate of one hour for every 15\u00c2\u00b0, or four minutes of time for each\\ndegree. Thus, to a place 15\u00c2\u00b0 east of Greenwich, it is 1 o clock,\\nP. M. when it is noon at Greenwich; and to a place 15\u00c2\u00b0 west of\\nthat meridian, it is 11 o clock, A. M. at the same instant. Hence,\\nthe difference of time at any two places, indicates their difference\\nof longitude.\\n274. The easiest method of finding the longitude is by means\\nof an accurate time piece, or chronometer. Let us set out from\\nLondon with a chronometer accurately adjusted to Greenwich\\ntime, and travel eastward to a certain place, where the time is\\naccurately kept, or may be ascertained by observation. We find,\\nfor example, that it is 1 o clock by our chronometer, when it is\\n2 o clock and 30 minutes at the place of observation. Hence,\\nthe longitude is 15x1.5=221\u00c2\u00b0 E. Had we travelled westward\\nuntil our chronometer was an hour and a half in advance of the\\ntime at the place of observation, (that is, so much later in the\\nday,) our longitude would have been 22^\u00c2\u00b0 W. But it would not\\nbe necessary to repair to London in order to set our chronometer\\nto Greenwich time. This might be done at any observatory, or\\nany place whose longitude had been accurately determined. For\\nexample, the time at New York is 4h. 56m. 4 S .5 behind that of\\nGreenwich. If, therefore, we set our chronometer so much be-\\nfore the true time at New York, it will indicate the time at Green-\\nwich. Moreover, on arriving at different places, any where on\\nthe earth, whose longitude is accurately known, we may learn\\nwhether our chronometer keeps accurate time or not, and if not,\\nthe amount of its error. Chronometers have been constructed of\\nsuch an astonishing degree of accuracy, as to deviate but a few\\nseconds in a voyage from London to Baffin s Bay and back, during\\nan absence of several years. But chronometers which are suffi-\\nciently accurate to be depended on for long voyages, are too ex-\\npensive for general use, and the means of verifying their accuracy\\nare not sufficiently easy. Moreover, chronometers by being trans-\\nported from one place to another, change their daily rate, oi de-\\npart from that mean rate which they preserve at a fixed station.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0188.jp2"}, "189": {"fulltext": "LONGITUDE. 163\\nA chronometer, therefore,, cannot be relied on for determining the\\nlongitudes of places where the greatest degree of accuracy is re-\\nquired, especially where the instrument is conveyed over land,\\nalthough the uncertainty attendant on one instrument may be\\nnearly obviated by employing several and taking their mean\\nresults.*\\n275. Eclipses of the sun and moon are sometimes used for de-\\ntermining the longitude. The exact instant of immersion or of\\nemersion, or any other definite moment of the eclipse which pre-\\nsents itself to two distant observers, affords the means of com-\\nparing their difference of time, and hence of determining their\\ndifference of longitude. Since the entrance of the moon into\\nthe earth s shadow, in a lunar eclipse, is seen at the same instant\\nof absolute time at all places where the eclipse is visible, (Art.\\n262,) this observation would be a very suitable one for finding\\nthe longitude were it not that, on account of the increasing dark-\\nness of the penumbra near the boundaries of the shadow, it is\\ndifficult to determine the precise instant when the moon enters the\\nshadow. By taking observations on the immersions of known\\nspots on the lunar disk, a mean result may be obtained which will\\ngive the longitude with tolerable accuracy. In an eclipse of the\\nsun, the instants of immersion and emersion may be observed with\\ngreater accuracy, although, since these do not take place at the\\nsame instant of absolute time, the calculation of the longitude from\\nobservations on a solar eclipse are complicated and laborious.\\nA method very similar to the foregoing, by observations on\\neclipses of Jupiter s satellites, and on occultations of stars, will\\nbe mentioned hereafter.\\n276. The Lunar method of finding the longitude, at sea, is m\\nmany respects preferable to every other. It consists in measuring\\n(with a sextant) the angular distance between the moon and the\\nsun, or between the moon and a star, and then turning to the Nau-\\ntical Almanac,f and finding what time it was at Greenwich when\\nWoodhouse, p. 838.\\nt The Nautical Almanac is a book published annually by the British Board of\\nLongitude, containing various tables and astronomical information for the use of", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0189.jp2"}, "190": {"fulltext": "164 the Moorr.\\nthat distance was the same. The moon moves so rapidly, that this\\ndistance will not be the same except at very nearly the same in-\\nstant of absolute time. For example, at 9 o clock, A. M., at a cer-\\ntain place, we find the angular distance of the moon and the sun to\\nbe 72\u00c2\u00b0 and on looking into the Nautical Almanac, we find that\\nat the time when this distance was the same for the meridian of\\nGreenwich was 1 o clock, P. M. hence we infer that the longi-\\ntude of the place is four hours, or 60\u00c2\u00b0 west.\\nThe Nautical Almanac contains the true angular distance of\\nthe moon from the sun, from the four large planets, (Venus, Mars,\\nJupiter, and Saturn,) and from nine bright fixed stars, for the be-\\nginning of every third hour of mean time for the meridian of\\nGreenwich and the mean time corresponding to any intermediate\\nhour, may be found by proportional parts.*\\n277. It would be a very simple operation to determine the lon-\\ngitude by Lunar Distances, if the process as described in the\\npreceding article were all that is necessary but the various cir-\\ncumstances of parallax, refraction, and dip of the horizon, would\\ndiffer more or less at the two places, even were the bodies whose\\ndistances were taken in view from both, which is not necessarily\\nthe case. The observations, therefore, require to be reduced to\\nthe center of the earth, being cleared of the effects of parallax and\\nrefraction. Hence, three observers are necessary in order to take\\na lunar distance in the most exact manner, viz. two to measure\\nthe altitudes of the two bodies respectively, at the same time that\\nthe third takes the angular distance between them. The altitudes\\nof the two luminaries at the time of observation must be known,\\nin order to estimate the effects of parallax and refraction.\\n278. Although the lunar method of finding the longitude at\\nsea has many advantages over the other methods in use, yet it\\nnavigators. The American Almanac also contains a variety of astronomical informa-\\ntion, peculiarly interesting to the people of the United States, in connexion with a\\nvast amount of statistical matter. It is well deserving a place in the library of the\\nstudent.\\nSee Bow ditch s Navigator, Tenth Ed. p. 226.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0190.jp2"}, "191": {"fulltext": "TIDES. 165\\nhas also its disadvantages. One is, the great exactness requisite\\nin observing the distance of the moon from the sun or star, as a\\nsmall error in the distance makes a considerable error in the longi-\\ntude. The moon moves at the rate of about a degree in two\\nhours, or one minute of space in two minutes of time. There-\\nfore, if we make an error of one minute in observing the distance,\\nwe make an error of two minutes in time, or 30 miles of longitude\\nat the equator. A single observation with the best sextants, may\\nbe liable to an error of more than half a minute but the accuracy\\nof the result may be much increased by a mean of several obser-\\nvations taken to the east and west of the moon. The imperfection\\nof lunar tables was until recently considered as an objection to this\\nmethod. Until within a few years, the best lunar tables were\\nfrequently erroneous to the amount of one minute, occasioning an\\nerror of 30 miles. The error of the best tables now in use will\\nrarely exceed 7 or 8 seconds.*\\nTIDES.\\n279. The tides are an alternate rising and falling of the waters\\nof the ocean, at regular intervals. They have a maximum and a\\nminimum twice a day, twice a month, and twice a year. Of the\\ndaily tide, the maximum is called High tide, and the minimum\\nLow tide. The maximum for the month is called Spring tide, and\\nthe minimum Neap tide. The rising of the tide is called Flood\\nand its falling Ebb tide.\\nSimilar tides, whether high or low, occur on opposite sides of\\nthe earth at once. Thus at the same time it is high tide at any\\ngiven place, it is also high tide on the inferior meridian, and the\\nsame is true of the low tides.\\nThe interval between two successive high tides is 12h. 25m.\\nor, if the same tide be considered as returning to the meridian,\\nafter having gone around the globe, its return is about 50 minutes\\nlater than it occurred on the preceding day. In this respect, as\\nwell as in various others, it corresponds very nearly to the motions\\nof the moon.\\nBrinkley s Elements of Astronomy, p. 241.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0191.jp2"}, "192": {"fulltext": "166 THE MOON.\\nThe average height for the whole globe is about 2^ feet or,\\nif the earth were covered uniformly with a stratum of water, the\\ndifference between the two diameters of the oval would be 5 feet,\\nor more exactly 5 feet and 8 inches but its natural height at\\nvarious places is very various, sometimes rising to 60 or 70 feet,\\nand sometimes being scarcely perceptible. At the same place\\nalso the phenomena of the tides are very different at different\\ntimes.\\nInland lakes and seas, even those of the largest class, as Lake\\nSuperior, or the Caspian, have no perceptible tide.\\n280. Tides are caused by the unequal attraction of the sun and\\nmoon upon different parts of the earth.\\nSuppose the projectile force by which the earth is carried for-\\nward in her orbit, to be suspended, and the earth to fall towards\\none of these bodies, the moon, for example, in consequence of\\ntheir mutual attraction. Then, if all parts of the earth fell\\nequally towards the moon, no derangement of its different parts\\nwould result, any more than of the particles of a drop of watei\\nin its descent to the ground. But if one part fell faster than an-\\nother, the different portions would evidently be separated from\\neach other. Now this is precisely what takes place with respect\\nto the earth in its fall towards the moon. The portions of the\\nearth in the hemisphere next to the moon, on account of being\\nnearer to the center of attraction, fall faster than those in the op-\\nposite hemisphere, and consequently leave them behind. The\\nsolid earth, on account of its cohesion, cannot obey this impulse,\\nsince all its different portions constitute one mass, which, is acted\\non in the same manner as though it were all collected in the cen-\\nter but the waters on the surface, moving freely under this im-\\npulse, endeavor to desert the solid mass and fall towards the\\nmoon. For a similar reason the waters in the opposite hemisphere\\nfalling less towards the moon than the solid earth, are left behind,\\nor appear to rise from the center of the earth.\\n281. Let DEFG (Fig. 56,) represent the globe and, for the sake\\nof illustrating the principle, we will suppose the waters entirely to\\ncover the globe at a uniform depth. Let defg represent the solid", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0192.jp2"}, "193": {"fulltext": "TIDES.\\n167\\nglobe, and the circular ring exterior to\\nit, the covering of waters. Let C be\\nthe center of gravity of the solid mass,\\nA that of the hemisphere next to the\\nmoon, and B that of the remoter hemi-\\nsphere. Now the force of attraction\\nexerted by the moon, acts in the same\\nmanner as though the solid mass were\\nall concentrated in C, and the waters\\nof each hemisphere at A and B respec-\\ntively and (the moon being supposed above E) it is evident that\\nA w T ill tend to leave C, and C to leave B behind. The same must\\nevidently be true of the respective portions of matter, of which\\nthese points are the centers of gravity. The waters of the globe\\nwill thus be reduced to an oval shape, being elongated in the direc-\\ntion of that meridian which is under the moon, and flattened in\\nthe intermediate parts, and most of all at points ninety degrees dis-\\ntant from that meridian.\\nWere it not, therefore, for impediments which prevent the force\\nfrom producing its full effects, we might expect to see the great\\ntide- wave, as the elevated crest is called, always directly beneath\\nthe moon, attending it regularly around the globe. But the in-\\nertia of the waters prevents their instantly obeying the moon s\\nattraction, and the friction of the waters on the bottom of the\\nocean, still further retards its progress. It is not therefore until\\nseveral hours (differing at different places) after the moon has\\npassed the meridian of a place, that it is high tide at that place.\\n282. The sun has a similar action to the moon, but only one\\nthird as great. On account of the great mass of the sun com-\\npared with that of the moon, we might suppose that his action\\nin raising the tides would be greater than the moon s but the\\nnearness of the moon to the earth more than compensates for\\nthe sun s greater quantity of matter. Let us, however, form a\\njust conception of the advantage which the moon derives from her\\nproximity. It is not that her actual amount of attraction is thus\\nrendered greater than that of the sun but it is that her attraction\\nfor the different parts of the earth is very unequal, while that of", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0193.jp2"}, "194": {"fulltext": "168 THE MOON.\\nthe sun is nearly uniform. It is the inequality of this action, and\\nnot the absolute force, that produces the tides. The diameter of\\nthe earth is of the distance of the moon, while it is less than\\nro oo o of the distance of the sun.\\n283. Having now learned the general cause of the tides, we\\nwill next attend to the explanation of particular phenomena.\\nThe Spring tides or those which rise to an unusual height\\ntwice a month, are produced by the sun and moon s acting to-\\ngether and the Neap tides, or those which are unusually low\\ntwice a month, are produced by the sun and moon s acting in\\nopposition to each other. The Spring tides occur at the syzygies\\nthe Neap tides at the quadratures. At the time of new moon,\\nthe sun and moon both being on the same side of the earth, and\\nacting upon it in the same line, their actions conspire, and the\\nsun may be considered as adding so much to the force of the\\nmoon. We have already explained ho\\\\v the moon contributes to\\nraise a tide on the opposite side of the earth. But the sun as well\\nas the moon raises its own tide-wave, which, at new moon, coin-\\ncides with the lunar tide-wave. At full moon, also, the two lumina-\\nries conspire in the same way to raise the tide for we must recol-\\nlect that each body contributes to raise the tide on the opposite\\nside of the earth as well as on the side nearest to it. At both the\\nconjunctions and oppositions, therefore, that is, at the syzygies,\\nwe have unusually high tides. But here also the maximum effect\\nis not at the moment of the syzygies, but 36 hours afterwards.\\nAt the quadratures, the solar wave is lowest where the lunar\\nwave is highest hence the low tide produced by the sun is sub-\\ntracted from high water and produces the Neap tides. Moreover,\\nat the quadratures the solar wave is highest where the lunar wave\\nis lowest, and hence is to be added to the height of low water at\\nthe time of Neap tides. Hence the difference between high and\\nlow water is only about half as great at Neap tide as at Spring tide.\\n284. The power of the moon or of the sun to raise the tide is\\nfound by the doctrine of universal gravitation to be inversely as\\nthe cube of the distance* The variations of distance in the sun are\\nLa Place, Syst. du Monde, 1. iv, c. x.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0194.jp2"}, "195": {"fulltext": "TIDES.\\n169\\nnot great enough to influence the tides very materially, but the\\nvariations in the moon s distances have a striking effect. The\\ntides which happen when the moon is in perigee, are considerably\\ngreater than when she is in apogee and if she happens to be in\\nperigee at the time of the syzygies, the spring tide is unusually\\nhigh. When this happens at the equinoxes, the highest tides of\\nthe year are produced.\\n285. The declinations of the sun and moon have a considerable\\ninfluence on the height of the tide. When the moon, for example,\\nhas no declination, or is in the equator, as in figure 57,* the rota-\\ntion of the earth on its axis NS will make the two tides exactly\\nequal on opposite sides of the earth. Thus a place which is car-\\nried through the parallel TT will have the height of one tide T2\\nand the other tide T 3. The tides are in this case greatest at the\\nequator, and diminish gradually to the poles, where it will be low\\nwater during the whole day. When the moon is on the north side\\nof the equator, as in figure 58, at her greatest northern declination,\\nFig. 57. Fig. 58.\\na place describing the parallel TT will have T 3 for the height of\\nthe tide when the moon is on the superior meridian, and T2 for\\nthe height when the moon is on the inferior meridian. Therefore,\\nall places north of the equator will have the highest tide when the\\nmoon is above the horizon, and the lowest when she is below it\\nthe difference of the tides diminishing towards the equator, where\\nDiagrams like these are apt to mislead the learner, hy exhibiting the protuberance\\noccasioned by the tides as much greater than the reality. We must recollect that it\\namounts, at the highest, to only a very few feet in eight thousand miles. Were the\\ndiagram, therefore, drawn in just proportions, the alterations of figure produced by the\\ntides would be wholly insensible.\\n22", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0195.jp2"}, "196": {"fulltext": "170 THE MOON.\\nthey are equal. In like manner, places south of the equator have\\nthe highest tides when the moon is below the horizon, and the\\nlowest when she is above it. When the moon is at her greatest\\ndeclination, the highest tides will take place towards the tropics.\\nThe circumstances are all reversed when the moon is south of the\\nequator.*\\n286. The motion of the tide-wave, it should be remarked, is not\\na progressive motion, but a mere undulation, and is to be carefully\\ndistinguished from the currents to which it gives rise. If the\\nocean completely covered the earth, the sun and moon being in the\\nequator, the tide-wave would travel at the same rate as the earth\\non its axis. Indeed, the correct way of conceiving of the tide-\\nwave, is to consider the moon at rest, and the earth in its rotation\\nfrom west to east as bringing successive portions of water under\\nthe moon, which portions being elevated successively at the same\\nrate as the earth revolves on its axis, have a relative motion west-\\nward in the same degree.\\n287. The tides of rivers, narrow bays, and shores far from the\\nmain body of the ocean, are not produced in those places by the\\ndirect action of the sun and moon, but are subordinate waves\\npropagated from the great tide-wave.\\nLines drawn through all the adjacent parts of any tract of wa-\\nter, which have high water at the same time, are called cotidal\\nlines. -f We may, for instance, draw a line through all places in\\nthe Atlantic Ocean which have high tide on a given clay at 1 o clock,\\nand another through all places which have high tide at 2 o clock.\\nThe cotidal line for any hour may be considered as representing\\nthe summit or ridge of the tide-wave at that time and could the\\nspectator, detached from the earth, perceive the summit of the\\nwave, he would see it travelling round the earth in the open ocean\\nonce in twenty four hours, followed by another twelve hours dis-\\ntant, and both sending branches into rivers, bays, and other open-\\nings into the main land. These latter are called Derivative tides,\\nEd m. Encyc. Art. Astronomy, p. 623.\\nt Whewell, Phil. Transaction for 1833, p. 148.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0196.jp2"}, "197": {"fulltext": "TIDES.\\n171\\nwhile those raised directly oy the action of the sun and moon, are\\ncalled Primitive tides.\\n288. The velocity with which the wave moves will depend on\\nvarious circumstances, but principally on the depth, and probably\\non the regularity of the channel. If the depth be nearly uniform,\\nthe cotidal lines will be nearly straight and parallel. But if some\\nparts of the channel are deep while others are shallow, the tide\\nwill be detained by the greater friction of the shallow places, and\\nthe cotidal lines will be irregular. The direction also of the de-\\nrivative tide, may be totally different from that of the prim live.\\nThus, (Fig. 59,) if the great tide-\\nwave, moving from east to west,\\nbe represented by the lines 1, 2,\\n3, 4, the derivative tide which is\\npropagated up a river or bay,\\nwill be represented by the cotidal\\nlines 3, 4, 5, 6, 7. Advancing\\nfaster in the channel than next\\nthe banks, the tides will lag be-\\nhind towards the shores, and the\\ncotidal lines will take the form\\nof curves as represented in the\\ndiagram.\\nFig. 59.\\n289. On account of the retarding influence of shoals, and an\\nuneven, indented coast, the tide-wave travels more slowly along\\nthe shores of an island than in the neighboring sea, assuming con-\\nvex figures at a little distance from the island and on opposite\\nsides of it. These convex lines sometimes meet and become\\nblended in such a manner as to create singular anomalies in a sea\\nmuch broken by islands, as well as on coasts indented with numer-\\nous bays and rivers.* Peculiar phenomena are also produced,\\nwhen the tide flows in at opposite extremities of a reef or island,\\nas into the two opposite ends of Long Island Sound. In certain\\nSee an excellent representation and description of these different phenomena by\\nProfessor Whewell, Phil. Trans. 1833, p. 153.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0197.jp2"}, "198": {"fulltext": "172 THE MOON.\\ncases a tide-wave is forced into a narrow arm of the sea, and\\nproduces very remarkable tides. The tides of the Bay of Fundy\\n(the highest in the world) sometimes rise to the height of 60 or 70\\nfeet and the tides of the river Severn, near Bristol in England,\\nrise to the height of 40 feet.\\n290. The Unit of Altitude of any place, is the height of the\\nmaximum tide after the syzygies, (Art. 283,) being usually about\\n36 hours after the new or full moon. But as the amount of this\\ntide would be affected by the distance of the sun and moon from\\nthe earth, (Art. 284,) and by their declinations, (Art. 285,) these\\ndistances are taken at their mean value, and the luminaries are\\nsupposed to be in the equator the observations being so reduced\\nas to conform to these circumstances. The unit of altitude can be\\nascertained by observation only. The actual rise of the tide de-\\npends much on the strength and direction of the wind. When\\nhigh winds conspire with a high flood tide, as is frequently the\\ncase near the equinoxes, the tide rises to a very unusual height.\\nWe subjoin from the American Almanac a few examples of the\\nunit of altitude for different places.\\nCumberland, head of the Bay of\\nFundy,\\n71\\nBoston,\\nm\\nNew Haven,\\n8\\nNew York,\\n5\\nCharleston, S. C,\\n6\\n291. The Establishment of any port is the mean interval between\\nnoon and the time of high water, on the day of new or full moon.\\nAs the interval for any given place is always nearly the same, it\\nbecomes a criterion of the retardation of the tides at that place.\\nOn account of the importance to navigation of a correct know-\\nledge of the tides, the British Board of Admiralty, at the sugges-\\ntion of the Royal Society, recently issued orders to their agents\\nin various important naval stations, to have accurate observations\\nmade on the tides, with the view of ascertaining the establishment\\nand various other particulars respecting each station;* and the\\nLubbock, Report on the Tides, 1833.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0198.jp2"}, "199": {"fulltext": "TIDES. 173\\ngovernment of the United States is prosecuting similar investiga-\\ntions respecting our own ports.\\n292. According to Professor Whewell,* the tides on the coast\\nof North America are derived from the great tide-wave of the\\nSouth Atlantic, which runs steadily northward along the coast to\\nthe mouth of the Bay of Fundy, where it meets the northern tide\\nwave flowing in the opposite direction. Hence he accounts for\\nthe high tides of the Bay of Fundy.\\n293. The largest lakes and inland seas have no perceptible\\ntides. This is asserted by all writers respecting the Caspian and\\nEuxine, and the same is found to be true of the largest of the\\nNorth American lakes, Lake Superior.f\\nAlthough these several tracts of water appear large when taken\\nby themselves, yet they occupy but small portions of the surface\\nof the globe, as will appear evident from the delineation of them\\non an artificial globe. Now we must recollect that the primitive\\ntides are produced by the unequal action of the sun and moon\\nupon the different parts of the earth and that it is only at points\\nwhose distance from each other bears a considerable ratio to the\\nwhole distance of the sun or the moon, that the inequality of ac-\\ntion becomes manifest. The space required is larger than either\\nof these tracts of water. It is obvious also that they have no op-\\nportunity to be subject to a derivative tide.\\n294. To apply the theory of universal gravitation to all the va-\\nrying circumstances that influence the tides, becomes a matter of\\nsuch intricacy, that La Place pronounces the problem of the\\ntides the most difficult problem of celestial mechanics.\\n295. The Atmosphere that envelops the earth, must evidently be\\nsubject to the action of the same forces as the covering of waters,\\nand hence we might expect a rise and fall of the barometer, indi-\\ncating an atmospheric tide corresponding to the tide of the ocean,\\nPhil. Trans. 1833, p. 172.\\nt See Experiments of Gov. Cass, Am. Jour. Science.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0199.jp2"}, "200": {"fulltext": "174 THE PLANETS.\\nLa Place has calculated the amount of this aerial tide. It is too\\ninconsiderable to be detected by changes in the barometer, unless\\nby the most refined observations. Hence it is concluded, that\\nthe fluctuations produced by this cause are too slight to affect\\nmeteorological phenomena in any appreciable degree.*\\nCHAPTER IX.\\nOF THE PLANETS INFERIOR PLANETS, MERCURY AND VENUS.\\n296. The name planet signifies a wanderer,^ and is applied to\\nthis class of bodies because they shift their positions in the\\nheavens, whereas the fixed stars apparently always maintain the\\nsame places with respect to each other. The planets known\\nfrom a high antiquity, are Mercury, Venus, Earth, Mars, Jupi-\\nter, and Saturn. To these, in 1781, was added Uranus, J (or\\nUerschel, as it was formerly called, from the name of its discov-\\nerer,) and, as late as 1846, another large planet, Neptune, was\\nadded to the list, making eight in all of the regular series. Be-\\nsides these, there are found between Mars and Jupiter, a remarka-\\nble group of small planets, called Asteroids, numbering at present\\ntwenty-six. Of these, four, Ceres, Pallas, Juno, and Vesta, were\\ndiscovered near the commencement of the present century and\\nthe remaining twenty-two, Astrea, Hebe, Iris, Flora, Metis,\\nHygeia, Parthenope, Victoria, Egeria, Irene, Eunomia, Pysche,\\nThetis, Melpomene, Fortuna, Massalia, Lutetia, Calliope, Thalia,\\nThemis, Phocea, and Proserpina, have been discovered since the\\nyear 1845.\\nThe foregoing are called primary planets. Several of these\\nhave one or more attendants, or satellites, which revolve around\\nthem as they revolve around the sun. The Earth has one sat-\\nellite, namely, the moon Jupiter has four Saturn, eight Ura-\\nBowditch s La Place, IL 191. From, the Greek, nXav^-nj s.\\nFrom Ovpavou", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0200.jp2"}, "201": {"fulltext": "DISTANCES FROM THE SUN. 175\\nnus, six and Neptune, one. These bodies also are planets, but\\nin distinction from the others they are called secondary planets.\\nIt appears, therefore, that the whole number of planets known\\nat present are 54, viz., 8 primary, 20 secondary, and 26\\nasteroids.\\n297. The primary planets all (with the exception of the as-\\nteroids) have their orbits nearly in the same plane, and are never\\nseen far from the ecliptic. Mercury, whose orbit is most inclined\\nof all, never departs further from the ecliptic than about 7\u00c2\u00b0, while\\nmost of the other planets pursue very nearly the same path with\\nthe earth, in their annual revolution around the sun. The aste-\\nroids, however, make wider excursions from the plane of the\\necliptic, amounting, in the case of Pallas, to 34^-\u00c2\u00b0.\\n298. Mercury and Venus are called inferior planets, because\\ntheir orbits are nearer to the sun than that of the earth while\\nall the others being more distant from the sun than the earth,\\nare called superior planets. The planets present great diver-\\nsities among themselves in respect to distance from the sun, mag-\\nnitude, time of revolution, and density. They differ also in\\nregard to satellites, of which, as we have seen, the Earth and\\nNeptune have each one, Jupiter has four, Saturn eight, and\\nUranus six while Mercury, Venus, and Mars, have none at all.\\nIt will aid the memory, and render our view of the planetary\\nsystem more clear and comprehensive, if we classify, as far as\\npossible, the various particulars comprehended under the fore-\\ngoing heads.\\n299. DISTANCES FROM THE SUN.f\\n1. Mercury, 37,000,000 0.3870981\\n2. Venus, 68,000,000 0.7233316\\nRespecting the number of satellites belonging to Uranus, there is some doubt,\\nwhich will be considered under the history of that planet.\\nThe distances in miles, as expressed in the first column, are to be treasured\\nup in the memory, while the second column expresses the relative distance, that of\\nthe Earth being 1, from which a more exact determination may be made when re-\\nquired, the Earth s distance being taken at 95,298,260 miles.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0201.jp2"}, "202": {"fulltext": "176 THE PLANETS.\\n3. Earth, 95,000,000 1.0000000\\n4. Mars, 145,000,000 1.5236923\\n5. Asteroids, 250,000,000 2.6612885\\n6. Jupiter, 495,000,000 5.2027760\\n7. Saturn, 900,000,000 9.5387861\\n8. Uranus, 1,800,000,000 19.1823900\\n9. Neptune, 2,800,000,000 30.0318000\\nThe dimensions of the planetary system are seen from this\\ntable to be vast, comprehending a circular space nearly six\\nthousand millions of miles in diameter. A railway car, travelling\\nnight and day at the rate of 20 miles an hour, and of course\\nmaking 480 miles a day, would require about 50 days to travel\\nround the Earth on a great circle, and about 500 days to reach\\nthe moon but it will give some idea of the vastness of the\\nplanetary spaces to reflect, that setting out from the sun, and\\ntravelling from planet to planet at the same rate, to reach Mer-\\ncury would require about 200 years Venus, nearly 400 the\\nEarth, 542 Mars, more than 800 Jupiter, towards 3,000 Sat-\\nurn, above 5,000; Uranus, 10,000 Neptune, more than 16,000\\nand to cross the entire orbit of Neptune would require upwards\\nof 32,000 years.\\nIt may aid the memory to remark, that in regard to the plan-\\nets nearest the sun, the distances increase in an arithmetical\\nratio, while those most remote increase in a geometrical ratio.\\nThus, if we add 30 to the distance of Mercury, it gives us\\nnearly that of Venus 30 more gives that of the Earth while\\nSaturn is nearly twice the distance of Jupiter, and Uranus twice\\nthat of Saturn. If this, however, were a perfectly correct rule,\\nNeptune would be twice as far from the sun as Uranus, and\\ntherefore 3,600 millions of miles, whereas its actual distance is\\nshort of 3,000 millions. Between the orbits of Mars and Jupi-\\nter a great chasm appeared, which broke the continuity; but\\nthe discovery of the Asteroids has filled the void. A more exact\\nlaw of the series is that called Bodes law. It is as follows if\\nwe represent the distance of Mercury by 4, and increase the fol-\\nlowing terms by the product of 3 into the ascending powers of 2,\\nwe shall obtain the relative distances of the planets from the\\nsun. Thus,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0202.jp2"}, "203": {"fulltext": "i\\nM.\\n\\\\GNITUDES.\\nMercury, 4\\n4\\nVenus,\\n4+3.2\u00c2\u00b0\\n7\\nEarth,\\n4 3.2 1\\n10\\nMars,\\n4 3.2 2\\n16\\nCeres,\\n4 3.2 3\\n28\\nJupiter,\\n4+3.2 4\\n52\\nSaturn,\\n4+3.2 5\\n=100\\nUranus,\\n4 3.2 6\\n19.6\\nNeptune,\\n4+3.2 7\\n388\\nFor example, b\\ny this\\nlaw,\\nthe distances of the\\nearth an\\n177\\nter are to each other as 10 to 52. Their actual distances, as\\ngiven in the table, (Art. 299,) are as 1 to 5.202776, which num-\\nbers are nearly as 10 to 52.\\nThe mean distances of the planets from the sun, may also be\\ndetermined by Kepler s law, that the squares of the periodic\\ntimes are as the cubes of the distances, (Art. 192.) Thus the\\nearth s distance being previously ascertained by means of the\\nsun s horizontal parallax, (Art. 87,) and the period of any other\\nplanet as Jupiter, being learned from observation, we may say as\\nthe square of the earth s period (365.256 days) is to the square\\nof Jupiter s period, (4332.586 days,) so is the cube of 1 year to\\nthe cube of Jupiter s period, the cube root of which will be the\\nperiod itself. Or, to express the same truth more concisely,\\n365.256 2 4332.586 2 I s 5.202 3\\nJ00. MAGNITUDES.\\nDiameter Mean apparent\\nin Miles. Diameter.\\nMass. Volume,\\nMercury,\\n2950* 8\\n4,865,75 If iV\\nVenus,\\n7800 17\\n401,839 t 9 q\\nEarth,\\n7912\\n389,551 1\\nMars,\\n4500 6\\n2,680,337\\nCeres,\\n160 0 .5\\nJupiter,\\n89000 37\\n1,048 1400\\nSaturn,\\n79000 16\\n3,502 1000*\\nUranus\\n35000 4\\n24,905 86\\nNeptune\\n31000* 2 .5\\n18,780 60\\nHind.\\nf Herschel. The num\\n)ers of this column express\\nthe denominators of frao-\\ntions, of which the numerator is 1, denoting the suris mass.\\n23", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0203.jp2"}, "204": {"fulltext": "178 THE PLANETS.\\nDiagrams and orreries, as usually constructed, wholly fail of\\ngiving any just conceptions of the distances of the planets from\\nthe sun and from each other. If we represent, for instance, the\\ndistance of the earth by 1 foot, we shall require 30 feet in order\\nto reach the place of Neptune and when we have constructed\\na diagram on so enlarged a scale, we must still bear in mind that\\neach foot represents a space of nearly 100 millions of miles.*\\nWe remark here a great diversity in regard to magnitude a\\ndiversity which does not appear to be subject to any definite\\nlaw. While Venus, an inferior planet, is nine-tenths as large\\nas the earth, Mars, a superior planet, is only one-sixth, while\\nJupiter is fourteen hundred times as large. Although sev-\\neral of the planets, when nearest to us, appear brilliant and\\nlarge when compared with the fixed stars, yet the angle which\\nthey subtend is very small, that of Venus, the greatest of all,\\nnever exceeding about 1 or more exactly 61 .2, and that of\\nJupiter, when greatest, being only about f of a minute.\\nThe distance of one of the near planets, as Venus or Mars,\\nmay be determined from its parallax and the distance being\\nknown, its real diameter can be estimated from its apparent\\ndiameter, in the same manner as we estimate the diameter of the\\nsun. (Art. 145.)\\n301.\\nPERIODIC TIMES.\\nSidereal revolution.\\nMean daily motion.\\nMercury,\\n3 months\\nor\\n88 days,\\n4\u00c2\u00b0\\n5 32 .6\\nVenus,\\n1 2\\n(C\\nu\\n224\\na\\n1\u00c2\u00b0\\n36 7 .8\\nEarth,\\n1 year,\\na\\n365\\na\\n0\u00c2\u00b0\\n59 8 .3\\nMars,\\n2\\n687\\na\\n0\u00c2\u00b0\\n31 26 .7\\nCeres,\\n4J\\n1687\\n0\u00c2\u00b0\\n12 50 .9\\nJupiter,\\n12\\nu\\n4332\\na\\n0\u00c2\u00b0\\n4 59 .3\\nSaturn,\\n29\\nit\\nk\\n10759\\na\\n0\u00c2\u00b0\\n2 0 .6\\nUranus,\\n84\\net\\nc\\n30686\\na\\n0\u00c2\u00b0\\n0 42 .4\\nNeptune,\\n164J\\n(C\\n60127\\nit\\n0\u00c2\u00b0\\n0 21 .5\\nFor the purposes of illustration to a class or to a popular audience, the follow-\\ning plan of representation is recommended, not only for the entire solar system, but\\nfor each of the subordinate systems, as that of Jupiter or of Saturn. Procure a\\nfew sheets of black paper cut it into strips a foot wide, and paste them to-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0204.jp2"}, "205": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 170\\nFrom this view it appears that the planets nearest the sun\\nmove most rapidly. Thus Mercury performs nearly 350 revolu-\\ntions while Uranus performs one. This is evidently not owing\\nmerely to the greater dimensions of the orbit of Uranus, for the\\nlength of its orbit is not 50 times that of the orbit of Mercury,\\nwhile the time employed in describing it is 350 times that of\\nMercury. Indeed, this ought to follow from Kepler s law, that\\nthe squares of the periodic times are as the cubes of the distan-\\nces from which it is manifest that the times of revolution in-\\ncrease faster than the dimensions of the orbit. Accordingly, the\\napparent progress of the most distant planets is exceedingly slow,\\nthe rate of Uranus being only 42 4 per day so that for weeks\\nand months, and even years, this planet but slightly changes its\\nplace among the stars.\\nThe planets are divided into two classes, first, the inferior,\\nwhich have their orbits nearer to the sun than that of the earth\\nand secondly, the superior, which have their orbits exterior to\\nthe earth s orbit.\\nTHE INFERIOR PLANETS, MERCURY AND VENUS.\\n302. The inferior planets, Mercury and Venus, having their\\norbits far within that of the earth, appear to us as attendants\\nupon the sun. Mercury never appears further from the sun than\\n29\u00c2\u00b0, (28\u00c2\u00b0 48 and seldom so far and Venus never more than\\nabout 47\u00c2\u00b0, (47\u00c2\u00b0 12 Both planets, therefore, appear either in\\nthe west soon after sunset, or in the east a little before sunrise.\\nIn high latitudes, where the twilight is prolonged, Mercury can\\nseldom be seen with the naked eye, and then only at the periods\\nof its greatest elongation.* The reason of this will readily ap-\\npear from the following diagram.\\ngether, so as to form a continuous sheet. For the solar system, this may be about\\n30 feet long. Cut out of white paper figures representing the sun and each of the\\nplanets, (and, if desired, each of the satellites,) which paste on the long sheet at\\ndistances corresponding to their respective ratios, that of the Earth being 1. This\\nenlarged diagram may be exhibited on a wall, or on a base made of boards ex-\\ntended along in a line with each other, and hung upon a wall.\\nCopernicus is said to have lamented on his death-bed that he had never been\\nable to obtain a sight of Mercury, and Delambre, a great French astronomer, saw\\nit but twice.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0205.jp2"}, "206": {"fulltext": "180\\nTHE PLANETS.\\nLet S represent the sun, E the earth, and MN Mercury at\\nits greatest elongations from the sun, and OZP a portion of the\\nsky. Then, since we refer all distant bodies to the same concave\\nsphere of the heavens, we should see the sun at Z, and Mercury\\nat O, when at its greatest eastern elongation, and at P when at\\nits greatest western elongation and while passing from M to N\\nthrough Q, it would appear to describe the arc OP and while\\npassing from N to M through R, it would appear to run back\\nacross the sun on the same arc. It is further evident, that it\\nwould be visible only when at or near one of its greatest elonga-\\ntions being at all other times so near the sun as to be lost in\\nhis light.\\nFig. 60.\\n303. A planet is said to be in conjunction with the sun, when\\nit is seen in the same part of the heavens with the sun, or\\nwhen it has the same longitude. Mercury and Venus have each\\ntwo conjunctions, the inferior and the superior. The inferior\\nconjunction is its position when in conjunction on the same side\\nof the sun with the earth, as at Q, in the figure: the superior\\nconjunction is its position when on the side of the sun most dis-\\ntant from the earth, as at R.\\n304. The period occupied by a planet between two successive\\nconjunctions with the earth, is called its synodical revolution.\\nBoth the planet and the earth being in motion, the time of the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0206.jp2"}, "207": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 181\\nsynodical revolution exceeds that of the sidereal revolution of\\nMercury or Venus for when the planet comes round to the\\nplace where it before overtook the earth, it does not find the\\nEarth at that point, but far in advance of it. Thus, let Mercury\\ncome into conjunction with the earth at Q, (Fig 60.) In about\\n88 days the planet will come round to the same point again\\nbut meanwhile the earth has moved forward through nearly a\\nfourth part of her revolution, and will continue to move onward\\nwhile Mercury, with a swifter motion, is following on to over-\\ntake her, the case being analogous to the hour and second-hand\\nof a clock. Having the sidereal period of a planet, which may\\nalways be accurately determined by observation, we may ascer-\\ntain its synodical period as follows.\\nBy the table in article 301, the mean daily motion of Mercury\\nis 4\u00c2\u00b0 5 32 .6= 14732 .6, and that of the earth is 59 8 .3=3548 .3.\\nTherefore 14732 .6-3548 .3=11184 .3, which is the average\\ngain of Mercury over the earth in a day. But in order to over-\\ntake the earth, Mercury must complete one revolution, and as\\nmuch of another as the earth has performed until the planet over-\\ntakes it; that is, the planet must gain an entire revolution.\\nNow,\\n11184 .3 1 day 360\u00c2\u00b0 115.8 days, the synodical period of\\nMercury. In like manner, the daily gain of Venus is 2219 .5,\\nand\\n2219 .5 1 day 360\u00c2\u00b0 583.9 days, the synodical period of\\nVenus.\\n305. The motion of an inferior planet is direct in passing\\nthrough its superior conjunction, and retrograde in passing\\nthrough its inferior conjunction.\\nThus Venus, while going from B through D to A, (Fig. 61,)\\nmoves in the order of the signs, or from west to east, and would\\nappear to traverse the celestial vault B S A from right to left\\nbut in passing from A through C to B, her course would be ret-\\nrograde, returning on the same arc from left to right. If the\\nearth were at rest, therefore, (and the sun of course at rest,) the\\ninferior planets would appear to oscillate backwards and forwards\\nacross the sun. But, it must be recollected that the Earth is", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0207.jp2"}, "208": {"fulltext": "182\\nTHE PLANETS.\\nmoving in the same direction with the planet, as respects the signs,\\nbut with a slower motion. This modifies the apparent motions of\\nthe planet, accelerating it in the superior, and retarding it in the\\ninferior conjunctions. Thus, in Figure 61, Venus, while moving\\nthrough BDA, would seem to move in the heavens from B to A\\nwerfc the earth at rest but meanwhile the earth changes its po-\\nsition from E to E by which means the planet is not seen at A\\nbut at A being accelerated by the arc A A in consequence\\nof the earth s motion. On the other hand, when the planet is\\npassing through its inferior conjunction ACB, it would appear to\\nFig. 61.