{"1": {"fulltext": "", "height": "4421", "width": "2638", "jp2-path": "introductionto00olms_0001.jp2"}, "2": {"fulltext": "Class\\nBook XI i\u00c2\u00a3\\n|S4$", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0002.jp2"}, "3": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0003.jp2"}, "4": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0004.jp2"}, "5": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0005.jp2"}, "6": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0006.jp2"}, "7": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0007.jp2"}, "8": {"fulltext": "Tig.l\\nTiqA\\n1. Telescopic -view o\u00c2\u00a3 thfi fuB. ^ooix,\\n2. io io of a T rxt of -^JfowiMar cjuaOiaiure\\ni?- I; SJt iinrtersen\\nl.Telescopic -sievr o\u00c2\u00a3 Saturn T*K Tnigs.\\nI of Jirofctex 8cl-iisIMJo\u00c2\u00abns.", "height": "4173", "width": "2576", "jp2-path": "introductionto00olms_0008.jp2"}, "9": {"fulltext": "AN\\nINTRODUCTION\\nfO^T-\\nASTRONOMY:\\nDESIGNED AS A\\nTEXT-BOOK\\nFOE THE USE OF\\nSTUDENTS IK COLLEGE,\\nU BY\\nDENISON OLMSTED, LLD.,\\nLATE PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN\\nYALE COLLEGE.\\nREVISED\\nBy E. S. SNELL, LL.D.,\\nPROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN\\nAMHERST COLLEGE.\\nNEW YORK:\\nCOLLINS BROTHER,\\nNO. 84 LEONARD STREET.\\n1863.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0009.jp2"}, "10": {"fulltext": "7492\\nEntered according to Act of Congress, in the year 1844,\\nBy DENISON OLMSTED,\\nIn the Clerk s Office of the District Court of Connecticut.\\nRevised Edition.\\nEntered according to Act of Congress, in the year 1861,\\nBy JULIA M. OLMSTED,\\nFoe the Children op Denison Olmsted, deceased,\\nIn the Clerk s Office of the District Court of the District of Connecticut.\\nRennie, Shea Lindsay,\\nstereotypers and electrotypers,\\n81, 83, 85 CENTRE-STREET,\\nNefio goi-ft.\\nC. A. AI/VORD,\\nPrinter,\\n15 Vandewater-street, New York.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0010.jp2"}, "11": {"fulltext": "PREFACE TO THE REVISED EDITION.\\nThis work was revised by its author in 1S54, at which time\\nwere introduced notices of the recent discoveries in Astronomy.\\nThe changes made in the present edition are mostly of a differ-\\nent character. While there have been added brief accounts of\\nstill later discoveries, and of new methods of observation, it\\nhas been especially my aim to give more clearness to certain\\ndescriptions and demonstrations, which my experience as a\\nteacher has shown me to be perplexing to the learner. The\\ndiscussion of central forces is entirely remodeled, and the great\\nlaw of gravitation throughout the solar system is deduced, by\\na more direct and less cumbrous mode of reasoning, from the\\nthree laws of Kepler, which are taken as facts established by\\nobservation.\\nTo those numerous teachers who approve the general design\\nof Professor Olmsted in the preparation of this work, as set\\nforth in his preface, and who have themselves tested the utility\\nof that design, it is hoped that the changes now made will\\ncommend themselves as improvements.\\nE. S. SNELL.\\nAmherst College, March, 1861.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0011.jp2"}, "12": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0012.jp2"}, "13": {"fulltext": "AUTHOR S PREFACE.\\nNearly all who have written Treatises on Astronomy, designed for\\nyoung learners, appear to have erred in one of two ways they have\\neither disregarded demonstrative evidence, and relied on mere popular\\nillustration, or they have exhibited the elements of the science in naked\\nmathematical formulas. The former are usually diffuse and superficial\\nthe latter, technical and abstruse.\\nIn the following Treatise, we have endeavored to unite the advantages\\nof both methods. We have sought, first, to establish the great princi-\\nples of astronomy on a mathematical basis and, secondly, to render the\\nstudy interesting and intelligible to the learner, by easy and familiar\\nillustrations. We would not encourage any one to believe that he can\\nenjoy a full view of the grand edifice of astronomy, while its noble\\nfoundations are hidden from his sight nor would we assure him that\\nhe can contemplate the structure in its true magnificence, while its\\nbasement alone is within his field of vision. W T e would, therefore, that\\nthe student of astronomy should confine his attention neither to the ex-\\nterior of the building, nor to the mere analytic investigation of its struc-\\nture. We would desire that he should not only study it in models and\\ndiagrams, and mathematical formulas, but should at the same time\\nacquire a love of nature herself, and cultivate the habit of raising his\\nviews to the grand originals. Nor is the effort to form a clear concep-\\ntion of the motions and dimensions of the heavenly bodies, less favorable\\nto the improvement of the intellectual powers, than the study of pure\\ngeometry.\\nBut it is evidently possible to follow oat all the intricacies of an ana-\\nlytical process, and to arrive at a full conviction of the great truths of\\nastronomy, and yet know very little of nature. According to our expe-\\nrience, however, but few students in the course of a liberal education\\nwill feel satisfied with this. They do not need so much to be convinced\\nthat the assertions of astronomers are true, as they desire to know what\\nthe truths are, and how they were ascertained and they will derive", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0013.jp2"}, "14": {"fulltext": "VI\\nfrom the stud) of astronomy little of that moral and intellectual eleva-\\ntion which they had anticipated, unless they learn to look upon the\\nheavens with new views, and a clear comprehension of their wonderful\\nmechanism.\\nMuch of the difficulty that usually attends the early progress of the\\nastronomical student, arises from his being too soon introduced to the\\nmost perplexing part of the whole subject,\u00e2\u0080\u0094 the planetary motions. In\\nthis work, the consideration of these is for the most part postponed until\\nthe learner has become familiar with the artificial circles of the sphere,\\nand conversant with the celestial bodies. We then first take the most\\nsimple view possible of the planetary motions by contemplating them as\\nthey really are in nature, and afterwards proceed to the more difficult\\ninquiry, why they appear as they do. Probably no science derives such\\nsignal advantage from a happy arrangement, as astronomy an order,\\nwhich brings out every fact or doctrine of the science just in the place\\nwhere the mind of the learner is prepared to receive it.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0014.jp2"}, "15": {"fulltext": "ANALYSIS.\\nPRELIMINARY OBSERVATIONS.\\nArticle.\\nAstronomy, and its divisions 1\\nDescriptive, physical, practical 1\\nHistory. Ancient nations who culti-\\nvated astronomy 2\\nPythagoras his time his views. 2\\nAlexandrian school Hipparchus. 2\\nPtolemy the Almagest 2\\nCopernicus, Tycho Brahe, Kepler, Ga-\\nlileo, Newton, La Place 2\\nAstrology Natural\u00e2\u0080\u0094 Judicial 8\\nAccuracy aimed at in astronomy. 4\\nTruths not always to be proved when\\nstated 5\\nCoperniean system its doctrines. 6\\nPlan of the work 7\\nPAET I. THE EARTH.\\nChapter I. Of the figure and size of\\nTHE EARTH, AND THE DOCTRINE OF THE\\nSPHERE.\\nFigure of the earth proofs 8\\nDip of the horizon 9\\nIts relation to height table 10\\nThe exact form 11\\nDimensions of the earth 12\\nHow found 13, 14\\nErroneous ideas of up and down 15\\nDoctrine of the sphere 16\\nSections by a plane 17\\nAxis of a circle poles 18, 19\\nGreat circles bisect each other 20\\nSecondaries 21\\nMeasure of inclination. 22\\nTerrestrial and celestial spheres 23\\nHorizon\u00e2\u0080\u0094 rational and sensible 24\\nZenith and Nadir. 25\\nVertical circles meridian, prime ver-\\ntical 26\\nCo-ordinates for the horizon, ampli-\\ntude, or azimuth altitude, or ze-\\nnith distance 27\\nAxis and poles of the earth 28\\nEquator\u00e2\u0080\u0094 equinoctial 29\\nIts secondaries\u00e2\u0080\u0094 the meridians, or\\nhour circles 30\\nLatitude polar distance 31\\nLongitude 32\\nThe ecliptic inclination to the equa-\\ntor 33\\nVernal and autumnal equinoxes 34\\nSolstices\u00e2\u0080\u0094 signs of the zodiac 85\\nArticle.\\nColures equinoctial, solstitial 36\\nCo-ordinates to the equinoctial right\\nascension, declination 37\\nCo-ordinates to the ecliptic, celestial\\nlongitude and latitude 37\\nParallels of latitude 38\\nTropics 39\\nPolar circles 40\\nZones 41\\nZodiac 42\\nElevation of the pole 43\\nElevation of the equator 44\\nPolar distance 45\\nChapter II. Diurnal revolution Arti-\\nficial GLOBES ASTRONOMICAL PROBLEMS,\\nCircles of Diurnal Ee volution 46\\nSidereal day defined 47\\nAppearance of the circles of diurnal\\nrevolution at the equator 49\\nA Right Sphere defined 49\\nA Parallel Sphere 50-52\\nAn Oblique Sphere 53\\nCircle of Perpetual Apparition 54\\nCircle of Perpetual Occupation 55\\nHow are the circles of daily motion\\ncut by the horizon in the different\\nspheres 56\\nExplanation of the peculiar appear-\\nances of each sphere, from the revo-\\nlution of the earth on its axis. .57-60\\nArtificial Globes terrestrial and ce-\\nlestial 61\\nMeridian how represented how\\ngraduated 62\\nHorizon how represented how gra-\\nduated 62\\nHour Circles how represented 63\\nHour Index described 64\\nQuadrant of Altitude its use 65\\nTo rectify the globe for any place. 66\\nProblems on thk Terrestrial Globe\\n\u00e2\u0080\u0094To find the latitude and longitude\\nof a place 67\\nTo find place, its latitude and longi-\\ntude being given 68\\nTo find the bearing and distance of\\ntwo places 69\\nTo determine the difference of time of\\ntwo places 70\\nThe hour being given at any place, to\\ntell what hour it is in any other part\\nof the world 71\\nTo find the antoeci, periceci, and antipo-\\ndes 72", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0015.jp2"}, "16": {"fulltext": "Vlll\\nANALYSIS.\\nArt.\\nTo rectify the globe for the sun s\\nplace 73\\nThe latitude of the place being given,\\nto find the time of the sun s rising\\nand setting 74\\nProblem.? on the Celestial Globe.\\nTo find the right ascension and decli-\\nnation 75\\nTo represent the appearance of the\\nheavens at any time 76\\nTo find the altitude and azimuth of a\\nstar 77\\nTo find the angular distance of two\\nstars from each other 78\\nTo find the sun s meridian altitude,\\nthe latitude and day of the month\\nbeing given 79\\nChapter III. Parallax Refraction\\nTwilight.