\\nmove backwards in the heavens A to B if the earth were at\\nrest, but from A to B if the earth has in the mean time moved\\nfrom E to E being retarded by the arc B B Although the\\nmotions of the earth have the effect to accelerate the planet in\\nthe superior, and to retard it in the inferior conjunction, yet on\\naccount of the greater distance, the apparent motion of the\\nplanet is much slower in the superior than in the inferior con-\\njunction.\\n306. When passing from the superior to the inferior conjunc-\\ntion, or from the inferior to the superior through the points of\\ngreatest elongation, the inferior planets are stationary.\\nIf the earth were at rest, the stationary points would be at the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0208.jp2"}, "209": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 183\\ngreatest elongations, as at A and B, for then the planet would be\\nmoving directly towards or from the earth, and would be seen\\nfor some time in the same place in the heavens but the earth\\nitself is moving nearly at right angles to the line of the planet s\\nmotion hence a direct apparent motion is given to the planet\\nby this cause. When the planet, however, has passed this line,\\nby its superior velocity it soon overcomes this tendency of the\\nearth to give it an apparent motion eastward, and becomes ret-\\nrograde as it approaches the inferior conjunction. Its station-\\nary point evidently lies between its place of greatest elongation,\\nand the place where its motion becomes retrograde. Mercury\\nis stationary at an elongation from 1 5\u00c2\u00b0 to 2:0\u00c2\u00b0 from the sun, and\\nVenus at about 29\u00c2\u00b0. The former continues to retrograde during\\n22 days; the latter, about 42.*\\n307. Mercury and Venus exhibit to the telescope phases similar\\nto those of the moon. -.y^\\nWhen on the side of their inferior conjunction, as from A to\\nB through C, (Fig. 61,) these planets appear horned, like the\\nmoon in her first and last quarters; and when=on;t,he^side of\\ntheir superior conjunctions, as from B to A through L), tbeyap-:\\npear gibbous. At the moment of su^7^X^PjU$^on f {fi^|\\nwhole enlightened orb of the planet is turned towards: the earth,\\nand the appearance would be that of the full moon, but the\\nplanet is too near the sun to be commonly visible. All these\\nchanges of figure resulting from the different^ =pos5ttons:pi the\\nplanet with respect to the sun and earth,-will be readily, under--\\nstood by inspecting the diagram, (Fig. 01;)\\nThese different phases show that these bodies are. bpake, and\\nshine only as they reflect to us the light of the sun and the\\nsame remark applies to all the planets. i\\n308. The distance of an inferior planet from the sun, mayov\\nfound by observations at the time of its greatest elongation.\\nThus if E (Fig. 62) be the place of the earth, and C that of\\nVenus at the time of her greatest elongation the angle 3CE will be\\nHerschel s Outlines, 2*78 Woodhouse, Wl.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0209.jp2"}, "210": {"fulltext": "184\\nTHE PLANETS.\\nFig. 62.\\nknown, being a right angle. Also the angle SEC\\nis known from observation. Hence the ratio of\\nSC to SE becomes known or, since SE is\\ngiven, being the distance of the earth from the\\nsun. SC the radius of the orbit of the planet is\\ndetermined. If, therefore, we already know\\nthe distance of the earth from the sun, we can\\nby this problem easily find the distance of Mer-\\ncury or Venus or, if neither were actually\\nknown, their ratio to each other would be\\nfound by this method. If the orbits were\\nboth circles, this method would be very exact\\nbut being elliptical, we obtain the mean value of the radius\\nSC by observing its greatest elongation in different parts of\\nits orbit.*\\n308. The orbit of Mercury is the most eccentric, and the\\nmost inclined of all the planets ;f while that of Venus varies but\\nlittle from a circle, and lies much nearer to the ecliptic.\\nThe eccentricity of the orbit of Mercury is nearly J of its semi-\\nmajor axis, while that of Venus is fh and that of the earth\\nonly 3 V the inclination of Mercury s orbit is 7\u00c2\u00b0, while that of\\nVenus is only 3J\u00c2\u00b0.J At the perihelion, Mercury is only 29 mil-\\nlions of miles from the sun, while at the aphelion his distance is\\n44 millions, a variation of 15 millions, and more than five times\\nas great as in the case of the earth. On account of his differ-\\nent distances from the earth, Mercury is also subject to much\\nvariation in his apparent diameter, which is 12 in perigee, but\\nonly 5 in apogee.\\n310. The most favorable time for determining the sidereal\\nrevolution of a planet, is when its conjunction takes place at one\\nof its nodes for then the sun, the earth, and the planet, being\\nin the same straight line, it is referred to its true place in the\\nHerschel s Outlines, p. 275.\\nI The asteroids are of course excepted.\\nBaily s Tables.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0210.jp2"}, "211": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 185\\nheavens, whereas, in other positions, its apparent place is more\\nor less affected by perspective.\\n311. An inferior planet is brightest at a certain point be-\\ntween its greatest elongation and inferior conjunction.\\nIts maximum brilliancy would happen at its inferior conjunc-\\ntion, (being then nearest to us,) if it shone by its own light but\\nin that position its dark side is turned towards us. Still its max-\\nimum cannot be when most of the illuminated side is turned\\ntowards us for then, being at the superior conjunction, it is at\\nits greatest distance from us. The maximum must, therefore,\\nbe somewhere between the two. Venus gives her greatest light\\nwhen about 40\u00c2\u00b0 from the sun.\\n312. Mercury and Venus both revolve on their axes in nearly\\nthe same time with the earth.\\nThe diurnal period of Mercury is a little greater than that\\nof the earth, being 24h. 5m. 28s., and that of Venus is a little\\nlegs than the earth s, being 23h. 21m. 7s. The revolutions on\\ntheir axes have been determined by means of some spot or mark\\nseen by the telescope, as the revolution of the sun on his axis is\\nascertained by means of his spots.\\n313. Venus is regarded as the most beautiful of the planets,\\nand is well known as the morning and evening star. The most\\nancient nations did not indeed recognize the evening and morn-\\ning star as one and the same body, but supposed they were dif-\\nferent planets, and accordingly gave them different names, calling\\nthe morning star Lucifer, and the evening star Hesperus. At\\nher period of greatest splendor, Venus casts a shadow, and is\\nsometimes visible in broad daylight. This occurred in a very\\nstriking mannner in September, 1852, Venus being on the merid-\\nian about 9 o clock, A. M., and her northern declination nearly\\n15 degrees. Although not 45\u00c2\u00b0 from the inferior conjunction, and\\nconsequently exposing only a portion of her disk, like that of the\\nmoon when three or four days old, yet her light is then estimated\\nas equal to that of twenty stars of the first magnitude.* At her\\nFrancceur, Uranography, p. 125.\\n24", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0211.jp2"}, "212": {"fulltext": "186 THE PLANETS.\\nperiod of greatest elongation, Venus is visible from three to four\\nhours after the setting, or before the rising of the sun.\\n314. Every eight years, Venus forms her conjunctions with the\\nsun in the same part of the heavens.\\nThe sidereal period of Venus being 224.7 days, and that of the\\nearth 365.256 days, thirteen revolutions of Venus are accom-\\nplished in nearly the same time as eight revolutions of the earth\\nfor 224.7 X 13 2921, and 365.256 X -8= 2922. At the end\\ntherefore of 2922 days, or eight years, the two bodies will come\\nround to the same point of the heavens, and be in the same situ-\\nation with respect to each other, as at the beginning. Conse-\\nquently, whatever appearances of this planet arise from its posi-\\ntions with respect to the earth and the sun, (as, for example,\\nbeing visible in the daytime,) they are repeated every eight years\\nin nearly the same form. .-,_\\nTRANSITS OF THE INFERIOR PLANETS\\n315. The transit of Mercury or Venus, is its passage across\\nthe sun s disk, as the moon passes over it in a solar eclipse.\\nAs a transit takes place only when the planet is in inferior\\nconjunction, at which time her motion is retrograde, (Art. 305,)\\nit is always from left to right, and the planet is seen projected\\non the solar disk in a black round spot. Were the orbits of these\\nplanets coincident with the earth s orbit, a transit would occur at\\nsome part of the earth at every inferior conjunction, as there\\nwould be an eclipse of the sun at every new moon, were the\\nmoon s revolution in the plane of the ecliptic. But the orbit; of\\nVenus makes an angle of 3^\u00c2\u00b0 with that of the earth, and the orbit\\nof Mercury an angle of 7\u00c2\u00b0 and, moreover, the apparent diame-\\nter of each of these bodies is very small, both of which circum.\\nstances conspire to render a transit a comparatively rare occur-\\nrence, since it can happen only when the sun, at the time of an\\ninferior conjunction, happens to be at, or extremely near the\\nplanet s node. The nodes of Mercury lie in that part of the\\nearth s orbit which it passes in the months of May and Novem-\\nber. It is only in these months, therefore, that transits of Mer-\\ncury can occur. For a similar reason, those of Venus occur only", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0212.jp2"}, "213": {"fulltext": "TRANSITS OF THE INFERIOR PLANETS. 187\\nin June and December. Since the nodes of both planets have a\\nsmall retrograde motion, the months in which transits occur,\\nwill change in the course of ages but the months for transits\\nwill for a long time remain the same as at present, since the\\nnodes of Mercury change their places only in 13 and those of\\nVenus only 31 in a century.*\\nThe first prediction of this phenomenon was made by Kepler,\\nand was that of a transit of Mercury which occurred on the 7th\\nof November, 1631. As early as 1629, Kepler announced to as-\\ntronomers that his tables gave the latitude of Mercury, at ihe~\\nconjunction which was to take place on that day, less than the\\nsun s semi-diameter; consequently, that the planet in passing by\\nthe sun would be nearer the sun s center than the length-. of the\\nsun s radius, and of course appear on his disk. The event cor-\\nresponded to the prediction. The latest transit of Mercury\\noccurred on the 8th of November, 1848, being the 25th since the\\none predicted by Kepler, averaging nearly one in 8 years, although\\nthey take place at very unequal intervals.\\n316. The shortest interval between two successive transits of\\nMercury is 3 years, and of Venus 8 years but sometimes they\\nare separated by long intervals, especially those of Venus. Not\\na single one of these will occur during the 20th century. The\\nnext transit of Mercury will take place November 11th, 1861,\\nand of Venus, December 8th, 1874. At the same node the\\nshortest period for Mercury is 7 years; but as there are two\\nnodes, a transit may occur at one node 3j years after it oc-\\ncurred at the other. Thus there will be transits of Mercury in\\nMay, 1891, and November, 1894. More of the transits of Mer-\\ncury happen in November than in May, because the orbit of\\nthis planet, (which has a great eccentricity, Art. 308,) is so sit-\\nuated, that in November the planet is near its perihelion, and is\\nthen more likely to be projected on the sun in passing its inferior\\nconjunction, than in a part of its orbit more distant from the\\nsun.\\nLet us see how the intervals between the transits of Mercury\\nHind.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0213.jp2"}, "214": {"fulltext": "188 THE PLANETS.\\nor Venus are found. Since Venus, for example, completes one\\nrevolution around the sun in 224.7 days, and the earth in 365.256,\\nand since the number of times each will revolve in a given pe-\\nriod is inversely as the time of one revolution, therefore in 224,700\\nrevolutions of the earth, and 365,256 revolutions of Venus, the\\ntwo bodies would meet exactly at the same node as before. But\\n224,700 365,256 8 13 nearly so that transits of Venus are\\nsometimes repeated at intervals of 8 years, and if the ratio of 8\\nto 13 were exactly that of the two first terms of the proportion, we\\nshould have a transit of Venus every 8 years. The ratio of 227 to\\n369 is still nearer that of those terms and hence a transit after\\n227 years is still more probable but since there are two nodes\\nthe chance is doubled, so that a transit is highly probable after\\nan interval of 113J years. The latest transit of Venus was that\\nof June, 1769, one having previously occurred 8 years before\\nand the next transit will take place in December, 1874, and the\\nnext after that in December, 1882. From June, 1769, to Decem-\\nber, 1882, is a period of 113^ years but it so happens that Venus\\nand the Earth will meet near enough to the node 8 years before\\nto occasion a transit, thus anticipating the regular interval of\\n1 13J years, and reducing it to 105^ years. If at the occurrence of\\na previous transit Venus had passed her node, the next transit,\\nat the other node, happens 8 years sooner than the usual period\\nof 113 J years.\\n317. The great interest attached by astronomers to a transit\\nof Venus, arises from its furnishing the most accurate means in\\nour power of determining the suns horizontal parallax an ele-\\nment of great importance, since it leads to a knowledge of the\\ndistance of the earth from the sun, and consequently, by the ap-\\nplication of Kepler s third law, (Art. 183,) of the distances of all\\nthe other planets. Hence, in 1769, great efforts were made\\nthroughout the civilized world, under the patronage of different\\ngovernments, to observe this phenomenon under circumstances\\nthe most favorable for determining the parallax of the sun. The\\nmethod of finding the parallax of a heavenly body, described in\\nArt. 85, cannot be relied on to a greater degree of accuracy than", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0214.jp2"}, "215": {"fulltext": "TRANSITS OF THE INFERIOR PLANETS. 189\\n4 In the case of the moon, whose greatest parallax amounts to\\nabout 1\u00c2\u00b0, this deviation from absolute accuracy is not material;\\nbut it amounts to nearly half the entire parallax of the sun and\\nsince the distance is inversely as the horizontal parallax, such an\\nerror would make the distance of the sun either twice too great\\nor twice too small, according as the parallax was 4 below or 4\\nabove the truth.\\n318. If the sun and Venus were equally distant from us, they\\nwould be equally affected by parallax as viewed by spectators in\\ndifferent parts of the earth, and consequently their relative situa-\\ntion would not be altered by such a difference in the points of\\nview but since Venus at the inferior conjunction is only about\\none-third as far off as the sun, her parallax is proportionally\\ngreater, and therefore spectators, at distant points, will see Venus\\nprojected on different parts of the solar disk and as the planet\\ntraverses the disk, she will appear to describe chords of different\\nlengths, by means of which the duration of the transit may be\\nestimated at different places. The difference in the duration of\\nthe transit, as viewed from opposite parts of the earth, does not\\namount to many minutes but to make it as large as possible,\\nplaces very distant from each other are selected for observation.\\nThus, in the transit of 1769, among the places selected, two of\\nthe most favorable were Wardhus in Lapland, and Otaheite, (now\\nwritten Tahiti) one of the Society Island, in the South Pacific\\nOcean, to which place the celebrated Captain Cook was dis-\\npatched by the British government for the express purpose of\\nobserving the transit.\\nAlthough the exact determination of the sun s horizontal par-\\nallax by this method is a very complicated and difficult problem,\\nyet the principle on which the process depends, admits of an\\neasy illustration. Let E, (Fig. 63,) be the earth, V Venus, and\\nS the sun. Suppose A and B two spectators at opposite extrem-\\nities of that diameter of the earth which is perpendicular to the\\necliptic. The spectator at A will see Venus on the sun s disk at\\na, and the spectator at B will see Venus at b and since AV and\\nBV may be considered as equal to each other, as also Yb and", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0215.jp2"}, "216": {"fulltext": "190 THE PLANETS.\\nVa; therefore the triangles are equiangular and similar, and\\nAV aV AB ab. But the ratio of AV to aV is known, (Art.\\n308 hence the ratio of AB to ah is known, and when the an-\\ngular value of ah as seen from the earth is found, that of AB\\nbecomes known as seen from the sun and half AB, or the semi-\\ndiameter of the earth as seen from the sun, is the sun s horizon-\\nFig. 63.\\ntal parallax, (Art. 82.) If, for example, ah is found to be 2^\\ntimes the diameter of the earth AB, or 5 times the semi-diameter,\\nthen, if the line AB be supposed to be on the sun, (for the sake\\nof comparing it with ab,) it would subtend an angle at the eye\\nequal to J^ of ab. But if viewed from the sun, the distance being\\nthe same, its apparent diameter would be the same, and ab would\\nbe five times the angular value of the semi-diameter of the earth\\nas seen from the sun, and consequently (Art. 82) five times the\\nsun s horizontal parallax. We have only then to find the angu-\\nlar value of the line ab. We can ascertain the angular value of\\neach chord EF or GH by the time occupied in describing it, since\\nthe motions of Venus and those of the sun are accurately known\\nfrom the tables. Each chord being double the sine of half the\\narc cut off* by it, therefore the sine of half the arc; and of course\\nthe versed sine becomes known, and the difference of the two\\nversed sines ce (equal to cd\u00e2\u0080\u0094ed)=ab.\\nThe appearance of Venus on the sun s disk being that of a\\nwell-defined black spot, and the exactness with which the mo-\\nment of external or internal contact may be determined, are cir-\\ncumstances favorable to the accuracy of the result and astron-\\nomers repose so much confidence in the estimation of the sun s\\nhorizontal parallax, as derived from the observations on the tran-\\nsit of 1769, that this important element is thought to be certainly", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0216.jp2"}, "217": {"fulltext": "TRANSITS OF THE INFERIOR PLANETS. 191\\nascertained within one-tenth of a second. The general result of\\nall these observations, gives the sun s horizontal parallax 8 6, or\\nmore exactly 8 .5776.*\\nVenus when on the side of her inferior conjunction, and Mars\\nwhen near his opposition, each comes comparatively near to the\\nearth, and at these times exhibits a large horizontal parallax.\\nTha*t of Venus, especially, may be obtained with great accuracy\\nwhen she is near her greatest elongation and since it is easy,\\nby Article 308, to determine, at that time, the ratio of her dis-\\ntance from the sun to the earth s distance, it is a matter of great\\ninterest to astronomy to have the parallax of Venus, when thus\\nsituated, accurately found. For this purpose, the government of\\nthe United States, in 1849, sent an expedition, under Lieutenant\\nGilliss, to Chili, in order to take observations on Mars and Venus,\\nespecially the latter, during 1850, 1851, and 1852, in concert with\\nthe Observatory at Washington. These researches, when com-\\npleted, will, it is hoped, afford a more accurate determination of\\nthe sun s horizontal parallax than any yet obtained.\\n319. During the transits of Venus over the sun s disk in 1761\\nand 1769, a sort of penumbral light was observed around the\\nplanet by several astronomers, which was thought to indicate an\\natmosphere. This appearance was particularly observable w 7 hile\\nthe planet was coming on and going off the solar disk. The\\ntotal immersion and emersion were not instantaneous but as\\ntwo drops of water when about to separate form a ligament\\nbetween them, so there was a dark shade stretched out between\\nVenus and the sun, and when the ligament broke, the planet\\nseemed to have got about an eighth part of her diameter from the\\nlimb of the sun.f The presence of an atmosphere is also indica-\\nted by appearances of twilight and indications of a horizontal\\nrefraction.J\\nAlthough no satellite has hitherto been discovered attending\\neither Mercury or Venus, yet suspicions have, at different times,\\nDelambre, t. 2. Vince, Complete Syst. yol. I Woodhouse, p. 754. Herschel s\\nOutlines, p. 255.\\nf Ed. Encyc. Art. Astronomy. Hind.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0217.jp2"}, "218": {"fulltext": "192 THE PLANETS.\\nbeen entertained of a satellite belonging to Venus. None has\\nbeen seen in any of the transits of Venus and although the dis-\\ntance of the satellite (if one exists) from the primary might have\\nbeen too great to be projected with the primary on the sun, yet\\nits absence on each of these occasions has strengthened the be-\\nlief of astronomers that no such satellite exists.\\nCHAPTER X.\\nOF THE SUPERIOR PLANETS, MARS, JUPITER, SATURN, URANUS, AND\\nNEPTUNE J AND OF THE NEW PLANETS, OR ASTEROIDS.\\n320. The Superior planets are distinguished from the Inferior,\\nby being seen at all distances from the sun from 0\u00c2\u00b0 to 180\u00c2\u00b0.\\nHaving their orbits exterior to that of the earth, they of course\\nnever come between us and the sun, that is, they have never\\nany inferior conjunction like Mercury and Venus, but they\\nare seen in superior conjunction and in opposition. Nor do\\nthey, like the inferior planets, exhibit to the telescope different\\nphases, but, with a single exception, they always present the side\\nthat is turned towards the earth fully enlightened. This is owing\\nto their great distance from the earth for were the spectator to\\nstand upon the sun, he would of course always have the illumin-\\nated side of each of the planets turned towards him but so dis-\\ntant are all the superior planets except Mars, that they are viewed\\nby us very nearly as they would be if we actually stood on\\nthe sun.\\n321. Mars is a small planet, his diameter being only about\\nhalf that of the earth, or 4500 miles.* He also, at times, comes\\nnearer to us than any other planet except Venus. His mean dis-\\ntance is 145,200,000 miles but in consequence of the eccentricity\\nof his orbit, the distance varies greatly, the difference between\\nHind.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0218.jp2"}, "219": {"fulltext": "MARS. 193\\nthe perihelion and aphelion distances being 27,000,000 miles.\\nMars is always near the ecliptic, never varying from it 2\u00c2\u00b0. He\\nis distinguished from all the other planets by his deep red color\\nand fiery aspect but his brightness and apparent magnitude vary\\nmuch at different times, being sometimes nearer to us than at\\nothers by the whole diameter of the earth s orbit, that is, by\\nabout 190,000,000 miles. When Mars is on the same side of the\\nsun with the earth, or at his opposition, he comes within\\n50,000,000 miles of the earth, and, rising about the time the sun\\nsets, surprises us by his magnitude and splendor but when he\\npasses to the other side of the sun to his superior conjunction, he\\ndwindles to the appearance of a small star, being then 240,000,000\\nmiles from us. Thus, let M, (Fig. 64,) represent Mars in opposi-\\ntion, and M in superior conjunction, it is obvious that, the planet\\nFia:. 64.\\nmust be nearer to us in the former situation than in the latter\\nby the whole diameter of the earth s orbit.\\n322. Mars is the only one of the superior planets which ex-\\nhibits phases. When he is towards the quadratures at Q or Q/,\\nit is evident from the figure that only a part of the circle of illu-\\nmination is turned towards the earth, such a portion of the\\nremoter part of it being concealed from our view as to render the\\nform more or less gibbous.*\\n323. When viewed with a powerful telescope, the surface of\\n25", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0219.jp2"}, "220": {"fulltext": "194 THE PLANETS.\\nMars appears diversified with numerous varieties of light and\\nshade. The region around the poles is marked by white spots,\\nwhich vary their appearance with the changes of the sea\\nsons in the planet. Hence Dr. Herschel conjectured that they\\nare owing to ice or snow which occasionally accumulates and\\nmelts, according to the position of each pole with respect to the\\nsun.* It has been common to ascribe the ruddy light of this\\nplanet to an extensive and dense atmosphere, which was sup-\\nposed to be distinctly indicated by the gradual diminution of\\nlight, observed in a star as it approached very near to the planet\\nin undergoing an occultation but more recent. observations afford\\nno such evidence of an atmosphere. f By observations on the\\nspots, we learn that Mars revolves on his axis in very nearly\\nthe same .time with the earth, (24h. 39m. 21.3s.;) and that the\\ninclination of his axis to the plane of his orbit, is also nearly the\\nsame, making his obliquity 28\u00c2\u00b0 42 that of the earth being 23\u00c2\u00b0\\n28 so that the changes of seasons in Mars must resemble\\nour own.\\nNo satellite has ever been discovered belonging to Mars,\\nalthough being situated at a greater distance from the sun\\nthan our globe, it might seem more especially to need such a\\nluminary to cheer its dark nights. As the diurnal rotation of\\nMars is performed in nearly the same time as the earth, we\\nshould expect a similar flattening of the poles. Such is the\\nfact, and the ellipticity of Mars exceeds that of the earth, being\\nabout one fiftieth, J while the earth s ellipticity is one three-hun-\\ndredth. This difference in the conjugate diameters may be\\nreadily observed when the planet is in opposition, the whole\\nenlightened disk being then presented to us.\\n324. Mars being comparatively near to us when on the same\\nside of the sun with the earth, and the ratio of his distance\\nfrom the sun to that of the earth being easily obtained, as-\\ntronomers have sought by means of his parallax, as by that of\\nVenus, to find the sun s horizontal parallax. But the method by\\nPhil. Trans. 1784.\\nf Sir James South, Phil. Trans. 1833. Hind", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0220.jp2"}, "221": {"fulltext": "JUPITER. 195\\nobservations on Venus, as described in Art. 318, is more to be\\nrelied on.\\n325. Jupiter is distinguished from all the other planets by\\nhis great magnitude. His diameter is 89,000 miles, being more\\nthan 11 times, and his volume more than 1400 times that of the\\nearth. His figure is strikingly spheroidal, the equatorial exceed-\\ning the polar diameter in the ratio of 107 to 100,* which is 21\\ntimes as great as the earth s ellipticity. This flattening of the\\npoles is indeed quite perceptible by the telescope, and is obvious\\nto the eye in a correct drawing of the planet. (See Frontis-\\npiece.) Such a figure might naturally be expected from the\\nrapidity of his diurnal revolution, which is accomplished in\\nabout 10 hours, (9h. 55m. 21.3s.)f\\nA place on the equator of Jupiter must revolve 450 miles\\nper minute, or 27 times as fast as a place on the terrestrial equa-\\ntor. The distance of Jupiter from the sun is 495,000,000 miles\\n(495,817,000)4 His axis of rotation is but slightly inclined to\\nthe plane of his orbit, (only about 3\u00c2\u00b0,) and consequently his cli-\\nmate experiences but a slight change of seasons.\\n326. The view of Jupiter through a good telescope, is one of\\nthe most magnificent and interesting spectacles among the heav-\\nenly bodies. The disk expands into a large and bright orb like\\nthe full moon the spheroidal figure which theory assigns to re-\\nvolving worlds, is here palpably exhibited to the eye across the\\ndisk, arranged in parallel stripes, are discerned several dusky\\nbands, called belts and four bright satellites, always in attend-\\nance, but ever varying their positions, compose a splendid retinue.\\nIndeed, astronomers gaze with peculiar interest on Jupiter and\\nhis moons, as affording a miniature representation of the whole\\nsolar system, repeating, on a smaller scale, the same revolutions,\\nand exemplifying, in a manner more within the compass of our\\nobservation, the same law r s as regulate the entire assemblage of\\nsun and planets.\\nHerscheL Airy, Hind", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0221.jp2"}, "222": {"fulltext": "196 THE PLANETS.\\n327. The Belts of Jupiter are variable in their number and\\ndimensions. With smaller telescopes only one or two are seen\\nacross the equatorial regions but with more powerful instru-\\nments the number is increased, covering a great part of the disk.\\nOccasionally these belts retain nearly the same form and posi-\\ntions for many months together, while at other times they\\nundergo great and sudden changes, and in one or two instances,\\nthey have been observed to break up and spread themselves over\\nthe whole face of the planet. The prevailing opinion among\\nastronomers in reference to the nature of these belts is, that they\\nare produced by disturbances in the planet s atmosphere, which\\noccasionally render its dark body visible and, as the belts are\\nfound to traverse the disk in lines uniformly parallel to Jupiter s\\nequator, they are inferred to be connected with the rotation of\\nthe planet upon its axis, the great rapidity of which would nat-\\nurally produce peculiarities in its atmospheric phenomena.\\n328. The Satellites of Jupiter may be seen with a telescope of\\nvery moderate powers. Even a common spy-glass will enable\\nus to discern them. Indeed, being nearly equal in brilliancy to\\nthe smallest stars visible to the naked eye, a slight increase of\\noptical power brings them into view and some few persons, en-\\ndowed with extraordinary powers of vision, have supposed that,\\nthey saw one of these little bodies without the aid of instru-\\nments but on applying the telescope it has been found that\\nthree of the satellites have approached so near together as to\\nappear like one.* In the largest telescopes, they severally ap-\\npear as bright as Sirius does to the naked eye. With such\\nan instrument, the view of Jupiter with his moons and belts is\\ntruly a magnificent spectacle a world within itself. As the\\norbits of the satellites do not deviate far from the plane of the\\necliptic, and but little from the equator of the planet, (which\\nnearly coincides with the ecliptic,) they are usually seen almost\\nHind.\\nRev. Mr. Stoddard, a graduate of Yale College, missionary to the ISTestorians,\\nhas repeatedly seen one of these bodies with the naked eye, from Mount Seir, near\\nOroomiah. Mr. Stoddard is known to the author as an excellent observer, and his\\ntestimony on this point may be fully relied on.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0222.jp2"}, "223": {"fulltext": "JUPITER.\\nlgft\\nin a straight line extending across the central part of the disk.\\n(See Frontispiece.)\\n329. Jupiter s satellites are distinguished from one another by\\nthe denominations of first, second, third, and fourth, according to\\ntheir relative distances from the primary, the first being that\\nwhich is nearest to him.* Their apparent motion is oscillatory,\\nlike that of a pendulum, going alternately from their greatest\\nelongation on one side to their greatest elongation on the other,\\nsometimes in a straight line, and sometimes in an elliptical\\ncurve, according to the different points of view in which we\\nobserve them from the earth. Their motion is alternately direct\\nand retrograde they are sometimes stationary and, in short,\\nthey exhibit in miniature all the phenomena of the planetary\\nsystem. Various particulars of the system are exhibited in the\\nfollowing table, the diameters being in miles, and the distances\\nbeing taken from the center of the primary. f\\nSatellite.\\nDiameter.\\nDistances.\\nSidereal Revolution.\\n1\\n2\\n3\\n4\\n2440\\n2190\\n3580\\n3060\\n278,500\\n443,300\\n707,000\\n1,243,500\\nId. 18h. 28m.\\n3 13 15\\n7 3 43\\n16 16 32\\nHence it appears, first, that Jupiter s satellites are all some-\\nwhat larger than the moon, except the second, which is nearly\\nof the same size with the moon. The third, the largest of the\\nwhole, has still only ^th the diameter of the primary. The\\ngreater distances also of these moons compared with ours, reduces\\ntheir apparent size and light as seen from Jupiter. Thus the\\nlargest of them would exhibit to a spectator on the equator of\\nthe planet, a diameter of only 36 which is only a little greater\\nthan that of the moon, while the smallest would appear only one-\\nfourth as large secondly, that the distance of the innermost\\nMythological names were long since proposed for the satellites of Jupiter,\\nviz., Io, Europa, Ganymede, Calisto but the mode of designating them by numbers\\ngenerally prevails. f Hind.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0223.jp2"}, "224": {"fulltext": "198 THE PLANETS.\\nsatellite from the planet is but a little more than three times\\nhis diameter or if reckoned from the surface of the primary,\\nnearly the same as the distance of the moon from the earth,\\nwhile that of the outermost satellite is more than four times as\\nfar thirdly, that the first satellite completes its revolution around\\nthe primary in about a day and three quarters, while the fourth\\nrequires nearly sixteen days and three quarters.\\n330. The orbits of the satellites are nearly or quite circular,\\nand deviate but little from the plane of the planet s equator, and\\nof course are but slightly inclined to the plane of his orbit. They\\nare, therefore, in a similar situation with respect to Jupiter as\\nthe moon would be with respect to the earth, if her orbit nearly\\ncoincided with the ecliptic, in which case she would eclipse the\\nsun every new moon, and be herself eclipsed every full moon.\\n331. The eclipses of Jupiter s satellites, in their general con-\\nception, are perfectly analogous to those of the moon, but in\\ntheir details they differ in several particulars. Owing to the\\nmuch greater distance of Jupiter from the sun, and its greater\\nmagnitude, the cone of its shadow is more than sixty times\\nthat o c the earth, stretching off into space more than 55,000,000\\nmiles. On this account, as well as on account of the little incli-\\nnation of their orbits to that of their primary, the three inner\\nsatellites of Jupiter pass through the shadow and are totally\\neclipsed at every revolution. The fourth satellite, owing to the\\ngreater inclination of its orbit, sometimes though rarely escapes\\neclipse, and sometimes merely grazes the limits of the shadow,\\nor suffers a partial eclipse.* These eclipses, moreover, are not\\nseen by us, as is the case with those of the moon, from the center\\nof their motion, but from a remote station, and one whose situ-\\nation, with respect to the line of the shadow, is variable. This\\nof course makes no difference in the times of the eclipses, but a\\nvery great difference in their visibility, and in their apparent sit-\\nuations with respect to the planet at the moment of their enter-\\ning or quitting the shadow.\\nHerschel s Ask p. 285", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0224.jp2"}, "225": {"fulltext": "JUPITER.\\n199\\n332. The eclipses of Jupiter s satellites present some curious\\nphenomena, which will be best understood from a diagram. Let\\nA, B, C, (Fig. 65,) represent the earth in different parts of its\\norbit, A being the western and C the eastern side, and B the place\\nof opposition. Let J represent Jupiter, a the first and b the fourth\\nsatellite and let xy represent the concave sphere of the heav-\\nens. When the earth is westward of the place of opposition, as\\nat A, the immersions only are seen, the emersions being hidden\\nbehind the planet, as will be evident on observing the rela-\\nFig. 65.\\ntion of the satellite in passing through the shadow to the\\nlines of vision drawn from the spectator to the primary and sec-\\nondary respectively. When the earth is eastward of the place\\nof opposition, the emersions only are seen, as is also evident by\\nconceiving lines drawn as before. This, however, is strictly true\\nonly of the first satellite for the third and fourth, and sometimes\\neven the second, occasionally disappear and reappear on the\\nsame side of the disk. Thus, lines drawn from the eye to xy\\nthrough b the place of immersion, and b that of emersion, will\\nstrike the concave sphere of the heavens at c and d, while the\\nplanet will be seen at e. The same mode of illustration will show-\\nthat when the earth is to the eastward of the planet, the immer-\\nsions and emersions of the outermost satellite will be seen on the\\neast side of the disk. When the earth is at B, the place of oppo-\\nsition, or at D, the place of superior conjunction, both the im-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0225.jp2"}, "226": {"fulltext": "200 THE TLANETS.\\nmersions and emersions take place behind the planet, and close\\nto the disk.\\n333. When one of the satellites is passing between Jupiter and\\nthe sun, it casts its shadow upon its primary, as the moon does\\n\u00c2\u00a3i the earth in a solar eclipse, which is seen by the telescope\\ntravelling across the disk of Jupiter, as the shadow of the moon\\nwould be seen to traverse the earth by a spectator favorably sit-\\nuated in space. When the earth is to the westward of Jupiter,\\nas at A, the shadow reaches the disk of the planet, or is seen on\\nthe disk, before the satellite itself reaches it. Thus, (Fig. 65,) it\\nwill be seen that the line of projection drawn from A to any part of\\nthe shadow of the satellite, meets the planet sooner than the line\\ndrawn through the satellite and that just the opposite is the case\\nwhen the earth has passed to C. We do not usually see the\\nsatellite itself projected on the disk of the primary, for, being\\nilluminated like the primary, it is not readily distinguishable from\\nit but sometimes, when it happens to be projected on one of\\nthe belts, it is seen, as a bright spot, making its transit across\\nthe disk. Occasionally, also, it is seen as a dark spot of smaller\\ndimensions than the shadow. This curious fact has led to the\\nconclusion that certain of the satellites have sometimes on their\\nown bodies, or in their atmospheres, obscure spots of great\\nextent.*\\n334. A very singular relation subsists between the mean mo-\\ntions of the three first satellites of Jupiter. The mean longitude\\nof the first, plus twice that of the third, minus three times that\\nof the second, always equals 180 degrees. A curious consequence\\nof this relation is, that the three satellites can never be all\\neclipsed at the same time for then, having severally the same\\nlongitude as the primary, their longitudes would be equal, and\\nthat of the first, plus twice that of the third, minus three times\\nthat of the second, would be nothing, and of course could not be\\n180 degrees. f These phenomena are such as would present\\nthemselves to a spectator on Jupiter, and not to a spectator on\\nthe earth.\\nSir J. HerscheL f Biot", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0226.jp2"}, "227": {"fulltext": "JUPITER. 201\\n335. The discovery of the system of Jupiter and his satellites,\\nsoon after the invention of the telescope, lent a powerful support\\nto the Copernican sv stem of astronomy, then just beginning to be\\nreceived by astronomers, since it presented to the eye an exact\\nminiature of the solar system, and exhibited an actual model of\\nthat arrangement of the sun and planets which had before only\\nbeen contemplated by the eye of the mind; and the laws of the\\nplanetary system, discovered by Kepler, were here actually seen\\nto be verified, in the motions of this miniature system. More-\\nover, the eclipses of Jupiter s satellites, furnished one of those in-\\nstantaneous events, occurring at the same moment of absolute\\ntime wherever seen, which are available for finding the longitudes\\nof different places and at that period, it was deemed a more\\neligible method of determining this great practical problem of\\nastronomy, than any method then in use.\\n336. The eclipses of these satellites seem to have various\\nrequisites for determining longitudes, being, as already remarked,\\nseen at the same moment at all places where the planet is vis-\\nible, being wholly independent of parallax, and being predicted\\nbeforehand with great accuracy the instant they occur at Green-\\nwich, and given in the Nautical Almanac but several circum-\\nstances conspire to render this method of finding the longitude\\nless eligible than several other methods at present in use. The\\nextinction of light in the satellite at its immersion, and the re-\\ncovery of its light at its emersion, are not instantaneous but\\ngradual for the satellite, like the moon, occupies some time in\\nentering into the shadow or in emerging from it which occasions\\na progressive diminution or increase of light. The better the\\nlight afforded by the telescope with which the observation is\\nmade, the later the satellite will be seen at its immersion, and the\\nsooner at its emersion.* In noting the eclipses even of the first\\nsatellite, the time must be considered as uncertain to the amount\\nof 20 or 30 seconds and those of the other satellites involve\\nstill greater uncertainty. Two observers, in the same room, ob-\\nThis is the reason why observers are directed, in the Nautical Almanac, to use\\ntelescopes of a certain power.\\n26", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0227.jp2"}, "228": {"fulltext": "202 THE PLANETS.\\nserving, with different telescopes, the same eclipse, will frequently\\ndisagree in noting its time to the amount of 15 or 20 seconds, and\\nthe difference will always be the same way.* Better methods,\\ntherefore, of finding the longitude are now employed, although\\nthe facility with which the necessary observations can be made,\\nand the little calculation required, still render this method eligible\\nin many cases where extreme accuracy is not required. As a\\ntelescope is essential for observing an eclipse of one of these sat-\\nellites, this method cannot be practised at sea.\\n337. The grand discovery of the progressive motion of light,\\nwas first made by observations on the eclipses of Jupiter s satel-\\nlites. In the year 1675, it was remarked by Roemer, a Danish\\nastronomer, on comparing together observations of these eclipses\\nduring many successive years, that they take place sooner by\\nabout sixteen minutes (10m. 26.6s.) when the earth is on the\\nsame side of the sun with the planet, than when she is on\\nthe opposite side. This difference he ascribed to the progres-\\nsive motion of light, which takes that time to pass through the\\ndiameter of the earth s orbit. Now, 16m. 26.6s. 986.6s.\\n986.6 sec. 190,000,000 miles 1 sec. 192,600 miles the\\nvelocity of light per second, equal to nearly 12,000,000 miles per\\nminute. So great a velocity startled astronomers at first, and\\nproduced some degree of distrust of this explanation of the phe-\\nnomenon but the subsequent discovery of the aberration of light,\\n(Art. 195,) led to an independent estimation of the velocity of\\nlight with nearly the same result.