\\nParallax defined diurnal 80\\nTrue place 81\\nRelation of parallax to the zenith dis-\\ntance, and distance from the center\\nof the earth 82\\nTo find the horizontal parallax from\\nthe parallax at any altitude 83\\nAmount of parallax in the zenith and\\nin the horizon 83\\nEffect of parallax upon the altitude of\\na body 84\\nMode of determining the horizontal\\nparallax of a body 85\\nAmount of the sun s hor. par 86\\nUse of parallax 87\\nRefraction. Its effect upon the alti-\\ntude of a body 88\\nIts nature illustrated 88\\nIts amount at different angles of ele-\\nvation 89\\nHow the amount is ascertained 90-91\\nSources of inaccuracy in estimating\\nthe refraction 92\\nEffect of refraction upon the sun and\\nmoon when near the horizon 93\\nOval figure of these bodies explained. 94\\nApparent enlargement of the sun and\\nmoon near the horizon 95\\nTwilight.\u00e2\u0080\u0094 its, cause explained 96\\nLength of twilight in different lati-\\ntudes 97\\nHow the atmosphere contributes to\\ndiffuse the sun s light 98\\nChapter IV.\u00e2\u0080\u0094 Time.\\nTime defined 99\\nWhat period is a sidereal day 100\\nUniformity of sidereal days 100\\nSolar time, how reckoned 101\\nWhy solar days are longer than side-\\nreal 101\\nApparent time defined 102\\nMean time 103\\nAn astronomical day 103\\nEquation of time defined 104\\nWhen do apparent time and mean\\ntime differ most 104\\nWhen do they come together 104\\nArt.\\nEffect of a change in the place of the\\nearth s perihelion 104\\nCauses of the inequality of the solar\\ndays 105\\nExplain the first cause, depending on\\nthe unequal velocities of the sun. 105\\nExplain the second cause, depending\\non the obliquity of the ecliptic. .106-108\\nWhen does the sidereal day com-\\nmence 109\\nThe Calendar.\u00e2\u0080\u0094 Astronomical year de-\\nfined 110\\nHow the most ancient nations deter-\\nmined the number of days in the\\nyear Ill\\nJulius Caesar s reformation of the cal-\\nendar explained Ill\\nErrors of this calendar 112\\nReformation by Pope Gregory 112\\nRule for the Gregorian calendar 112\\nNew style, whenadopted in England. 113\\nWhat nations still adhere to the old\\nstyle 113\\nWhat number of days is now allowed\\nbetween old and new style 114\\nHow the common year begins and\\nends 115\\nHow leap year begins and ends 115\\nDoes the confusion of different calen-\\ndars affect astronomical observations 116\\nChapter V. Astronomical Instruments\\nand Problems Figure and Density\\nof the Earth.\\nHow the most ancient nations acquired\\ntheir knowledge of astronomy 117\\nUse of Instruments in the Alexan-\\ndrian School 117\\nDitto, by Tycho Brahe 117\\nDitto, by the Astronomers Royal 117\\nSpace occupied by on the limb of\\nan instrument 117\\nExtent of actual divisions on the limb/ 118\\nVernier defined 118\\nIts use illustrated 119\\nChief astronomical instruments eau-\\nmerated 120\\nObservations taken on the meridian. 120\\nReasons of this. 120\\nTransit Instrument defined 121\\nDitto, described 121\\nMethod of placing it in the meridian. 122\\nLine of collimation defined 123\\nSystem of wires in the focus 123\\nAstronomical Clock\u00e2\u0080\u0094 how regulated 124\\nWhat does it show 124\\nHow to test its accuracy 124\\nRate and error 124\\nAmerican method 125\\nMural Circle its object 126\\nDescribe it 126\\nHow the different parts contribute to\\nthe object 126\\nUse of the Mural Circle for arcs of\\ndeclination 127\\nAltitude and Azimuth Instrument de-\\nfined 128\\nIts use 12S", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0016.jp2"}, "17": {"fulltext": "ANALYSIS.\\nIX\\nArt.\\nDescribe it 128\\nSextant described 129\\nHow to measure the angular distance\\nof the moon from a star. 129\\nHow to take the altitude of a heavenly-\\nbody 129\\nUse of the artificial horizon 130\\nIn what consists the peculiar value of\\nthe sextant 130\\nAstronomical Problems. Given the\\nsun s right ascension and declina-\\ntion, to find his longitude and the\\nobliquity of the ecliptic 132\\nNapier s rule of circular parts 132\\nGiven the sun s declination to find his\\nrising and setting at any place whose\\nlatitude is known 133\\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. 134\\nThe latitudes and longitudes of two\\ncelestial objects being given, to find\\ntheir distance apart 135\\nFigure and Density of the Earth\\nreason for ascertaining it with great\\nprecision 136\\nHow found from the centrifugal force. 137\\nFrom measuring an arc of the meridian 138\\nFrom observations with the pendulum 139\\nFrom the motions of the moon 140\\nFrom precession 141\\nDensity of the earth 141\\nHow ascertained by Dr. Maskelyne.. 141\\nWhy an important element 141\\nPart II. -OF THE SOLAR SYSTEM.\\nChapter I. The Sun Solar Spots Zo-\\ndiacal Light.\\nFigure of the sun 143\\nAngle subtended by a line of 400 miles 143\\nDistance from the earth 144\\nIllustrated by motion on a railway car. 144\\nApparent diameter of the sun how\\nfound 145\\nHow to find the linear diameter 145\\nHow much larger is the sun than the\\nearth 145\\nIts density and mass compared with\\nthe earth s 146\\nWeight at the surface of the sun 146\\nVelocity of falling bodies at the sun. 146\\nSolar Spots. Their number 147\\nSize 147\\nDescription 147\\nWhat region of the sun do they occupy 147\\nProof that they are on the sun 148\\nHow we learn the revolution of the\\nsun on his axis 148\\nTime of the revolution 148\\nApparent paths of the spots 149\\nInclination of the solar axis 149\\nSun s Nodes when does the sun pass\\nthem? 150\\nFaculae 151\\nArt.\\nTheory of the spots 151\\nZodiacal Light. Where seen 152\\nIts form 152\\nAspects at different seasons 152\\n1 ts motions 152\\nIts nature 152\\nChapter II. Apparent Annual Motion\\nof the Sun Seasons Figure of thb\\nEarth s Orbit.\\nApparent motion of the sun 153\\nHow both the sun and earth are said\\nto move from west to east 154\\nNature and position of the sun s orbit,\\nhow determined 155\\nChanges in declination, how found. 155\\nDitto, in right ascension 156\\nInferences from a table of the sun s\\ndeclinations 156\\nDitto, of right ascensions 156\\nPath of the sun, how proved to be a\\ngreat circle 156\\nObliquity of the ecliptic, how found. 157\\nHow it varies 157\\nGreat dimensions of the earth s orbit. 158\\nEarth s daily motion in miles 158\\nDitto, hourly, ditto 158\\nDiurnal motion at the equator per hour 158\\nSeasons. Causes of the change of\\nseasons 159\\nHow each cause operates 159\\nIllustrated by a diagram 160\\nChange of seasons had the equator\\nbeen perpendicular to the ecliptic. 161\\nFigure of the Earth s Orbit. Proof\\nthat the earth s orbit is not circular. 161\\nRadius vector defined 162\\nFigure of the earth s orbit, how ob-\\ntained 162\\nRelative distances of the earth from\\nthe sun, how found 163\\nPerihelion and Aphelion defined 164\\nVariations in the sun s apparent diam-\\neter 164\\nAngular velocities of the sun at the\\nperihelion and aphelion 165\\nRatio of these velocities to the dis-\\ntances 165\\nHow to calculate the relative distances\\nof the earth from the sun s daily mo-\\ntions 165\\nProduct of the angle described in any\\ngiven time by the square of the dis-\\ntance 167\\nSpace described by the radius vector\\nof the solar orbit in equal times. 168\\nHow to represent the sun s orbit by a\\ndiagram 168\\nChapter III. Central Forces Gravita-\\ntion.\\nTwo forces in curved motion 170\\nCentripetal and centrifugal 170\\nKepler s laws 171\\nFirst law second third 171\\nFirst principles in mechanics and as-\\ntronomy identical 171\\nKepler s first law proved 172", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0017.jp2"}, "18": {"fulltext": "ANALYSTS.\\nArt.\\nIts converse 173\\nMeasure of velocity in an orbit 174\\nModification for those nearly circular. 174\\nCentrifugal force 175\\nFirst law of central force in circular\\norl.it 176\\nSecond ditto 177\\nLaw of gravity in an elliptical orbit. 178\\nProof. 179\\nSame law for different orbits\u00e2\u0080\u0094 proof. 181\\nBodies on the earth compared with\\nthe moon 182\\nSame law explains disturbances 182\\nGravity as quantity of matter. 182\\nProjectiles 183\\nWhy parabola, not ellipse 183\\nTime of complete revolution of a pro-\\njectile 183\\nDifferent forms of projectile paths. 184\\nPlace of perigee and apogee 184\\nAnnual and diurnal rotation by one\\nimpulse 185\\nEffect of impulse on the system 186\\nTwo bodies supposed 186\\nMotion of center 186\\nMotion of each body 186\\nEpicycloids, two forms 186\\nWhere retrograde motion 186\\nHow center can be kept at rest 186\\nWhy planet returns from aphelion. 187\\nWhy it departs from perihelion 187\\nChange in centrifugal force, compared\\nwith that in centripetal 187\\nChapter IV. Precession of the Equi-\\nnoxes Nutation Aberration Mean\\nand True Places of the Sun.\\nPrecession of the equinoxes defined. 188\\nWhy so called 188\\nAmount of precession annually 189\\nEevolution of the equinoxes 189\\nRevolution of the pole of the equator\\naround the pole of the ecliptic 190\\nChanges among the stars caused by\\nprecession 190\\nThe present pole-star not always such. 190\\nWhat will be the pole-star 13,000 years\\nhence? 190\\nCause of the precession of the equi-\\nnoxes 191\\nExplain how the cause operates 191\\nProportionate effect of the sun and\\nmoon in producing precession 192\\nThe law of compound rotations 192\\nTropical year defined 193\\nHow much shorter than the sidereal\\nyear 193\\nUse of the precession of the equinoxes\\nin chronology 193\\nNutation, defined 1 94\\nExplain its operation 194\\nCause of nutation 194\\nAberration, defined 195\\nIllustrated by a diagram 195\\nAmount of aberration 195\\nEffect on the places of the stars 195\\nMotion of the Apsides the fact\\nstated 196\\nArt.\\nDirection of this motion Iy6\\nTime of revolution of the line of ap-\\nsides 196\\nPresent longitude of the perihelion. 196\\nCause of advance of apsides 196\\nAnomaly defined 197\\nAnomalistic year, its length 197\\nSlow change in duration of the seasons. 198\\nMean and True Places of the Sun. 199\\nMean Motion defined 199\\nIllustrated by surveying a field 199\\nMean and true longitudedistinguished 199\\nEquations defined 200\\nTheir object 200\\nMean and True Anomaly defined 200\\nEquation of the center 200\\nExplain from the figure 200\\nChapter V. The Moon Lunar Geogra-\\nphy Phases of the Moon Her Revo-\\nlutions.\\nDistance of the moon from the earth. 201\\nHer mean horizontal parallax 201\\nHer diameter 201\\nVolume, density, and mass 201\\nShines by reflected light 202\\nAppearance in the telescope 202\\nTerminator defined 203\\nIts appearance 203\\nProofs of mountains and valleys. 20D\\nForm of the valleys 204\\nRing-mountains\u00e2\u0080\u0094 bulwark plains 204\\nLava-lines seen at full moon 205\\nWater, clouds, vegetation 205\\nExplain the method of estimating the\\nheight of lunar mountains 206\\nHas the moon an atmosphere? 