\\n338. Saturn comes next in the series as we recede from the\\nsun, and has, like Jupiter, a system within itself, on a scale of\\ngreat magnificence. In size it is, next to Jupiter, the largest of\\nthe planets, being 79,000 miles in diameter, or nearly 10 times\\nas large as the earth in diameter, and about 1000 times as la*ge\\nin volume. It has likewise belts on its surface, and is attended\\nby eight satellites. But a still more wonderful appendage is its\\nRing, a broad wheel encompassing the planet at a great distance\\nWoodhouse, p. 840.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0228.jp2"}, "229": {"fulltext": "SATURN. 203\\nfrom it. We have already intimated that Saturn s system is on\\na grand scale. As, however, Saturn is distant from us nearly\\n900,000,000 miles, we are unable to obtain the same clear and\\nstriking views of his phenomena that we do of the phenomena of\\nJupiter, although they really present a more wonderful mechan-\\nism. The figure of Saturn has usually been described, on the\\nauthority of Sir William Herschel, as approaching that of a cube\\nbut more recent and refined measurements have shown that it is\\nelliptical, being much compressed at the poles, the equatorial\\nexceeding the polar diameter by about one-tenth.\\nThe belts of Saturn, although clearly discerned by a good tel-\\nescope, are far more indistinct than those of Jupiter. Spots,\\nwhich occasionally appear on the belts, have enabled astronomers\\nto determine the time of the diurnal rotation of Saturn, which is\\nfound to be about ten hours and a half, (lOh. 29m.)\\n339. Saturn s ring, when viewed with powerful telescopes, is\\nfound to consist of two concentric rings, separated from each\\nother by a dark space. f (See Frontispiece.) Although this\\ndivision of the rings appears to us, on account of our immense\\ndistance, as only a fine line, yet it is in reality an interval of nearly\\n1800 miles. The dimensions of the whole system are in round\\nnumbers, as follows :J\\nMiles.\\nDiameter of the planet, 79,000\\nFrom the surface of the planet to the inner ring, 20,000\\nBreadth of the inner ring, 17,000\\nInterval between the rings, 1,800\\nBreadth of the, outer ring, 10,500\\nExtreme dimensions from outside to outside 176,000\\nThe figure represents Saturn as it appears to a powerful teles-\\ncope, surrounded by its rings, and having its body striped with\\nHind.\\nA greater number of divisions of the rings have been occasionally seen, and the\\nresearches of Mr. G. P. Bond and of Professor Peirce, render it probable that the\\nnumber is variable. (See Trans. Amer. Academy.)\\nProfessor Struve, Mem. Art. Soc. III. 301.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0229.jp2"}, "230": {"fulltext": "204 THE PLANETS.\\ndark belts, somewhat similar, but broader and less strongly\\nmarked, than those of Jupiter, and owing doubtless to a similar\\ncause.* That the ring is composed of matter of considerable\\ndensity, is shown by its throwing a deep shadow on the body of\\nthe planet on the side nearest the sun, and on the other side re-\\nceiving that of the body.f\\nFrom the parallelism of the belts with the plane of the ring, it\\nmay be conjectured that the axis of rotation of the planet is per-\\npendicular to that plane; and this conjecture is confirmed by\\nthe occasional appearance of extensive dusky spots on its surface,\\nwhich, when watched, indicate a rotation parallel to the ring in\\nabout ten hours and a half, (lOh. 29m. 17s.) This motion, it will\\nbe remarked, is nearly the same with the diurnal motion of Jupi-\\nter, subjecting places on the equator of the planet to a very swift\\nrevolution, and occasioning its striking spheroidal figure and\\nthe axis of rotation, like that of the earth, preserves its parallelism\\nto itself during the motion of the planet in its orbit. According\\nto Sir William Herschel, the planet is surrounded with a very\\ndense atmosphere, which is indicated by the refraction experi-\\nenced by the satellites when they are passing behind the planet,\\nand by periodical changes of color and shade in the polar\\nregions.\\nIt requires a telescope of high magnifying powers and a strong\\nlight to give a full and striking view of Saturn with his rings and\\nbelts and satellites for we must bear in mind that at that dis-\\ntance, one second of angular measurement corresponds to 4000\\nmiles, a space equal to the semi-diameter of our globe. But with\\na telescope of moderate powers, the leading phenomena of the\\nring itself may be observed.\\n340. Saturn s ring, in its revolution around the sun, always\\nremains parallel to itself.\\nIf we hold opposite to the eye a circular ring or disk, like a\\nSir J. Herschel.\\nf Recent investigations of Mr. George P. Bond, of the Observatory of Harvard\\nUniversity, and of Professor Peirce, indicate that the rings are composed of matter\\nin the fluid state.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0230.jp2"}, "231": {"fulltext": "SATURN. 205\\npiece of coin, it will appear as a complete circle when it is at\\nright angles to the axis of vision but when oblique to that axis,\\nit will be projected into an ellipse more and more acute as its\\nobliquity is increased, until, when its plane coincides with the\\naxis of vision, it is projected into a straight line. Let us place\\non the table a lamp or a ball to represent the sun, and, holding\\nthe ring at a certain distance, inclined a little towards the cen-\\ntral body, let us carry it round, always keeping it parallel to\\nitself. During its revolution it will twice present its edge to the\\nlamp or ball at opposite points, and twice at 90\u00c2\u00b0 distance from\\nthose points, it will present its broadest face towards the central\\nbody. At intermediate points, it will exhibit an ellipse more or\\nless open, according as it is nearer one or the other of the pre-\\nceding positions. It will be seen also that in one half of the\\nrevolution, the lamp shines on one side of the ring, and in the\\nother half of the revolution on the other side. Such would be\\nthe successive appearances of Saturn s ring to a spectator on the\\nsun and since the earth is in respect to so distant a body as\\nSaturn, very near the sun, those appearances are presented to\\nus nearly in the same manner as though we viewed them from\\nthe sun. Accordingly, we sometimes see Saturn s ring under the\\nform of a broad ellipse, which grows continually more and more\\nacute until it passes into a line, and we either lose sight of it alto-\\ngether, or, with the aid of the most powerful telescopes, we see\\nit as a fine line drawn across the disk, and projecting out from it\\non each side. As the whole revolution occupies nearly 30 years,\\nand the edge is presented to us twice in the revolution, this last\\nphenomenon, namely, the disappearance of the ring, takes place\\nevery 15 years, when sometimes two and sometimes three dis-\\nappearances occur very near together.\\n341. The learner may perhaps gain a clearer idea of the fore-\\ngoing appearances from the following diagram.\\nLet A, B, C, c, represent successive positions of Saturn and\\nhis ring in different parts of his orbit, while ah represents the\\norbit of the earth.* Were the ring when at C and G perpendic-\\nIt may be remarked by the learner, that these orbits are made so elliptical, not", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0231.jp2"}, "232": {"fulltext": "206\\nTHE PLANETS.\\nular to the line joining CG, it would be seen by a spectator situated\\nat a or as a perfect circle, but being inclined to the line of vision\\n28\u00c2\u00b0 11 it is projected into an ellipse. This ellipse contracts in\\nbreadth as the ring passes towards its nodes at A and E, where\\nit dwindles into a straight line. From E to G the ring opens\\nFig. 66.\\nagain, becomes broadest at G, and again contracts until it be-\\ncomes a straight line at A, and from this point it expands until it\\nrecovers its original breadth at C, in which case the breadth is\\nvery nearly half the length of the ellipse. These successive ap-\\npearances are all visible in a telescope of moderate powers, as\\nrepresented in the foregoing diagram.\\n342. The several circumstances which occasion the disappear\\nance of the ring two or three times within a short period ever}\\nfifteen years, may be understood from the following explanation\\nLet S, (Fig. 67,) be the sun, ABCD a part of Saturn s orbit\\nwhich includes the node at C, and CS will, of course, be the line\\nof the nodes. Let EFGH be the earth s orbit, and EB, GD, lines\\nparallel to CS, and touching the earth s orbit in E and G. Since\\nthe ring always remains parallel to itself, its plane can nowhere\\npresent its edge to the earth s orbit, except when the planet is\\nbetween B and D, during which time and then only can a disap-\\npearance take place. Since Saturn is 9.54 times as far from the\\nsun as the earth is, therefore,\\nto represent the eccentricity of either the earth s or Saturn s orbit, but merely\\nthe projection of circles seen very obliquely.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0232.jp2"}, "233": {"fulltext": "SATURN.\\n207\\n9.54 1 Rad Sin. SBE 6\u00c2\u00b0 l BSC, and the whole angle\\nBSD=12\u00c2\u00b0 2 an arc which is described by Saturn at his mean\\nrate, in 359.46 days, or nearly a year, of which it falls short only\\nabout 5f days. Let the earth set out from G when the planet\\nsets out from B, and let Ga be the arc of the earth s orbit de-\\nscribed from G in 5 J days. Then, if at the moment of Saturn s\\nFig. 67.\\narrival at B, the earth is at a, a spectator on the earth will see\\nthe plane of the ring advancing parallel to itself towards him, and\\nwill come into such a position that its edge will be presented to\\nhim somewhere in the quadrant HE, since the earth will de-\\nscribe half its entire orbit while the ring is moving from B to C.\\nLet M be the point where the earth passes the ring. It will then\\nbe on the dark side of the ring, and continue so until the ring\\nhas passed the sun at C, when it will again become visible, and\\nremain visible until the earth again comes up with it at G. In\\nthis case there will be two disappearances, one while the ring is\\nmoving from K to C, a period of considerable duration, (the dark\\nside being all this while turned towards the earth,) and the other\\nbut momentary, since the earth overtakes it just at the moment\\nof the planet s quitting the arc BD, beyond which its edge can\\nnowhere be presented towards the earth s orbit. If, when Sat-\\nurn is at B, the earth is in any part of the arc \u00c2\u00abHE, it will\\nmeet and pass the ring in the quadrant HE and the earth will\\novertake it before it reaches D, and passing round G, will meet it\\nagain in the quadrant GH so that in this case there will be\\nthree disappearances of the ring in the course of a year. But\\nshould the earth be at E when the ring is at B, the motion of the\\nearth being at that time directly towards the ring, the latter will", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0233.jp2"}, "234": {"fulltext": "208 THE PLANET3.\\nleave it behind, (still presenting its dark side to the earth but\\nthe earth, by its more rapid revolution, will soon pass the ring\\nsomewhere in the quadrant EF. But before the earth has made\\nanother entire circuit, the ring will have advanced beyond D, so\\nthat, in this case, there will be only one disappearance. It ap-\\npears, therefore, that there are three causes for the disappear-\\nance of Saturn s ring first, when the edge of the ring is pre-\\nsented to the sun secondly, when the edge is presented to the\\nearth and, thirdly, when the unilluminated side is towards the\\nearth.\\n343. Saturn s ring revolves in its own plane in about 10J\\nhours, (lOh. 32m. 15.4s.) La Place inferred such a revolution\\nfrom the doctrine of universal gravitation. He proved that such\\na rotation was necessary, otherwise the matter of which the ring\\nis composed would be precipitated upon its primary. He showed\\nthat in order to sustain itself, its period of rotation must be equal\\nto the time of the revolution of a satellite, circulating around\\nSaturn at a distance from it equal to that of the middle of the\\nring, which period would be about 10J- hours. By means of spots\\non the ring, Dr. Herschel followed it in its rotation, and actually\\nfound its period to be the same as assigned by La Place.*\\nThe thickness of the ring, according to Sir John Herschel,\\ndoes not exceed a hundred miles. It is not quite concentric with\\nthe body of the planet, an arrangement which is essential to its\\nstability, since, were it perfectly circular, of uniform density, and\\nconcentric with the planet, it would be in a condition of unstable\\nequilibrium, ready to fall on the planet by the least disturbing\\nforce, like the attraction of one of the satellites.!\\nWithin the double ring of Saturn, as exhibited to ordinary tel-\\nescopes, there has recently been discovered a new ring, less\\nluminous than the others, and therefore concealed from previous\\nobservers. This was first discovered by Mr. G. P. Bond, with\\nthe great refractor of Harvard Observatory.\\n344. The rings of Saturn must present a magnificent spectacle\\nSystem du Monde, 1. ir. c. 8. f Herschel s Outlines, p. 279.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0234.jp2"}, "235": {"fulltext": "SATURN. 209\\nfrom those regions of the planet which lie on their illuminated\\nsides, appearing as vast arches spanning the sky from horizon to\\nhorizon, and holding an invariable situation among the stars.\\nOn the other hand, in the region beneath the dark side, a solar\\neclipse, of fifteen years duration, must afford an inhospitable\\nabode to animated beings, but ill-compensated by the full light of\\nits satellites.*\\n345. Saturn is attended by eight satellites. Although bodies of\\nconsiderable size, varying from 500 to 2850 miles,t their great\\ndistance prevents their being visible to any telescopes but such\\nas afford a strong light and high magnifying powers. The outer-\\nmost satellite is distant sixty-four times the radius of the primary,\\na reach of 2.500,000 miles. The whole extent, therefore, of the\\nsystem of Saturn is immense a realm within itself, being from\\nside to side nearly five millions of miles. When represented in\\na diagram, on a scale in w T hich the diameter of the planet is only\\none foot, the satellites reach out through the long line of thirty-\\ntwo feet on each side. It is only representations of this kind\\nthat give any just ideas of the amplitude of the celestial system,\\nwhile the contracted and crowded figures of ordinary diagrams,\\nor even of orreries, help to form only erroneous and wholly inade-\\nquate views of these systems.\\nThe names of the satellites of Saturn are Mimas, Ence-\\nladus, Tethys, Dione, Rhea, Titan, Hyperion, and Japetus. The\\nseventh, Hyperion, was recently discovered by Professor Bond,\\nwith the great Cambridge refractor. At the time of the disap-\\npearance of the rings, (to ordinary telescopes,) the satellites were\\nseen by Sir William Herschel, with his great telescope, projected\\nalong the edge of the ring, and threading, like beads, the thin\\nfibre of light to w r hich the ring is then reduced. Owing to the\\nobliquity of the ring and of the orbits of the satellites to that of\\nthe primary, there are no eclipses of the satellites, the two interior\\nones excepted, until near the time when the ring is seen edge-\\nwise.!\\nSir J. Herschel. f Hind. J Sir J. HerscheL\\n27", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0235.jp2"}, "236": {"fulltext": "210 THE PLANETS.\\n346. Uranus, the next planet in the series, was discovered by\\nSir William Herschel, in 1781. Previous to this time, Saturn\\nhad, from a high antiquity, been considered as the outermost boun-\\ndary of the solar system but this discovery doubled the dimen-\\nsions of the system, bringing to light a large planet at about twice\\nthe distance of Saturn from the sun, and about 19 times the dis-\\ntance of the earth, or 1800 millions of miles. It was named by\\nthe discoverer the Georgian, in honor of his patron George III.\\nbut this name being unacceptable to astronomers of other coun-\\ntries, the planet was called Herschel in America, after the name\\nof the discoverer, and Uranus- on the continent of Europe, which\\nlast appellation is now universally adopted. The diameter of\\nUranus is about 35,000 miles, and consequently its volume more\\nthan 80 times that of the earth. Its revolution around the sun\\noccupies nearly 84 years, so that its position among the stars\\nvaries but little for several years in succession, since it shifts its\\nplace only a little more than four degrees in a year, and of course\\nwould remain in the same sign of the Zodiac seven years. Its\\npath lies very near the ecliptic, being inclined to it less than\\n0\u00c2\u00b0 47 The sun himself, when seen from Uranus, dwindles al-\\nmost to a star, subtending, as it does, an angle of only 1 40 so\\nthat the surface of the sun would appear there nearly 400 times\\nless than it does to us.\\n347. The satellites of Uranus are exceedingly minute objects,\\nand visible only to the most powerful telescopes. Although Sir\\nWilliam Herschel assigned six satellites to this planet, yet only\\ntwo of the number (the second and fourth in the order of dis-\\ntances) have, until quite recently, been seen by other astrono-\\nmers. Two others have of late been added, and an increasing\\nconfidence is beginning to be felt that the entire number an-\\nnounced by Herschel will be identified. The orbits of these sat\\nellites, says Sir John Herschel, offer remarkable, and indeed quite\\nunexpected and unexampled peculiarities. Contrary to the un-\\nbroken analogy of the whole planetary system, whether of pri-\\nmaries or secondaries, the planes of their orbits are nearly\\nFrom ovpavos, the father of Saturn.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0236.jp2"}, "237": {"fulltext": "NEPTUNE. 211\\nperpendicular to the ecliptic, being inclined no less than 78 58\\nto that plane, and in these orbits their motions are retrograde.\\nInstead of advancing from west to east, as is the case with every\\nother planet and satellite, they move in the opposite direction, or\\nfrom east to west. With this exception, all the motions of the\\nplanets, whether around their own axes or around the sun, and\\nthat of the sun himself on his axis, are from west to east.\\n348. Neptune is (so far as is known) the last planet of the series,\\nbeing removed from the sun to the immense distance of nearly\\n3000 millions of miles (2,862,457,000). Its diameter is a little less\\nthan that of Uranus, being 31,000 miles.* Its volume is nearly\\nsixty times that of the earth. Its periodic time is 164J years,\\nwhich is about twice that of Uranus. Its orbit is nearly circu-\\nlar, and but little inclined to the ecliptic, (1\u00c2\u00b0 47\\nThe discovery of the planet Neptune is the most remarkable\\nastronomical event of our times, and is generally considered as the\\nmost extraordinary discovery ever made in physical science. The\\nleading steps of the process were as follows. The planet Ura-\\nnus had long been known to be subject to certain irregularities\\nin its revolution around the sun, not accounted for by all the\\nknown causes of perturbation. In some cases the deviation from\\nthe true place, as given by the tables, differs from actual obser-\\nvation two minutes of a degree a quantity indeed which seems\\nsmall, but which is still far greater than occurs in the case of\\nthe other planets, and far too great to satisfy the extreme ac-\\ncuracy required by modern astronomy. This fact long since\\nsuggested to astronomers the possibility of one or more addi-\\ntional planets, hitherto undiscovered, which, by their attractions,\\nexert on Uranus a great disturbing influence. Le Verrier, a dis-\\ntinguished French astronomer, assuming the existence of such a\\nplanet, applied himself, by the aid of the calculus, guided by the\\nlaw of universal gravitation, to the inquiry where the hidden\\nplanet was situated at what distance from the sun and at what\\npoint of the starry heavens From Bode s law of the planetary\\ndistances, (Art. 299,) according to which Saturn is nearly twice\\nHindi", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0237.jp2"}, "238": {"fulltext": "212 THE PLANETS.\\nas far from the sun as Jupiter, and Uranus twice as far as Sat-\\nurn, he inferred that, if a planet exists beyond Uranus, its distance\\nis probably about twice that of Uranus, or about 3600 millions of\\nmiles from the sun, which is nearly thirty-eight times that of\\nthe earth. He assumed it, however, to be thirty-six times the\\nearth s mean distance. The corresponding periodic time would\\nbe 216 years. After reasoning from analogy, and the doctrine\\nof universal gravitation, respecting the position and mass which\\na body must have in order to account for the perturbations of\\nUranus, equations were formed between these perturbations and\\nthe elements of the body in question, both known and unknown.\\nThese equations were exceedingly complex and difficult of reduc-\\ntion but, by the most ingenious artifices, the several unknown\\nquantities were successively eliminated, either directly or by re-\\npeated approximations, until the great geometer arrived at\\nexpressions for the elements of the unknown planet, which indi-\\ncated its place among the stars, its quantity of matter, the shape\\nof its orbit, and the period of its revolution. Having placed the\\nbody in various positions in the orbit thus determined, he found\\nthat when situated at a point in the constellation Capricornus,\\nits effect upon Uranus would be such as corresponded to the irreg-\\nularities to be accounted for that on the 1st of January, 1847,\\nthe hidden planet would have a longitude of 326\u00c2\u00b0 32 and would\\nlie about five degrees eastward of the well-known star Delta Ca-\\npricorni. He further asserted that it would have an apparent\\ndiameter of about 3 and therefore be visible to large telescopes.\\n349. Having communicated these results to the French Acad-\\nemy, at their sitting on the 31st of August, 1846, Le Verrier soon\\nafterwards made them known to Dr. Galle, one of the astronomers\\nof the Royal Observatory of Berlin, with the request that he would\\nsearch for the stranger with the powerful telescope at his com-\\nmand. On the same evening that Dr. Galle received the com-\\nmunication, namely, on the 23d of September, he directed his\\ntelescope towards the spot assigned for the planet, and there\\nit was, within less than a degree of the place indicated by Le\\nVerrier, and having an apparent magnitude within half a second\\nof that assigned. To show the near correspondence between", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0238.jp2"}, "239": {"fulltext": "NEPTUNE. 213\\ntheory and observation, we may remark that the predicted lon-\\ngitude, for the 23d of September, at midnight, was 324\u00c2\u00b0 58 and\\nthe observed longitude was 325\u00c2\u00b0 52 .8 the predicted diurnal\\nmotion in longitude was 69 and the observed 74 These re-\\nsults struck the scientific world with astonishment, and their\\nconfirmation was one of the greatest achievements of the human\\nmind.\\n350. It has often happened, in the history of great discoveries,\\nthat the same hidden truth is revealed simultaneously to different\\ninquirers, and accordingly, by a singular coincidence, a young\\nmathematician of the University of Cambridge, (Eng.,) Mr.\\nAdams, had, without the least knowledge of what M. Le Verrier\\nwas doing, arrived at the same great result. But having failed\\nto publish his paper until the world was made acquainted with\\nthe facts through the other medium, he has lost much of the\\nhonor which the priority of discovery would have gained for\\nhim. Thus two distinguished mathematicians, unknowm to each\\nother, and by entirely independent processes, had arrived at the\\nsame results, as regarded both the existence of the supposed planet,\\nand the region of the starry heavens where at that moment it\\nlay concealed and, to crown all, astronomers, in obedience to\\nthe direction of one of them, had pointed their telescopes to -the\\nspot, and found it there. The conviction on the mind of every\\none was, that nothing but absolute truth could abide a test so\\nunequivocal. It still remained, however, to determine by obser-\\nvation whether the body actually conformed, in all respects, to\\nthe results of theory. To settle this point completely, that is, to\\ndetermine with precision the elements of the orbit from observa-\\ntion, would require a long time in a planetary body whose mo-\\ntion was so slow that more than two centuries, as was supposed,\\nwould be required to complete a single revolution. But if it\\nshould be found that, among preceding catalogues of the stars,\\nthis body might have been included, and its place recorded as a\\nfixed star, then, by comparing that place with its present posi-\\ntion, and noting the interval of time between the two observa-\\ntions, we might thus learn the rate of its motion, and its peri-\\nodic time, and might thence deduce various other particulars", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0239.jp2"}, "240": {"fulltext": "214 THE PLANETS.\\ndependent on these elements. Our distinguished countryman,\\nMr. Sears C. Walker, then connected with the observatory at\\nWashington, undertook this investigation. First, from the ob-\\nservations already accumulated, he calculated the path which\\nthe planet must have pursued for the last fifty or sixty years, and,\\nby tracing this path among the stars of Lalande s catalogue, he\\nfound that it passed within two minutes of a star of the seventh\\nmagnitude, which was recorded as being seen in May, 1795.\\nProfessor Hubbard, of the same observatory, on reconnoiterincr\\nfor this star, found that it was missing. Little doubt remained\\nthat the star seen by Lalande, was the planet of Le Verrier and\\nthis conclusion was confirmed by calculating its orbit on this\\nsupposition, and comparing ths results with the places it has\\nactually occupied since it fell within the sphere of observation.\\nThe results thus obtained, however, were materially different\\nfrom those of Le Verrier and Adams. Instead of a period of\\n216 years, they give only a period of 164^ years and instead\\nof a distance of 3600 millions of miles, the new period would re-\\nquire a distance of only 2862 millions. The eccentricity of the\\norbit, moreover, according to Walker, is much less than had been\\nassigned to it, the orbit being in fact very nearly circular, while,\\nby Le Terrier s estimate, it was considerably elliptical. The\\nlongitude, in fact, proved to be nearly the same as that assigned\\nto it, and this rendered the discovery of it with the telescope\\nso easy. The elements thus corrected account fully and com-\\npletely for the irregularities of Uranus sought to be explained,\\nwithin a single second, as determined by Professor Peirce.*\\nNEW PLANETS, OR ASTEROIDS.\\n351. The commencement of the present century was rendered\\nmemorable in the annals of astronomy, by the discovery of four\\nnew planets between Mars and Jupiter. Kepler, from some\\nanalogy which he found to subsist among the distances of the\\nplanets from the sun, had long before suspected the existence of\\na planet at this distance and his conjecture was rendered more\\nAmer. Journal of Science, New Series, voL v. p. 436.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0240.jp2"}, "241": {"fulltext": "NEW PLANETS, OR ASTEROIDS. 215\\nprobable by the discovery of Uranus, which follows the analogy\\nof the other planets. So strongly were astronomers impressed\\nwith the idea that a planet would be found between Mars and\\nJupiter, that, in hope of discovering it, an association was formed\\non the continent of Europe of twenty-four observers, who divi-\\nded the sky into as many zones, one of which was allotted to\\neach member of the association. The discovery of the first of\\nthese bodies was, however, made accidentally by Piazza, an as-\\ntronomer of Palermo, on the 1st of January, 1801. It was\\nshortly afterwards lost sight of, on account of its proximity to\\nthe sun, and was not seen again until the close of the year, when\\nit was rediscovered in Germany. Piazza called it Ceres, in\\nhonor of the tutelary goddess of Sicily, and her emblem, the\\nsickle 9, has been adopted as the appropriate symbol. The dif-\\nficulty of finding Ceres, induced Dr. Olbers, of Bremen, to\\nexamine, with particular care, all the small stars that lie near her\\npath, as seen from the earth and, while prosecuting these obser-\\nvations, in March, 1802, he discovered another similar body,\\nvery nearly at the same distance from the sun, and resembling\\nthe former in many other particulars. The discoverer gave to\\nthis second planet the name of Pallas, choosing for its symbol\\nthe lance the characteristic of Minerva.\\n352. The most surprising circumstance connected with the\\ndiscovery of Pallas, was the existence of two planets at nearly\\nthe same distance from the sun, and apparently having a common\\nnode a circumstance that indicated an identity of origin. On\\naccount of this singularity, Dr. Olbers was led to conjecture that\\nCeres and Pallas are only fragments of a larger planet which had\\nformerly circulated around the sun at this distance, and been\\nshattered by some great convulsion.\\nIn 1804, near one of the nodes of Ceres and Pallas, a third\\nplanet was discovered. This was named Juno, and the charac-\\nter o was adopted for its symbol, representing the starry sceptre\\nof the goddess. In 1807, a fourth planet, Vesta, was discovered,\\nand for its symbol the character was chosen an altar sur-\\nmounted with a censer holding the sacred fire. It is the largest\\nof the asteroids, and has sometimes been seen by the naked eye.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0241.jp2"}, "242": {"fulltext": "216 THE PLANETS.\\n353. From 1807 to 1845, a period of nearly forty years, no\\nmore of these small planets were discovered, and, up to this time,\\nby the asteroids were meant the four little planets already enu-\\nmerated Ceres, Pallas, Juno, and Vesta. Meanwhile, very\\naccurate maps of the stars, including all up to the tenth magni-\\ntude, had been published, especially in the region of the zodiac,\\nand astronomers scrutinized these with such extreme closeness\\nthat any wanderer appearing among them, was likely to be im-\\nmediately detected. Since 1845 to the present time, (December,\\n1853,) no fewer than 23 more asteroids have been discovered,\\nmaking the entire number at present 27, as enumerated in arti-\\ncle 296. The average distance of the asteroids from the sun, is\\nabout 21 times that of the earth, or 240,000,000 miles but these\\ndistances vary considerably among themselves Flora being only\\nabout 200, and Hygeia nearly 300 millions of miles from the sun.\\nAs they are found to be governed by Kepler s law, like the other\\nmembers of the solar system, their average time of revolution\\nabout the sun is nearly 4 years although the nearest asteroid\\ncompletes its period in a little more than 3, while the most dis-\\ntant requires about 5j years. Some of these bodies have their\\norbits much more eccentric and highly inclined to the ecliptic than\\nthose of the old planets. Juno and Pallas move in orbits more\\neccentric even than that of Mercury and the inclination of\\nVesta exceeds 34 degrees, while those of several others are much\\nmore highly inclined than the orbit of Mercury. Their small\\nsize constitutes one of their most remarkable peculiarities. The\\ndifficulty of estimating the apparent diameter of bodies at once\\nso very small and so far, would lead us to expect that the esti-\\nmates of different observers would vary but all agree that their\\ndiameters are only a few hundred miles at most.\\n354. We have waited until the learner may be supposed to be\\nfamiliar with the heavenly bodies, individually, before inviting his\\nattention to a systematic view of the planets in their revolutions\\naround the sun, and their grand laws. The time has now ar-\\nrived for entering more advantageously upon this subject than\\ncould have been done at an earlier period.\\nThere are two methods of arriving at a knowledge of the mo-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0242.jp2"}, "243": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 217\\ntions of the heavenly bodies. One is, to begin with the apparent,\\nand from these to deduce the real motions the other is to begin\\nwith considering things as they really are in nature, and then to\\ninquire why they appear as they do. The latter of these methods\\nis by far the more eligible. It is much easier than the other\\nand proceeding from the less difficult to that which is more so\\nfrom motions which are very simple to such as are complicated,\\nit finally puts the learner in possession of the whole machinery of\\nthe heavens. We shall in the first place, therefore, endeavor to\\nintroduce the student to an acquaintance with the simplest mo-\\ntions of the planetary system, and afterwards to conduct him\\ngradually through such as are more complicated and difficult.\\n355. When viewed from the center of their motions, the revo-\\nlutions of the planets would appear simple and harmonious, all\\ncoursing around the spectator from west to east in regular order,\\nin nearly the same great highway, though with very different de-\\ngrees of velocity. Let us, then, suppose ourselves standing on\\nthe sun, and contemplate the revolutions of the planets, first, sev-\\nerally, and then as forming one grand whole, consisting of nu-\\nmerous parts, but bound together under the same laws in one\\nvast empire. We should see Mercury making very perceptible\\nprogress from night to night, like the moon in its motions about\\nthe earth, his daily progress eastward being about one-third as\\ngreat as that of the moon, since he completes his entire revolu-\\ntion in about three months. It will, at first, aid our conceptions\\nof the respective positions of the planetary orbits, to imagine the\\necliptic to be marked out on the face of the visible heavens in a\\npalpable line distinctly visible to the eye. If w r e watch the mo-\\ntions of Mercury from night to night, we shall see it cross the\\necliptic in two opposite points of the heavens, constituting its\\nnodes and we shall see it, when half way between the nodes, at\\nan angular distance from the ecliptic of about 7\u00c2\u00b0, this being the\\ninclination of its orbit. Knowing the position of the orbit of\\nMercury with respect to the ecliptic, we may now, in imagina-\\ntion, represent that orbit in a great circle passing through the\\ncentre of the planet and the center of the sun, and cutting the\\nplane of the ecliptic in two opposite points in an angle of 7 de-\\n28", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0243.jp2"}, "244": {"fulltext": "218 THE PLANETS.\\ngrees. The planes of both the ecliptic and the orbit of Mercury\\nmay be conceived of as indefinitely extended until they meet the\\nsphere of the fixed stars but the lines which the earth and Mer-\\ncury describe in those planes, that is, their orbits, may be con-\\nceived of as comparatively near to the sun. Could we now for\\na moment be permitted to imagine that the planes of the earth s\\norbit, and of the orbit of Mercury, were made of thin plates of\\nglass, and that the paths of the respective planets were marked\\nout on their planes in distinct lines, we should perceive the orbit\\nof the earth to be almost a perfect circle, while that of Mercury\\nwould appear distinctly elliptical, and we should see visibly rep-\\nresented to the eye the several relations of these two orbits to\\neach other. But having once made use of a palpable surface and\\nvisible lines to aid us in giving position and figure to the plane-\\ntary orbits, let us now throw aside these devices, and hereafter\\nconceive of these planes and orbits as ,they are in nature, and\\nlearn to refer a body to a mere mathematical plane, and to trace\\nits path in that plane through absolute space.\\n356. A clear understanding of the motions of Mercury, and\\nof the relations of its orbit to the plane of the ecliptic, will ren-\\nder it easy to understand the same particulars in regard to each\\nof the other planets. Standing on the sun, we should see each\\nof the planets pursuing a similar course to that of Mercury, all\\nmoving from west to east, differing from each other chiefly in\\ntwo respects, namely, in their velocities, and in the distances to\\nwhich they recede from the ecliptic, or their inclinations. We\\nhave supposed the observer to select the plane of the earth s orbit\\nas his standard of reference, and to see how each of the other\\norbits is related to it but such a selection of the ecliptic is en-\\ntirely arbitrary the spectator on the sun, who views the motions\\nof the planets as they actually exist in nature, would make no\\ndistinction between the different orbits, but merely inquire how\\nthey are mutually related to each other. Taking, however, the\\necliptic as the plane to which all the others are referred, we do\\nnot, as in the case of the other planets, inquire how its plane is\\ninclined, nor what are its nodes, since it has neither inclination\\nnor node.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0244.jp2"}, "245": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM.\\n219\\n357. Such, in general, are the real motions of the planets, and\\nsuch the appearances which the planetary system would exhibit\\nto a spectator at the center of motion. But, in order to repre-\\nsent correctly the positions of the planetary orbits, at any given\\ntime, three things must be regarded the Inclination of the orbit\\nto the ecliptic the position of the line of the Nodes and the\\nposition of the line of the Apsides. In our common diagrams, the\\norbits are incorrectly represented, being all in the same plane, as\\nFig. 68.\\nin the following diagram, where AEB (Fig. 68) represents the\\norbit of Mercury as lying in the same plane with the ecliptic.\\nTo exhibit its position justly, AB being taken as the line of the\\nnodes, the plane should be elevated on one side about 7\u00c2\u00b0, and\\ndepressed the same number of degrees on the other side, turn-\\ning on the line AB as on a hinge. But even then the represen-\\ntation may be incorrect in other respects, for we have taken it\\nfor granted that the line of the nodes coincides with the line\\nof the apsides, or that the orbit of Mercury cuts the ecliptic in\\nthe line AB, the major axis of the orbit, whereas it may lie in\\nany given position with respect to the line of apsides, according", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0245.jp2"}, "246": {"fulltext": "220 THE PLANETS.\\nto the longitude of the nodes. If, for example; the line of nodes\\nhad chanced to pass through Taurus and Scorpio instead of Can-\\ncer and Capricorn, then it would have been represented by the\\nline 8 H instead of the line passing though and the plane when\\nelevated or depressed with respect to the plane of the ecliptic,\\nwould be turned on this line in our figure. Moreover, our dia-\\ngram represents the line of apsides as passing through Cancer and\\nCapricorn, whereas it may have any other position among the\\nsigns, according to the longitudes of the perigee and apogee.\\n358. Having acquired as correct an idea as we are able of the\\nplanetary system, as seen from the sun, and of the positions of the\\norbits with respect to the ecliptic, let us next inquire into the na-\\nture and causes of the apparent motions. The apparent motions\\nof the planets are exceedingly unlike the real motions, a fact\\nwhich is owing to two causes first, we view them out of the\\ncenter of their orbits secondly, we are ourselves in motion.\\nFrom the first cause, the apparent places of the planets are\\ngreatly changed by perspective and, from the second cause, we\\nattribute to the planets changes of place which arise from our\\nown motions, of which we are unconscious.\\n359. The situation of a heavenly body, as seen from the center\\nof the sun, is called its heliocentric place as seen from the center\\nof the earth, its geocentric place. The geocentric motions of the\\nplanets must, according to what has just been said, be far more\\nirregular and complicated than the heliocentric, as will be evi-\\ndent from the following diagram, which represents the geocen-\\ntric motions of Mercury for two entire revolutions, embracing a\\nperiod of nearly six months. Let S (Fig. 69) represent the sun,\\n1, 2, 3, c, the orbit of Mercury, a,b,c, c, that of the earth, and\\nGT the concave sphere of the heavens. The orbit of Mercury\\nis divided into 12 equal parts, each of which he describes in 7j\\ndays and a portion of the earth s orbit described by that body\\nin the time that Mercury describes the two complete revolutions,\\nis divided into 24 equal parts. Let us now suppose that Mercury\\nis at the point 1 in his orbit, when the earth is at the point a\\nMercury will then appear in the heavens at A. In 7J days", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0246.jp2"}, "247": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM.\\n221\\nMercury will have reached 2, while the earth has reached b t\\nwhen Mercury will appear at B. By laying a ruler on the point\\nc and 3, d and 4, and so on, in the order of the alphabet, the suc-\\ncessive apparent places of Mercury in the heavens will be ob-\\ntained. From A to C, the apparent motion is direct, or in the\\nFig. 69.\\norder of the signs from C to G it is retrograde at G it is sta-\\ntionary a while, and then direct through the whole arc GT. At\\nI the planet is again stationary, and afterwards retrograde along\\nthe arc TX. Hence it appears that the motions of an inferior\\nplanet, as viewed from the earth, are exceedingly irregular and\\ncomplicated, although it is all the while pursuing its course at a\\nnearly uniform rate, and in the same unvarying direction around\\nthe sun. It moves forward when near the superior conjunction,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0247.jp2"}, "248": {"fulltext": "222 THE PLANETS.\\nbackward when near the inferior, and is stationary near the points\\nof greatest elongation. The planet moves sometimes very\\nslowly, and then rapidly at one time backward over a small space,\\nand then forward for a great distance. Yet all these apparent\\nirregularities are owing to the two causes already adverted to,\\nviz., the effects produced by perspective, and by the motions of\\nthe spectator himself. Venus exhibits a variety of motions sim-\\nilar to those of Mercury, except that the changes do not succeed\\neach other so rapidly, since her period of revolution approaches\\nmore nearly to that of the earth.\\n360. The apparent motions of the superior planets are, like those\\nof Mercury and Venus, alternately direct and retrograde, and be-\\ntween the two the planets are stationary. In this case, however,\\nthe earth moves faster than the planet, and the planet has its\\nopposition, but no inferior conjunction; whereas an inferior\\nplanet has its inferior conjunction, but no opposition. These\\ndifferences render the apparent motions of the superior planets\\nin some respect unlike those of Mercury and Venus. On the\\nside of the sun most remote from the earth, the motion of a\\nsupsrior planet is direct, because, as is the case with Venus in\\nher superior conjunction, (see Figure 61,) the only effect of the\\nearth s motion is to accelerate it but when the planet is in op-\\nposition, the earth is moving past it with greater velocity, and\\nmakes the planet seem to move backwards, like the apparent\\nbackward motion of a vessel when we overtake it and pass rapidly\\nby it in a steamboat.\\n361. Let ABCD (Fig. 70) represent the earth in different posi-\\ntions in its orbit, M a superior planet as Mars, and NR an arc of\\nthe concave sphere of the heavens. First, suppose the planet to\\nremain at rest in M, and let us see what apparent motions it\\nwould receive from the real motions of the earth. When the\\nearth is at B, it will see the planet in the heavens at N and as\\nthe earth moves successively through CDEF, the planet will\\nappear to move through OPQR B and F are the two points of\\ngreatest elongation of the earth from the sun, as seen from the\\nplanet between these two points, while passing through the part", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0248.jp2"}, "249": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM.\\n223\\nof its orbit most remote from the planet, (at which time the planet\\nis seen in superior conjunction,) the earth, by its own motion,\\ngives an apparent motion to the planet in the order of the signs\\nthat is, the apparent motion given by the earth s motion, when\\nthe planet is seen towards its superior conjunction, is direct.\\nBut in passing from F to B through A, when the planet is seen\\ntowards its opposition, the apparent motion given to the planet\\nby the earth s motion is retrograde. But the superior planets\\nFig. 10.\\nare not in fact at rest, as we have supposed, but are all the while\\nmoving eastward, though w 7 ith a slower motion than the earth.\\nIndeed, with respect to the remotest planets, as Saturn and Ura-\\nnus, the forward motion is so exceedingly slow, that each remains\\nfor a long time in the same sign of the zodiac. Still, the effect\\nof the real motions of all the superior planets eastward, is to in-\\ncrease the direct apparent motion communicated by the earth,\\nand to diminish the retrograde motion, as will be readily seen\\nfrom the figure.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0249.jp2"}, "250": {"fulltext": "CHAPTER XI.\\nDETERMINATION OF THE PLANETARY ORBITS-\\nELEMENTS OF THE ORBIT OF A PLANET QUANTITY OF MAT-\\nTER IN THE SUN AND PLANETS.\\n362. In Chapter II. we have shown that the figure of the earth s\\norbit is an ellipse, having the sun in one of the foci, and that the\\nearth s radius describes equal spaces in equal times and in Chap-\\nter III. we have remarked that these are only particular exam-\\nples under the law of Universal Gravitation, as is also the addi-\\ntional fact, that the squares of the periodic times of the planets\\nare as the cubes of the major axes of their orbits. We may now\\nlearn more particularly the process by which the illustrious Kep-\\nler was conducted to the discovery of these grand laws of the\\nplanetary system. From the apparent motions of the heavenly\\nbodies as seen projected on the face of the sky, the ancient as-\\ntronomers inferred that their orbits were necessarily circular,\\nand the motions actually uniform. Still, Hipparchus and Ptolemy\\nwere not ignorant of the fact, that the sun moves faster through\\nthe winter than through the summer signs, performing the half\\nof his revolution around the earth nearly eight days sooner\\nfrom the autumnal to the vernal, than from the vernal to the\\nautumnal equinox. This led them to infer that the earth is not\\nin the center of the circle, but nearer to one side of the circle\\nthan to the other, by which means the sun would appear to move\\nmore rapidly in that part of its orbit than in the opposite part,\\njust as a steamboat appears to a spectator on the shore to move fast-\\ner when nearer than when more remote from the shore, although\\nher actual speed is the same in both cases. On a similar suppo-\\nsition, Tycho Brahe made a great number of very accurate ob-\\nservations on the planetary motions, which served Kepler as\\nstandards of comparison for results which he deduced from cal-\\nculations, founded on the application of geometrical reasoning to", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0250.jp2"}, "251": {"fulltext": "DETERMINATION OF THE PLANETARY ORBITS. 225\\nvarious hypotheses which he successively assumed as to the fig-\\nure of the planetary orbits first supposing the orbit to be of a\\ncertain figure, then determining from the geometrical properties\\nof the curve what motions the body would appear to us to have\\nwhen moving in such a path, and finally testing his conclusions\\nby comparing them with the facts, as determined by Tycho, from\\nobservation.\\n363. Kepler first applied himself to investigate the figure of the\\norbit of Mars, the motions of which planet appeared more irreg-\\nular than those of any other planet except Mercury, which, being\\nseldom seen, had been very little studied. Like Ptolemy and\\nTycho, he first supposed the orbit to be circular, and the planet\\nto move uniformly about a point at a certain distance from the\\nsun. He made seventy suppositions before he obtained one that\\nagreed with observation, the calculation of which was extremely\\nlong and tedious, occupying him more than five years.* The\\nsupposition of an equable motion in a circle, however varied,\\ncould not be made to conform to the observations of Tycho,\\nwhereas the supposition that the orbit was an oval figure, de-\\npressed at the sides, but coinciding with a circle at the perihelion,\\nagreed so nearly with observation as to leave no doubt that the\\norbit of Mars is an ellipse, having the sun in one of its foci. He\\nimmediately inferred that the same is true of the orbits of all the\\nother planets and a similar comparison of this hypothesis with\\nobservation, confirmed its truth. Thus he established the first\\ngreat law, viz., The planets revolve about the sun in ellipses, hav-\\ning the sun in one of the foci.\\n364. Kepler also discovered from observation, that the veloci-\\nties of the planets, when in their apsides, are inversely as the\\ndistances respectively, and therefore the product of the velocity\\nLogarithms were invented during the age of Kepler, but were not available\\nto him until his most laborious calculations had been performed. In relation to\\nthese, he expresses himself thus Si te hujus laboriosce metlwdi pertcesum fueritjure\\ntnei te misereat, qui earn ad minimum septuagies ivi cum plurima temporia jactura\\net mirari desines hunc quintum jam annum abire, ex quo Martem aggressus sum.\\n29", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0251.jp2"}, "252": {"fulltext": "226 THE PLANETS.\\ninto the distance is a constant quantity, as was proved of the\\nsolar orbit, (Art. 167.) From this it follows that the radius vec-\\ntor in each case describes equal areas in equal times, since the\\nproduct of a triangle or circular sector into the perpendicular, is\\na measure of its area. But in this case the base is the space\\ndescribed by the planet in a given time, and the perpendicular is\\nthe radius vector, (Fig. 32, p. 86.) Although he could not prove,\\nfrom observation, that the same was true in every point of the\\norbit, yet analogy suggested that such was probably the fact. 1\\nTherefore, assuming this principle as true, and hence deducing\\nthe equation of the center, (Art. 200,) he found the result to\\nagree with observation, and therefore concluded in general, that\\nthe radius vectors of the planetary orbits describe about the sun\\nequal areas in equal times.\\n365. Having in his researches, that led to the discovery of\\nthe first of the above laws, found the relative mean distances\\nof the planets from the sun, (Art. 308,) and, knowing their\\nperiodic times from observation, Kepler next endeavored to\\nascertain if there was any relation between the distances and\\ntimes of revolution, having a strong passion for tracing analogies\\nin nature. He saw at once that the more distant a planet is from\\nthe sun, the slower it moves so that the periodic times of the\\nremoter planets are increased on two accounts first, because\\nthey have a longer path to traverse and secondly, because they\\nactually move more slowly in their orbits than the planets nearer\\nthe sun. Saturn, for example, is 9j times further from the sun\\nthan the earth is and since the circumferences of circles are as\\ntheir radii, the orbit of Saturn must be larger than the earth s in\\nthe same ratio so that if the periodic time of Saturn were longer\\nthan the earth s merely because its orbit is larger, that period\\nwould be 9| years, whereas it is 30 years. Hence it is evident,\\nthat the periodic times of the planets increase in a greater ratio\\nthan their distances from the sun, but in a less ratio than the\\nsquares of the distances, for then the time of Saturn would be\\nabout 90 years. Kepler then compared the squares of the times\\nwith the cubes of the distances, and found an exact agreement\\nbetween them. Thus he discovered the famous law, the squares", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0252.jp2"}, "253": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 227\\nof the periodic times of all the planets, are as the cubes of their\\nmean distances from the sun*\\n366. This law is strictly true only in relation to planets whose\\nquantity of matter in comparison with that of the central body is\\ninappreciable. When this is not the case, the periodic time is\\nshortened in the ratio of the square root of the sun s mass divi-\\nded by the sun s plus the planet s mass, as expressed by the\\nformula P. The mass of the planets is, however, so\\n\\\\M mf\\nsmall compared to the sun s, that this modification of the law is\\nunnecessary except where extreme accuracy is required.\\nELEMENTS OF THE PLANETARY ORBITS.\\n367. The particulars necessary to be known in order to deter-\\nmine the precise situation of a planet at any instant, are called\\nthe Elements of its Orbit. They are seven in number, of which\\nthe first two determine the absolute situation of the orbit, and the\\nother five relate to the motion of the planet in its orbit. These\\nelements are,\\n(1.) The position of the line of the nodes.\\n(2.) The inclination to the ecliptic.\\n(3.) The periodic time.\\n(4.) The mean distance from the sun, or semi-axis major.\\n(5.) The eccentricity.\\n(6.) The place of the perihelion.\\n(7.) The place of the planet in its orbit at a particular epoch.\\n368. It may at first view be supposed that we can proceed to\\nfind the elements of the orbit of a planet in the same manner as\\nwe did those of the solar or lunar orbit, namely, by observations\\non the right ascension and declination of the body, converted into\\nlatitudes and longitudes by means of spherical trigonometry, (See\\nArt. 132.) But in the case of the moon, we are situated in the\\ncenter of her motions, and the apparent coincide with the real\\nmotions and, in respect to the sun, our observations on his appa-\\nrent motions give us the earth s real motions, allowing 180\u00c2\u00b0 differ-\\nVince s Complete System, L 98.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0253.jp2"}, "254": {"fulltext": "228 THE PLANETS.\\nence in longitude. But as we have already seen, the motions of\\nthe planets appear exceedingly different to us, from what they\\nwould if seen from the center of their motions. It is necessary\\ntherefore to deduce from observations made on the earth the cor-\\nresponding results as they would be if viewed from the center of\\nthe sun that is, in the language of astronomers, having the geo-\\ncentric place of a planet, it is required to find its heliocentric place.\\n369. The first steps in this process are the same as in the case\\nof the sun and moon. That is, for the purpose of finding the right\\nascension and declination, the planet is observed on the meridian\\nwith the Transit Instrument and Mural circle, (See Arts. 155 and\\n230,) and from these observations, the planet s geocentric longi-\\ntude and latitude are computed by spherical trigonometry. The\\ndistance of the planet from the sun is known nearly by Kepler s\\nlaw. From these data it is required to find the heliocentric lon-\\ngitude and latitude.\\nLet S and E (Fig. 71) be the sun and earth, P the planet, PO\\na line drawn from P perpendicular to the ecliptic, SA the direc-\\nFig. 71.\\ntion of Aries, and EH parallel to SA, and therefore (on account\\nof the immense distance of the fixed stars) also in the direction\\nof Aries. Then OEH, being the apparent distance of the planet\\nfrom Aries in the direction of the ecliptic, is the geocentric longi-\\ntude, and OEP, being the apparent distance of the planet from the\\necliptic taken on a secondary to the ecliptic, is the geocentric\\nlatitude. It is obvious also that the angles OSA and PSO are", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0254.jp2"}, "255": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 229\\nthe heliocentric longitude and latitude. The planet s angular dis-\\ntance from the sun, PES, is also known from observation. Hence,\\nin the triangle SEP, we know SP and SE and the angle SEP, from\\nwhich we can find PE and knowing PE and the angle PEO, we\\ncan find OE, since OEP is a right angled triangle. Hence in the\\ntriangle SEO, ES and EO, and the angle SEO (=OEH-SEH=\\ndifference of longitude of the planet and the sun) are known, and\\nhence we can obtain OSE, which added to the sun s longitude\\nESA,* gives us OSA the planet s heliocentric longitude.\\nAlso, because PS Rad. OP Sin. PSO.\\nPS x Sin. PSO=OPxRad.\\nBut EP Rad. OP Sin. OEP.\\nEPxSin. OEP^OPxRad.\\nPS x Sin. PSO=EPxSin. OEP.\\nPS EP Sin. OEP Sin. PSO.\\nThe first three terms of this proposition being known, the last\\nis found, which is the heliocentric latitude.\\n370. Having now learned how observations made at the earth\\nmay be converted into corresponding observations made at the\\nsun, we may proceed to explain the mode of finding the several\\nelements before enumerated although our limits will not permit\\nus to enter further into detail on this subject, than to explain the\\nleading principles on which each of these elements is determined.}\\n371. First, to determine the position of the Nodes, and the In-\\nclination of the Orbit.\\nThese two elements, which de- Fi g- 72\\ntermine the situation of the orbit.\\n(Art. 367,) maybe derived from two\\nheliocentric longitudes and latitudes.\\nLet AR and AS (Fig. 72) be two\\nStrictly, ESA, being the supplement of the angle SEH, is the supplement of\\nthe sun s longitude.\\nf Brinkley s Elements of Astronomy, p. 164.\\nMost of these elements admit of being determined in several different ways, an\\nexplanation of which may be found in the larger works on Astronomy, as Vince s\\nComplete System, YoL L Gregory s Aet. p. 212. Woodhouse, p. 562.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0255.jp2"}, "256": {"fulltext": "230 THE PLANETS.\\nheliocentric longitudes, PR and QS the heliocentric latitudes,\\nand N the ascending node. Then, by Napier s theorem,\\n(Art. 132,)\\nSin. NR (=AR-AN) _ pNR= sin. NS (=AS-AN)\\ntan. PR C tan. QS\\n.-.Sin. ARxcos. AN-cos. ARxsin. AN* _\\ntan. PR\\nsin. AS x cos. AN\u00e2\u0080\u0094 cos. AS x sin. AN\\nBut tan. AN=\\ntan. QS\\nsin. AN Sin. ARxtan. QS-sin. AS x tan. PR\\ncos. AN Cos. AR x tan. QS\u00e2\u0080\u0094 cos. AS x tan. PR\\nBut AN is the longitude of the ascending node and its value\\nis found in terms of the heliocentric longitudes and latitudes pre-\\nviously determined, (Art. 369.)\\nAgain, since AN is found, we may deduce from the first\\nequation above the value of PNR, which is the inclination of the\\norbit. f\\n372. Secondly, to find the Periodic Time.\\nThis element is learned, by marking the interval that passes\\nfrom the time when a planet is in one of the nodes until it returns\\nto the same node. We may know when a planet is at the node,\\nbecause then its latitude is nothing. If, from a series of observa-\\ntions on the right ascension and declination of a planet, we deduce\\nthe latitudes, and find that one of the observations gives the lati-\\ntude 0, we infer that the planet was at that moment at the node.\\nBut if, as commonly happens, no observation gives exactly 0, then\\nwe take two latitudes that are nearest to 0, but on opposite sides\\nof the ecliptic, one south and the other north, and as the sum of the\\narcs of latitude is to the whole interval, so is one of the arcs to the\\ncorresponding time in which it was described, which time being\\nadded to the first observation, or subtracted from the second, will\\ngive the precise moment when the planet was at the node.\\nBy repeated observations it is found, that the nodes of the plan-\\nets have a very slow retrograde motion.\\n373. If the orbit of a planet cut the ecliptic at right angles, then\\nDay s Trig. Art. 208. f Brinkley, p. 166.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0256.jp2"}, "257": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 231\\nsmall changes of place would be attended by appreciable differ-\\nences of latitude but in fact the planetary orbits are in general\\nbut little inclined to the ecliptic, and some of them lie almost in\\nthe same plane with it. Hence arises a difficulty in ascertaining\\nthe exact time when a planet reaches its node. Among the most\\nvaluable observations for determining the elements of a planet s\\norbit, are those made when a superior planet is in or near its op-\\nposition to the sun, for then the heliocentric and geocentric lon-\\ngitudes are the same. When a number of oppositions are\\nobserved, the planet s motion in longitude, as would be observed\\nfrom the sun, will be known. The inferior planets also, when in\\nsuperior conjunction, have their geocentric and heliocentric lon-\\ngitudes the same. When in inferior conjunction, these lon-\\ngitudes differ 180\u00c2\u00b0; but the inferior planets can seldom be\\nobserved in superior conjunction, on account of their proximity\\nto the sun, nor in inferior conjunction except in their transits,\\nwhich occur too rarely to admit of observations sufficiently nu-\\nmerous. Therefore, we cannot so readily ascertain by simple\\nobservation, the motions of the inferior planets seen from the sun,\\nas we can those of the superior.*\\n374. Hence, in order to obtain accurately the periodic time of\\na planet, we find the interval elapsed between two oppositions\\nseparated by a long interval, when the planet was nearly in the\\nsame part of the zodiac. From the periodic time, as determined\\napproximately by other methods, it may be found when the planet\\nhas the same heliocentric longitude as at the first observation.\\nThus the time of a complete number of revolutions will be\\nknown, and thence the time of one revolution. The greater the\\ninterval of time between the two oppositions, the more accurately\\nthe periodic time will be obtained, because the errors of observa-\\ntion will be divided between a great number of periods there-\\nfore by using very accurate observations, much precision may be\\nattained. For example, the planet Saturn was observed in the\\nyears 228 B. C, March 2, (according to our reckoning of time,)\\nto be near a certain star called y Virginis, and it was at the same\\nBrinkley, p. 16?.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0257.jp2"}, "258": {"fulltext": "232 THE PLANETS.\\ntime nearly in opposition to the sun. The same planet was again\\nobserved in opposition to the sun, and having nearly the same\\nlongitude, in Feb. 1714. The exact difference between these\\ndates was 1943y. 118d. 21h. 15m. It is known from other sources,\\nthat the time of a revolution is 29J years nearly, and hence it was\\nfound that in the above period there were 66 revolutions of Sat-\\nurn; and dividing the interval by this number, we obtain 29*444\\nyears, which is nearly the periodic time of Saturn according to\\nthe most accurate determination.\\n375. Thirdly, to determine the distance from the sun, andmajo?\\naxes of the planetary orbits.\\nThe distance of the earth from the sun being known, the mean\\ndistance of any planet (its periodic time being known) may be\\nfound by Kepler s law, that the squares of the periodic times are\\nas the cubes of the distances. The method of finding the dis-\\ntance of an inferior planet from the sun by observations at the\\ngreatest elongation, has been already explained, (see Art. 308.)\\nThe distance of a superior planet may be found from observations\\non its retrograde motion at the time of opposition. The periodic\\ntimes of two planets being known, we of course know their mean\\nangular velocities, which are inversely as the times. Therefore,\\nlet Ee (Fig. 73) be a very small portion of the earth s orbit, and\\nMm a corresponding portion of that of a superior planet, de-\\nscribed on the day of opposition, about the sun S, on which day\\nFiff. Hz.\\nthe three bodies lie in one straight line SEMX. Then the angle\\nESe and MSm, representing the respective angular velocities of\\nthe two bodies are known. Now if em be joined, and prolonged\\nto meet SM continued in X, the angle EXe, which is equal to the\\nalternate angle Xey, being equal to the retrogradation of the planet\\nin the same time, (being known from observation,) is also given.\\nEe, therefore, and the angle EXe being given in the right-angled\\ntriangle EXe, the side EX is easily calculated, and thus SX be-\\ncomes known. Consequently, in the triangle SmX, we have", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0258.jp2"}, "259": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 233\\ngiven the side SX, and the two angles ??*SX and rriXS, whence\\nthe other sides Sm and niX. are easily determined. Now Sm is\\nthe radius of the orbit of the superior planet required, which, in\\nthis calculation, is supposed circular, as well as that of the earth,\\na supposition not exact, but sufficiently so to afford a satisfac-\\ntory approximation to the dimensions of its orbit, and which, if\\nthe process be often repeated, in every variety of situation at\\nwhich the opposition can occur, will ultimately afford an average\\nor mean value of its distance fully to be depended on.*\\n376. Fourthly, to determine the place of the perihelion the\\nepoch of passing the perihelion and the eccentricity.\\nAn easy method of finding the place of the perihelion, and\\nof course the position of the line of the apsides, of a planetary\\norbit, and the eccentricity, is the following. From a series of\\nobservations on the greatest elongations of a planet from the\\nsun, we shall find one that is a minimum, and another that is a\\nmaximum. The former denotes the place of the perihelion, the\\nlatter of the aphelion. Thus, (Fig. 60,) if in a long series of ob-\\nservations on the greatest elongations of Mercury, the value of\\nSB were at any time to be the least of all, we should know that\\nthat point is the place of the perihelion, and of course the point\\ndiametrically opposite is the place of the aphelion. Moreover, by\\ncalculating the relative distances of the planet from the sun at\\nthese two points, as in Art. 308, we ascertain the length of the\\nleast and the greatest radius vector, and half the difference of\\nthese two lines constitutes the eccentricity. This method, how-\\never, is applicable only to the inferior planets Mercury and Ve-\\nnus. The place of the nodes also can be determined by a series\\nof observations on the latitudes of a planet, being at those points\\nwhere the latitude is nothing. In most cases, indeed, the geo-\\ncentric would be different from the true heliocentric latitude,\\nand of course observation would not give the exact positions of\\nthe nodes but when, as is sometimes the case, the planet is in\\nconjunction or in opposition at the time of passing the node, then\\nit js seen in the same place as if viewed from the sun the geo-\\nSir J. HerscheL\\n30", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0259.jp2"}, "260": {"fulltext": "234\\nTHE PLANETS.\\ncentric coincides with the heliocentric place, and the observed\\nis the true place of the node.\\nBut trigonometry, building on a few instrumental observations,\\naffords other modes of arriving at the elements of a planetary\\norbit, one of which is derived from the greatest equation of the\\ncenter, (Art. 200.) For since the two points in the orbit where\\nthis becomes greatest are equally distant from the apsides, by\\nbisecting the interval between these\\ntwo points, we obtain the position of\\nthe perihelion and aphelion. Let\\nAEBF (Fig. 74) be the orbit of the\\nplanet, having the sun in the focus at\\nS. In an ellipse, the square root of\\nthe product of the semi-axes gives\\nthe radius of a circle of the same\\narea as the ellipse.* Therefore,\\nwith the center S, at the distance\\nSE= \\\\/AR x OK, describe the circle\\nCEGF, then will the area of this cir-\\ncle be equal to that of the ellipse. At\\nthe same time that a body departs\\nfrom A the aphelion, let a body begin to move with a uniform\\nmotion from C through the periphery CEGF, and perform a whole\\nrevolution in the same period that the planet describes the ellipse\\nthe motion of this body will represent the equable or mean motion\\nof the planet, and it will describe around S areas or sectors of\\ncircles which are proportional to the times, and equal to the ellip-\\ntic areas described in the same time by the planet. Let the\\nequable motion, or the angle about S proportional to the time, be\\nCSM, and take ASP equal to the sector CSM then the place of\\nthe planet will be P MSC will be the mean anomaly, (Art. 200,)\\nDSC the true anomaly, and MSD the equation of the center.\\nSince the sectors CSM and ASP are equal, and the part CSD is\\ncommon to both, PACD and MSD are equal and therefore\\nPACD is the measure of the equation of the center, which is\\ngreatest when PACD becomes ACE, that is, at the point where\\nFig. 74.\\n\u00e2\u0096\u00a0^J\\nK\\nM^U\\nK\\neK\\n^s\\nwVkX/\\nx^\\nB\\nDay s Mensuration.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0260.jp2"}, "261": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 235\\nthe ellipse and the circle intersect one another. For since the\\nsemi-ellipse AEB and the semicircle CEG are equal, the planet,\\nstarting from the aphelion A, will at first fall behind the body\\nmoving in the circle, and will not overtake it till it arrives at B.\\nTaking from the ellipse and the circle the common part CEB,\\nthe remainders AEC and BEG are equal. The true anomaly\\nequals ASm, the mean anomaly ASV, and the difference or\\nmSV equals the equation of the center. But since ACE=GBE,\\ntherefore GBE CSR CSR -f ERm+wSV GBE-ERm=\\nwiSV. Hence the equation of the center becomes less than GBE\\nor ACE after passing the point E, and consequently, the equation\\nof the center is greatest at the point E, where the real motion of\\nthe planet is equal to its mean motion. The mean motion for\\nany given time is easily found for the time of revolution is to\\n360\u00c2\u00b0 as the given time is to the number of degrees for that time.\\nObservation shows when the actual motion of the planet is the\\nsame with this. Now, the equation of the center is greatest\\ntwice in the revolution, on opposite sides of the orbit, as at E and\\nF, which points lie at equal distances from the apsides A and B\\nand since the whole arc EAF or EBF is known, from the time\\noccupied in describing it, therefore, by bisecting the arc, we find\\nthe points A and B, the aphelion and perihelion, and, consequently,\\nthe position of the line of the apsides. The time of describing\\nthe area EBF being known, by bisecting this interval we obtain\\nthe moment of passing the perihelion, w T hich gives us the place\\nof the planet in its orbit at a particular epoch*\\n377. The amount of the greatest equation evidently depends\\non the eccentricity of the orbit, since it arises w T holly from the\\ndeparture of the ellipse from the figure of a perfect circle hence\\nthe greatest equation affords the means of determining the eccen-\\ntricity itself. In orbits of small eccentricity, as is the case with\\nmost of the planetary orbits, it is found that the arc which meas-\\nures the greatest equation is very nearly equal to the distance\\nbetween the foci, which always equals twice the eccentricity, the\\nmeasure of the eccentricity being the distance from the focus to\\nGregory s Astronomy, p. 197.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0261.jp2"}, "262": {"fulltext": "236 THE PLANETS.\\nthe center of the ellipse. The angular value of radius is 57\u00c2\u00b0 17\\n44 .8; for,\\n3.14159 1 180\u00c2\u00b0 57\u00c2\u00b0 17 44 .8.\\nTherefore, 57\u00c2\u00b0 17 44 8 radius half the greatest equation\\nof the center the eccentricity*\\nThe foregoing explanations of the methods of finding the ele-\\nments of the orbits, will serve in general to show the learner how\\nthese particulars are or may be ascertained yet the methods\\nactually employed are usually more refined and intricate than\\nthese. In astronomy, scarcely an element is presented simple\\nand unmixed with others. Its value when first disengaged, must\\npartake of the uncertainty to which the other elements are sub-\\nject, and can be supposed to be settled to a tolerable degree of\\ncorrectness, only after multiplied observations and many revi-\\nsions.! Indeed, a large part of the most arduous labors of astron-\\nomers have been employed in finding the elements of the plane-\\ntary orbits, with the wonderful degree of precision which has\\nfinally been attained.\\nQUANTITY OF MATTER IN THE SUN AND PLANETS.\\n378. It would seem at first view very improbable, that an in-\\nhabitant of this earth would be able to weigh the sun and planets,\\nand estimate the exact quantity of matter which they severally\\ncontain. But the principles of Universal Gravitation conduct\\nus to this result, by a process remarkable for its simplicity. By\\ncomparing the relations of a few elements that are known to us,\\nwe ascend to the knowledge of such as appeared beyond the pale\\nof human investigation. We learn the quantity of matter in a\\nbody by the force of gravity it exerts. Let us see how this force\\nis ascertained.\\n379. The quantities of matter in two bodies, may be found in\\nterms of the distances and periodic times of two bodies revolving\\naround them respectively, being as the cubes of the distances divi-\\nded by the squares of the periodic times.\\nVince s Complete System, 1.118. f Woodhouse, p. 51 9.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0262.jp2"}, "263": {"fulltext": "is to that in the sun. That is, 1 353,385.\\nQUANTITY OF MATTER IN THE SUN AND PLANETS. 237\\nThe force of gravity G in a body whose quantity of matter is\\nM and distance D, varies directly as the quantity of matter, and\\nM\\ninversely as the square of the distance that is, G cc r\u00e2\u0080\u0094. But it\\nis shown by writers on Central Forces, that the force of gravity\\nalso varies as the distance divided by the square of the periodic\\nD M D D 3\\ntime, or Ga Therefore, 2 oc and Mac p 2 Thus we\\nmay find the respective quantities of matter in the earth and the\\nsun, by comparing the distance and periodic time of the moon, re-\\nvolving around the earth, with the distance and periodic time of\\nthe earth revolving around the sun. For the cube of the moon s\\ndistance from the earth divided by the square of her periodic time,\\nis to the cube of the earth s distance from the sun divided by the\\nsquare of her periodic time, as the quantity of matter in the earth\\n238,545 3 95,0 00,00 s\\nYllftF 365.256 2\\nThe most exact determination of this ratio, gives for the mass\\nof the sun 354,936 times that of the earth. Hence it appears\\nthat the sun contains more than three hundred and fifty-four\\nthousand times as much matter as the earth. Indeed, the sun\\ncontains eight hundred times as much matter as all the planets.\\nAnother method, well suited to popular illustration, of weigh-\\ning the earth against the sun, is the following. Knowing the\\nradii of the solar and lunar orbits respectively, we can easily find\\nthe space which the moon descends towards the earth, and the\\nearth towards the sun, in any given time, as an hour. Thus,\\n(Fig. 75.) if we know the radius AE of the orbit, we can deter-\\nmine the length of the arc Kb, described in an hour, and also the\\nlength of the hypothenuse BE. But BE AE B the space\\nthrough which the central attracts the revolving body in the\\ngiven time. The earth draws the moon towards itself about 11\\nmiles per hour, and the sun draws the earth towards itself 24.4\\nmiles per hour that is, the sun exerts a force 2j greater on the\\nearth than the earth does on the moon. But were the sun at the\\nsame distance as the moon, his force of attraction would be the\\nOlmsted s Natural Philosophy, Art. 185.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0263.jp2"}, "264": {"fulltext": "238\\nTHE PLANETS.\\nsquare of 400, or 160,000 times as great as it is now that is, it\\nwould be 2Jx 160,000 times as great as the earth s attraction,\\nand, consequently, must have 2^x160,000=352,000 times as\\nmuch matter, a result agreeing nearly with the former. The\\nagreement would be exact if more precise numbers were em-\\nployed, but our object is here merely to illustrate the method.\\n380. The mass of each of the other planets that have satellites\\nmay be found, by comparing the periodic time of one of its sat-\\nellites with its own periodic time around the sun. By this means\\nwe learn the ratio of its quantity of matter to that of the sun.\\nThe masses of those planets which have no satellites, as Venus\\nor Mars, have been determined, by estimating the force of at-\\ntraction which they exert in disturbing the motions of other\\nbodies. Thus, the effect of the moon in raising the tides, leads\\nto a knowledge of the quantity of matter in the moon and the\\neffect of Venus in disturbing the motions of the earth, indicates\\nher quantity of matter.*\\n381. The quantity of matter in bodies varies as their magni-\\ntudes and densities conjointly. Hence, their densities vary as\\nThese estimates are made by the most profound investigations in Laplace s\\nMe*canique Celeste, Vol HI.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0264.jp2"}, "265": {"fulltext": "QUANTITY OF MATTER IN THE SUN AND PLANETS.\\n239\\ntheir masses divided by their magnitudes and since we know\\nthe magnitudes of the planets, and can compute as above their\\nmasses, we can thus learn their densities, which, when reduced\\nto a common standard, give us their specific gravities, or show\\nus how much heavier they are than water. Worlds, therefore,\\nare weighed with almost as much ease as a pebble, or an article\\nof merchandise.\\nThe densities and specific gravities of the sun, moon, and\\nplanets, are estimated as follows\\nSun,\\nMoon,\\nMercury,\\nVenus,\\nEarth,\\nMars,\\nJupiter,\\nSaturn,\\nUranus,\\nNeptune,\\nFrom this table it appears that the sun consists of matter but\\nlittle heavier than water but that the moon is more than three\\ntimes as heavy as water, though less dense than the earth, which\\nis five and a half times heavier than water. It also appears\\nthat the planets near the sun are, as a general fact, more dense\\nthan those more remote, Mercury being as heavy as many of\\nthe metallic ores, while Saturn is as light as a cork. The\\ndecrease of density, however, is not entirely regular, since Venus\\nis a little lighter than the earth, and Saturn than Uranus.\\nDensity.\\nSpecific Gravity.\\n0.25\\n1.37f\\n0.56\\n3.27\\n1.12\\n6.13\\n0.92\\n5.04\\n1.00\\n5.48\\n0.95\\n5.20\\n0.24\\n1.31\\n0.14\\n0.76\\n0.24\\n1.31\\n0.14\\n0.76\\nHerschel.\\nf The earth being taken, according to Baily, at 5.48, the specific gravities of the\\nother bodies (which are found by multiplying the density of each by the specific\\ngravity of the earth) are here stated somewhat higher than they are given in\\nmost works", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0265.jp2"}, "266": {"fulltext": "CHAPTER XII.\\nPERTURBATIONS OF THE PLANETS STABILITY OF THE SYSTEM\\nNUMERICAL RELATIONS OF THE PLANETS PROBLEMS.\\n382. The perturbations occasioned in the motions of the plan-\\nets by their action on each other are very numerous, since every\\nbody in the system exerts an attraction on every other, in confor-\\nmity with the law of universal gravitation. Venus and Mars,\\napproaching as they do at times comparatively near to the earth,\\nsensibly disturb its motions and Jupiter and Saturn, although\\nvery far asunder, still, in consequence of their great masses,\\nexert on each other, w r hen on the same side of the heavens es-\\npecially, a decided influence. Moreover, the sun, by his unequal\\naction on the several planets, in consequence of the peculiar fig-\\nure of each, produces various irregularities in their motions. As\\nin the case of the earth and moon, (Art. 243.) these perturbations\\nare divided into periodical and secular: periodical, when com-\\npleted in comparatively short periods, as those, for example,\\nwhich undergo all their changes during one revolution of the\\nplanet and secular, when completed only in very long periods,\\nas those which affect the form and inclination of the orbits.\\n383. If the only bodies in the system were a central body like\\nthe sun, and a revolving body like Venus, then, when the planet\\nwas once put in motion with such a projectile force as to make\\nit describe an ellipse, it would forever continue to describe the\\nsame figure without the least variation, the radius vector always\\npassing over equal spaces in equal times but now introduce a\\nthird body so near as to exert on it a decided attraction, and its\\nmotions no longer retain their simplicity, but become complica-\\nted by the conflicting influences of the two attracting bodies.\\nThe sun, however, in consequence of its mass, which is eight\\nhundred times as great as that of all the planets, and, of course,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0266.jp2"}, "267": {"fulltext": "PERTURBATIONS OF THE PLANETS. 241\\nvastly greater than that of any one of them, exerts a force so\\nmuch superior to that of any or all the other disturbing bodies,\\nthat the elliptical figure of the orbits is nearly maintained, and a\\nnear approximation to the place of a planet is obtained, by neg-\\nlecting all those minor forces, and simply contemplating it as re-\\nvolving in an elliptical orbit. Still it is essential, in order to find\\nthe exact place of a planet at any given time, that all these irreg-\\nularities, minute as they may be, be carefully summed up, and\\ntheir resultant applied to the elliptical motions. To investigate\\nthese perturbations, to estimate their precise amount, and to reg-\\nister them in tables, for the use of the practical astronomer, have\\nconstituted a large part of the labors of modern astronomy. The\\nknowledge gained by astronomers of the planetary motions, con-\\nsidering the very numerous irregularities, both periodical and\\nsecular, to which they are subject, is truly wonderful. The mo-\\ntion of Jupiter, for instance, is so perfectly calculated, that\\nastronomers have computed ten years beforehand the time at\\nwhich it will pass the meridian of different places, and we find\\nthe prediction correct within half a second of time.* The\\nmore obvious irregularities have been detected by observation\\nthe more minute, by following out the consequences of universal\\ngravitation. Even those at first revealed to the instruments of\\nthe astronomer, have been confirmed and estimated with greater\\naccuracy, by the same far-reaching principle and many of the\\nirregularities have been first brought to light by this theory,\\nwhich had before eluded observation although, when once\\npointed out as a result of the principle of gravitation, careful\\ninstrumental measurements have confirmed them, except in cases\\nwhere the force was too minute to be reached by the most re-\\nfined observation. Periodical perturbations among the bodies of\\nthe solar system, maybe compared to the regular flux and reflux\\nof the tides, by which the ocean daily oscillates about its mean\\nlevel, without any permanent change of level, w 7 hile secular per-\\nturbations would resemble any slow changes of level, which, accu-\\nmulating from time to time, might finally become obvious to\\nmeasures of the depths of the ocean, as recorded from age to age.\\nAiry.\\n31", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0267.jp2"}, "268": {"fulltext": "242 THE PLANETS.\\nAs an example of the extreme minuteness of some of these secular\\nperturbations, we may instance the changes in the eccentricity\\nof the earth s orbit. The entire eccentricity is so small that the\\nfigure, when drawn on paper in just proportions, can scarcely be\\ndistinguished from a circle, the focus of the ellipse being distant\\nfrom the center only about part of the semi-major axis. But\\nthe change of eccentricity in a century, is only the twenty-five\\nthousandth part of the whole, or the hundred and fifty thousandth\\npart of the semi-major axis.\\n384. But although the secular inequalities of the planetary mo-\\ntions are exceedingly slow, yet may they not in time accumulate\\nso as to derange the whole system and do they not at least indi-\\ncate that the system carries within it the seeds of its own dissolu-\\ntion So far is this from being the case, that the stability of the\\nsolar system is a fact established on the most satisfactory evidence,\\nand its demonstration is among the finest triumphs of physical\\nastronomy. Even a superficial view of the system will convince\\nus that care has been bestowed on this point by several obvious\\narrangements. One is, that the planets have severally so small\\nmasses compared with the sun, as to interfere but little, at most,\\nwith the supremacy of his control over the planetary motions.\\nAnother is, that the planets are placed at such great distances from\\neach other, a distance which is greatest among the largest bod-\\nies, as Jupiter and Saturn, than among the smaller, as the earth\\nand Venus and another still, that the orbits are less eccentric\\nwhen the masses of the bodies are greater, by which provision\\nthey are always maintained at a remote distance from the sun.\\nWere the orbit of Jupiter as eccentric as that of Mars, he would\\napproach so near the earth at his perihelion, as greatly to endanger\\nits stability. But if even these general considerations might\\nconvince us that the stability of the solar system is provided for,\\na more profound investigation will reveal this truth in a far more\\nadmirable light. This object is especially secured by the follow-\\ning remarkable provisions.\\nFirst, by the invariability of the grand axes, and of the peri-\\nodic times secondly, by the fact, that whatever irregularities a\\nplanet undergoes on one side of its orbit, (so far as respects the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0268.jp2"}, "269": {"fulltext": "STABILITY OF THE SYSTEM. 243\\nperiodical perturbations,) they are compensated on the other\\nside so that, when it returns to a given point, as the node or\\nthe perihelion, any irregularities it may have felt in different parts\\nof its orbit, neutralize one another, and therefore do not consti-\\ntute an accumulating mass of errors and, thirdly, by this, that\\nall the secular perturbations are restricted within narrow limits,\\noscillating to and fro but, before they can proceed so far on one\\nside as to endanger the stability of the system, they turn about\\nand proceed, for a similar period, in the opposite direction.\\n385. These truths have been established by the most rigorous\\nmathematical demonstrations, by the successive labors of three\\nvery celebrated mathematicians, Euler, Lagrange, and Laplace.