209\\nImprobability of identifying artificial\\nstructures in the moon 210\\nPhases of the Moon, their cause... 211\\nSuccessive appearances of the moon\\nfrom one new moon to another 211\\nSyzygies defined 211\\nExplain the phases of the moon from\\nfigure 46 212\\nRevolutions of the Moon. Period\\nof her revolutions about the earth.. 213\\nHer apparent orbit a great circle 213\\nA sidereal month defined 213\\nA synodical do. 213\\nLength of each 213\\nWhy the synodical is longer 213\\nHow each is obtained 213\\nInclination of the lunar orbit 214\\nNodes defined 214\\nWhy the moon sometimes runs high\\nand sometimes low 215\\nHarvest moon defined 216\\nDitto explained 216\\nExplain why the moon is nearer to us\\nwhen on the meridian than when\\nnear the horizon 217\\nTime of the moon s revolution on its\\naxis 218\\nHow known 218\\nLibrations explained 219\\nDiurnal libration 21 9\\nLength of the lunar days 220", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0018.jp2"}, "19": {"fulltext": "ANALYSIS.\\nXI\\nEarth never seen on the opposite side\\nof the moon 220\\nAppearances of the earth to a specta-\\ntor on the moon 220\\nWhv the earth would appear to remain\\nfixed 220\\nPath of the moon in space 221\\nHow much more is the moon attracted\\ntoward the sun than toward the\\nearth? 222\\nWhen does the sun act as a disturbing\\nforce upon the moon 222\\nWhy does not the moon abandon the\\nearth at the conjunction 222\\nThe moon s orbit concave toward the\\nsun 223\\nChapter VI. Lunar Irregularities.\\nSpecify their general cause 225\\nUnequal action of the sun upon the\\nearth and moon 225\\nOblique action of earth and sun 225\\nGravity of the moon toward the earth\\nat the syzygies 226\\nGravity at the quadratures 226\\nExplain the disturbances in the\\nmoon s motions from figure 48 228\\nFigure of the moon s orbit 230\\nHow its figure is ascertained 230\\nMoon s greatest and least apparent\\ndiameters 230\\nHer greatest and least distances from\\nthe earth 230\\nPerigee and Apogee defined 230\\nEccentricities of the solar and lunar\\norbits compared 230\\nMoon s nodes, their change of place. 231\\nRate of this change per annum. 231\\nPeriod of their revolution 231\\nIrregular curve described by the\\nmoon 232\\nCause of the retrograde motion of\\nnodes 232\\nExplain from figure 50 232\\nSvnodical revolution of the node de-\\nstined 233\\nIts period 233\\nThe Saros explained 233\\nThe Metonic Cycle. 234\\nGolden Number 234\\nRevolution of the line of apsides 235\\nIts period 235\\nHow the places of the perigee may be\\nfound 235\\nMoon s anomaly defined. 235\\nCause of the revolution of the apsides, 236\\nAmount of the equation of the center. 237\\nEjection defined 238\\nIts cause explained 239\\nVariation defined 240\\nIts cause 240\\nAnnual Equation explained 241\\nHow these irregularities were first dis-\\ncovered 242\\nHow many equations are applied to\\nthe moon s motions 242\\nMethod of proceeding in finding the\\nmoon s place 242\\nSuccessive degrees of accuracy at-\\ntained 242\\nPeriodic and secular irregularities dis-\\ntinguished 243\\nAcceleration of the moon s mean mo-\\ntion explained 243\\nIts consequences 243\\nLunar inequalities of latitude and\\nparallax 244\\nChapter VII.\u00e2\u0080\u0094 Eclipses.\\nEclipse of the moon, when it happens. 245\\nEclipse of the sun, when it happens. 245\\nWhen only can each occur 245\\nWhy an eclipse does not occur at\\nevery new and full moon 245\\nWhy eclipses happen at two opposite\\nmonths 245\\nCircumstances which affect the length\\nof the earth s shadow 246\\nSemi-angle of the cone of the earth s\\nshadow, to what equal 247\\nLength of the earth s shadow 248\\nIts breadth where it eclipses the moon. 249\\nLunar ecliptic limit defined. 250\\nSolar do. 250\\nAmount of the lunar ecliptic limit. 251\\nAppulse defined. 251\\nPartial, total, central eclipse, each de-\\nfined 251\\nPenumbra defined 252\\nSemi-angle of the moon s penumbra,\\nto what equal 253\\nSemi-angle of a section of the penum-\\nbra where the moon crosses it 254\\nMoon s horizontal parallax increased\\nA wh y 255\\nWhy the moon is visible in a total\\neclipse 256\\nCalculation of eclipses, general mode\\nof proceeding 257\\nTo find the exact time of the begin-\\nning, end, duration, and magnitude\\nof a lunar eclipse, by figures 53, 54. 258\\nElements of an eclipse defined 259\\nDigits defined 260\\nHow the shadow of the moon travels\\nover the eartli in a solar eclipse. 262\\nWhy the calculation of a solar eclipse\\nis more complicated than a lunar. 262\\nVelocity of the moon s shadow 263\\nDifferent ways in which the shadow\\ntraverses the earth, according as\\nthe conjunction is near the node or\\nnear the limit 263\\nWhen do the greatest eclipses happen 264\\nCase in which the moon s shadow\\nnearly reaches the earth 265\\nHow far may the shadow reach beyond\\nthe center of the earth 265\\nGreatest diameter of the moon s shad-\\now where it traverses the earth. 266\\nGreatest portion of the earth s surface\\never covered by the moon s penum-\\nbra 267\\nMoon s apparent diameter compared\\nwith the sun s 268\\nAnnular eclipse, its cause 26S", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0019.jp2"}, "20": {"fulltext": "Xll.\\nANALYSIS.\\nArt.