\\nIt was demonstrated that the major axes of the planetary orbits,\\nand the times of their revolutions around the sun, are subject to no\\nsecular perturbations, nor to any variation whatever, but such as,\\nin the course of a single revolution, exactly compensate and neu-\\ntralize each other. This is a most important point in relation to\\nthe stability of the system for if the lengths of the major axes\\nvaried, then, of course, the times of revolution would vary,\\n(since, by Kepler s 3d law, the squares of the periodic times are\\nin a constant ratio to the cubes of the major axes,) and we\\nshould have years of unequal length, and the earth, by approach-\\ning at one time nearer to the sun, and at another receding fur-\\nther from it, would render the changes of temperature too great\\nfor the existence of animal or vegetable life and similar evils,\\nit is probable, would result to the economy of the other planets.\\nIt was next established, that the eccentricities of the planetary\\norbits, although they have been undergoing constant changes in\\nall time past, and will continue to undergo them in all future\\nages, can never vary beyond a certain moderate limit, entirely\\nwithin the bounds of safety to the stability of the system. The\\neccentricity of the earth s orbit, for example, has been diminish-\\ning from the creation of the world and although, as we have\\nseen, the rate of diminution is exceedingly slow, yet, in the pro-\\ngress of centuries, it would totally change the character of the\\nearth s orbit first reducing it to the circular form, and finally\\ncarrying its eccentricity to a fatal extreme. In like manner, the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0269.jp2"}, "270": {"fulltext": "244 THE PLANETS.\\ninclination of the earth s orbit to the equator is constantly di-\\nminishing, and is now about two-fifths of a degree less than it\\nwas in the days of Aristotle and, were this to proceed in the\\nsame direction, the equator and ecliptic would coincide, the\\nchange of seasons would cease, and the whole economy of na-\\nture would be subverted. But Laplace has demonstrated, that\\nsuch an event can never occur, nor can the entire extent of this\\nvariation exceed three degrees. It is worthy of remark, that\\nthose perturbations, such as changes in the place of the peri-\\nhelion, affecting a change of direction in space of the major axis\\nof the orbit, or in the place of the nodes, which, by accumulating,\\ndo not endanger the stability of the system, proceed onward\\nthrough the entire circuit of the heavens, while perturbations\\nwhich, by indefinite accumulation, would bring ruin to the sys-\\ntem, such as variations of eccentricity and of inclination, are not\\nprogressive, but oscillatory, waving to and fro within the limits\\nof entire safety.\\n386. These great ends would not have been secured, had the\\nsystem been constructed differently from what it is. Numerous\\nconditions must concur in order to produce these results the\\nmass of the sun must have greatly exceeded that of any or all the\\nplanets the eccentricities of the orbits must have been small\\nand the planets must all have revolved around the sun in the\\nsame direction, and in planes but little inclined to each other.*\\nIt was also necessary that the periodic times of the planets should,\\nin general, be incommensurable for were their periods such that\\none planet would revolve a certain number of times exactly,\\nwhile another planet, next to it, revolved a certain other even\\nnumber of times, then, when they once came into the sphere of\\neach other s influence, they might remain under it so long,\\nand return to their relative position so often, as seriously to de-\\nrange their orbits. An instance of this, in fact, occurs in the\\ncase of Jupiter and Saturn, five revolutions of Jupiter being\\nnearly equal to two of Saturn, a relation which gives rise to\\nwhat is called the long inequality of Saturn and Jupiter. Similar\\nLaplace, Sys. du Monde. Herschel s Outlines. Grant s History of Physical\\nAstronomy. Pontecoulant s Trait. Elemen. de Phys. Celeste.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0270.jp2"}, "271": {"fulltext": "RELATIONS BETWEEN BODIES OF THE SOLAR SYSTEM. 245\\neffects result from a near commensurability of the mean motions\\nof any other two planets. One exists between the earth and Ve-\\nnus, 13 times the period of Venus being very nearly equal to 8\\ntimes that of the earth still the influence of this disturbing cause\\nis so nicely compensated, and its effects so distributed, that, ac-\\ncording to Mr. Airy, (who was the first to detect it,) it amounts,\\nat its finaximum, to no more than a few seconds for a period of\\n240 years. The laws which regulate the eccentricities and in-\\nclinations of the planetary orbits, (says an able writer on Physical\\nAstronomy,) combined with the invariability of the mean distan-\\nces, secure the permanence of the solar system throughout an\\nindefinite lapse of ages, and offer to us an impressive indication\\nof the Supreme Intelligence which presides over nature, and per-\\npetuates her beneficent arrangements. When contemplated\\nmerely as speculative truths, they are unquestionably the most\\nimportant which the transcendental analysis has disclosed to the\\nresearches of the geometer and their complete establishment\\nwould suffice to immortalize the names of Lagrange and La-\\nplace, even although these great geniuses possessed no other\\nclaims to the recollection of posterity.*\\nNUMERICAL RELATIONS BETWEEN THE BODIES OF THE SOLAR\\nSYSTEM.\\n387. If we contemplate the relations subsisting between a cen-\\ntral body, as the sun, and a revolving body, as one of the planets,\\nit will be readily understood, that if the quantity of matter in the\\ncentral body is increased, while the distance of the revolving\\nbody remains the same, the velocity of the revolving body must\\nbe increased also, in order to generate a sufficient centrifugal\\nforce to counterbalance the increased force of attraction in the\\ncentral body, arising from the increase of its mass and that,\\nwere the force of attraction diminished by removing the body to\\na greater distance from the center, then the rate of its motion\\nGrant s Hist. Phys. Ast.p. 56.\\nf In the preparation of this article, the author has derived much assistance from\\na small work, now nearly out of print, containing the substance of three lectures\\ndelivered to the students of Tale College in 1781, by Rev. Nehemiah Strong, at\\nthat time Professor of Mathematics and Natural Philosophy.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0271.jp2"}, "272": {"fulltext": "246 THE PLANETS.\\nwould also have to be diminished, otherwise the centrifugal force\\nwould overpower the force of attraction. It is a remarkable\\nfact, that the members of the solar system are so adjusted to each\\nother, in respect to their velocities, distances from the sun, peri-\\nodic times, and gravitation towards the central body, that if any\\none of these particulars is known, all the rest become known\\nalso. Thus, if it were found that a new-discovered planet\\nmoved in its orbit six times as slow as the earth, we should know\\nat once that its distance from the sun was thirty-six times as\\ngreat as the earth s distance, that its time of revolution was two\\nhundred and sixteen years, and that its gravitation towards the\\nsun was twelve hundred and ninety-six times less than that of the\\nearth for the distance is the square of the number expressing\\nthe rate of motion compared with thaj; of the body taken as a\\nstandard the periodic time is the cube and the gravitation to\\nthe sun is the biquadrate of t\\\\\\\\Q same number. All this follows\\nfrom Kepler s third law that the squares of the periodic times\\nare as the cubes of the distances and from the law of univer-\\nsal gravitation that the force of attraction is inversely as the\\nsquare of the distance. The four particulars named, therefore,\\nconstitute a series of numbers in geometrical progression, of\\nwhich the first term is equal to the ratio. The truth of this prop-\\nosition may be demonstrated as follows.\\nLet D be the mean distance of a planet from the sun, the\\nratio of the diameter to the circumference of a circle, and P the\\ntime of revolution around the sun, or periodic time then the ex-\\nr i -rr 2 D D Tr D 2\\npression tor the velocity is V p- x-^-. And V^oc^. But,\\nD 2 I\\nby Kepler s law, FxD 3 V 2 oc =r- 3 or V 2 ac -j?. Since a body\\nmore remote from the sun moves more slowly in its orbit than a\\nnearer body, and the comparative slowness, or retardation, is in-\\nversely as the velocity, in order to avoid fractional terms, we may\\nput the retardation (R) in the place of V, and then R 2 ac D, (1.)\\nIf, therefore, R indicates how much slower a planet moves than\\nanother, as the earth, taken as a standard, the square of R will\\nshow how much farther from the sun the planet is than the\\nearth.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0272.jp2"}, "273": {"fulltext": "NUMERICAL RELATIONS. 247\\nD D 3\\nAgain, since Vac -p, Vac But, ky Kepler s law, D 3 x P 2\\nV s x \u00e2\u0080\u0094or Y 3 z and R 3 x P (2.)\\nConsequently, if R expresses the retardation of a planet in\\ncomparison with the earth, the cube of R will express the corre-\\nsponding periodic time.\\nFinally, by the law of gravitation, the force of gravitation to-\\nwards the central body varies as the square of the distance\\ninversely, or Goc But the diminution of gravity (L) being\\ninversely as the gravity, LacD 2 but Da R 2 D 2 ac R 4 and\\nLxR 4 (3.)\\nTherefore, if R denotes how much slower a planet moves in\\nits orbit than the earth, R 4 will denote how much less the same\\nbody gravitates towards the central body. Collecting these sev-\\neral results, it appears that the square of the rate of motion gives\\nthe distance, its cube the periodic time, and its fourth power the\\ndiminution of gravity, which numbers compose a series in geomet-\\nrical progression, of which the first term is the ratio.\\n388. A number of very useful and convenient rules, may be\\nderived from this numerical relation between the members of the\\nsolar system since, when any one of the four things named is\\ngiven, all the rest may be found from it and each of the four\\nmay be found in four different ways when the other members of\\nthe series are given. This will be obvious from a few examples.\\nI. Given the rate of motion or retardation, (R.)\\n1. Square the retardation for the distance.\\n2. Cube the retardation for the periodic time.\\n3. Take the fourth power of the retardation for the force of\\ngravitation.\\nII. Given the distance, (D.)\\n1. Take the square root of the distance for the rate of motion.\\n2. Take the cube of the square root of the distance for the\\nperiodic time.\\n3. Take the square of the distance for the force of gravitation.\\nIII. Given the periodic time, (P.)", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0273.jp2"}, "274": {"fulltext": "248 THE PLANETS.\\n1. Take the cube root of the periodic time for the rate of\\nmotion.\\n2. Take the square of the cube root of the periodic time for\\nthe distance.\\n3. Take the biquadrate of the cube root for the force of gravi-\\ntation.\\nIV. Given the diminished force of gravitation, (L.)\\n1. Take the fourth root for the rate of motion.\\n2. Take the square root for the distance.\\n3. Take the cube of the fourth root for the periodic time.\\nV. Required the rate of motion.\\nThis may be obtained by taking the square root of the distance,\\nor the cube root of the periodic time, or the biquadrate root of\\nthe force of gravitation, or by dividing the force of gravitation\\nby the periodic time.\\nVI. Required the distance.\\nTake the square of the retardation, or the square of the cube\\nroot of the time, or the square root of the force of gravitation, or\\ndivide the time by the retardation.\\nVII. Required the periodic time.\\nWe may take the cube of the retardation, or the cube of the\\nsquare root of the distance, or the cube of the fourth root of the\\ngravitation, or may divide the gravitation by the retardation.\\nVIII. Required the diminished gravitation.\\nIt may be found from the fourth power of the retardation, or\\nthe square of the distance, or the biquadrate of the cube root of\\nthe time, or by multiplying the periodic time by the retardation.\\nAccording to the foregoing rules tables may be formed, exhib-\\niting, in a striking light, the numerical relations of the members\\nof the solar system. In the following table the distances are taken\\nfrom Herschel s Astronomy, and from these the other particulars\\nare determined by the preceding rules. If Mercury were taken\\nas the standard of comparison, then the retardations of all the\\nother planets would be greater than unity but, as it is con-\\nvenient to take the earth as the standard, the retardations of\\nMercury and Venus will be less than unity showing that the\\nvelocity (which is expressed by the fraction inverted) is greater\\nthan that of the earth. In like manner, the force of gravitation", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0274.jp2"}, "275": {"fulltext": "PROBLEMS.\\n249\\nof an inferior planet, being greater than that of the earth, is the\\nreciprocal of the tabular number.\\nTable showing the Numerical Relations of the Primary\\nPlanets.\\nPlanets.\\nRetardations.\\nDistances.\\nPer. Times.\\nForce of Gravi-\\ntation.\\nMercury,\\n0.62217\\n0.38710\\n0.24084\\n0.14985\\nVenus,\\n0.85049\\n0.72333\\n0.61519\\n0.52321\\nEarth,\\n1.00000\\n1.00000\\n1.00000\\n1.00000\\nMars,\\n1.23440\\n1.52369\\n1.88080\\n2.32170\\nJupiter,\\n2.28100\\n5.20277\\n11.86700\\n27.06900\\nSaturn,\\n3.08850\\n9.53878\\n29.46100\\n90.98900\\nUranus,\\n4.37970\\n19.18239\\n84.01200\\n367.95000\\nNeptune,\\n5.49040\\n30.14512\\n165.51000\\n908.72000\\n389. Problems.\\nProb. 1. The planet Pallas was discovered to have a period\\nof about 4| years. How much slower does it move in its orbit\\nthan the earth how much further is it from the sun and how\\nmuch less does it gravitate towards the sun? Ans. R 1.67,\\nD=2.79, L=7.80.\\nBy applying the proportional numbers determined by this prob-\\nlem respectively to the earth s motion per second, to its distance\\nfrom the sun in miles, and to the space through which the earth\\ndeparts in a second from a tangent to her orbit, we may obtain\\nthe numerical value of each of these elements.\\nProb. 2.\u00e2\u0080\u0094 What would be the periodical time of a meteor or\\nplanet revolving close to the earth\\nAs the moon is a body revolving around the earth at a known\\ndistance, and with a known periodic time, it will evidently furnish\\nthe necessary standard of comparison. The distance of the moon\\nfrom the center of the earth being 60 times the earth s radius,\\nand, of course, 60 times that of the meteor, its rate of motion is\\n\\\\/60 times less. The retardation being V60, the periodic time\\nwill be 60 2 Now, what part of the moon s period is 60 2 Di-\\nvide the moon s period (27.32 days) by 60^, and we have for the\\nanswer, 1 hour, 24 minutes, 38.88 seconds.\\n32", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0275.jp2"}, "276": {"fulltext": "250 THE PLANETS.\\nProb. 3. What would be the periodic time of a body revolv-\\ning about the earth at the distance of 5000 miles from the cen-\\nter? Ans. lh. 59m. 23.28s.\\nProb. 4.\u00e2\u0080\u0094 How much faster must the earth revolve in order\\nthat bodies on its surface may lose all their gravity\\nAccording to problem 2, the period of a body revolving at the\\nsurface of the earth, is 1.4108 hours and since, in a circular\\norbit, the force of gravity and the centrifugal force are equal,\\ntherefore a body like that contemplated in problem 2, is in equi-\\nlibrium between these two forces consequently, such a body\\nmay be considered as having lost all its gravity, and being, by\\nthe supposition, close to the earth, we have only to inquire how\\nmuch its velocity exceeds that of the earth. Now, 24 divided by\\n1.4108 gives 17.01 which shows that were the earth to revolve\\non its axis about 17 times faster than it does at present, the bod-\\nies on the surface would lose all their weight and were the ve-\\nlocity greater than this, the centrifugal force would prevail over the\\ncentripetal, and the same would fly off from the earth in tangents.\\nProb. 5. Were the moon to be removed so far from the earth\\nas to revolve about it but once a year, how much greater would\\nbe its distance than at present, how much less its velocity, and\\nits gravitation towards the earth\\nIts period being increased 13.37 times, its retardation is 13.37s\\n=2.373; its distance 2.373 2 5.631 and its diminished gravity\\n5.631 2 31.71. Or R=2.373, D 5.631, and L 31.71.\\nMultiplying the present distance of the moon, 238,545 miles,\\nby 5.631, we obtain about 1,343,000 miles for the distance at\\nwhich the moon must have been placed in order to complete its\\nrevolution in one year.\\nProb. 6. Were the earth s mass equal to the sun s, and of\\ncourse 354,000 times as great as at present, in what time would\\nthe moon revolve around it\\nSince the masses are as the cubes of the distances divided\\nby the squares of the periodic times, letting the required time\\nbe denoted by x, 1 (the earth s mass) 354.000 (the sun s mass)\\nD 3 D 3 1 1 1 354,000 27.32 _,\\nx _ lh.\\n27 .32 2 x 2 27.32 2 x 2 x 2 27.32 2 ^354,000\\n6m. 7s.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0276.jp2"}, "277": {"fulltext": "PROBLEMS. 251\\nComets, in passing their perihelion, especially when that hap-\\npens to be very near the sun, as in the great comet of 1843, move\\nwith an astonishing rapidity requiring a velocity not merely\\nsufficient to generate the centrifugal force necessary to balance\\nthe powerful force of attraction exerted by the sun, but greatly to\\nexceed that force, since they are carried far without a circular\\norbit into an elliptical or even a hyperbolic orbit.\\nProb. 7. The perihelion distance of the great comet of 1843\\nbeing 532,000 miles from the center of the sun, what must have\\nbeen its velocity per hour at that period\\nProb. 8. How much must the mass of the earth be increased\\nin order that the moon may revolve about it in the same time\\nas at present, when removed to three times her present dis-\\ntance\\nProb. 9. How much must the mass of the earth be increased\\nto make the moon, at her present distance, revolve in 24 hours\\nProb. 10. The semi-diameter of Jupiter being 11 times that\\nof the earth, and the distance of its fourth satellite from the cen-\\nter of the planet being 27 times the radius of the planet also the\\nsidereal revolution of the satellite being 16.69 days, while that of\\nthe moon is 27.3217 days, and her distance 60 times the radius\\nof the earth How r much does the quantity of matter in Jupiter\\nexceed that of the earth Ans. 324.49 times.\\nProb. 11. Suppose volcanic matter to be thrown from the\\nmoon towards the earth, required the point where it would be in\\nequilibrium between the two, the mass of the moon being one-\\neightieth that of the earth? Ans. 24,000 miles from the center\\nof the moon, nearly.\\nProb. 12. Suppose that the only two bodies in the universe\\nwere a sphere two inches in diameter, of the same density with\\nthe earth, for the primary, and a material point for the satellite\\nWhat would be the periodic time of the satellite, at the distance\\nof one foot, in a circular orbit Ans. 2 days, 10 hours, 13\\nminutes.*\\nThe elements used in the solution of this problem are, for the diameter of the\\nearth, h t9l2.4; for the distance of the moon 238,545 miles and for its periodic\\ntime, 21.32 days. The solution, conducted in the ordinary mode, will be found", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0277.jp2"}, "278": {"fulltext": "CHAPTER XIII.\\nCOMETS METEORIC SHOWERS.\\n390. A Comet,* when perfectly formed, consists of three parts,\\nthe Nucleus, the Envelope, and the Tail. The Nucleus, or body\\nof the comet, is generally distinguished by its forming a bright\\npoint in the center of the head, conveying the idea of a solid, or\\nat least of a very dense portion of matter. Though it is usually\\nsusceptible of great abridgment. But the following ingenious method is still\\nshorter. It was suggested, to the author by one of his pupils, Mr. Samuel Emer-\\nson, of the class of 1848.\\nLemma. The periodic times of two satellites revolving about primaries of equal\\ndensities, at distances which are equimultiples of their radii, are equal.\\nDemonstration. Let\\nM, m, the masses of the two bodies respectively.\\nP, p the periodic times.\\nR, r the radii of the spheres.\\nD, c? the distances of their satellites.\\nD 3 d*\\nThen, M m\\nBut since D and d are equimultiples of R, r, by some number n, therefore\\nD 9 RV, and(f rV;\\niJ RV rW R 8 r 3 _ 3\\nHence, M m \u00e2\u0080\u00945- -=rz -7. But, R 3 and r 3 oc M and. m.\\npi ^2 p2 ^2\\n_ s Mm MXm MXm\\nTherefore, M m P\\nThe moon being distant 60.296 radii of the earth, (as would result from the above\\nelements,) at the distance of 60.296 inches that of the small satellite from its pri-\\nmary would be the same multiple of its radius, and, consequently, its periodic\\ntime the same. What then is its period at 12 inches?\\n2 f 7.32\u00c2\u00bb p 1 60.296 3 12 s p 2d. lOh. 13m.\\nCorollary. If any two spheres of the same density be taken, the periodic times\\nof satellites revolving about them close to the surface, will be the same in both\\nfor the case becomes this when n 1. Thus, the material point supposed in the\\nabove problem, will revolve about its little globe in the same time that the\\nmoon would revolve about the earth, both being situated close to the surfaces\\nof their respective primaries.\\nKfyjj, coma, from the bearded appearance of comets.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0278.jp2"}, "279": {"fulltext": "COMETS. 253\\nexceedingly small when compared with the other parts of the\\ncomet, yet it sometimes subtends an angle capable of being meas-\\nured by the telescope. The Envelope (sometimes called the\\ncoma) is a dense nebulous covering, which frequently renders the\\nedge of the nucleus so indistinct, that it is extremely difficult to\\nascertain its diameter with any degree of precision. Many com-\\nets have no nucleus, but present only a nebulous mass extremely\\nattenuated on the confines, but gradually increasing in density\\ntowards the center. Indeed, there is a regular gradation of com-\\nets, from such as are composed merely of a gaseous or vapory\\nmedium, to those which have a well-defined nucleus. In some\\ninstances on record, astronomers have detected with their tele-\\nscopes small stars through the densest part of a comet. The\\nTail is regarded as an expansion or prolongation of the coma\\nand presenting, as it sometimes does, a train of appalling magni-\\ntude, and of a pale, portentous light, it confers on this class of\\nbodies their peculiar celebrity.\\n391. The number of comets belonging to the solar system, is\\nprobably very great. Many, no doubt, escape observation by\\nbeing above the horizon in the day-time. Seneca mentions, that\\nduring a total eclipse of the sun, which happened 60 years before\\nthe Christian era, a large and splendid comet suddenly made its\\nappearance, being very near the sun. The elements of at least\\n180 comets have been computed, and arranged in a catalogue for\\nfuture comparison.* Of these, six are particularly remarkable,\\nviz., the comets of 1680, 1770, and 1843; and those which bear\\nthe names of Halley, Encke, and Biela. The comet of 1680 was\\ndistinguished not only for its astonishing size and splendor, but is\\nremarkable for having been the first comet whose elements were\\ndetermined on the sure basis of mathematics, as was done by Sir\\nIsaac Newton, it having appeared in his time. The comet of\\n1770 is memorable for the changes its orbit has undergone by\\nthe action of Jupiter, and for having approached very near to the\\nearth. The comet of 1843 was the most remarkable in its ap-\\npearance of all that have been seen in modern times, having been\\nSee a complete catalogue of comets, whose elements have been determined, in\\nthe American Almanac for 1847.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0279.jp2"}, "280": {"fulltext": "254\\nCOMETS.\\nFig. 76.\\nFig. 77.\\nCOMET OF 1811.\\nCOMET OF 1680.\\nvisible at noonday. Halley s comet (the same which reappeared\\nin 1835) is distinguished as that whose return was first success-\\nfully predicted, and whose orbit was first accurately determined\\nand Biela s and Encke s comets are well known for their short\\nperiods of revolution, which subject them frequently to the view\\nof astronomers. Biela s comet, at its return in 1846, displayed\\nanother remarkable feature -a separation into two distinct parts.\\nThis strange peculiarity was first seen from the Observatory of\\nYale College, by Messrs. Herrick and Bradley, but was first pub-\\nlicly announced from the Observatory at Washington. At one\\ntime, the distance of one nucleus from the other, was estimated\\nat 157,000 miles.\\n392. In magnitude and brightness, comets exhibit a great di-\\nversity. They are sometimes so bright as to be distinctly\\nvisible in the day-time, even at noon and in the brightest sun-\\nshine, as was the case with that of 1843 and such was the comet\\nseen at Rome a little before the assassination of Julius Caesar.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0280.jp2"}, "281": {"fulltext": "COMETS. 255\\nThe comet of 1680 covered an arc of the heavens of 97\u00c2\u00b0, and\\nits length was estimated at 123,000,000 miles.* That of 1811\\nhad a nucleus of only 428 miles in diameter, but a tail 132,000,000\\nmiles long.f Had it been coiled around the earth like a serpent,\\nit would have reached round more than 5,000 times. Other com-\\nets are of exceedingly small dimensions, the nucleus being esti-\\nmated at only 25 miles and some which are destitute of any\\nperceptible nucleus, appear to the largest telescopes, even when\\nnearest to us, only as a small speck of fog, or as a tuft of down.\\nThe majority of these bodies can be seen only by the aid of the\\ntelescope.\\nThe same comet, indeed, has often very different aspects, at its\\ndifferent returns. Halley s comet in 1305 was described by the\\nhistorians of that ag;e, as cometa horrendcs ma rrnitudinis in 1456\\nits tail reached from the horizon to the zenith, and inspired such\\nterror, that, by a decree of the Pope of Rome, public prayers were\\noffered up at noon-day in all the Catholic churches to deprecate\\nthe wrath of heaven, while in 1682, its tail was only 30\u00c2\u00b0 in length,\\nand in 1759 it was visible only to the telescope, until after it. had\\npassed its perihelion. At its recent return in 1835, the greatest\\nlength of the tail was about 12\u00c2\u00b0J These changes in the appear-\\nances of the same comet are partly owing to the different posi-\\ntions of the earth with respect to them, being sometimes much\\nnearer to them when they cross its track than at others also\\none spectator so situated as to see the comet at a higher angle of\\nelevation or in a purer sky than another, will see the train longer\\nthan it appears to one less favorably situated but the extent\\nof the changes are such as indicate also a real change in their\\nmagnitude and brightness.\\n393. The periods of comets in their revolutions around the sun,\\nare equally various. Encke s comet, which has the shortest\\nknown period, completes its revolution in 3j years, or more ac-\\ncurately, in 1205.23 days while that of 1811 is estimated to have\\nArago. f Milne s Prize Essay on Comets.\\nBut might be seen much longer by indirect vision. {Prof. Joslin, Am. Journ.\\nScience, xxxl 328.)", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0281.jp2"}, "282": {"fulltext": "256\\nCOMETS.\\na period of 3383 years.* The distances to which different com-\\nets recede from the sun, are also very various. While Encke s\\ncomet performs its entire revolution within the orbit of Jupiter,\\nHalley s comet recedes from the sun to twice the distance of\\nFig. 18.\\nw\\nUranus, or nearly 3600,000,000 miles. Figure 78 is a represen-\\ntation, in due proportions, of the orbit of this comet. Its vast\\ndimensions will be truly conceived of by reflecting that the ra-\\ndius of the small circle E of the earth s orbit implies a space of\\nnearly 100,000,000 miles; that, as the comet recedes from the\\nsun, it soon reaches the orbit of Jupiter, and successively traver-\\nses the orbits of Saturn, Uranus, and Neptune, reaching its aphe-\\nlion 600,000,000 miles beyond the present boundaries of the\\nplanetary system. Some comets, indeed, are thought to go to a\\nmuch greater distance from the sun than this, as that of 1811\\nmust have receded from it more than 45,000,000,000 miles, while\\nsome even are supposed to pass into parabolic or hyperbolic or-\\nbits, and never to return.\\n394. Comets shine by reflecting the light of the sun. In one or\\ntwo instances they have exhibited distinct phases,] although the\\nnebulous matter with which the nucleus is surrounded, would\\ncommonly prevent such phases from being distinctly visible, even\\nwhen they would otherwise be apparent. Moreover, certain\\nqualities of polarized light enable the optician to decide whether\\nthe light of a given body is direct or reflected and M. Arago,\\nMilne.\\nf Delambre, t. 3, p. 400.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0282.jp2"}, "283": {"fulltext": "COMETS. 257\\nof Paris, by experiments of this kind on the light of the comet of\\n1819, ascertained it to be reflected light.* The tail of a comet\\nusually increases very much as it approaches the sun and fre-\\nquently does not reach its maximum until after the perihelion\\npassage. In receding from the sun, the tail again contracts, and\\nnearly or quite disappears before the body of the comet is entirely\\nout of sight. The tail is frequently divided into two portions, the\\ncentral parts, in the direction of the axis, being less bright than\\nthe marginal parts. In 1744, a comet appeared which had six\\ntails, spread out like a fan.\\nThe tails of comets extend in a direct line from the sun, al-\\nthough they are usually more or less curved, like a long quill or\\nfeather, being convex on the side next to the direction in which\\nthey are moving, (Fig. 77 a figure which may result from the\\nless velocity of the portions most remote from the sun. Expan-\\nsions of the Envelope have also been at times observed on the\\nside next the sun.f but these seldom attain any considerable\\nlength.\\n395. The quantity of matter in comets is exceedingly small.\\nTheir tails consist of matter of such tenuity that the smallest stars\\nare visible through them. They can only be regarded as great\\nmasses of thin vapor, susceptible of being penetrated through\\ntheir whole substance by the sunbeams, and reflecting them alike\\nfrom their interior parts and from their surfaces. It appears,\\nperhaps, incredible that so thin a substance should be visible by\\nreflected light, and some astronomers have held that the matter\\nof comets is self-luminous but it requires but very little light to\\nrender an object visible in the night, and a light vapor may be\\nvisible when illuminated throughout an immense stratum, which\\ncould not be seen if spread over the face of the sky like a thin\\ncloud. The highest clouds that float in our atmosphere, must be\\nlooked upon as dense and massive bodies, compared with the filmy\\nand all but spiritual texture of a comet. J The small quantity of\\nFrancoeur, 181.\\nf See Dr. Joslin s remarks on Halley s comet- Arner. Journ. Science, vol. 31.\\nX Sir J. HerscheL\\n33", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0283.jp2"}, "284": {"fulltext": "258 COMETS.\\nmatter in comets is further proved by the fact that they have some-\\ntimes passed very near to some of the planets without disturbing\\ntheir motions in any appreciable degree. Thus the comet of 1770,\\nin its way to the sun, got entangled among the satellites of Jupiter,\\nand remained near them four months, yet it did not perceptibly\\nchange their motions. The same comet also came very near the\\nearth so near, that, had its mass been equal to that of the earth,\\nit would have caused the earth to revolve in an orbit so much\\nlarger than at present, as to have increased the length of the\\nyear 2h. 47m. Yet it produced no sensible effect on the length\\nof the year, and therefore its .mass, as is shown by Laplace,\\ncould not have exceeded 5-0V o \u00c2\u00b0f lat \u00c2\u00b0f the earth, and might have\\nbeen less than this to any extent. It may indeed be asked, what\\nproof we have that comets have any matter, and are not mere\\nreflections of light. The answer is, that, although they are not\\nable by their own force of attraction to disturb the motions of\\nthe planets, yet they are themselves exceedingly disturbed by the\\naction of the planets, and in exact conformity with the laws of\\nuniversal gravitation. A delicate compass may be greatly agi-\\ntated by the vicinity of a mass of iron, while the iron is not sen-\\nsibly affected by the attraction of the needle.\\n396. By approaching very near to a large planet, a comet may\\nhave its orbit entirely changed. This fact is strikingly exempli-\\nfied in the history of the comet of 1770. At its appearance in\\n1770, its orbit was found to be an ellipse, requiring for a complete\\nrevolution only 5| years and the wonder was, that it had not\\nbeen seen before, since it was a very large and bright comet.\\nAstronomers suspected that its path had been changed, and that\\nit had been recently compelled to move in this short ellipse, by\\nthe disturbing force of Jupiter and his satellites. The French\\nInstitute, therefore, offered a high prize for the most complete\\ninvestigation of the elements of this comet, taking into account\\nany circumstances which could possibly have produced an altera-\\ntion in its course. By tracing back its movements for some\\nLaplace.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0284.jp2"}, "285": {"fulltext": "COMETS. 259\\nyears previous to 1770, it was found that, at the beginning\\nof 1767, it had entered considerably within the sphere of Jupi-\\nter s attraction. Calculating the amount of this attraction from\\nthe known proximity of the two bodies, it was found what\\nmust have been its orbit previous to the time when it became sub-\\nject to the disturbing action of Jupiter. The result showed that\\nit then moved in an ellipse of greater extent, having a period of\\n50 years, and having its perihelion instead of its aphelion near\\nJupiter. It was therefore evident why, as long as it continued to\\ncirculate in an orbit so far from the center of the system, it was\\nnever visible from the earth. In January, 1767, Jupiter and the\\ncomet happened to be very near each other, and as both were\\nmoving in the same direction, and nearly in the same plane, they\\nremained in the neighborhood of each other for several months,\\nthe planet being between the comet and the sun. The conse-\\nquence was, that the comet s orbit was changed into a smaller\\nellipse, in which its revolution was accomplished in 5J years.\\nBut as it was approaching the sun in 1779, it happened again to\\nfall in with Jupiter. It was in the month of June that the attrac-\\ntion of the planet began to have a sensible effect and it was not\\nuntil the month of October following that they were finally sep-\\narated.\\nAt the time of their nearest approach, in August, Jupiter was\\ndistant from the comet only T J T of its distance from the sun, and\\nexerted an attraction upon it 225 times greater than that of the\\nsun. By reason of this powerful attraction, Jupiter being further\\nfrom the sun than the comet, the latter was drawn out into a new\\norbit, which, even at its perihelion, came no nearer to the sun than\\nthe planet \u00e2\u0082\u00aceres. In this third orbit, the comet requires about\\n20 years to accomplish its revolution and being at so great a\\ndistance from the earth, it is invisible, and will forever remain so,\\nunless, in the course of ages, it shall undergo new perturbations\\nand move again in some smaller orbit as before.*\\nMilne.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0285.jp2"}, "286": {"fulltext": "260 COMETS.\\nORBITS AND MOTIONS OF COMETS.\\n397. The planets, as we have seen, (with the exception of the\\nasteroids, which seem to be an intermediate class of bodies be-\\ntween planets and comets,) move in orbits which are nearly-\\ncircular, and all very near to the plane of the ecliptic, and all\\nmove in the same direction from west to east. But the orbits of\\ncomets are far more eccentric than those of the planets they are\\ninclined to the ecliptic at various angles, being sometimes even\\nnearly perpendicular to it and the motions of comets are some-\\ntimes retrograde.\\n398. The Elements of a comet are fiVe, viz., (1) The perihelion\\ndistance (2) longitude of the perihelion (3) longitude of the node\\n(4) inclination of the orbit; (5) time of the perihelion passage.\\nThe investigation of these elements is a problem extremely in-\\ntricate, requiring for its solution a skilful and laborious applica-\\ntion of the most refined analysis. Newton himself pronounced it\\nProblema longe difficilimum and with all the advantages of the\\nmist improved state of science, the determination of a comet s\\norbit is considered one of the most complicated problems in as-\\ntronomy. This difficulty arises from several circumstances\\npeculiar to comets. In the first place, from the elongated form of\\nthe orbits which these bodies describe, it is during only a very\\nsmall portion of their course that they are visible from the earth,\\nand the observations made in that short period cannot afterwards\\nbe verified on more convenient occasions whereas in the case\\nof the planets, whose orbits are nearly circular, and whose move-\\nments may be followed uninterruptedly throughout a complete\\nrevolution, no such impediments to the determination of their\\norbits occur. There is also some unavoidable uncertainty in\\nobservations made upon bodies whose outlines are so ill-defined.\\nIn the second place, there are many comets which move in a\\ndirection opposite to the order of the signs in the zodiac, and\\nsometimes nearly perpendicular to the plane of the ecliptic so\\nthat their apparent course through the heavens is rendered ex-\\ntremely complicated, on account of the contrary motion of the\\nearth. In the third place, as there may be a multitude of ellip-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0286.jp2"}, "287": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 261\\ntic orbits, whose perihelion distances are equal, it is obvious that,\\nin the case of very eccentric orbits, the slightest change in the\\nposition of the curve near the vertex, where alone the comet can\\nbe observed, must occasion a very sensible difference in the length\\nof the orbit, (as will be obvious from Fig. 79;) and therefore,\\nthough a small error produces no perceptible discrepancy between\\nthe observed and the calculated course, while the comet remains\\nvisible from the earth, its effect, when diffused over the whole\\nextent of the orbit, may acquire a most material or even a fatal\\nimportance.\\nOn account of these circumstances, it is found exceedingly dif-\\nficult to lay down the path which a comet actually follows through\\nthe whole system, and least of all possible to ascertain with ac-\\ncuracy the length of the major axis of the ellipse, and conse-\\nquently the periodical revolution.* An error of only a few sec-\\nonds may cause a difference of many hundred years. In this\\nmanner, though Bessel determined the revolution of the comet of\\n1769 to be 2089 years, it was found that an error of no more\\nthan 5 in observation, would alter the period either to 2678\\nyears, or to 1692 years. Some astronomers, in calculating the\\nFor when we know the length of the major axis, we can find the periodic time\\nby Kepler s law, which applies as well to comets as to planets.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0287.jp2"}, "288": {"fulltext": "262 COMETS.\\norbit of the great comet of 1680, have found the length of its\\ngreater axis 426 times the earth s distance from the sun, and con-\\nsequently its period 8792 years whilst others estimate the greater\\naxis 430 times the earth s distance, which alters the period to\\n8916 years. Newton and Halley, however, judged that this\\ncomet accomplished its revolution in only 570 years.\\n399. Disheartened by the difficulty of attaining to any preci-\\nsion in the circumstances by which an elliptic orbit is charac-\\nterized, and, moreover, taking into account the laborious calcula-\\ntions necessary for its investigation, astronomers usually satisfy\\nthemselves with ascertaining the elements of a comet on the\\nsupposition of its describing a parabola p and, as this is a curve\\nwhose axis is infinite, the procedure is greatly simplified by leav-\\ning entirely out of consideration the periodic revolution. It is\\ntrue that a parabola may not represent, with mathematical\\nstrictness, the course which a comet actually follows but as a\\nparabola is the intermediate curve between the hyperbola and\\nellipse, it is found that this method, which. is so much more con-\\nvenient for computation, also accords sufficiently with observa-\\ntions, except in cases when the ellipse is a comparatively short\\none, as that of Encke s comet, for example. When the elements\\nof a comet are determined, Kepler s law of areas enables astron-\\nomers to find, by computation, the exact place of the comet in its\\norbit at any given time, on the supposition that its path is a pa-\\nrabola and comparing this place with that determined by obser-\\nvation for the same instant, it is seen whether the orbit is truly\\nparabolic, or whether its deviation from that path is such as to\\nindicate that its real path is an ellipse and the amount of such\\ndeviation will give some idea of the degree of eccentricity of the\\nellipse.\\n400. The elements of a comet, with the exception of its peri-\\nodic time, are calculated in a manner similar to those of the\\nplanets. Three good observations on the right ascension and\\ndeclination of the comet (which are usually found by ascertaining\\nits position with respect to certain stars, whose right ascensions", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0288.jp2"}, "289": {"fulltext": "ORBITS AND MOTIONS OF COMETS.\\n263\\nand declinations are accurately known) afford the means of cal-\\nculating these elements.\\nThe appearances of the same comet at different periods of its\\nreturn are so various, (Art. 392,) that we can never pronounce a\\ngiven comet to be the same with one that has appeared before,\\nfrom any peculiarities in its physical aspect. The identity of a\\ncomet with one already on record, is determined by the identity\\nof the elements. When a new comet appears, we first determine\\nits elements, and then turning to a catalogue of comets whose\\nelements have previously been found and placed on record, we\\nsee whether these new elements agree with any set of those in\\nthe catalogue. If they do, we infer that the present comet is\\nidentical with that on record and the interval between the two\\nappearances of the body will indicate its periodic time. If, for\\nexample, we find respecting a comet now visible in the sky, that\\nits path makes the same angle with the ecliptic as that of a cer-\\ntain comet in our catalogue, that it crosses the ecliptic in the same\\ndegree of longitude, that it comes to its perihelion in the same\\nplace, that its perihelion distance is the same, and its course the\\nsame in regard to the order of the signs, then we infer that the\\ntwo bodies are one and the same and the number of years that\\nhave elapsed since its former appearance, indicates the period of\\nits revolution around the sun. But if these particulars differ\\nwholly from any set of recorded elements, we infer that the pres-\\nent is a comet which has never visited our sphere before, or at\\nleast one whose elements have not been determined and recorded.\\nIt was by this means that Halley first established the identity\\nof the comet which bears his name, with one that had appeared\\nat several preceding ages of the world, of which so many partic-\\nulars were left on record, as to enable him to calculate the ele-\\nments at each period. These were as in the following table.\\nTime of ap-\\nInclination of\\nLonscitude of\\nLongitude of\\nPerihelion\\nCourse.\\npearance.\\nthe Orbit\\nthe Node.\\nPerihelion.\\nDistance.\\n1456\\n17\u00c2\u00b0 56\\n48\u00c2\u00b0 30\\n301\u00c2\u00b0 00\\n0.58\\nRetrograde.\\n1531\\n17 56\\n49 25\\n301 39\\n0.57\\nRetrograde.\\n1607\\n17 02\\n50 21\\n302 16\\n0.58\\nRetrograde.\\n1682\\n17 42\\n50 48\\n301 36\\n0.58\\nRetrograde.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0289.jp2"}, "290": {"fulltext": "264 COMETS.\\nOn comparing these elements, no doubt could be entertained\\nthat they belonged to one and the same body and since the in-\\nterval between the successive returns was seen to be 75 or 76\\nyears, Halley ventured to predict that it would again return in\\n1758. Accordingly, the astronomers who lived at that period,\\nlooked for its return with the greatest interest. It w T as found,\\nhowever, that on its way towards the sun it would pass very\\nnear to Jupiter and Saturn, and by their action on it, would\\nbe retarded for a long time. Clairaut, a distinguished French\\nmathematician, undertook the laborious task of estimating the\\nexact amount of this retardation, and found it to be no less than\\n618 days, namely, 100 days by the action of Jupiter, and 518\\ndays by that of Saturn. This would delay its appearance until\\nearly in the year 1759, and Clairaut fixed its arrival at the peri-\\nhelion within a month of April 13th. It came to the perihelion\\non the 12th of March.\\n401. The return of H alley s comet in 1835, was looked for\\nwith no less interest than in 1759. Several of the most accurate\\nmathematicians of the age had calculated its elements with in-\\nconceivable labor. Their zeal was rewarded by the appearance\\nof the expected visitant at the time and place assigned it tra-\\nversed the northern sky, presenting the very appearances, in\\nmost respects, that had been anticipated and came to its peri-\\nhelion on the 16th of November, within one day of the time pre-\\ndicted by Pontecoulant, a French mathematician, who had, it\\nappeared, made the most successful calculation.* On its previous\\nreturn, it was deemed an extraordinary achievement to have\\nbrought the prediction within a month of the actual time.\\nMany circumstances m conspired to render this return of Hal-\\nley s comet an astronomical event of transcendent interest. Of\\nall the celestial bodies, its history was the most remarkable it\\nafforded most triumphant evidence of the truth of the doctrine\\nof universal gravitation, and consequently of the received laws of\\nastronomy and it inspired new confidence in the power of that\\nSee Professor Loomis s Observations on Halley s Comet, Amer. Journ. Science,\\nxxx. 209. Pontecoulant s Phys. Celeste Precis, p. 586.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0290.jp2"}, "291": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 265\\ninstrument (the Calculus) by means of which its elements had\\nbeen investigated.\\n402. Encke s comet, by its frequent returns, affords peculiar\\nfacilities for ascertaining the laws of its revolution and it has\\nkept the appointments made for it with great exactness. On its\\nreturn in 1839, it exhibited to the telescope a globular mass of\\nnebulous matter resembling fog, and moved towards its perihelion\\nwith great rapidity.\\nBut what has made Encke s comet particularly famous, is its\\nhaving first revealed to us the existence of a Resisting Medium\\nin the planetary spaces. It has long been a question whether the\\nearth and planets revolve in a perfect void, or whether a fluid of\\nextreme rarity may not be diffused through space. A perfect\\nvacuum was deemed most probable, because no such effects on\\nthe motions of the planets could be detected as indicated that\\nthey encountered a resisting medium. But a feather or a lock\\nof cotton propelled with great velocity, might render obvious the\\nresistance of a medium which would not be perceptible in the\\nmotions of a cannon-ball. Accordingly, Encke s comet is thought\\nto have plainly suffered a retardation from encountering a resist-\\ning medium in the planetary regions. The effect of this resist-\\nance, from the first discovery of the comet to the present time,\\nhas been to diminish the time of its revolution about two days.\\nSuch a resistance, by destroying part of the projectile force,\\nwould cause the comet to approach nearer to the sun, and thus\\nto have its periodic time shortened. The ultimate effect of this\\ncause will be to bring the comet nearer to the sun at every rev-\\nolution, until it finally falls into that luminary, although many\\nthousand years will be required to produce this catastrophe.* It\\nis conceivable, indeed, that the effects of such a resistance may\\nbe counteracted by the attraction of one or more of the planets\\nnear which it may pass in its successive returns to the sun. It\\nis peculiarly interesting to see a portion of matter of a tenuity\\nexceeding the thinnest fog. pursuing its path in space, in obe-\\nHalley s comet, at its return in 1835, did not appear to be affected by the sup-\\nposed resisting medium, and its existence is considered as still doubtful.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0291.jp2"}, "292": {"fulltext": "266 COMETS.\\ndience to the same laws as those which regulate such large and\\nheavy bodies as Jupiter or Saturn. In a perfect void, a speck\\nof fog, if propelled by a suitable projectile force, would revolve\\naround the sun, and hold on its way through the widest orbit,\\nwith as sure and steady a pace as the heaviest and largest bodies\\nin the system.\\n403. The most remarkable comet of the present century hith-\\nerto observed, was the great comet of 1843. (See Plate I. at the\\nend of the volume.) On the 28th of February of that year, the\\nattention of numerous observers in various parts of the world,\\nwas arrested by a comet seen in the broad light of day, a little\\neastward of the sun. In Mexico it was observed, and its alti-\\ntude repeatedly measured with a sextant, from nine in the morn-\\ning until sunset. In New England, it was seen at several places\\nfrom half-past seven in the morning until after three in the\\nafternoon, when the sky became obscured by haziness and clouds.\\nAccurate measures were taken by Capt. Clark, at Portland, Maine,\\nof the distance of the nucleus from the sun s limb. At 3h. 2m.\\n15s. mean time, the distance of the sun s farthest limb from the\\nnearest limb of the nucleus, was 4\u00c2\u00b0 6 15 The comet resem-\\nbled a white cloud of great density, being nearly equally shining\\nthroughout, with a nucleus as bright as the full moon at midnight\\nin a clear sky. During the first week in March, the appearance\\nof this body was splendid and magnificent, enhanced in both\\nrespects by the transparency of a tropical sky, and the higher\\nangle of elevation above that at which it was seen by northern\\nobservers. At New Haven, it was first seen after sunset, on the\\n5th of March. It then lay far in the southwest. On account of\\nthe presence of the moon, it was not seen most favorably until\\nthe evening of the 17th. It then extended along the constellation\\nEridanus to the ears of the Hare, below the feet of Orion, reach-\\ning nearly to Sirius, being about 40\u00c2\u00b0 in length, although in the\\ntropical regions its apparent length, at its maximum, was nearly\\n70\u00c2\u00b0. It was slightly curved like a goose-quill, and colored with\\na slight tinge of rose-red, which in a few evenings disappeared,\\nand left it nearly a pearly white. Our diagram (Plate I. at the\\nend of the volume) presents a pretty accurate idea of its appear-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0292.jp2"}, "293": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 267\\nance on the 20th of March. All the astronomers of the age have\\nagreed in the opinion that this is one of the most remarkable ex-\\nhibitions of a comet ever witnessed, although the} are not fully\\nagreed respecting the elements of its orbit, or its periodic time.\\nIts elements resemble those of the comet pf 1688, which would\\ngive a period of 175 years and to this periodic time authority\\nat present inclines but Prof. Hubbard, of the Washington Ob-\\nservatory, after an elaborate discussion of all the observations,\\nthinks the most probable period 170 years.\\nOf all the comets on record, the great comet of 1843 approached\\nnearest to the sun. It came within about 60,000 miles of his lumin-\\nous surface, or only about one-fourth of the distance of the moon\\nfrom the earth. It will be recollected that to a spectator on the\\nearth the sun s angular diameter but a little exceeds half a de-\\ngree but were we to approach as near to the sun as this body\\ndid in its perihelion, that diameter would appear no less than\\n121\u00c2\u00b0, 32 and the light and heat (which increase as the square\\nof the distance is diminished) would be 47,000 times as great as\\nat present, the heat exceeding nearly twenty-five times that pro-\\nduced by Parker s great burning lens, although this instrument\\nis capable of producing effects beyond those of the most powerful\\nblast furnace. The velocity of the comet was still more aston-\\nishing, being at the rate of more than one and a quarter million\\nof miles per hour, a velocity sufficient to carry it through 180\u00c2\u00b0,\\nor half round the sun, in two hours, f\\n404. Of the physical nature of comets, little is understood. It\\nis usual to account for the variations which their tails undergo\\nby referring them to the agencies of heat and cold. The intense\\nheat to which they are subject in approaching so near the sun as\\nsome of them do, is alleged as a sufficient reason for the great\\nexpansion of the thin nebulous atmospheres forming their tails; and\\nthe inconceivable cold to which they are subject in receding to\\nsuch a distance from the sun, is supposed to account for the con-\\nSee American Almanac for 1844, p. 94. Amer. Journ. of Science, xlv. 188,\\nAstronomical Journal, Yol. II. p. 156.\\nf Herschel s Outlines, p. 318.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0293.jp2"}, "294": {"fulltext": "268 COMETS.\\ndensation of the same matter until it returns to its original dimen-\\nsions. The temperature experienced by the comets of 1680 and\\n1843 at their perihelion, would be sufficient to volatilize the most\\nobdurate substances, and to expand the vapor to vast dimensions\\nand the opposite effects of the extreme cold to which it would be\\nsubject in the regions remote from the sun, would be adequate to\\ncondense it into its former volume.\\nThis explanation, however, does not account for the direction\\nof the tail, extending, as it usually does, only in a line opposite to\\nthe sun. Some writers therefore, as Delambre,* suppose that the\\nnebulous matter of the comet, after being expanded to such a vol-\\nume that the particles are no longer attracted to the nucleus un-\\nless by the slightest conceivable force, is carried off in a direc-\\ntion from the sun by the impulse of the solar rays themselves.\\nOthers conceive of a force of repulsion, independent of any\\nmechanical impulse emanating from the sun. But to assign such\\na power of communicating motion to the sun s rays while they\\nhave never been proved to have any momentum, or to a repulsive\\nforce which has no independent proof of its existence, is unphil-\\nosophical and we are compelled to place the phenomena of\\ncomets tails among the points of astronomy yet to be ex-\\nplained.!\\n405. Since those comets which have their perihelion very near\\nthe sun, like the comet of 1680, cross the orbits of all the planets,\\nthe possibility that one of them may strike the earth, has frequently\\nbeen suggested. Still, it may quiet our apprehensions on this\\nDelambre s Astronomy, t. 3, p. 401.\\nf Professor W. A. Norton, in an essay on the Formation of Comets Tails, main-\\ntains that the head and tail of a comet do not compose one connected mass, revolving\\nas one body, but that the tail is made up of particles of matter continually in the act\\nof flowing away from the head, (Amer. Journal, xlvii. 104.) William Mitchell, of Nan-\\ntucket, in an article, published in the 38th Vol. of the American Journal, holds that\\na comet s tail does not consist of matter at all that has the least connection with the\\ncomet, but is formed by the sun s rays, slightly refracted by the nucleus in traversing\\nthe envelope of the comet, and uniting in an infinite number of points beyond it,\\nthrowing a stronger than ordinary light on the etherial medium, near to or more remote\\nfrom the comet, as the ray from its relative position and direction is more or less\\nrefracted.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0294.jp2"}, "295": {"fulltext": "METEORIC SHOWERS. 269\\nsubject, to reflect on the vast extent of the planetary spaces, in\\nwhich these bodies ai*e not crowded together as we see them\\nerroneously represented in orreries and diagrams, but are sparsely\\nscattered at immense distances from each other. They are like\\ninsects flying in the expanse of heaven. If a comet s tail lay\\nwith its axis in the plane of the ecliptic when it was near the\\nsun, we can imagine that the tail might sweep over the earth\\nbut the tail may be situated at any angle with the ecliptic as w r ell\\nas in the same plane with it, and the chances that it will not be\\nin the same plane, are almost infinite. It is also extremely im-\\nprobable that a comet will cross the plane of the ecliptic precisely\\nat the earth s path in that plane, since it may as probably cross\\nit at any qther point nearer or more remote from the sun. Still,\\nsome comets have occasionally approached near to the earth.\\nThus Biela s comet, in returning to the sun in 1832, crossed the\\necliptic very near to the earth s track, and had the earth been\\nthen at that point of its orbit, it might have passed through a\\nportion of the nebulous atmosphere of the comet. The earth was\\nwithin a month of reaching that point. This might at first view-\\nseem to involve some hazard; yet we must consider that a month\\nshort implied a distance of nearly 50,000,000 miles. Laplace has\\nassigned the consequences that would ensue in case of a direct\\ncollision between the earth and a comet but terrible as he has\\nrepresented them on the supposition that the nucleus of the comet\\nis a solid body, yet considering a comet (as most of them doubt-\\nless are) as a mass of exceedingly light nebulous matter, it is not\\nprobable, even were the earth to make its way directly through\\na comet, that a particle of the comet would reach the earth. The\\nportions encountered by the earth, would be arrested by the at-\\nmosphere, and probably inflamed and they would perhaps exhibit,\\non a more magnificent scale than was ever before observed, the\\nphenomena of shooting stars, or meteoric showers.\\nMETEORIC SHOWERS.\\n406. The remarkable exhibitions of shooting stars which have\\noccurred within a few years past, have excited great interest\\nSyst. du Monde, 1. iv. c. 4.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0295.jp2"}, "296": {"fulltext": "270 METEORIC SHOWERS.\\namong astronomers, and led to some new views respecting the\\nconstruction of the solar system. Their attention was first turned\\ntowards this subject by the great meteoric shower of Novembei\\n13th, 1833. On that morning, from two o clock until broad day-\\nlight, the sky being perfectly serene and cloudless, the whole\\nheavens were lighted with a magnificent display of celestial fire-\\nworks. At times, the air was filled with streaks of light, occa-\\nsioned by fiery particles darting down so swiftly as to leave the\\nimpression of their light on the eye, (like a match ignited and\\nwhirled before the face,) and drifting to the northwest like flakes\\nof snow driven by the wind while, at short intervals, balls of\\nfire, varying in size from minute points to bodies larger than\\nJupiter and Venus, and in a few instances as large as the full\\nmoon, descended more slowly along the arch of the sky, often\\nleaving after them long trains of light, which were, in some in-\\nstances, variegated with different prismatic colors.\\nOn tracing back the lines of direction in which the meteors\\nmoved, it was found that they all appeared to radiate from the\\nsame point, which was situated near one of the stars (Gamma\\nLeonis) of the sickle, in the constellation Leo and, in every rep-\\netition of the meteoric shower of November, the radiant point\\nhas occupied nearly the same situation.\\nThis shower pervaded nearly the whole of North America,\\nhaving appeared in almost equal splendor from the British pos-\\nsessions on the north, to the West India Islands and Mexico on\\nthe south, and from sixty-one degrees of longitude east of the\\nAmerican coast, quite to the Pacific ocean on the west. Through-\\nout this immense region, the duration was nearly the same. The\\nmeteors began to attract attention by their unusual frequency and\\nbrilliancy, from nine to twelve o clock in the evening were most\\nstriking in their appearance from two to four arrived at their\\nmaximum, in many places, about four o clock and continued\\nuntil rendered invisible by the light of day. The meteors moved\\nin right lines, or in such apparent curves, as, upon optical prin-\\nciples, can be resolved into right lines. Their general tendency\\nwas towards the northwest, although by the effect of perspective\\nthey appeared to move in all directions.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0296.jp2"}, "297": {"fulltext": "METEORIC SHOWERS. 271\\n407. Soon after this occurrence, it was ascertained that a sim-\\nilar meteoric shower had appeared in 1799, and what was re-\\nmarkable, almost exactly at the same time of the year, namely,\\non the morning of the 12th of November and it soon appeared,\\nby accounts received from different parts of the world, that this\\nphenomenon had occurred on the same 13th of November, in\\n1830, 1831, and 1832. Hence, this was evidently an event inde-\\npendent of the casual changes of the atmosphere for, having a\\nperiodical return, it was undoubtedly to be referred to astronom-\\nical causes, and its recurrence, at a certain definite period of the\\nyear, plainly indicated some relation to the revolution of the\\nearth around the sun.\\nIt remained, however, to develop the nature of this relation, by\\ninvestigating, if possible, the origin of the meteors. The views\\nto which the author of this work was led, suggested the proba-\\nbility that the same phenomenon would recur at the correspond-\\ning seasons of the year for at least several years afterwards and\\nsuch proved to be the fact, although the appearances, at every\\nsucceeding return, were less and less striking, until 1839, when,\\nso far as is known, they ceased altogether.\\nMeanwhile, three other distinct periods of meteoric showers\\nhave also been determined one on the 9th of August, and (more\\nrare) on the 21st of April and 7th of December respectively.\\n408. The following conclusions respecting the meteoric shower\\nof November, are believed to be well established, and most of\\nthem are now generally admitted by astronomers, though we\\ncannot here exhibit the evidence on which they were founded.*\\nIt is considered, then, as established, that the periodical me-\\nteors of November (and most of the conclusions apply equally to\\nthose of August) have their origin beyond the atmosphere, de-\\nscending to us from some body (which, from the known consti-\\ntution of the meteors, may be called a nebulous body) with which\\nthe earth falls in, and near or through the borders of which it\\nWe beg leave to refer the reader to various publications on the subject, by the\\nauthor and others, in the American Journal of Science, commencing with the 25th\\nvolume and also to Letters on Astronomy, by the author of this work.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0297.jp2"}, "298": {"fulltext": "272 METEORIC SHOWERS.\\npasses that this body has an independent existence as a member\\nof the solar system, its periodic time being nearly commensurable\\nwith the earth s, either a year or half a year, so that for a number\\nof years in succession the two bodies meet near the same part of\\nthe earth s orbit. It is further established, that the meteors con-\\nsist of light combustible matter that they move with great\\nvelocities, amounting, in some instances, to not less than that of\\nthe earth in its orbit, or 19 miles per second that some of them\\nare bodies of large size, sometimes several thousand feet in diam-\\neter that when they enter the atmosphere, they rapidly and\\npowerfully condense the air before them, and thus elicit the heat\\nthat sets them on fire, as a spark is elicited in the air-match, by\\nbeing suddenly condensed by means of a piston and cylinder\\nand that they are burned up at a considerable height above the\\nearth, sometimes not less than 30 miles.\\n409. Calling the body from which the meteors descended the\\nmeteoric body, it is inferred that it is a body of great extent,\\nsince, without apparent exhaustion, it has been able to afford such\\ncopious showers of meteors at so many different times and hence\\nw T e regard the part that has descended to the earth only as the\\nextreme portions of a body or collection of meteors, of unknown\\nextent, existing in the planetary spaces. Since the earth fell in\\nwith the meteoric body, in the same part of its orbit for several\\nyears in succession, the body must either have remained there\\nwhile the earth was performing its whole revolution around the\\nsun, or it must itself have had a revolution, as well as the earth.\\nNo body can remain stationary within the planetary spaces for,\\nunless attracted to some nearer body, it would be drawn directly\\ntowards the sun, and could not have been encountered by the\\nearth again in the same part of her orbit. Nor can any mode be\\nconceived in which this event could have happened so many\\ntimes in regular succession, unless the body had a revolution of\\nits own around the sun. Finally, to have come into contact\\nwith the earth at the same part of her orbit, in two or more suc-\\ncessive years, the body must have a period which is either nearly\\nthe same with the earth s period, or some aliquot part of it. No", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0298.jp2"}, "299": {"fulltext": "METEORIC SHOWERS. 273\\nperiod will fulfil these conditions, but either a year or half a year.\\nWhich of these is the true period of the meteoric body, is not\\nfully determined.\\nThere are some reasons for believing that the Zodiacal Light\\n(Art. 152) is the body which affords the meteoric showers, con-\\nforming, as it does, to many or all of the conditions required of\\nthe body in question.*\\nSee a paper on this subject by the author of the present work, in the Transac-\\ntions of the American Association for the Advancement of Knowledge, for 1851\\nor American Journal of Science, for November, 1851.\\n35", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0299.jp2"}, "300": {"fulltext": "PART IE.\u00e2\u0080\u0094 OF THE FIXED STARS AND SYSTEM OF THE\\nWORLD.\\nCHAPTER I.\\nOF THE FIXED STARS CONSTELLATIONS.\\n410. The Fixed Stars are so called, because, to. common\\nobservation, they always maintain the same situations with re-\\nspect to one another.\\nThe stars are classed by their apparent magnitudes. The\\nwhole number of magnitudes recorded are sixteen, of which the\\nfirst six only are visible to the naked eye the rest are telescopic\\nstars. As the stars which are now grouped together under one\\nof the first six magnitudes are very unequal among themselves, it\\nhas recently been proposed to subdivide each class into three,\\nmaking in all eighteen instead of six magnitudes visible to the\\nnaked eye. These magnitudes are not determined by any very\\ndefinite scale, but are merely ranked according to their relative\\ndegrees of brightness, and this is left in a great measure to the\\ndecision of the eye alone, although it would appear easy to meas-\\nure the comparative degree of light in a star by a photometer,\\nand upon such measurement to ground a more scientific classifi-\\ncation of the stars. The brightest stars to the number of 15 or\\n20 are considered as stars of the first magnitude the 50 or 60\\nnext brightest, of the second magnitude the next 200 of the\\nthird magnitude and thus the number of each class increases\\nrapidly as we descend the scale, so that no less than fifteen or\\ntwenty thousand are included within the first seven magnitudes.\\n411. The stars have been grouped in Constellations from the\\nmost remote antiquity a few, as Orion, Bootes, and Ursa Major,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0300.jp2"}, "301": {"fulltext": "FIXED STARS. 275\\nare mentioned in the most ancient writings under the same names\\nas they bear at present. The names of the constellations are\\nsometimes founded on a supposed resemblance to the objects to\\nwhich the names belong as the Swan and the Scorpion were\\nevidently so denominated from their likeness to those animals\\nbut in most cases it is impossible for us to find any reason for\\ndesignating a constellation by the figure of the animal or the hero\\nwhich is employed to represent it. These representations were\\nprobably once blended with the fables of pagan mythology. The\\nsame figures, absurd as they appear, are still retained for the con-\\nvenience of reference since it is easy to find any particular star,\\nby specifying the part of the figure to which it belongs, as when\\nwe say a star is in the neck of Taurus, in the knee of Hercules,\\nor in the tail of the Great Bear. This method furnishes a gen-\\neral clue to its position but the stars belonging to any constel-\\nlation are distinguished according to their apparent magnitudes,\\nas follows first, by the Greek letters, Alpha, Beta, Gamma, c.\\nThus a Orionis, denotes the largest star in Orion, (3 Andromedce,\\nthe second star in Andromeda, and 7 Leonis, the third brightest star\\nin the Lion. Where the number of the Greek letters is insuffi-\\ncient to include all the stars in a constellation, recourse is had to\\nthe letters of the Roman alphabet, a, b, c, c. and, in cases\\nwhere these are exhausted, the final resort is to numbers. This\\nis evidently necessary, since the largest constellations contain\\nmany hundreds or even thousands of stars. Catalogues of par-\\nticular stars have also been published by different astronomers,\\neach author numbering the individual stars embraced in his list,\\naccording to the places they respectively occupy in the catalogue.\\nThese references to particular catalogues are sometimes entered\\non large celestial globes. Thus we meet with a star marked\\n84 H., meaning that this is its number in Herschel s catalogue,\\nor 140 M., denoting the place the star occupies in the catalogue\\nof Mayer.\\n412. The earliest catalogue of the stars was made by Hippar-\\nchus, of the Alexandrian School, about 140 years before the\\nChristian era. A new star appearing in the firmament, he was\\ninduced to count the stars and to record their positions, in order", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0301.jp2"}, "302": {"fulltext": "276 FIXED STARS.\\nthat posterity might be able to judge of the permanency of the\\nconstellations. His catalogue contains all that were conspicuous\\nto the naked eye in the latitude of Alexandria, being 1022. Most\\npersons unacquainted with the actual number of the stars which\\ncompose the visible firmament, would suppose it to be much\\ngreater than this but it is found that the catalogue of Hipparchus\\nembraces nearly all that can now be seen in the same latitude,\\nand that on the equator, where the spectator has the northern and\\nsouthern hemispheres both in view, the number of stars that can\\nbe counted does not exceed 3000. A careless view of the firma-\\nment in a clear night, gives us the impression of an infinite multi-\\ntude of stars but when we begin to count them, they appear\\nmuch more sparsely distributed than we supposed, and large\\nportions of the sky appear almost destitute of stars.\\nBy the aid of the telescope, new fields of stars present them-\\nselves of boundless extent the number continually augmenting\\nas the powers of the telescope are increased. Lalande, in his\\nHistoire Celeste, has registered the positions of no less than\\n50,000 and the whole number visible in the largest telescopes\\namount to many millions.\\n413. It is strongly recommended to the learner to acquaint\\nhimself with the leading constellations at least, and with a few of\\nthe most remarkable individual stars. The task of learning them\\nis comparatively easy, when they are taken up at suitable inter-\\nvals throughout the year, the moon being absent and the sky clear.\\nAfter becoming familiar with such constellations as are visible on\\nany given evening, (suppose the first of January,) these may be\\ncarefully reviewed after an interval of a month, and the several\\nnew ones added which have in the mean time risen above the\\neastern horizon. By repeating this process near the beginning\\nof every month of the year, the learner will acquire a competent\\nknowledge of the whole that are visible in his latitude, and with\\na small expenditure of time. It may at first be advisable to ob-\\ntain, for an evening or two, the assistance of some one who is\\nacquainted with the constellations, to point out such as are then\\nvisible in the evening sky. Then, by the aid of a celestial map,\\nor, what is better, a celestial globe, the learner will pursue the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0302.jp2"}, "303": {"fulltext": "CONSTELLATIONS. 277\\nstudy without difficulty. We begin by rectifying the globe for\\nthe time, according to the directions given in Article 76.\\nIn the following sketch of the leading constellations, we will\\npoint out a few of the marks by which they may be severally\\nrecognized, adding occasionally a few particulars, and leaving\\nit to the learner to fill up the outline by the aid of his map or\\nglobe, one of which, indeed, is presumed to be before him.*\\nLet us begin with the constellations of the Zodiac, w T hich, suc-\\nceeding each other as they do in a know T n order, are most easily\\nfound, f\\nAries (The Ram) the first constellation of the Zodiac, is known\\nby two bright stars, Alpha (a) on the northeast, and Beta (/3) on\\nthe southwest, 4\u00c2\u00b0 J apart, forming the head. South of Beta, at\\nthe distance of 2\u00c2\u00b0, is a smaller star, Gamma (j). The next bright-\\nest star of the Ram, Delta (6), is in the tail, 15\u00c2\u00b0 southeast of Alpha.\\nThe feet of the figure rest on the head of the Whale. It has\\nbeen already intimated, (Art. 193,) that the vernal equinox was\\nnear the head of Aries, when the signs of the Zodiac received their\\npresent names, but that the equinox is now found 30\u00c2\u00b0 westward\\nof a Arietis, in consequence of the precession of the equinoxes.\\nTaurus (The Bull) will be readily found by the seven stars,\\nA celestial globe, sufficient for studying the constellations, mar be purchased\\nfor a small sum, and is, in other respects, a valuable possession to the astronomical\\nstudent but even cheap maps of the stars, like those of Burnt t or Kendal, will\\nanswer for beginners; and the Celestial Atlas, published by the Society for the\\nDiffusion of Useful Knowledge, which is suitable for the more advanced student,\\nmay be procured at a moderate expense.\\nf It will be expedient, where it is practicable, for the learner to study the con-\\nstellations in separate portions, at different seasons of the year, as at the equinoxes\\nand at the solstices, according to the directions given in the closing article of this\\nchapter.\\nThese measures are not intended to be stated with minute accuracy, but only\\nwith such a degree of exactness as may serve for a general guide. The learner\\nwill find it greatly for his advantage to accustom himself to make an accurate esti-\\nmate with the eye of distances in degrees on the celestial sphere and he may, at\\nthe outset, fix on the distance between Alpha and Beta Arietis as a standard meas-\\nure (4\u00c2\u00b0) by which to estimate other angular distances among the stars. Thus, half\\nthis length applied from Beta to Gamma, indicates that the two latter stars are 2\u00c2\u00b0\\napart; and two and a half times the same measure (10\u00c2\u00b0) will reach from the\\nPleiades to Aldebaran. Or the Pointers in the Great Bear will furnish a measure cf 5\u00c2\u00b0", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0303.jp2"}, "304": {"fulltext": "278 FIXED STARS.\\nor Pleiades, which lie in the neck, 24\u00c2\u00b0 eastward of a Arietis.\\nThe largest star in Taurus is Aldebaran, of the first magnitude,\\nin the Bull s eye, 14\u00c2\u00b0 southeast of the Pleiades. It has a reddish\\ncolor, and resembles the planet Mars. The other eye of the fig-\\nure is Epsilon (s), 3\u00c2\u00b0 northwest of Aldebaran. Five small stars,\\nsituated a little west of Aldebaran, in the face of the Bull, con-\\nstitute the Hyades. Although the Pleiades are usually denom-\\ninated the seven stars, yet it has been remarked, from a high\\nantiquity, that only six are present.\\nQuae septem dici, sex tamen esse solent.* Ovid.\\nSome persons, however, of remarkable powers of vision, are\\nstill able to recognize seven, and even a greater number, f With\\na moderate telescope, not less than 50 or 60 stars, of considerable\\nbrightness, may be counted in this group, and a much larger num-\\nber of very small stars are revealed to the more powerful tele-\\nscopes. The beautiful allusion, in the book of Job, to the sweet\\ninfluences of the Pleiades/ and the special mention made of this\\ngroup by Homer and Hesiod, show how early it had attracted\\nthe attention of mankind. The horns of the Bull are two stars,\\nBeta and Zeta, situated 25\u00c2\u00b0 east of the Pleiades, being 8\u00c2\u00b0 apart.\\nThe northern horn, Beta, also forms one of the feet of Auriga,\\nthe Charioteer.\\nGemini (The Twins) is represented by two well-known stars,\\nCastor and Pollux, in the head of the figure, 5\u00c2\u00b0 asunder. Castor,\\nthe northern, is of the first, and Pollux of the second magnitude.\\nFour conspicuous stars, extending in a line from south to north,\\n25\u00c2\u00b0 S. W. of Castor, form the feet, and two others parallel to\\nthese at the distance of six or seven degrees northeastward, are\\nin the knees.\\nCancer (The Crab). There are no large stars in this constel-\\nlation, and it is regarded as less remarkable than any other in the\\nTheir names were Electra, Maia, Taygeta, Alcyone, Celaeno, Asterope, and\\nMerope, the last beiDg the Lost Pleiad of the poets. Alcyone, according to a\\nrecent celebrated hypothesis, is distinguished as the center around which the starry\\nhost revolve.\\nf Smyth s Cycle, II. 86.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0304.jp2"}, "305": {"fulltext": "CONSTELLATIONS. 279\\nZodiac. The two most conspicuous stars, Alpha and Beta, are\\nin the southern claws of the figure, and in its body are the\\nnorthern and southern Asellus, which may be readily found on a\\ncelestial globe. But the most remarkable object in this constel-\\nlation, is a misty group of very small stars, so close together\\nwhen seen by the naked eye as to resemble a comet, but easily\\nseparated by the telescope into a beautiful collection of brilliant\\npoints. It is called Prcesepe, or the Beehive.\\nLeo (The Lion) is a very large constellation, and has many\\ninteresting members. Regulus (a Leonis) is a star of the first\\nmagnitude, which lies very near the ecliptic, and is much used\\nin astronomical observations. North, of Regulus lies a semi-\\ncircle of five bright stars, arranged in the form of a sickle, of\\nwhich Regulus is the handle, and extending over the shoulder\\nand neck of the Lion.* Denebola, a conspicuous star in the\\nLion s tail, lies 25\u00c2\u00b0 east of Regulus. Twenty bright stars in all\\nhelp to compose this beautiful constellation. It ranges from west\\nto east along the Zodiac, over more than 40\u00c2\u00b0 of longitude, all\\nparts of the figure excepting the feet lying north of the ecliptic.\\nVirgo (The Virgin) extends along the Zodiac eastward from\\nthe Lion, covering an equally wide region of the heavens, al-\\nthough less distinguished by brilliant stars. Spica, however, is a\\nstar of the first magnitude, and lies a little east of the vernal\\nequinox. Vindemiatrix, in the arm of Virgo, 18\u00c2\u00b0 east of Dene-\\nbola, and 23\u00c2\u00b0 north of Spica, is easily found, and directly south\\nof Denebola 13\u00c2\u00b0, is (3 Virginis w T hile four other conspicuous\\nstars, in the form of a trapezium, between this and Vindemiatrix,\\nlie in the wing and shoulders of the figure. The feet are near\\nthe Balance.\\nLibra (The Balance) is composed of a few scattered mem-\\nbers situated between the feet of Virgo and the head of Scorpio,\\nbut has no very distinctive marks. Two stars of the second mag-\\nnitude, Alpha on the south, and Beta 8\u00c2\u00b0 northeast of Alpha,\\ntogether with a few smaller stars, form the scales.\\nAs the Meteors of November always appear to radiate from a point in the bend\\nof the sickle, near the star Gamma, it may be noted that the names of the six stars\\ncomposing this figure, beginning with Kegulus, are a, tj, y, c.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0305.jp2"}, "306": {"fulltext": "280 FIXED STARS.\\nScorpio (The Scorpion) is one of the finest of the constella-\\ntions of the Zodiac, and is manifestly so called from its resem-\\nblance to the animal whose name it bears. The head is composed\\nof five stars, arranged in a line slightly curved, which is crossed\\nin the center by the ecliptic, nearly at right angles, a degree\\nsouth of the brightest of the group f3 Scorpionis. Nine degrees\\nsoutheast of this is a remarkable star of the first magnitude,\\ncalled Antares, and sometimes the Heart of the Scorpion, (Cor\\nScorpionis.) It is of a red color, resembling the planet Mars.\\nSouth and east of this, a succession of not less than nine bright\\nstars sweep round in a semicircle, terminating in several small\\nstars forming the sting of the Scorpion. The tail of the figure\\nextends into the Milky Way.\\nSagittarius (The Archer). Ten degrees eastward of the\\nScorpion s tail, on the eastern margin of the Milky Way, we come\\nto the bow of Sagittarius, consisting of three stars about 6\u00c2\u00b0 apart,\\nthe middle one being the brightest, and situated in the bend of\\nthe bow, while a fourth star, 4\u00c2\u00b0 westward of it, constitutes the\\narrow. The archer is represented by the figure of a Centaur,\\n(half horse and half man.) and proceeding about ten degrees east\\nfrom the bow. we come to a collection of seven or eight stars of\\nthe second and third magnitudes, which lie in the human or upper\\npart of the figure.\\nCapricornus, (The Goat,) represented with the head of a goat\\nand the tail of a fish, comes next to Sagittarius, about 20\u00c2\u00b0 east-\\nward of the group that form the upper portions of that constella-\\ntion. Two stars of the second magnitude, a on the north, and\\n(3 on the south, 3\u00c2\u00b0 apart, constitute the head of Capricornus,\\nwhile a collection of stars of the third magnitude, lying 20\u00c2\u00b0 south-\\neast of these, form the tail.\\nAquarius (The Water Bearer) is closely in contact with trie\\ntail of Capricornus, immediately north of which, at the distance\\nof 10\u00c2\u00b0, is the western shoulder (/3), and 10\u00c2\u00b0 further east is the east-\\nern shoulder (a) of Aquarius. About 3\u00c2\u00b0 southeast of a is 7\\nAquarii, which, together with the other two, makes an acute tri-\\nangle, of which /3 forms the vertex. In the eastern arm of\\nAquarius are found four stars, which together make the figure Y,\\nthe open part being westward, or towards the shoulders of the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0306.jp2"}, "307": {"fulltext": "CONSTELLATIONS. 281\\nconstellation. Aquarius ranges nearly 30\u00c2\u00b0 from north to south,\\nbeing nearly bisected by the ecliptic.\\nPisces (The Fishes). Three figures of this kind, at a great\\ndistance apart, two north and one south of the ecliptic, compose\\nthis constellation. The Southern Fish, Piscis Australis, otherwise\\ncalled Fomalhaut, lies directly below the feet of Aquarius, and\\nbeing the only conspicuous star in that part of the heavens, is\\nmuch used in astronomical measurements. It is 30\u00c2\u00b0 south of the\\nequator.\\nAbout 12\u00c2\u00b0 east of the figure Y in the arm of Aquarius, is an\\nassemblage of five stars, forming a pretty regular pentagon, which\\nis one of the northern members of the Constellation Pisces and far\\nto the northeast of this figure, north of the head of Aries, lies the\\nthird member, the three being represented as connected together\\nby a ribbon, or wavy band, composed of minute stars.\\n414. The Constellations of the Zodiac being first w T ell learned,\\nso as to be readily recognized, will facilitate the learning of others\\nthat lie north and south of them. Let us therefore next review\\nthe principal Northern Constellations, beginning at the North\\nPole.\\nUrsa Minor (The Little Bear). The Pole-star (Polaris)\\nis in the extremity of the tail of the Little Bear. It is of the\\nthird magnitude, and being within less than a degree and a half\\nof the North Pole of the heavens, it serves at present to indicate\\nthe position of the pole. It will be recollected, however, that on\\naccount of the precession of the equinoxes, the pole of the heav-\\nens is constantly shifting its place from east to west, revolving\\nabout the pole of the ecliptic, and will in time recede so far from\\nthe pole-star, that this will no longer retain its present distinction,\\n(Art. 190.) Three stars in a straight line, 4\u00c2\u00b0 or 5\u00c2\u00b0 apart, com-\\nmencing with Polaris, lead to a trapezium of four stars, the whole\\nseven together forming the figure of a dipper, the trapezium being\\nthe body, and the three first-mentioned stars being the handle.\\nUrsa Major (The Great Bear) is one of the largest and most\\ncelebrated of the constellations. It is usually recognized by the\\nfigure of a larger and more perfect dipper than the one in the\\nLittle Bear three stars, as before, constituting the handle, and\\n36", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0307.jp2"}, "308": {"fulltext": "282 FIXED STARS.\\nfour others, in the form of a trapezium, the body of the figure.\\nThe two western stars of the trapezium, ranging nearly with the\\nNorth Star, are called the Pointers and beginning with the\\nnorthern of these two, and following round from left to right\\nthrough the whole seven, they correspond in rank to the succes-\\nsion of the first seven letters of the Greek alphabet, Alpha, Beta,\\nGamma, Delta, Epsilon, Zeta, Eta. Several of them also are\\nknown by their Arabic names. Thus, the first in the tail, cor-\\nresponding to Epsilon, is Alioth, the next (Zeta) Mizar, and the\\nlast (Eta) Benetnasch. These are all bright and beautiful stars,\\nAlpha being of the first magnitude, Beta, Gamma, Delta, of the\\nsecond, and the three forming the tail, of the third. But it must\\nbe remarked that this very remarkable figure of a dipper or ladle\\ncomposes but a small part of the entire constellation, being merely\\nthe hinder half of the body and the tail of the Bear. The head\\nand breast of the figure, lying about ten or twelve degrees west of\\nthe Pointers, contain a great number of minute stars in a trian-\\ngular group? One of the fourth magnitude, Omicron, is in the\\nmouth of the Bear. The feet of the figure may be looked for\\nabout 15\u00c2\u00b0 south of those already described, the two hinder paws\\nconsisting each of two stars very similar in appearance, and only\\na degree and a half apart. The two paws are distant from each\\nother about 18\u00c2\u00b0 and following westward about the same number\\nof degrees, we come to another very similar pair of stars, which\\nconstitute one of the fore paws, the other fbot being without any\\ncorresponding pair.