\\nDirection in \u00e2\u0080\u00a2which the eclipse passes\\non the sun s disk 269\\nGreatest duration of total darkness.. 269\\nEclipses of the sun more frequent\\nthan of the moon, why 269\\nLunar eclipses oftener visible, why 269\\nEadiation of light in a total eclipse of\\nthe sun 269\\nInteresting phenomena of a total\\neclipse of the sun 271\\nBaily s Beads 271\\nFlame-colored projections. 271\\nChapter VI! I. Longitude Tides.\\nObjects of the ancients in studying\\nastronomy 272\\nDitto of the moderns 272\\nLongitude. How to find the differ-\\nence of longitude between two\\nplaces 273\\nMethod by the Chronometer explained 274\\nHow to set the chronometer to Green-\\nwich time, 274\\nAccuracy of some chronometers 274\\nObjections to them 274\\nLongitude by eclipses explained 275\\nLunar method of finding the longi-\\ntude 276\\nCircumstances which render this\\nmethod somewhat difficult 277\\nDifference of longitude accurately ob-\\ntained by magnetic telegraph 278\\nTides, defined. 279\\nHigh, Low, Spring, Neap, Flood, and\\nEbb Tide, severally defined 279\\nSimilar tides on opposite sides of the\\nearth 279\\nInterval between two successive high\\ntides 279\\nAverage height for the whole globe.. 279\\nExtreme height 279\\nCause of the tides 280\\nExplain by figure 56 281\\nTide- wave defined 281\\nComparative effects of the sun and\\nmoon in raising the tide. 282\\nWhy the moon raises a higher tide\\nthan the sun 282\\nSpring tides accounted for 283\\nNeap tides, ditto 283\\nPower of the sun or moon to raise the\\ntide, in what ratio to its distance,. 284\\nInfluence of the declinations of the\\nsun and moon on the tides 2S5\\nExplain from figures 57 and 58 235\\nMotion of the tide-wave not progres-\\nsive 286\\nTides of rivers, narrow bays, how\\nproduced 2S7\\nCotidal Lines defined 287\\nDerivative and Primitive tides distin-\\nguished 287\\nVelocity of the tide-wave, circum-\\nstances which affect it 288\\nExplain by figure 59 2^9\\nExamples of very high tides 289\\nUnit of altitude defined 290\\nUnit of altitude for different places. 290\\nArt.\\nEstablishment of a port. 291\\nTides on the coast of North America,\\nwhence derived 292\\nWhy no tides in lakes and seas 293\\nIntricacy of the problem of the tides. 294\\nAtmospheric tide 295\\nChapter IX. The Planets Inferior:\\nPlanets Mercury and Venus.\\nSignification of the term planet 296\\nPlanets known from antiquity 296\\nPlanets added in 1781 and 1846 296\\nAsteroids 296\\nPrimarv and Secondary Planets dis-\\ntinguished 296\\nNumber of each 296\\nInclination of the planetary orbits to\\nthe ecliptic 297\\nInferior and Superior planets distin-\\nguished 295\\nHow the planets differ among them-\\nselves 298\\nDistances from the sun in miles 299\\nGreat dimensions of the planetary\\nsystem 299\\nIllustrated by the motion of a railway\\ncar 299\\nOrder by which the distances of the\\nplanets increase 299\\nBode s law of distances 299\\nMean distances, how determined 299\\nDiameters in miles 300\\nGreat diversity in respect to magni-\\ntude 300\\nHow the real diameters are found from\\nthe apparent 300\\nPeriodic Times in months and years 301\\nWhich of the planets move rapidly\\nand which slowly. 301\\nInferior Planets. Proximity to the\\nsun 302\\nIllustration by Fig. 60 302\\nConjunction defined inferior and\\nsuperior 303\\nSynodical revolution denned 304\\nHow to find the synodical from the\\nsidereal 304\\nMotion of an inferior planet, when\\ndirect and when retrograde 305\\nHow these motions are affected by the\\nearth s motions 305\\nWhen the inferior planets are station-\\nary 306\\nElongation of the stationary points-\\nfor Mercury and Venus 306\\nPhases of the inferior planets 307\\nRelative distances from the sun 3f 8\\nEccentricity of their orbits. 309\\nMode of finding the period in time. 310\\nWhen is an inferior planet brightest? 311\\nDiurnal revolutions of Mercury and\\nVenus 312\\nVenus as the morning and evening star 313\\nPhenomena every eight years 314\\nTransits of the Inferior Planets\\ndefined 315\\nWhen they occur why not at every\\ninferior conjunction 315", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0020.jp2"}, "21": {"fulltext": "ANALYSIS.\\nXlll\\nArt.\\nWhy those of Mercury in May and\\nNovember 315\\nWhy those of Venus in June and De-\\ncember 315\\nIntervals between the transits of Mer-\\ncury 31\\nIntervals between the transits of\\nVenus 316\\nHow found 316\\nWhy so great an interest is attached\\nto the transits of Venus 317\\nWhy the sun s horizontal parallax\\ncannot be found like the moon s.. 317\\nWhy distant places of observation\\nare taken..... 318\\nProcess for the sun s hor. par. ex-\\nplained from Fig. 63 318\\nSun s hor. par. in seconds 318\\nTo find the hor. par. of Venus and of\\nMars 318\\nAtmosphere of Venus 319\\nSatellites of Mercury and of Venus? 319\\nChapter X.\u00e2\u0080\u0094 Superior Planets\u00e2\u0080\u0094 Aster-\\noids\u00e2\u0080\u0094 Motions of the Planets.\\nSuperior Planets, how distinguished\\nfrom the Inferior 320\\nMars\u00e2\u0080\u0094 size\u00e2\u0080\u0094 distance from the sun 321\\nChanges in apparent magnitude and\\nbrightness 321\\nPhases of Mars, Fig. 64 322\\nTelescopic appearances 323\\nSatellite ellipticity 323\\nTo find the hor. par. of Mars 324\\nAsteroids\u00e2\u0080\u0094 history of the first four. 325\\nDistance from the sun\u00e2\u0080\u0094 size\u00e2\u0080\u0094 orbits 326\\nModes of naming 327\\nJupiter\u00e2\u0080\u0094 magnitude\u00e2\u0080\u0094 figure\u00e2\u0080\u0094 diurnal\\nrevolution 328\\nInclination of the axis to the orbit,\\nand change of seasons 328\\nTelescopic appearances 329\\nBelts described and explained 330\\nSatellites\u00e2\u0080\u0094 how seen names 331\\nMagnitude\u00e2\u0080\u0094 distances periods 332\\nOrbits form inclination 333\\nEclipses their various phenomena,\\nFig. 65 334-335\\nShadows cast by the satellites on the\\nPrimary 336\\nLongitude from the eclipses of Ju-\\npiter s satellites 338-339\\nVelocity of light, how discovered. 340\\nSaturn size ring\u00e2\u0080\u0094 telescopic view. 341\\nKing described 342\\nDimensions of the system 342\\nThinness of the rings 342\\nRevolution of the ring around the\\nsun 343-344\\nIts changes and disappearances ex-\\nplained 345-346\\nRevolution of the ring in its own\\nplane 347\\nSatellites of Saturn number and\\nnames s 348\\nEclipses 348\\nUranus\u00e2\u0080\u0094 its discovery 340\\nSize periodic time inclination 349\\nArt.\\nSatellites number peculiarities 350\\nNeptune distance diameter\\nperiod 351\\nHistory of its discovery 351-353\\nAgreement of observation with theory 353\\nSimultaneous discovery 353\\nResults obtained by Walker 353\\nPlanetary Motions two methods\\nof studying them 354\\nAppearances viewed from the sun. 355\\nMotions of Mercury explained 355\\nForm of orbit not seen from the sun. 355\\nWhy diagrams and orreries represent\\nthem erroneously 357\\nApparent motions of the planets 858\\nTwo causes make them unlike the\\nreal 358\\nApparent motions illustrated by\\nFig. 69 359\\nApparent motions of the Superior\\nPlanets 360\\nIllustrated by Fig. 70 361\\nChapter XL Determination of the\\nPlanetary Orbits\u00e2\u0080\u0094 Kepler s Discov-\\neries Elements of the Orbits of the\\nPlanets Masses.\\nFigure of the planetary orbits an-\\ncient ideas 362\\nNotions of Ptolenry anil Hipparchus. 362\\nKepler Investigation of the motions\\nof Mars 363\\nDiscovery of the first law the second\\n\u00e2\u0080\u0094the third 363-365\\nModification of the third law 366\\nElements of the Planetary Orbits\\nenumerated 367\\nWhy not found like the lunar and\\nsolar orbits 368\\nFirst steps of the process for finding\\nthe elements 369\\nTo convert geocentric longitudes and\\nlatitudes into heliocentric, Fig. 71. 369\\nTo determine the position of the\\nnodes 371\\nTo determine the inclination 371\\nTo find the periodic time. 372\\nThe position of a planet which is\\nmost favorable for finding the ele-\\nments 373\\nExemplified in finding the periodic\\ntime of Saturn 374\\nTo determine the distance from the\\nsun 375\\nHow the mean distance is found 375\\nHow the distance at any point in the\\norbit 375\\nMethod for the Inferior Planets 375\\nMethod for the Superior, Fig. 73 375\\nTo determine the place of ike perihe-\\nlion 376\\nTo determine the epoch of passing the\\nperihelion 376\\nTo find the eccentricity 377\\nQuantity of Matter in the Sun and\\nPlanets 37$\\nHow found in terms of the distances\\nand periodic times 379", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0021.jp2"}, "22": {"fulltext": "XIV\\nANALYSIS.\\nArt.\\nHow found by the spaces fallen\\nthrough, Fig. 75 379\\nHow found in planets which have no\\nsatellites 380\\nDensities, how found 381\\nSpecific gravities of the sun and plan-\\nets respectively 381\\nComparative densities 381\\nChapter XII. Perturbations of Planets\\nStability of the System Numeri-\\ncal Kelations Problems.\\nPerturbations Numerous causes. 382\\nPeriodical and secular perturbations\\ndistinguished 382\\nCase where the only bodies are a cen-\\ntral and a revolving body 383\\nHow these irregularities have been\\ndiscovered 383\\nMinuteness of some perturbations. 383\\nWhether the perturbations accumu-\\nlate indefinitely 384\\nStability of the system\u00e2\u0080\u0094 how muin-\\ntained 384\\nNature of the evidence to prove the\\nstability 384\\nInvariability of the major axes 384\\nLimits to the variation of the eccen-\\ntricity 385\\nAlso to that of the inclination 385\\nWhat kind of perturbations are cu-\\nmulative and what are oscillatory.. 385\\nConditions essential to this stability. 386\\nLong inequality of Jupiter and Sat-\\nurn 386\\nAlso of the Earth and Venus 386\\nNumerical Eelations of the Plan-\\netary System 387\\nChange of velocity necessary on in-\\ncreasing the mass 387\\nAlso on increasing the distance 387\\nMembers of the solar system, how ad-\\njusted 387\\nEelation between the rate of motion,\\ndistance, periodic time, and force of\\ngravity 387\\n.Demonstration of the rules 387\\nThe rules stated 388\\nGiven, the velocity, to find the other\\nterms 388\\nGiven, the distance 388\\nGiven, the periodic time 3S8\\nGiven, the force of gravitation 388\\nEequired, the rate of motion, dis-\\ntance, period, and force of gravita-\\ntion respectively 388\\nProblems 389\\nChapter XIIT. Comets Meteoric\\nShowers.\\nComets their several parts 390\\nNumber belonging to the system 391\\nThe six most remarkable 391\\nVariations in magnitude and bright-\\nness 392\\nTo what owing 392\\nPeriods of revolution 393\\nDistances from the sun 393\\nArt.\\nFigure of the orbit of Halley s comet. 393\\nSource of the light 394\\nDirection of the tails 394\\nQuantity of matter in comets 395\\nHow the orbit of a comet may be\\nchanged 396\\nExample in the comet of 1770 396\\nOrbits and Motions of Comets 397\\nHow they differ from those of planets. 