\\nIn a clear winter s night, when the whole constellation is above\\nthe pole, these various parts may be easily recognized, and the\\nentire figure will be seen to resemble a large animal, readily ac-\\ncounting for the name given to this constellation from the ear-\\nliest ages.\\nDraco (The Dragon) is also a very large constellation, extend-\\ning for a great length from east to west. Beginning at the tail,\\nwhich lies halfway between the Pointers and the Pole-star, and\\nwinding round between the Great and the Little Bear, by a con-\\ntinued succession of bright stars from 5 P to 10\u00c2\u00b0 asunder, it coils\\naround under the feet of the Little Bear, sweeps round the pole\\nof the ecliptic, and terminates in a trapezium formed by four con-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0308.jp2"}, "309": {"fulltext": "CONSTELLATIONS. 283\\nspicuous stars, from thirty to thirty-five degrees from the North\\nPole. A few of the members of this constellation are of the sec-\\nond, but the greater part of the third magnitude, and below it.\\n415. With the constellations already described as general land-\\nmarks, we may now proceed with each of the principal remaining\\nones, by stating its boundaries, as we do those of countries in\\ngeography their relative situations being thus first learned from\\na map, or (what is better) from a celestial globe, and then being\\nseverally traced out on the sky itself. We will begin with those\\nwhich surround the North Pole.\\nCepheus (The King) is bounded N. by the Little Bear, E. by\\nCassiopeia, S. by the Lizard, and W. by the Dragon. The head\\nlies in the Milky Way, and the feet extend towards the pole.\\nIt contains no stars above the third magnitude.\\nCassiopeia is bounded N. and W. by Cepheus, E. by Camel-\\nopardalus, and S. by Andromeda, and is one of the Constellations\\nof the Milky Way. It is readily distinguished by the figure of a\\nchair inverted, of which two stars constitute the back, and four,\\nin the form of a square, the body of the chair. It is on the op-\\nposite side of the pole from the Great Bear, and nearly at the\\nsame distance from it.\\nCamelopaedalus (The Giraffe) is bounded N. by the Little\\nBear, E. by the head of the Great Bear, S. by Auriga and Per-\\nseus, and W. by Cassiopeia. Although this Constellation occu-\\npies a large space, yet it has no conspicuous stars.\\nAndromeda is bounded N. by Cassiopeia, E. by Perseus, S. by\\nPegasus, and W. by the Lizard. The direction of the figure is\\nfrom S. W. to N. E., the head coming down within 30\u00c2\u00b0 of the\\nequator, and being recognized by a star of the second magnitude,\\nwhich forms the northeastern corner of the great square in Pega-\\nsus, to be described hereafter. At the distance of six or seven\\ndegrees from the head, are three conspicuous stars in a row,\\nranging from north to south, which lie in the breast of the figure\\nand about the same distance from these, and parallel to them,\\nthree more, which constitute the girdle of Andromeda. Near the\\nnorthernmost of the three, is a faint, misty object, often mistaken", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0309.jp2"}, "310": {"fulltext": "284 FIXED STARS.\\nfor a comet, but is a nebula, and one of the most remarkable in\\nthe heavens.\\nPerseus is bounded N. by Cassiopeia, E. by Auriga, S. b^\\nTaurus, and W. by Andromeda. The figure extends from north\\nto south, and is represented by a giant holding aloft a sword in\\nhis right hand, while his left grasps the head of Medusa, a group\\nof stars on the western side of the figure, embracing the celebra-\\nted star Algol. A series of bright stars descend along the shoul-\\nders and the waist, and there divide into the two legs. The\\nwestern foot is 8\u00c2\u00b0 north of the Pleiades. The eastern leg is bent\\nat the knee, which is distinguished by a group of small stars.\\nNear the sword handle, under Cassiopeia s chair, is a fine cluster\\nof stars, so close together as scarcely to be separable by the eye.\\nAuriga (The Wagoner) is bounded N. by Camelopardalus,\\nE. by the Lynx, S. by Taurus, and W. by Perseus. He is rep-\\nresented as bearing on his left shoulder the little Goat Capella, a\\nwhite and beautiful star of the first magnitude, (a Aurigse,) while\\nBeta forms the right shoulder, 8\u00c2\u00b0 east of Capella. These two\\nbright stars form, with the northern horn of the Bull, at the dis-\\ntance of 18\u00c2\u00b0, an isosceles triangle.\\nLeo Minor (The Lesser Lion) is bounded N. by Ursa Major,\\nE. by Coma Berenices, S. by Leo, and W. by the Lynx. It lies\\ndirectly under the hind feet of the Great Bear, and over the sickle\\nin Leo, and is easily distinguished. Four stars in the central\\npart of the figure, from 4\u00c2\u00b0 to 5\u00c2\u00b0 apart, form a pretty regular par-\\nallelogram.\\nCanes Venatici (The Greyhounds). This Constellation lies\\nbetween the hind legs of the Great Bear on the west, and Bootes\\non the east Cor Caroli, a solitary star of the third magnitude,\\n18\u00c2\u00b0 south of Alioth, in the tail of the Great Bear, will serve to\\nmark this Constellation.\\nComa Berenices (Berenice s Hair) is a cluster of small stars,\\ncomposing a rich group, 15\u00c2\u00b0 N. E. of Denebola, in the Lion s\\ntail, in a line between this star and Cor Caroli, and half way be-\\ntween the two.\\nBootes is bounded N. by Draco, E. by the Crown and the\\nhead of Serpentarius, S. by Virgo, and W. by Coma Berenices and\\nthe Hounds. It reaches for a great distance from north to south,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0310.jp2"}, "311": {"fulltext": "CONSTELLATIONS. 285\\nthe head being within 20\u00c2\u00b0 of the Dragon, and the feet reaching\\nto the Zodiac. In the knee of Bootes is Arcturus, a star of the\\nfirst magnitude. The next brightest star, Beta, is in the head of\\nBootes, 23\u00c2\u00b0 north of Arcturus, and 15\u00c2\u00b0 east of the last star in the\\ntail of the Great Bear.\\nCorona Borealis (The Northern Crown) is bounded N. and\\nE. by Hercules, S. by the head of Serpentarius, and W. by\\nBootes. It is formed of a semicircle of bright stars, six in num-\\nber, of which Gemma, near the center of the curve, is of the sec-\\nond magnitude.\\nHercules is bounded N. by Draco, E. by Lyra, S. by Ophiu-\\nchus, and W. by Corona Borealis. It is a very large Constellation,\\nand contains some brilliant objects for the telescope, although its\\ncomponents are generally very small. The figure lies north and\\nsouth, with the head near the head of Ophiuchus, and the feet un-\\nder the head of Draco. Being between the Crown and the Lyre,\\nits locality is easily determined. The eastern foot of Hercules\\nforms an isosceles triangle with the two southern stars of the tra-\\npezium in the head of Draco while the head of Hercules is far\\nin the south, within 15\u00c2\u00b0 of the equator, being 6\u00c2\u00b0 west of a similar\\nstar which constitutes the head of Ophiuchus.\\nLyra (The Lyre) is bounded N. by the head of Draco, E. by\\nthe Swan, S. and W. by Hercules. Alpha Lyra?, or Vega, is of\\nthe first magnitude. It is accompanied by a small acute triangle\\nof stars. Its color is a shining white, resembling Capella and the\\nEagle.\\nCygnus (The Swan) extends along the Milky Way, below\\nCepheus, and immediately eastward of the Lyre, and has the fig-\\nure of a large bird flying along the Milky Way from north to\\nsouth, with outstretched wings and long neck. Commencing\\nwith the tail, 25\u00c2\u00b0 east of Lyra, and following down the Milky\\nWay, we pass along a line of conspicuous stars which form the\\nbody and neck of the figure and then returning to the second of\\nthe series, we see two bright stars at eight or nine degrees on the\\nright and left (the three together ranging across the Milky Way)\\nwhich form the wings of the Swan. This Constellation is among\\nthe few, which exhibit some resemblance to the animals whose\\nnames they bear.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0311.jp2"}, "312": {"fulltext": "286 FIXED STARS.\\nVulpecula (The Little Fox) is a small Constellation, in which\\na fox is represented as holding a goose in his mouth. It lies in\\nthe Milky Way, between the Swan on the north and the Dolphin\\nand the Arrow on the south.\\nAauiLA (The Eagle) stretches across the Milky Way, and is\\nbounded N. by Sagitta, a small Constellation which separates it\\nfrom the Fox, E. by the Dolphin, S. by Antinous, and W. by\\nTaurus Poniatowski, (the Polish Bull,) which separates it from\\nOphiuchus. It is distinguished by three bright stars in the neck,\\nknown as the three stars, which lie in a straight line about 2\u00c2\u00b0\\napart, on the eastern margin of the Milky Way. The central\\nstar is of the first magnitude. Its Arabic name is Altair.\\nAntinous lies across the equator, between the Eagle on the\\nnorth, and the head of Capricorn on the south.\\nDelphinus (The Dolphin) is situated east and north of Altair,\\nand is composed of five stars of the third magnitude, of which\\nfour, in the form of a rhombus, compose the head, and the fifth\\nforms the tail.\\nPegasus (The Flying Horse) is a very large Constellation, and\\nis bounded N. by the Lizard and Andromeda, E. and S. by Pisces,\\nW. by the Dolphin. The head is near the Dolphin, while the\\nback rests on Pisces, and the feet extend towards Andromeda.\\nA large square, composed of four conspicuous members, one\\n(Markab) of the first, and three others of the second magnitude,\\ndistinguish this Constellation. The corners of the square are\\nabout 15\u00c2\u00b0 apart; the northeastern corner being in the head of\\nAndromeda.\\nOphiuchus is another very large Constellation, the head being\\nnear the head of Hercules, and the feet reaching to Scorpio, the\\nwestern foot being almost in contact with Antares. The figure\\nis that of a giant holding a serpent in his hands. The head of\\nthe serpent is a little south of the Crown, and the tail reaches\\nfar eastward towards the Eagle.\\n416. Of the Constellations which lie south of the Zodiac, we shall\\nnotice only Cetus, Orion, Lepus, Monoceros, Canis Major, Canis\\nMinor, Hydra, Crater, and Corvus.\\nCetus (The Whale) is distinguished rather for its extent than", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0312.jp2"}, "313": {"fulltext": "CONSTELLATIONS. 287\\nits brilliancy, occupying a large tract of the sky south of the Con-\\nstellations Pisces and Aries. The head is directly below the head\\nof Aries, and the tail reaches westward 45\u00c2\u00b0, being about 10\u00c2\u00b0 south\\nof the vernal equinox. Menkar, (a Ceti,) the largest of its com-\\nponents, is situated in the mouth, 25\u00c2\u00b0 southeast of a Arietis and\\nMir a (o Ceti) in the neck, 14\u00c2\u00b0 west of Menkar, is celebrated as a\\nvariable star, which exhibits different magnitudes at different\\ntimes.\\nOrion is one of the most magnificent of the Constellations, and\\none of those that have longest attracted the admiration of man-\\nkind, being alluded to in the book of Job, and mentioned by Ho-\\nmer. The head of Orion lies southeast of Taurus, 15\u00c2\u00b0 from\\nAldebaran, and is composed of a cluster of small stars. Two very\\nbright stars, Betalgeuse of the first, and Bellatrix of the second\\nmagnitude, form the shoulders three more, resembling the three\\nstars of the Eagle, compose the girdle and three smaller stars,\\nin a line inclined to the girdle, form the sword. Rigel, of the first\\nmagnitude, makes the west foot, but the corresponding star, 9\u00c2\u00b0\\nsoutheast of this, which is sometimes taken for the other foot, is\\nabove the knee, this foot being concealed behind the Hare.\\nOrion s club is marked by three stars of the fifth magnitude, close\\ntogether, in the Milky Way, just below the southern horn of the\\nBull. Orion is a favorite Constellation with the practical astron-\\nomer, abounding, as it does, in addition to the splendor of its\\ncomponents, with fine nebulae, double stars, and other objects of\\npeculiar interest when viewed with the telescope. It embraces\\n70 stars, plainly visible to the naked eye, including two of the\\nfirst, four of the second, and three of the third magnitude.\\nLepus (The Hare). Below Rigel, the western foot of Orion,\\nis a small trapezium of stars, which forms the ears of the Hare\\nand an assemblage of nine stars, of the third and fourth magni-\\ntudes, south and east of these, make up the remaining parts of the\\nfigure.\\nCanis Major (The Greater Dog) lies directly east of the\\nHare, and is highly distinguished by containing Sirius, the most\\nsplendid of all the fixed stars, which lies in the mouth of the fig-\\nure. In the fore paw, 6\u00c2\u00b0 west of Sirius, is a star of the second\\nmagnitude, ((3 Canis Maj oris) and from 10\u00c2\u00b0 to 15\u00c2\u00b0 south of Sir-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0313.jp2"}, "314": {"fulltext": "288 FIXED STARS.\\nius, is a collection of stars of the second and third magnitudes,\\nwhich make up the hinder portions of the figure. The Egyptians,\\nwho anticipated the rising of the Nile by the appearance of Sir-\\nius in the morning sky, represented the Constellation by the figure\\nof a dog, the symbol of a faithful watchman.\\nCanis Minor (The Lesser Dog). About 25\u00c2\u00b0 north of Sirius,\\nis the bright star Procyqn, also of the first magnitude, which\\nmarks the side of the Lesser Dog. A star of the third magnitude\\n(/3), 4\u00c2\u00b0 northwest of this, in the head of the figure, forms with\\nProcyon the lower side of an elongated parallelogram, of which\\nCastor and Pollux, 25\u00c2\u00b0 north, form the upper side.\\nMonoceros is a large Constellation, occupying the space be-\\ntween the Greater and the Lesser Dog, but has no conspicuous\\nmembers.\\nHydra occupies a long space south of Leo, Virgo, and Libra.\\nIts head, which is south of the fore paws of the Lion, consists of\\nfour stars of the fourth magnitude, of nearly uniform appearance\\nand about 15\u00c2\u00b0 S. E. of these is the Heart, {Cor Hy dree) 23\u00c2\u00b0 south\\nof Regulus. Resting on Hydra, and south of the hind feet of\\nLeo, is Crater, (the Cup) consisting of six stars of the fourth\\nmagnitude, arranged in the form of a semicircle and a little\\nfurther east, also perched on the back of Hydra, is Corvus, (the\\nCrow,) the two brightest components of which are situated in one\\nof the wings of the figure, in a line between Crater and Spica\\nVirginis.\\n417. According to an intimation given in a note on p. 277, the\\nConstellations may be advantageously studied at four different\\nperiods of the year, as near the equinoxes and the solstices, accord-\\ning to the following directions. The latitude supposed is 41\u00c2\u00b0.\\nLesson I. For the middle of September, from 8 to 10 o clock.\\nAt 8 o clock Scorpio is near setting in the S. W., Antares being\\n10\u00c2\u00b0 high. The bow of Sagittarius is seen on the eastern margin\\nof the Milky Way, the arrow being directed to a point a little\\nbelow Antares. At 9 o clock, the horns of the Goat come upon\\nthe meridian and at 10 o clock, the western shoulder of Aqua-\\nrius. The other shoulder, and the figure Y in the arm, may also", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0314.jp2"}, "315": {"fulltext": "CONSTELLATIONS. 289\\nbe easily found from the description given on p. 280 also, the\\nPentagon, in Pisces, and Fomalhaut, (the Southern Fish,) a soli-\\ntary bright star far in the south, only 16\u00c2\u00b0 above the horizon.\\nThe head of Aries appears in the east, and the Pleiades are but\\nlittle above the horizon, while Aldebaran is just rising. Return-\\ning now to the west, (at 10 o clock,) the Crown is seen a little\\nnorth of west, about 20\u00c2\u00b0 high Lyra is 30\u00c2\u00b0 west of the zenith the\\nSwan is nearly overhead and following down the Milky Way,\\nthe Eagle is seen on its eastern margin over against Lyra on the\\nwestern; and the Dolphin, a little eastward of the Eagle, and as\\nfar above the horns of Capricornus, as the latter are above the\\nsouthern horizon. Following on east of the meridian, the great\\nsquare in Pegasus may next be identified and since the north-\\neastern corner of the square is in the head of Andromeda, this\\nConstellation may next be learned and then Perseus and Auri-\\nga, which appear still further east, Directly north of Perseus, is\\nCassiopeia s chair; and next to that we may take the Pole Star,\\nthe Little Bear, and the Great Bear, the Dipper only being\\ntraced for the present. Commencing now at the tail of the\\nDragon, we may trace round this figure between the two Bears\\nto the head, which brings us back to Lyra and the head of Her-\\ncules. The boundaries of this Constellation, and of Ophiuchus,\\nwhich lies south of it, will end the first lesson.\\nLesson II. For the middle of December, horn. 7 to 10 o clock.\\nOf the Constellations of the Zodiac, Taurus and Gemini are now\\nfavorably situated for observation in the east. At 7 o clock, the\\ntail of Cetus just reaches the meridian, its head being seen below\\nthe feet of Aries. Orion is just risen in the S. E. At 9 o clock,\\njust above the western horizon, are seen in succession from south\\nto north, Aquarius, the Dolphin, the Eagle, the Lyre, and the\\nDragon s head. Between the Eagle and the Lyre, at a little\\nhigher altitude, we perceive the Swan, flying directly downwards.\\nBetween the tail of the Swan and the Pole Star, is Cepheus\\nand from the pole, along the meridian, we trace Cassiopeia, the\\nfeet of Andromeda, the head of Aries, and the neck of the Whale.\\nAt 10 o clock, Perseus has reached the meridian, the star Algol,\\nin the head of Medusa, being directly over head. The Pleiades\\n37", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0315.jp2"}, "316": {"fulltext": "290 FIXED STARS.\\nare but little eastward of the zenith and following along south\\nfrom the pole, at the interval of from one to two hours east of the\\nmeridian, we may trace in succession, Camelopard, Auriga, Tau-\\nrus, Orion, and the Hare. Turning along the eastern horizon,\\nwe find Canis Major, Monoceros, Canis Minor, the head of Hy-\\ndra, (just rising,) Cancer, Leo, the sickle just appearing about 3\u00c2\u00b0\\nnorth of the east point. Leo Minor and Ursa Major complete the\\nsurvey; and we may now advantageously trace out the various\\nparts of the Great Bear, as described on p. 281 the two stars\\ncomposing its hindmost paw being scarcely above the horizon.\\nLesson III. For the middle of March, from 8 to 10 o clock.\\nAt 8 o clock, we see the Twins nearly overhead, and Procyon\\nand Sirius, at different intervals, towards the south. Along the\\nwest we recognize the neck and head of- the Whale, the head of\\nAries, and the head of Andromeda; next above these, Orion,\\nTaurus, Perseus, Cassiopeia, and Cepheus; and north of the head\\nof Orion, we see Auriga and Camelopard. In the S. W., Hydra\\nis now fully displayed; and following on north, we obtain fine\\nviews of the Greater and the Lesser Lion, and the Great Bear.\\nAt 9 o clock, Crater and Corvus appear in the S. E. on the back\\nof Hydra Virgo extends from Leo down to the horizon, Spica\\nVirginis being about 5\u00c2\u00b0 high and north of Virgo, we trace in\\nsuccession Coma Berenices, Cor Caroli, Bootes, with Arcturus,\\nand the Crown lying far in the N. E.\\nLesson IV. For the middle of June, from 9 to 10 o clock.\\nAt 9 o clock, Bootes, Corona Borealis, the head of Libra, the Ser-\\npent, and Scorpio, lie along on either side of the meridian. Castor\\nand Pollux are just setting, and Leo is about an hour high. East\\nof Leo, Virgo is seen extending along towards the meridian, Spica\\nbeing about 30\u00c2\u00b0 above the southern horizon. North of Leo and\\nVirgo, we recognize Leo Minor, Coma Berenices, Cor Caroli,\\nand Ursa Major. At 10 o clock, we trace along the eastern side\\nof the meridian, Draco, Hercules, and Ophiuchus and east of\\nthese, the Lyre, the Eagle, Antinous, Sagittarius, and Capricor-\\nnus. North of the Eagle, and round to the east, we find Cepheus", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0316.jp2"}, "317": {"fulltext": "DOUDLE STARS. 291\\nand Cassiopeia, Andromeda rising in the northeast, Pegasus in\\nthe east, and Aquarius in the southeast. Thus we may advan-\\ntageously complete a review of the Constellations.\\nCHAPTER II.\\nDOUBLE STARS TEMPORARY STARS VARIABLE STARS CLUSTERS\\nAND NEBULJS.\\n418. The view hitherto taken of the starry heavens presents\\nlittle that is new, since most of the Constellations, visible in our\\nlatitude, and the most conspicuous of the individual stars, have\\nbeen known from antiquity. But the objects to be described in\\nthe present chapter, are chiefly such as have been discovered by\\nmodern astronomy, aided by the powerful telescopes which, since\\nthe time of Sir William Herschel, have been directed to the heav-\\nens. Different orders and systems of stars have been brought to\\nlight, and a new and still more wonderful class of bodies, called\\nNebulae, have been reached in the depths of the stellar universe.\\n419. The introduction into practical astronomy of Herschel s\\ngreat Forty Feet Reflector, in 1789, was a great event in the\\nstudy of the stars. This instrument, in its previous humble\\nforms, had been very little employed upon the stars, they being\\nsupposed to be too remote for its powers, which seemed only\\nsuited to nearer worlds, as the sun and planets. It was not, how-\\never, an increase of magnifying power that was wanted for\\nresearches on these distant objects, but an increase of light, by\\nwhich a few scattered rays sent to us from bodies hidden in the\\ndepths of space, might be collected in such numbers, and directed\\ninto the eye, as would render visible objects otherwise invisible,\\nnot because they do not transmit to us any light, but because not\\nenough of what they transmit enters the small pupil of the eye\\nfor the purposes of distinct vision. Telescopes of great aperture,\\ntherefore, by collecting a large beam of light and conveying it to", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0317.jp2"}, "318": {"fulltext": "292 FIXED STARS.\\nthe eye, greatly enlarge the powers of this organ, and enable it to\\npenetrate proportionally further into the most distant regions of\\nthe universe. Sir W. Herschel himself made wonderful progress\\nin the knowledge of the starry heavens, and by his own researches\\ndiscovered a large portion of those bodies which we are now to\\ndescribe and his son, Sir John Herschel, has cultivated, with\\ngreat success, the same field, and especially, by a residence of\\nfive years at the Cape of Good Hope, devoted assiduously to ob-\\nservations with large instruments, has greatly augmented our\\nknowledge of the stellar systems of the southern hemisphere.\\nMoreover, telescopes of still greater power than that of the elder\\nHerschel, and especially instruments capable of nicer angular\\nmeasurements, have recently enriched the department of practical\\nastronomy. The most remarkable of these are the grand ^Re-\\nflector constructed by Lord Rosse, an Irish nobleman, and\\nthe great Refractors belonging respectively to the Pulkova and\\nCambridge Observatories. Lord Rosse s telescope considerably\\nexceeds in dimensions and in power the forty feet reflector of Sir\\nW. Herschel, being 50 feet in focal length, and having a diame-\\nter of 6 feet, whereas that of the Herschelian telescope was only\\n4 feet. This unexampled magnitude makes this instrument su-\\nperior to all others in light, and fits it pre-eminently for observa-\\ntions on the most remote and obscure celestial objects, such as\\nthe faintest nebulae. But its unwieldy size, and its liability to\\nloss of power, by the tarnishing or temporary blurring of the great\\nspeculum, will render it far less available for actual research than\\nthe great refractors which come in competition with it. Until\\nrecently, it was thought impossible to form perfect achromatic\\nobject-glasses of more than about five inches diameter but they\\nhave been successively enlarged, until we can no longer set\\nbounds to the dimensions which they may finally assume. The\\nPulkova telescope (at St. Petersburgh) has a clear aperture of about\\n15 inches, and a focal length of 22 feet. The telescope recently\\nacquired by Harvard University, is perhaps the finest refractor\\nhitherto constructed. It was made by the same artists, and upon\\nthe same scale with that, but its performances are thought even\\nto exceed those of the Pulkova instrument. We now proceed to\\nreview some ol the discoveries among the stars, which the re-", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0318.jp2"}, "319": {"fulltext": "DOUBLE STARS. 293\\nsearches made with such instruments as the foregoing have\\nbrought to light.\\nDOUBLE STARS.\\n420. Double Stars are those which appear single to the naked\\neye, but are resolved into two by the telescope or if not visible\\nto the naked eye, are seen in the telescope very close together.\\nSometimes three or more stars are found in this near connection,\\nconstituting triple or multiple stars.* Castor, for example, when\\nseen by the naked eye, appears as a single star but in a tele-\\nscope, even of moderate powers, it is resolved into two stars, be-\\ntween the third and fourth magnitudes, within 5 of each other.\\nThese two stars are of nearly equal size, but frequently one is\\nexceedingly small in comparison with the other, resembling a sat-\\nellite near its primary, although in distance, in light, and in other\\ncharacteristics, each has all the attributes of a star, and the com-\\nbination, therefore, cannot be that of a planet w T ith a satellite.\\nThe distance between these objects varies from a fraction of a\\nsecond to thirty-two seconds. In some cases, the extreme close-\\nness, and the exceeding minuteness of double stars, require, for\\ntheir separation, the best telescope, united with the most acute\\npowers of observation. Indeed, certain of these objects are re-\\ngarded as the severest tests both of the excellence of the instru-\\nment, and of the skill of the observer.\\n421. When Sir William Herschel began his observations on\\ndouble stars, about the year 1780, he was acquainted with only 4.\\nBy his own researches he extended the number to 2400. Sir\\nJohn Herschel, Sir James South, and M. Struve, the great Russian\\nastronomer, prosecuted the same line of research and when\\nSir John Herschel left England for the Cape of Good Hope, in\\n1833, the whole number of double stars enrolled was 3346 and\\nthis number was increased, by that eminent astronomer, by adding\\nthose of the southern hemisphere, to 5542. It appears, therefore,\\nthat the number of double stars considerably exceeds all the stars\\nSee several figures of double and multiple stars, in Plate III. at the end of\\nthe volume.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0319.jp2"}, "320": {"fulltext": "294 FIXED STARS.\\nvisible to the naked eye. In some instances, this proximity arises\\nundoubtedly from the two members lying nearly in the same line\\nof vision, and therefore being projected very near to each other\\non the face of the sky but in most cases the double stars are\\nproved to have a physical relation to each other, and are therefore\\nsaid to be physically double, while the former are said to bo opti-\\ncally double. There is no longer any doubt that among the stars\\nare separate systems, in which two, three, and eveo. in one in-\\nstance at least, six stars are bound together in relations of mutual\\ndependance, suns with suns, as the members of the solar system\\ncompose an individual province in the great empire of nature. A\\nstar in Orion s sword (Tketa Orionis) has been for some time\\nknown as a quadruple stai, the members of which form a small\\ntrapezium and recent observations I*ave detected u\\\\ two of these,\\nseverally, companions of extreme minuteness, the whole com-\\nposing a figure like the follow iog\\nMany of la*, double stars a**3 distinguished by the componen\\nexhibiting -aiffbrent colors, often fineVy contrasted with each othe^\\nas orange with blue w green, yellow with blue, and white with\\npurple. Gamma Apdromedse is a close double star, the compo-\\nnents of which are both green. Insulated stars of a red color,\\nalmost as deep as that of blood, occur in many parts of the heav-\\nens, but, no green or blue star of any decided hue has ever been\\nnoticed unassociated with a companion brighter than itself.*\\n422. TEMPORARY STARS.\\nTemporary Stars are new stars which have suddenly made\\ntheir appearance, and after a certain interval, as suddenly disap-\\npeared and returned no more. It was the appearance of a new\\nstar of this kind, 125 years before the Christian era, that prompted\\nHersclieL", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0320.jp2"}, "321": {"fulltext": "VARIABLE STARS. 295\\nHipparchus to form a catalogue of the stars, the first on record.\\nSuch also was the star which suddenly shone out, A. D. 389, in\\nthe Eagle, as bright as Venus, and after remaining three weeks,\\ndisappeared entirely. At other periods, at distant intervals, sim-\\nilar phenomena ha\\\\*e presented themselves. Thus the appear-\\nance of a new star in 1572 was so sudden, that Tycho Brahe,\\nreturning home one evening, was surprised to find a collection of\\ncountry people gazing at a star, which he was sure did not exist\\nhalf an hour before. It was then as bright as Sirius, and continued\\nto increase until it surpassed Jupiter when brightest, and was visi-\\nble at midday. In a month it began to diminish, and in three\\nmonths afterwards it had entirely disappeared. Some stars are\\nnow missing which were registered in the older catalogues. In\\none instance, at least, (that of Neptune,) the supposed star has\\nproved to have been a planet.\\n423. VARIABLE STARS.\\nVariable Stars are those which undergo a periodical change\\nof brightness. One of the most remarkable is the star Mira, in\\nthe neck of the Whale (Omicron Ceti). It appears once in 11\\nmonths, remains at its greatest brightness about a fortnight, being-\\nthen, on some occasions, equal to a star of the second magnitude.\\nIt then decreases about three months, until it becomes completely\\ninvisible, and remains so about five months, when it again be-\\ncomes visible, and continues increasing during the remaining\\nthree months of its period.\\nAnother very remarkable variable star is Algol (/3 Persei). It\\nis suddenly visible as a star of the second magnitude, and con-\\ntinues such for 2d. 14h., when it begins rapidly to diminish in\\nsplendor, and in about 3J hours is reduced to the fourth magni-\\ntude. It then begins again to increase, and in 3J hours more, is\\nrestored to its usual brightness, going through all its changes in\\nless than three days. This remarkable law of variation appears\\nstrongly to suggest the revolution round it of some opake body,\\nwhich, when interposed between us and Algol, cuts off a large\\nportion of its light. It is (says Sir J. Herschel) an indication of\\na high degree of activity in regions where, but for such evidence,", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0321.jp2"}, "322": {"fulltext": "296 FIXED STARS.\\nwe might conclude all to be lifeless. Our sun requires almost nine\\ntimes this period to perform a revolution on its axis. On the\\nother hand, the periodic time of an opake revolving body, suffi-\\nciently large, which would produce a similar temporary obscura-\\ntion of the sun, seen from a fixed star, would be less than fourteen\\nhours.\\nThe duration of these periods is extremely various. While that\\nof (3 Persei, above mentioned, is less than three days, others are\\nmore than a year, and others many years.\\n424. CLUSTERS AND NEBULiE.\\nIn various parts of the firmament are seen large groups, or\\nclusters, which, either by the naked eye, or by the aid of the\\nsmallest telescope, are perceived to consist of a great number of\\nsmall stars. Such are the Pleiades, Coma Berenices, and Prae-\\nsepe, or the Bee-hive, in Cancer. The Pleiades, or Seven Stars,\\nas they are called, in the neck of Taurus, is the most conspicuous\\ncluster. When we look directly at this group, we cannot distin-\\nguish more than six stars, but by turning the eye sideways* upon\\nit, we discover that there are many more. The telescope only\\ncan, however, display the real magnificence of the Pleiades. (See\\nPlate III. Fig. 1.) Coma Berenices has fewer stars, but they are\\nof a larger class than those which compose the Pleiades. The\\nBee-hive, or Nebula of Cancer, is one of the finest objects of this\\nkind for a small telescope, being, by its aid, converted into a rich\\ncongeries of shining points. A cluster in the sword-handle of\\nPerseus, below Cassiopeia s chair, though but a dim speck to the\\nnaked eye, is a very elegant object to a large telescope, being\\nseparated into bright and beautiful stars, embracing several dis-\\ntinct subordinate clusters of exceedingly minute stellar points.\\nThe head of Orion affords an example of another cluster, though\\nless remarkable than the others.\\nIndirect vision is far more delicate than direct. Thus we can see the Zodiacal\\nLight or a comet s tail much more distinctly and better defined, (partly, perhaps,\\nby the effect of contrast,) if we fix one eye on a part of the sky at some distance,\\nand turn the other eye obliquely upon the object.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0322.jp2"}, "323": {"fulltext": "CLUSTERS AND NEBULAE. 297\\n425. Nebulae are faint misty objects seen in various parts of the\\nfirmament, always maintaining a fixed position, which resemble\\ncomets, or a speck of fog. The Galaxy, or Milky Way, presents\\na constant succession of large nebulae. Of the individual nebu-\\nlae, seen by the naked eye, the most conspicuous is that near the\\ngirdle of Andromeda. It is the oldest known nebula, having at-\\ntracted the attention of star-gazers as early as the beginning of\\nthe tenth century,* although it is commonly said to have been\\ndiscovered by Simon Marius, in 1612. No powers of the tele-\\nscope have been able to resolve this into separate stars, although\\nthe great Cambridge telescope reveals a vast number of stars,\\nmore than 1500, of various degrees of brightness, scattered over\\nits surface but these appear not to belong to the nebula itself,\\nwhich has hitherto afforded no evidence of resolution. f Its\\ndimensions are astonishingly great, since it covers a space of a\\nquarter of a degree in diameter and we must bear in mind that,\\nat such a distance as the fixed stars, a space of 15 implies an im-\\nmense extent. Its figure is oval, and elliptical nebulae constitute\\na common variety among the figures which these bodies exhibit.\\n(See Plate III. Fig. 2, for a representation of the great nebula of\\nAndromeda.) Another very common figure are the globular\\nnebulae. A grand specimen of this variety may be easily found\\nin the Constellation Hercules, between Zeta and Eta. Draw a\\nline from Lyra to Gemma of the Crown, and 3\u00c2\u00b0 above the center\\nof that line will be the place of this nebula. When viewed with\\na small telescope, it exhibits only a globular cloud, (Plate III.\\nFig. 3, a.) but to a more powerful instrument it reveals its real\\nglories in a form truly exciting to the beholder, (Fig. 3, b.) About\\n4000 nebulae have been detected and described, of which about\\n1700 have recently been added by Sir John Herschel, from his Re-\\nsults of Observations at the Cape of Good Hope. Among the latter\\nare two remarkable spots, well known to navigators, situated near\\nthe south pole, called Magellanic Clouds by sailors, but by as-\\ntronomers, the Nubecula Major and the Nubecula Minor. They\\nare found to consist of a wonderful collection of nebulae, the\\nSmyth s Cycle, II. 16.\\nf Memoirs of the Amer. Acad. Vol. IIL\\n38", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0323.jp2"}, "324": {"fulltext": "298 FIXED STARS.\\ngreater embracing 278 nebulae, and the lesser 37. Both together\\ncompose a most magnificent assemblage. In the sword of Orion\\nis a celebrated nebula, long known, which, until recently, had\\nresisted all attempts to resolve it into stars but the great Reflec-\\ntor of Lord Rosse, and more recently the great Refractor of the\\nCambridge Observatory, have succeeded in a partial resolution,\\nat least, of this grand object, and have authorized the anticipation\\nthat, with a small increase of telescopic power, the whole will be\\nshown to consist of an immense collection of exceedingly minute\\nstars.\\nThese great telescopes, by the superior light they afford,\\ndisplay their peculiar powers in this department of astronomy,\\nand those astronomers who, for the first time, have gazed at these\\nsidereal pictures as seen in the Leviathan of Lord Rosse, have\\nexpressed, in glowing terms, their mingled delight and astonish-\\nment. The perfect forms, and strange but symmetrical config-\\nurations, exhibited by these instruments, of nebulae that were\\nbefore seen of irregular or fantastic shapes, afford grounds for\\nbelieving that such irregularities are often if not always owing to\\nthe objects being but partly developed. Thus the Crab Nebula\\nof Lord Rosse (Plate III. Fig. 5) had been long known as a faint,\\nill-defined nebula of an elliptical shape but the higher powers of\\nthat instrument exhibit the before concealed appendages which\\nare essential to the completeness of the figure. The Whirlpool\\nNebula of Rosse, (Plate III. Fig. 6,) when seen in separate parts,\\nexhibited no signs of order or symmetry but when viewed with\\nthe great Reflector, it develops the wonderful structure of a per-\\nfect spiral.\\n426. Nebulae were formerly divided into two classes, resolvable\\nand irresolvable, the former term implying that the body was\\nshown by the telescope to consist of stars, and the latter implying\\nthat the body is not composed of stars, but of a shining cloudy\\nkind of matter diffused throughout the mass. Astronomers, at\\npresent, include all resolvable nebulae under the head of clusters,\\nappropriating the term nebulae exclusively to such of these bodies\\nas have never been resolved. The question whether this distinc-\\ntion is not merely relative to the powers of the telescope, and", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0324.jp2"}, "325": {"fulltext": "CLUSTERS AND NEBULAE. 299\\nwhether, on the increase of these powers, this class of bodies\\nwould not all be resolved into stars, is not easily determined, since\\nthe same increase of telescopic power which converts existing\\nnebulae into clusters, brings to light a greater number of those\\nwhich are irresolvable.\\nThese remote objects of the universe occasionally exhibit traces\\nof that regard to beauty which everywhere, in these nether\\nworlds, characterizes the works of the Creator. In the Cross, a\\nbrilliant constellation of the southern hemisphere, for example, is a\\ncluster surrounding the star Kappa Cruris, which consists of about\\n110 stars from the seventh magnitude downwards, eight of the\\nmore conspicuous of which are colored with various shades of\\nred, green, and blue, so as to give to the whole the appearance of\\na rich piece of jewelry.\\n427. Nebulous stars are such as exhibit a sharp and brilliant\\nstar, surrounded by a disk or atmosphere of nebulous matter.\\nThese atmospheres, in some cases, present a circular, in others an\\noval figure and in certain instances, the nebula consists of a\\nlong, narrow, spindle-shaped ray, tapering away at both ends to\\npoints. Annular Nebulce (Ring-shaped) are among the rarest\\nobjects in the heavens. The most conspicuous of this class is in\\nthe Constellation Lyra, between the stars Beta and Gamma, about\\n6\u00c2\u00b0 S. E. of Alpha Lyrae. This remarkable objeet is believed to\\nbe in fact a resolvable nebula or cluster, and yet the greatest\\npowers of the telescope hitherto applied have only effected such\\nchanges as are regarded as giving signs of resolvability, but its\\nperfect resolution has not been attained. Should it be achieved\\nby an increased power of the instrument, astronomers look for a\\nsplendid coronet of stars, more glorious, perhaps, than any thing\\nhitherto discovered in the starry heavens.\\nPlanetary Nebulce constitute another variety, and are very re-\\nmarkable objects. They have, as their name imports, exactly the\\nappearance of planets. Whatever may be their nature, they\\nmust be of enormous magnitude. One of them is to be found in\\nthe parallel of v Aquarii, and about 5m. preceding that star. Its\\napparent diameter is about 20 Another in the Constellation\\nAndromeda, presents a visible disk of 12 perfectly defined and", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0325.jp2"}, "326": {"fulltext": "300 FIXED STABS.\\nround. Granting these objects to be equally distant from us with\\nthe stars, their real dimensions must be such as, on the lowest\\ncomputation, would fill the orbit of Uranus. It is no less evident\\nthat, if they be solid bodies, of a solar nature, the intrinsic splen-\\ndor of their surfaces must be almost infinitely inferior to that of\\nthe sun. A circular portion of the sun s disk, subtending an\\nangle of 20 would give a light equal to 100 full moons while\\nthe objects in question are hardly, if at all, discernible with the\\nnaked eye.*\\n428. The Milky Way, or Galaxy, is a well-known luminous\\nzone, encircling the sphere nearly in the direction of a great cir-\\ncle. Near the Swan, in the northern sky, it is seen to be divided\\ninto two bands, which remain asunder for 150\u00c2\u00b0, and then reunite.\\nThe Galaxy owes its peculiar appearance to the blended light of\\nmyriads of small stars too minute to be individually recognized by\\nthe naked eye, but which are seen in their true character by a\\ntelescope of only moderate powers. Sir William Herschel esti-\\nmated that, on one occasion, in forty-one minutes, no less than\\n258,000 stars passed through the small field of his telescope. f In\\napproaching the border of the Milky Way, there is found a regu-\\nlar but rapid increase in the number-of stars, even before entering\\nthe limits of the luminous zone itself. Sir J. Herschel computes\\nthe whole number of stars in the Milky Way at five and a half\\nmillions, including such only as are visible in his twenty feet\\nreflector. The Galaxy is itself supposed to be a nebula, of which\\nour sun with its planets forms a constituent part and that it ap-\\npears so much greater than other nebulae only in consequence\\nof our situation with respect to it, and its greater proximity to\\nour system. J\\nHerschel.\\nf Plate II. Fig. 1, exhibits a telescopic view of a part of the southern portion of\\nthe Milky Way.\\nIn the course of instruction given to the students of Yale College, topics of thia\\nkind are more fully discussed in lectures on astronomy.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0326.jp2"}, "327": {"fulltext": "CHAPTER I ll.\\nMOTIONS OF THE FIXED STARS DISTANCES NATURE.\\n429. In 1803, Sir William Herschel first determined and an-\\nnounced to the world, that there exist among the stars separate\\nsystems, composed of two stars, revolving about each other in\\nregular orbits. These he denominated Binary Stars, to distinguish\\nthem from other double stars where no such motion is detected,\\nand whose proximity to each other may possibly arise from cas-\\nual juxtaposition, or from one being in the range of the other.\\nAt present, more than a hundred of the binary stars are known,\\nand as the number of such revolutions known among the double\\nstars is constantly increasing as the times of comparison increase,\\nit may be anticipated that, in after ages, so large a proportion of\\nall the double stars will be found to possess this character, as to\\nauthorize the belief that they universally consist of subordinate\\nsystems, of which the members have a revolution around a common\\ncenter of gravity. The periodic times of the binary stars are\\nvery various. While some (as Hercules, and ?j Coronce) complete\\ntheir revolutions in 30 or 40 years, others (as y Virginis) re-\\nquire more than 170, and others still (as 65 Piscium) take up the\\nlong period of 3000 years.* Their orbits are in general more\\neccentric than those of the planets. That of Gamma Virginis,\\nincluding the relative positions of the two components from 1837\\nto 1860, is figured on Plate II. as drawn by Mr. E. P. Mason,\\nin 1840-f\\nSmyth s Cycle, I. 300.\\nf Sir John Herschel had computed the orbit of y Virginis, and had given it at\\n625 years. Mason, from a discussion of all the observations, published to the date\\nof 1838, combined with his own of 1840, found that this period was too great, and\\nassigned as the true period 171 years, which is now acknowledged by the highest\\nauthorities, and even by Herschel himself, to be nearly its real time of revolution.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0327.jp2"}, "328": {"fulltext": "302 FIXED STARS.\\n430. The revolutions of the binary stars have assured us of\\nthis most interesting fact, that the law of gravitation extends to\\nthe fixed stars. Before these discoveries, we could not decide,\\nexcept by a feeble analogy, that this law transcended the bounds\\nof the solar system. Indeed, our belief of the fact rested more\\nupon our idea of unity of design in all the works of the Creator,\\nthan upon any certain proof; but the revolution of one star\\naround another in obedience to forces which must be similar to\\nthose that govern the solar system, establishes the grand conclu-\\nsion, that the law of gravitation is truly the law of the material\\nuniverse.\\nWe have the same evidence (says Sir John Herschel) of the\\nrevolutions of the binary stars about each other, that we have of\\nthose of Saturn and Uranus about the sun and the correspond-\\nence between their calculated and observed places in such elon-\\ngated ellipses, must be admitted to carry with it a proof of the\\nprevalence of the Newtonian law of gravity in their systems, of\\nthe very same nature and cogency as that of the calculated and\\nobserved places of comets round the center of our own system.\\nBut (he adds) it is not with the revolutions of bodies of a plan-\\netary or cometary nature round a solar center that we are now\\nconcerned it is with that of sun around sun, each, perhaps, ac-\\ncompanied with its train of planets and their satellites, closely\\nshrouded from our view by the splendor of their respective suns,\\nand crowded into a space, bearing hardly a greater proportion to\\nthe enormous interval which separates them, than the distances\\nof the satellites of our planets from their primaries, bear to their\\ndistances from the sun itself.\\n431. Some of the fixed stars appear to have a Proper Motion,\\nor a real motion in space.\\nThe apparent change of place in the stars arising from the pre-\\ncession of the equinoxes, the nutation of the earth s axis, the\\ndiminution of the obliquity of the ecliptic, and the aberration of\\nlight, have been already mentioned but after all these corrections\\nare made, changes of place still occur, which cannot result from\\nany changes in the earth, but must arise from changes in the stars\\nthemselves. Such motions are called the proper motions of the", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0328.jp2"}, "329": {"fulltext": "MOTIONS OF THE FIXED STARS. 303\\nstars. Nearly 2000 years ago, Hipparchus and Ptolemy made\\nthe most accurate determinations in their power of the relative\\nsituations of the stars, and their observations have been trans-\\nmitted to us in Ptolemy s Almagest from which it appears that\\nthe stars retain at least very nearly the same places now as they\\ndid at that period. Still, the more accurate methods of modern\\nastronomers, have brought to light minute changes in the places of\\ncertain stars which force upon us the conclusion, either that our\\nsolar system causes an apparent displacement of certain stars, by\\na motion of its own in space, or that they have themselves a proper\\nmotion. Possibly, indeed, both these causes may operate.\\n432. If the sun, and of course the earth which accompanies\\nhim, is actually in motion, the fact may become manifest from\\nthe apparent approach of the stars in the region which he is leav-\\ning, and the recession of those which lie in the part of the heav-\\nens towards which he is travelling. Were two groves of trees\\nsituated on a plain at some distance apart, and we should go\\nfrom one to the other, the trees before us would gradually\\nappear further and further asunder, while those we left behind\\nwould appear to approach each other. Some years since, Sir\\nWilliam Herschel supposed he had detected changes of this kind\\namong two sets of stars in opposite points of the heavens, and an-\\nnounced that the solar system was in motion towards a point in\\nthe Constellation Hercules.* As, for many years after this an-\\nnouncement, other astronomers failed to find evidence of such a\\nmotion of the solar system, the doctrine was generally discredited,\\nuntil, within a few years, new and very* refined researches have\\nbeen instituted by several of the most eminent astronomers, which\\nhave fully confirmed the observations of Herschel. The great\\nRussian astronomer, Struve, by a comparison of the best observa-\\ntions, finds the exact point towards which the solar system is mov-\\ning is in a line which joins the two stars and f* Herculis,f a\\npoint which can be easily found on the celestial globe, and thence\\ntransferred tc the heavens. (Right ascension 259\u00c2\u00b0, declination\\nPhil. Trans. 1183, 1805, and 1806.\\nf fitudes d Astronomie Stellaire, p. 108.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0329.jp2"}, "330": {"fulltext": "304 FIXED STARS.\\n341\u00c2\u00b0.) The researches of the younger Struve have conducted\\nhim to the velocity with which the solar system is moving in\\nspace. For having found that the arc traversed by the sun in a\\nyear is 0 3392, if viewed at the mean distanced the stars of the\\nfirst magnitude, and having previously ascertained that the mean\\nparallax of the stars of this class amounts to 0 .209, he infers that\\nthe space through which the sun moves annually is 154,000,000\\nmiles. Great as this space is, yet it may be remarked that it\\nis only about one-fourth that traversed by the earth in its revo-\\nlution around the sun. Within the comparatively short period\\nduring which these observations on the solar motion have been\\ncontinued, the direction appears rectilinear but all analogy leads\\nto the belief that it is in fact a motion of revolution, although on\\naccount of the immense size of the orbit, and, consequently, its\\nsmall curvature, many years will be requisite in order to determine\\nthe deviation from the line of the tangent.*\\n433. When we reflect on the immense distance of the stars,\\nwe may readily believe that they may be in fact in rapid motion,\\nand yet appear quiescent as a distant ship, under full sail, ap-\\npears at rest, although actually moving at the rate of ten knots\\nan hour. Thus we have seen above that a motion of the sun in\\nspace, as seen from the nearest fixed stars, would make it de-\\nscribe an arc of only about one-third of a second annually, although\\ntraversing a space of 154 millions of miles. But a small change\\nin the place of a star in a single year may, in a long series of\\nyears, accumulate to a very sensible amount. For example, the\\nlatitudes of the three bright stars, Sirius, Arcturus, and Aldebaran,\\nwere determined by Hipparchus 130 years before the Christian\\nera, and their assigned places are transmitted to us in the Alma-\\ngest of Ptolemy. About the year 1700, Dr. Halley found that\\nthese stars had, during the interval of nearly 2000 years, moved\\nsoutherly through the spaces respectively of 37 42 and 33\\nThe immense gains that have of late years been bestowed upon\\ncatalogues of the stars, and especially of particular portions of the\\nheavens, with the view of furnishing, to after ages, the most ac-\\nGrant s Hist. Phys. Ast. 557.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0330.jp2"}, "331": {"fulltext": "DISTANCES OF THE FIXED STARS. 305\\ncurate data for comparison, will enable future astronomers to\\nstudy the proper motions of the stars with far greater advantages\\nthan the present generation enjoys. In most cases where a proper\\nmotion in certain stars has been suspected, its annual amount has\\nbeen so small, that many years are required to assure us that the\\neffect is not owing to some other than a real progressive motion\\nin the stars themselves but in a few instances the fact is too\\nobvious to admit of any doubt. A small star in the leg of the\\nGreat Bear has an annual motion away from the neighboring\\nstars of 7 and the two stars 61 Cygni, which are nearly equal,\\nhave remained constantly at the same, or nearly at the same\\ndistance of 15 for at least fifty years past. Meanwhile they have\\nshifted their local situation in the heavens, 4 23 the annual\\nproper motion of each star being 5. 3, by which quantity this\\nsystem is every year carried along in some unknown path, by a\\nmotion which for many centuries must be regarded as uniform\\nand rectilinear. A greater proportion of the double stars than of\\nany other indicate proper motions, especially the binary stars, or\\nthose which have a revolution around each other. Among stars\\nnot double, and no way differing from the rest in any other ob-\\nvious particular, f/. Cassiopeia? has a proper motion, amounting to\\nnearly 4 annually and another obscure star has been recently\\nfound to have a motion of nearly 8\\n434. DISTANCES OF THE FIXED STARS.\\nIt has long been considered one of the highest problems that can\\nbe proposed to the human mind, to measure the distance to any\\nof the fixed stars. Nothing more, indeed, would be necessary\\nhan to determine its horizontal parallax but this is so exceed-\\ningly small, that, until recently, all efforts to measure it had proved\\nunavailing. For all measurements relating to the distances of\\nthe sun and planets, the diameter of the earth furnishes the base\\nline, (Art. 87.) The length of this line being known, and likewise\\nthe horizontal parallax of the body whose distance is sought, we\\nreadily obtain the distance by the solution of a right-angled tri-\\nangle, (Art. 80, Fig. 6.) But any star viewed from the opposite\\nHerschel s Outlines, (Ed. 1851.)\\n39", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0331.jp2"}, "332": {"fulltext": "306 FIXED STARS.\\nsides of the earth, would appear from both stations to occupy pre-\\ncisely the same situation in the celestial sphere, and of course it\\nwould exhibit no horizontal parallax. But astronomers have\\nendeavored to find a parallax in some of the fixed stars, by taking\\nthe diameter of the earth s orbit as a base line. Yet even a\\nchange of position, amounting to 190 millions of miles, has, until\\nwithin a few years, proved insufficient to alter the apparent\\nplace of a single fixed star, from which it was concluded that the\\nfixed stars have not even any annual parallax or that the angle\\nsubtended by the semidiameter of the earth s orbit, at the nearest\\nfixed star, is insensible. The errors to which instrumental meas-\\nurements are subject, arising from defects of the instruments them-\\nselves, from errors of refraction, of aberration, of precession, of\\nnutation, and from imperfections of observation, are such, that the\\nangular determinations of celestial arcs, it was supposed, could\\nnot be relied on to less than 1 and the change of place in any star\\nthat had been examined for parallax being less than one second\\nwhen viewed at opposite extremities of the earth s orbit, the con-\\nclusion was, that the parallax of the fixed stars, if any exist, is too\\nminute ever to be measured by instruments. According to this,\\nthe diameter of the earth s orbit, when viewed from the nearest\\nfixed star, would be insensible the spider-line of the telescope\\nwould more than cover it. Fig. 80.\\nTaking, however, the annual parallax at 1 let ah (Fig.\\n80) represent the radius of the earth s orbit, and c a fixed\\nstar, the angle at c being 1 and the angle at b a right\\nangle then,\\nSin. 1 Rad. 1 200,000, nearly.\\nHence the hypothenuse of a triangle w*hose vertical\\nangle is 1 is about 200,000 times the base; conse-\\nquently, the distance in question must exceed 95,000,000 x\\n200,000=190,000,000X100,000, or one hundred thou-\\nsand times one hundred and ninety millions of miles. Of\\na distance so vast we can form no adequate conceptions,\\nand attempt to measure it only by the time that light\\n(which moves more than 192,000 miles per second) w r ould\\ntake to traverse it. Now,\\n192,000 Is. 19,000,000,000,000 3.1 years.\\nc", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0332.jp2"}, "333": {"fulltext": "DISTANCES OF THE FIXED STARS. 307\\n435. After many fruitless and delusory efforts to measure the\\nimmense interval that separates us from the fixed stars, the great\\nPrussian astronomer, Bessel, in the year 1838, determined this\\ninteresting and important element, by observations on a double\\nstar in the Swan, (61 Cygni.) This star was selected for the\\nfollowing reasons first, it was known to have a great proper\\nmotion, (Art. 433,) indicating a comparatively great prox-\\nimity to our system secondly, situated as it is among the\\ncircumpolar stars, observations could be made upon it nearly\\nevery night in the year and, thirdly, the great number of small\\nstars in the immediate neighborhood, furnished the opportunity\\nof selecting favorable stationary points from which (inasmuch as\\nthese more remote objects might be considered as entirely devoid\\nof parallax) any changes of place in the nearer, in consequence\\nof an annual parallax, might be readily estimated. By observa-\\ntions of the last degree of refinement, conducted for a period of\\nseveral years, a parallax was decisively indicated, amounting to\\nabout one-third of a second or, more exactly, to 0. 3483, imply-\\ning a distance of 592,200 times the mean distance of the earth\\nfrom the sun, or a space which it would take light, moving at the\\nrate of twelve millions of miles per minute, nine and a quartet\\nyears to traverse. To form some familiar notions of this distance,\\nlet us suppose a railway-car to travel night and day, at the rate\\nof twenty miles an hour we should find it would take it about 547\\nyears to reach the sun but to reach 61 Cygni would require\\n324,000,000 of years.\\nThe observations of Bessel enabled him to estimate also the\\nperiod of revolution of the two stars composing the binary sys-\\ntem of 61 Cygni, and the dimensions of the orbit, and he found\\nthe periodic time about 540 years, and the length of the orbit\\nabout two and a half times that of Uranus. Knowing also the\\ndistance of this star, we can now determine from its proper mo-\\ntion (five seconds a year) the velocity of its motion this is found\\nto be about forty- four miles per second more than double that\\nof the earth in its orbit amounting to about one thousand mil-\\nlions of miles per annum.\\nOn account of the smallness of the supposed parallax thus\\nfound, it would not be unreasonable still to entertain a lingering", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0333.jp2"}, "334": {"fulltext": "308 FIXED STARS.\\nsuspicion, that it is nothing more than the unavoidable imperfec-\\ntion of instrumental measurements, as proved to be the case in\\nprevious attempts to find the same element but the most satis-\\nfactory evidence which the world can have that such is not the\\nfact in the present instance, but that the parallax is truly found,\\nis that the most celebrated astronomers of the age, after rigorous\\nscrutiny, have acknowledged the reality and soundness of the de-\\ntermination, Our confidence that the parallax of 61 Oygni was\\ntruly determined by Bessel, is strengthened by the fact that a sep-\\narate determination recently made by Peters at the Pulkova Ob-\\nservatory, gives almost precisely the same result, that of Bessel\\nbeing 0. 348, and that of Peters 0. 349. In the case of several stars\\nstill more distant, the parallax has been found, with more or less\\nprobability, but with sufficient to command the general confidence\\nof astronomers. Thus, the parallax of Arcturus, Alpha Lyras,\\nand Polaris, were also found by Peters to be respectively 0/ 127,\\n0. 123, 0. 067, that of the Pole-star being only one-fifth as great\\nas that of 61 Cygni and, consequently, if light would require\\n9J years to come from that star, it would require more than 46\\nyears to come to us from the Pole-star. A star in the southern\\nhemisphere, (a Centauri,) indicates a parallax of about 1 and\\nhence appears at present the nearest of the fixed stars.\\n436. NATURE OF THE STARS.\\nThe stars are bodies greater than our earth. If this were\\nnot the case they could not be visible at such an immense dis-\\ntance. Dr. Wollaston, a distinguished English philosopher,\\nattempted to estimate the magnitudes of certain of the fixed\\nstars from the light which they afford. By means of an accu-\\nrate photometer (an instrument for measuring the relative inten-\\nsities of light) he compared the light of Sirius with that of the\\nsun. He next inquired how far the sun must be removed from\\nus in order to appear no brighter than Sirius. He found the dis-\\ntance to be 141,400 times its present distance. But Sirius is more\\nthan 200,000 times as far off as the sun, (Art. 434.) Hence he\\ninferred that, upon the lowest computation, Sirius must actually\\ngive out twice as much light as the sun or that, in point of", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0334.jp2"}, "335": {"fulltext": "NATURE OF THE STARS. 309\\nsplendor, Sirius must be at least equal to two suns. Indeed, he\\nhas rendered it probable that the light of Sirius is equal to four-\\nteen suns.\\n437. The fixed stars are suns. We have already seen that\\nthey are large bodies that they are immensely further off than\\nthe furthest planet that they shine by their own light, as is evi-\\ndent by the nature of the light as tested by polarization in short,\\nthat their appearance is, in all respects, the same as the sun would\\nexhibit if removed to the region of the stars. Hence we infer\\nthat they are bodies of the same kind with the sun.\\n438. We are justified therefore by a sound analogy, in con-\\ncluding that the stars were made for the same end as the sun,\\nnamely, as the centers of attraction to other planetary worlds, to\\nwhich they severally dispense light and heat. Although the starry\\nheavens present, in a clear night, a spectacle of ineffable gran-\\ndeur and beauty, yet it must be admitted that the chief purpose\\nof the stars could not have been to adorn the night,* since by far\\nthe greatest part of them are w r holly invisible to the naked eye\\nnor as landmarks to the navigator, for only a very small propor-\\ntion of them are adapted for this purpose nor, finally, to influence\\nthe earth by their attractions, since their distance renders such\\nan effect entirely insensible. If they are suns, and if they exert\\nno important agencies upon our w T orld, but are bodies evidently\\nadapted to the same purpose as our sun, then it is as rational to\\nsuppose that they w 7 ere made to give light and heat, as that the\\neye was made for seeing and the ear for hearing. It is obvious\\nto inquire next, to what they dispense these gifts if not to plan-\\netary worlds and why to planetary worlds, if not for the use of\\npercipient beings We are thus led, almost inevitably, to the\\nidea of a Plurality of Worlds and the conclusion is forced upon\\nus, that the spot which the Creator has assigned to us is but a\\nhumble province of his boundless empire.*\\nSee this argument, in its full extent, in Dick s Celestial Scenery.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0335.jp2"}, "336": {"fulltext": "CHAPTER IV.\\nOF THE SYSTEM OF THE WORLD.\\n439. The arrangement of all the bodies that compose the ma-\\nterial universe, and their relations to each other, constitutes the\\nSystem of the World.\\nIt is otherwise called the Mechanism of the Heavens and in-\\ndeed in the System of the World, we figure to ourselves a machine,\\nall the parts of which have a mutual dependence, and conspire to\\none great end. The machines that are first invented (says\\nAdam Smith) to perform any particular movement, are always\\nthe most complex and succeeding artists generally discover that\\nwith fewer wheels and with fewer principles of motion than had\\noriginally been employed, the same effects may be more easily\\nproduced. The first systems, in the same manner, are always the\\nmost complex and a particular connecting chain or principle is\\ngenerally thought necessary to unite every two seemingly dis-\\njointed appearances but it often happens, that one great connect-\\ning principle is afterwards found to be sufficient to bind together\\nall the discordant phenomena that occur in a whole species of\\nthings. This remark is strikingly applicable to the origin and\\nprogress of systems of astronomy.\\n440. From the visionary notions which are generally under-\\nstood to have been entertained on this subject by the ancients,\\nwe are apt to imagine that they knew less than they actually did\\nof the truths of astronomy. But Pythagoras, who lived 500 years\\nbefore the Christian era, was acquainted with many important\\nfacts in our science, and entertained many opinions respecting\\nthe System of the World which are now held to be true. Among\\nother things well known to Pythagoras were the following\\n1. The principal Constellations. These had begun to be formed\\nin the earliest ages of the world. Several of them bearing the\\nsame names as at present are mentioned in the writings of Hesiod", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0336.jp2"}, "337": {"fulltext": "SYSTEM OF THE WORLD. 311\\nand Homer and the sweet influences of the Pleiades and the\\nbands of Orion, are beautifully alluded to in the Book of Job.\\n2. Eclipses. Pythagoras knew both the causes of eclipses and\\nhow to predict them not indeed in the accurate manner now\\nemployed, but by means of the Saros, (Art. 233.)\\n3. Pythagoras had divined the true system of the world, hold-\\ning that the sun, and not the earth, (as was generally held by the\\nancients, even for many years after Pythagoras,) is the center\\naround which all the planets revolve, and that the stars are so\\nmany suns, each the center of a system like our own.f Among\\nlesser things, he knew that the earth is round that its surface\\nis naturally divided into five zones and that the ecliptic is in-\\nclined to the equator. He also held that the earth revolves daily\\non its axis, and yearly around the sun that the galaxy is an as-\\nsemblage of small stars; and that it is the same luminary, namely,\\nVenus, that constitutes both the morning and the evening star,\\nwhereas all the ancients before him had supposed that each was\\na separate planet, and accordingly the morning star was called\\nLucifer, and the evening star Hesperus. J He held rlso that the\\nplanets were inhabited, and even went so far as to calculate the\\nsize of some of the animals in the moon.\u00c2\u00a7 Pythagoras was so great.\\nan enthusiast in music, that he not only assigned to it a conspicuous\\nplace in his system of education, but even supposed the heavenly\\nbodies themselves to be arranged at distances corresponding to\\nthe diatonic scale, and imagined them to pursue their sublime\\nmarch to notes created by their own harmonious movements,\\ncalled the music of the spheres but he maintained that this\\ncelestial concert, though loud and grand, is not audible to the\\nfeeble organs of man, but only to the gods.\\n441. With few exceptions, however, the opinions of Pythago-\\nras on the System of the World, were founded in truth. Yet they\\nwere rejected by Aristotle and by most succeeding astronomers\\ndown to the time of Copernicus, and in their place was substituted\\nLong s Astronomy, ii. 671.\\n\u00e2\u0080\u00a2j* Library of Useful Knowledge, History of Astronomy.\\nLong s Ast, ii. 673. Ed. Encyclopaedia.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0337.jp2"}, "338": {"fulltext": "312 SYSTEM OF THE WORLD.\\nthe doctrine of Crystalline Spheres, first taught by Eudoxus. Ac-\\ncording to this system, the heavenly bodies are set like gems in\\nhollow solid orbs, composed of crystal so pellucid that no anterior\\norb obstructs in the least the view of any of the orbs that lie behind\\nit. The sun and the planets have each its separate orb but the\\nfixed stars are all set in the same grand orb and beyond this is\\nanother still, the Primum Mobile, which revolves daily from east\\nto west, and carries along with it all the other orbs. Above the\\nwhole, spreads the Grand Empyrean, or third heavens, the abode\\nof perpetual serenity.*\\nTo account for the planetary motions, it was supposed that each\\nof the planetary orbs, as well as that of the sun, has a motion of its\\nown eastward, while it partakes of the common diurnal motion of\\nthe starry sphere. Aristotle taught that these motions are effected\\nby a tutelary genius of each planet, residing in it, and directing\\nits motions, as the mind of man directs his motions.\\n442. On coming down to the time of Hipparchus, who flourished\\nabout 150 years before the Christian era, we meet with astrono-\\nmers who acquired far more accurate knowledge of the celestial\\nmotions. Hipparchus was in possession of instruments for meas-\\nuring angles, and knew how to resolve spherical triangles. He\\nascertained the length of the year within 6m. of the truth. He\\ndiscovered the eccentricity of the solar orbit, (although he sup-\\nposed the sun actually to move uniformly in a circle, but the earth\\nto be placed out of the center,) and the positions of the sun s\\napogee and perigee. He formed very accurate estimates of the\\nobliquity of the ecliptic and of the precession of the equinoxes.\\nHe computed the exact period of the synodic revolution of the\\nmoon, and the inclination of the lunar orbit discovered the mo-\\ntion of her node and of her line of apsides and made the first\\nattempts to ascertain the horizontal parallaxes of the sun and moon.\\nSuch was the state of astronomical knowledge when Ptolemy\\nwrote the Almagest, in which he has transmitted to us an en-\\ncyclopaedia of the astronomy of the ancients.\\nLong s Ast. ii. 640 Robinson s Mech. Phil. ii. 83\u00e2\u0080\u0094 Gregory s Ast. 132\u00e2\u0080\u0094 Play-\\nfair s Dissertations, 118.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0338.jp2"}, "339": {"fulltext": "THE PTOLEMAIC SYSTEM. 313\\n443. The systems of the world which have been most celebrated\\nare three the Ptolemaic, the Tychonic, and the Copernican.\\nWe shall conclude this part of our work with a concise statement\\nand discussion of each of these systems of the Mechanism of\\nthe Heavens.\\nTHE PTOLEMAIC SYSTEM.\\n444. The doctrines of the Ptolemaic System were not originated\\nby Ptolemy, but being digested by him out of materials furnished\\nby various hands, it has come down to us under the sanction of\\nhis name.\\nAccording to this system, the earth is the center of the uni-\\nverse, and all the heavenly bodies daily revolve around it from\\neast to west. In order to explain the planetary motions, Ptolemy\\nhad recourse to deferents and epicycles, an explanation devised\\nby Apollonius, one of the greatest geometers of antiquity.* He\\nconceived that, in the circumference of a circle, having the earth\\nfor its center, there moves the center of another circle, in the\\ncircumference of which the planet actually revolves. The circle\\nsurrounding the earth was called the deferent, while the smaller\\ncircle, whose center was always in the periphery of the deferent,\\nwas called the epicycle. The motion in each was supposed to be\\nuniform. Lastly, it was conceived that the motion of the center\\nof the epicycle in the circumference of the deferent, and of the\\ndeferent itself, are in opposite directions, the first being towards\\nthe east, and the second towards the west.\\n445. But these views will be better understood from a diagram.\\nTherefore, let ABC (Fig. 81) represent the deferent, E being the\\nearth a little out of the center. Let abc represent the epicycle,\\nhaving its center at v, on the periphery of the deferent. Con-\\nceive the circumference of the deferent to be carried about the\\nearth every twenty-four hours in the order of the letters and at\\nthe same time, let the center v of the epicycle abed, have a slow\\nmotion in the opposite direction, and let a body revolve in this\\nPlayfair, Dissertation Second, 119.\\n40", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0339.jp2"}, "340": {"fulltext": "314\\nSYSTEM OF THE WORLD.\\ncircle in the direction abed. Then it will be seen that the body\\nwould actually describe the looped curves klmnop that it would\\nappear stationary at I and m, and at n and o that its motion\\nwould be direct from k to and then retrograde from /torn;\\ndirect again from m to n, and retrograde from n to o. Thus,\\nsuppose Mercury to be situated at b in its epicycle. By the rev-\\nolution of the deferent, it would be carried along with the other\\nheavenly bodies around the earth from left to right, every twenty-\\nfour hours but, meanwhile, the center of the epicycle shifting\\nits place slowly from right to left, while Mercury was moving\\nfrom b toe, c itself would change its place to r, and therefore the\\npath of the planet would be in the cycloidal arc br. Again, while\\nMercury was passing through cda, the point c would be still mov-\\ning eastward, which would have the effect apparently to compress\\nthe lower half of the epicycle into the looped curve nor and as\\non this side the motion in the epicycle is in the same direction\\nwith that of the deferent, but at a slower rate, the apparent path\\nis much shorter than where, as on the other side, the two motions\\nconspire.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0340.jp2"}, "341": {"fulltext": "THE TYCHONIC SYSTEM. 315\\n446. Such a deferent and epicycle may be devised for each\\nplanet as will fully explain all its ordinary motions but it is in-\\nconsistent with the phases of Mercury and Venus, which being\\nbetween us and the sun on both sides of the epicycle, would pre-\\nsent their dark sides towards us in both these positions, whereas\\nat one of the conjunctions they are seen to shine with full face.*\\nIt is moreover absurd to speak of a geometrical center, which, has\\nno bodily existence, moving around the earth on the circumference\\nof another circle and hence some suppose that the ancients\\nmerely assumed this hypothesis as affording a convenient geo-\\nmetrical representation of the phenomena, a diagram simply,\\nwithout conceiving the system to have any real existence in\\nnature.\\n447. The objections to the Ptolemaic system, in general, are the\\nfollowing First, it is a mere hypothesis, having no evidence in\\nits favor, except that it explains the phenomena. This evidence\\nis insufficient of itself, since it frequently happens that each of\\ntwo hypotheses, directly opposite to each other, will explain all\\nthe known phenomena. But the Ptolemaic system does not even\\ndo this, as it is inconsistent with the phases of Mercury and\\nVenus, as already observed. Secondly, now that we are ac-\\nquainted with the distances of the remoter planets, and especially\\nof the fixed stars, the swiftness of motion implied in a daily rev-\\nolution of the starry firmament around the earth, renders such a\\nmotion wholly incredible. Thirdly, the centrifugal force that\\nwould be generated in these bodies, especially in the sun, renders\\nit impossible that they can continue to revolve around the earth\\nas a center.\\nThese reasons are sufficient to show the absurdities of the\\nPtolemaic System of the World.\\nTHE TYCHONIC SYSTEM.\\n448. Tycho Brahe, like Ptolemy, placed the earth in the center\\nof the universe, and accounted for the diurnal motions in the same\\nVince s Complete System, i. 96.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0341.jp2"}, "342": {"fulltext": "316 SYSTEM OF THE WORLD.\\nmanner as Ptolemy had done, namely, by an actual revolution of\\nthe whole host of heaven around the earth every twenty-four\\nhours. But he rejected the scheme of deferents and epicycles,\\nand held that the moon revolves about the earth as the center of\\nher motions that the sun, and not the earth, is the center of the\\nplanetary motions and that the sun, accompanied by the planets,\\nmoves around the earth once a year, somewhat in the manner\\nthat we now conceive of Jupiter and his satellites as revolving\\naround the sun. The system of Tycho serves to explain all the\\ncommon phenomena of the planetary motions, but it is encum-\\nbered with the same objections as those that have been men-\\ntioned as resting against the Ptolemaic system, namely, that it is\\na mere hypothesis that it implies an incredible swiftness in the\\ndiurnal motions and that it is inconsistent with the known laws\\nof universal gravitation. But if the heavens do not revolve, the\\nearth must, and this brings us to the system of Copernicus.\\nTHE COPERNICAN SYSTEM.\\n449. Copernicus was born at Thorn, in Prussia, in 1473. The\\nsystem that bears his name was the fruit of forty years of intense\\nstudy and meditation upon the celestial motions. As already\\nmentioned, (Art. 6,) it maintains (1) That the apparent diurnal\\nmotions of the heavenly bodies, from east to west, is owing to the\\nreal revolution of the earth on its own axis from west to east\\nand (2) That the sun is the center around which the earth and\\nplanets all revolve from west to east. It rests on the following\\narguments\\nFirst, the earth revolves on its own axis.\\n1. Because this supposition is vastly more simple.\\n2. It is agreeable to analogy, since all the other planets that\\nafford any means of determining the question, are seen to revolve\\non their axes.\\n3. The spheroidal figure of the earth is the figure of equilib-\\nrium, that results from a revolution on its axis.\\n4. The diminished weight of bodies at the equator, indicates a\\ncentrifugal force arising from such a revolution.\\n5. Bodies let fall from a high eminence, fall eastward of their", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0342.jp2"}, "343": {"fulltext": "THE COPERNICAN SYSTEM. 317\\nlase, indicating that when further from the center of the earth\\nthey were subject to a greater velocity, which, in consequence of\\ntheir inertia, they do not entirely lose in descending to the lower\\nlevel.*\\nSecondly, the planets, including the earth, revolve about the sun.\\n1. The phases of Mercury and Venus are precisely such as\\nwould result from their circulating around the sun in orbits w r ithin\\nthat of the earth but they are never seen in opposition, as they\\nwould be if they circulated around the earth.\\n2. The superior planets do indeed revolve around the earth\\nbut they also revolve around the sun, as is evident from their\\nphases and from the known dimensions of their orbits and that\\nthe sun, and not the earth, is the center of their motions, is in-\\nferred from the greater symmetry of their motions as referred to\\nthe sun than as referred to the earth, and especially from the laws\\nof gravitation, which forbid our supposing that bodies so mucl\\nlarger than the earth, as some of these bodies are, can circulate\\npermanently around the earth, the latter remaining all the while\\nat rest.\\n3. The annual motion of the earth itself is indicated also by the\\nmost conclusive arguments. For, first, since all the planets with\\ntheir satellites, and the comets, revolve about the sun, analogy\\nleads us to infer the same respecting the earth and its satellite.\\nSecondly, the motions of the satellites, as those of Jupiter and\\nSaturn, indicate that it is a law of the solar system that the\\nsmaller bodies revolve about the larger. Thirdly, the direction\\nof the periodical meteors of November, which, in a majority of\\ncases, is from east to west, indicates the motion of the earth from\\nwest to east. Lastly, the aberration of light affords a sensible\\nproof of the motion of the earth, since that phenomenon indicates\\nboth a progressive motion of light, and a motion of the earth from\\nwest to east. (Art. 195.)\\n450. It only remains to inquire whether there subsist higher\\norders of relations between the stars themselves. The assem-\\nblage of bodies in clusters, as in the Pleiades, and still more, as in\\nBiot.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0343.jp2"}, "344": {"fulltext": "318 SYSTEM OF THE WORLD.\\nthe great nebula of Hercules, (Art. 425,) implies mutual relations\\nconstituting for each a system within itself; and the analogies of\\nall that portion of the heavenly bodies, whose motions fall within\\nour observation, and the known uniformity of the laws of nature,\\nconspire to prove that those relations are maintained by revolu-\\ntions around a common center. What theory would lead us to\\nexpect, we actually see exemplified in the revolutions of the binary\\nstars, (Art. 430,) and in the motion of the sun himself with his\\nattendant worlds, (Art. 432.) The Nebulce also compose peculiar\\nsystems, in which the members seem associated in mutual rela-\\ntions, and separated from all the other heavenly bodies, each\\ncomposing an island universe. Thus we ascend from the lower\\nto the higher combinations, according to a uniform plan, so char-\\nacteristic of ascending orders in every department of nature.\\nBeginning with the relation between the earth and its satellite,\\nwe see it sustained by the prevalence of forces which subject it\\nto Kepler s laws and the law of universal gravitation. We see\\nthe same principles carried out on a larger scale, but exactly on\\nthe same plan, in the system of Jupiter and his satellites, and in\\nthe respective systems of Saturn, Uranus, and Neptune. From\\nthis lowest order of combination, composed of planets and their\\nsatellites, we ascend to the next higher order, consisting of suns\\nand planets, in which the same plan is exemplified on a still grand-\\ner scale, but without any change in its peculiar features. We\\nnext ascend still higher to the third order, as in the binary stars.\\nwhere sun revolves around sun, upon the same unvarying plan\\nas before seen in these nearer worlds. At present, observation\\nleads us to no higher point of the scale in the structure of the\\nuniverse but the mind of man, obtaining from these lower sys-\\ntems a knowledge of the plan on which the universe is built, goes\\nforward to complete the grand machine. A bold attempt has\\nrecently been made by Maedler, an eminent European astrono-\\nmer, to fix the center around which not only our sun, but all the\\nstars of our firmament revolve. It must evidently be such a\\npoint, that the known proper motions detected among the fixed\\nstars will conform to it, like the motions of the planets around\\nthe sun. He places that center in the Pleiades, or, more exactly,\\nin Alcyone, the central star of the Pleiades, which body is therefore", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0344.jp2"}, "345": {"fulltext": "STRUCTURE OF THE UNIVERSE. 319\\ndenominated the Central Sun.* The proofs of this remarkable\\nhypothesis are deemed too incomplete at present to command\\nentire assent but the method of investigation pursued by this\\ndistinguished astronomer, opens a new field of observation and of\\nspeculation, and promises to lend a new interest to inquiries into\\nthe mechanism of the universe.\\n451. This fact being now established, that the stars are im-\\nmense bodies like the sun, and that they are subject to the laws\\nof gravitation, we cannot conceive how they can be preserved\\nfrom falling into final disorder and ruin, unless they move in har-\\nmonious concert like the members of the solar system. Otherwise,\\nthose that are situated on the confines of creation, being retained\\nby no forces from without, while they are subject to the attraction\\nof all the bodies within, must leave their stations, and move in\\nward with accelerated velocity, and thus all the bodies in the\\nuniverse would at length fall together in the common center of\\ngravity. The immense distances at which the stars are placed\\nfrom each other, would indeed delay such a catastrophe but such\\nmust be the ultimate tendency of the material world, unless sus-\\ntained in one harmonious system by nicely adjusted motions. f To\\nleave entirely out of view our confidence in the wisdom and pre-\\nserving goodness of the Creator, and reasoning merely from what\\nwe know of the stability of the solar system, we should be justi-\\nfied in inferring, that other worlds are not subject to forces\\nwhich operate only to hasten their decay, and to involve them in\\nfinal ruin.\\nWe conclude, therefore, that the material universe is one great\\nsystem that the combination of planets with their satellites con-\\nstitutes the first or lowest order of worlds that next to these,\\nplanets are linked to suns that these are bound to other suns,\\ncomposing a still higher order in the scale of being and, finally,\\nthat all the different systems of worlds move around their common\\ncenter of gravity.\\nPlate III. 1. f Robinson s Physical Astronomy.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0345.jp2"}, "346": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0346.jp2"}, "347": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0347.jp2"}, "348": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0348.jp2"}, "349": {"fulltext": "PLATE II.\\nNEBULA AND DOUBLE STARS\\n1. Castor. 2. y Leonis.\\n3. 39 Drac. 4. Oph. 5 11 Monoc\\n6^-Cancri.\\nBO\\nrj| 1 wt~ m\\nHi\\nRevolutions of 7 Virginis.\\nn\\n1837. 1838. 1839. 1840. 1845. 1850. 1860. Orbit.", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0349.jp2"}, "350": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0350.jp2"}, "351": {"fulltext": "PLATE III.\\nCLUSTERS AND NEBULA 1", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0351.jp2"}, "352": {"fulltext": "y 08", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0352.jp2"}, "353": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0353.jp2"}, "354": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0354.jp2"}, "355": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0355.jp2"}, "356": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0356.jp2"}, "357": {"fulltext": "", "height": "3995", "width": "2302", "jp2-path": "introductionto00olm_0357.jp2"}, "358": {"fulltext": "i", "height": "3797", "width": "2432", "jp2-path": "introductionto00olm_0358.jp2"}, "359": {"fulltext": "", "height": "3797", "width": "2432", "jp2-path": "introductionto00olm_0359.jp2"}, "360": {"fulltext": "LIBRARY OF CONGRESS\\n003 631 408 4", "height": "4308", "width": "2500", "jp2-path": "introductionto00olm_0360.jp2"}}