397\\nElements enumerated 398\\nTheir investigation, why difficult. 398-399\\nHow the return of a comet is predicted. 400\\nExemplified in Halley s comet 400\\nIts return in 1759 and 1835 400-401\\nWhy an astronomical event of great\\ninterest 401\\nEncke s comet its period 402\\nQuestion of a resisting medium. 402\\nComet of 1843 its remarkable pecu-\\nliarities 403\\nPhysical nature of comets 404\\nPossibility of their striking the earth. 405\\nMeteoric Showers\u00e2\u0080\u0094 great shower of\\nNovember, 1833 406\\nPoint of apparent radiation 406\\nExtent and duration 406\\nPeriods of its recurrence 407\\nWhy an astronomical or cosmical\\nphenomenon 407\\nOf the periods of meteoric showers. 407\\nConclusions respecting the meteors,\\nas to their origin, nature, velocity,\\nsize, light, and heat 408\\nSeasons for these conclusions 409\\nPart III.\u00e2\u0080\u0094 OF THE FIXED STAES\\nAND SYSTEM OF THE WOELD.\\nChapter I. Fixed Stars Constella-\\ntions.\\nWhy called fixed stars 410\\nClassification 410\\nNumber in each class 410\\nAntiquity of the constellations 411\\nTheir names how individual stars\\nare denoted 411\\nCatalogues of the stars 412\\nNumber in the catalogue of Hippar-\\nchus 412\\nNumber in Lalande s 412\\nUtility of learning the constellations. 413\\nConstellations of the Zodiac\u00e2\u0080\u0094 Aries,\\nTaurus 413\\nSeven stars in Pleiades 413\\nGemini, Cancer 413\\nPrsesepe, or the Bee-hive 413\\nLeo, Virgo, Libra 413\\nScorpio, Sagittarius, Capricornus,\\nAquarius, Pisces 413\\nNorthern Constellations 414\\nUrsa Minor, Ursa Major 414\\nDraco 414\\nCepheus, Cassiopeia, Camelopard,\\nAndromeda 415\\nPerseus, Auriga, Leo Minor, Canes\\nVenatici, Coma Berenices, Bootes.. 415", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0022.jp2"}, "23": {"fulltext": "ANALYSIS.\\nXV\\nArt.\\nCorona Borealis, Hercules, Lyra, Cyg-\\nnus 415\\nVulpecula, Aquila, Antinous, Del-\\nphinus, Pegasus, Ophiuchus 415\\nSouthern Constellations 416\\nOrion, Lepus, Canis Major 416\\nCanis Minor, Menoceros, Hydra 416\\nLesson for the middle of September. 417\\nLesson for the middle of December.. 417\\nLesson for the middle of March 417\\nLesson for the middle of June 417\\nChapter II. Double Stars Temporary\\nStars Variable Stars Clusters and\\nNebulae.\\nUse of great telescopes in studying\\nthe stars 418\\nHerschel s forty-feet telescope 419\\nEosse telescope 419\\nPulkova and Cambridge telescopes.. 419\\nDouble Stars denned 420\\nBy whom discovered 421\\nExamples number 421\\nWhen merely optically double 421\\nWhen physically double 421\\nSystem of double, triple, and multiple\\nstars 421\\nColors of the components 421\\nTemporary Stars defined 422\\nExamples 422\\nVariable Stars\u00e2\u0080\u0094 denned 423\\nExamples 423\\nEvidence of activity among the stars. 423\\nClusters\u00e2\u0080\u0094 examples 424\\nNebula\u00e2\u0080\u0094 defined 424\\nExamples nebula of Andromeda 425\\nNebula of Hercules 425\\nMagellanic clouds 425\\nNebula of Orion 425\\nUse of great telescopes for these ob-\\njects 425\\nSingular forms of nebulas 425\\nKesolvable and irresolvable distin-\\n_ guished 426\\nSigns of beauty and symmetry among\\nthe nebulas 426\\nNebulous Stars\u00e2\u0080\u0094 defined 427\\nAnnular Nebula defined 427\\nExample in Lyra 427\\nPlanetary Nebula 427\\nResemblance to planets great extent. 427\\nExample in Andromeda 427\\nMUky Way cause of its peculiar\\nlight 428\\nNumber of its component stars 428\\nChapter III. Motions of the Fixed\\nStars Distances Nature.\\nBinary Stars\u00e2\u0080\u0094 defined 429\\nNumber of these 429\\nPeriodic times examples 429\\nLaw of gravitation among the stars. 430\\nProper Motions of the stars 431\\nArt\\nKesult on comparing the places of cer-\\ntain stars in ancient and modern\\ncatalogues 431\\nMotion of the solar system in space. 432\\nPoint toward which it is moving. 432\\nEate of motion per annum 432\\nExamples of great annual proper mo-\\ntions 433\\nDistances of the Stars how found. 434\\nWhat is the base line for parallax?. 434\\nWhy it was supposed impossible to\\ndetermine a parallax of less than r 434\\nDistance implied by a parallax of 435\\nBessel s determination of the parallax\\nof 61 Cygni 435\\nHis method of investigation 435\\nDistance measured by the progress of\\nlight and by a railway car, respec-\\ntively 435\\nActual period of revolution of the\\ncomponents of 61 Cygni 435\\nSpace described by the star annually. 435\\nReliance to be placed on Bessel s de-\\ntermination 435\\nNature of the Stars 436\\nSize of Sirius compared with the sun. 436\\nProof that the fixed stars are suns. 437\\nEnd for which they were made 438\\nArguments for a plurality of worlds. 438\\nChapter IV. System of the World.\\nSystem of the world defined 439\\nComplex character of early systems. 439\\nThings known to Pythagoras 440\\nHis visionary notions 440\\nRejection of his system 441\\nCrystalline spheres of Eudoxus 441\\nHow the two motions were accounted\\nfor. 441\\nHipparchus truths discovered by\\nhim 442\\nAlmagest of Ptolemy 442\\nPtolemaic System explained 444\\nIllustrated by Fig. 81 445\\nDefects of this system 446\\nObjections to it 447\\nCopernican System explained 449\\nArguments on which it rests 449\\nProofs that the planets revolve about\\nthe sun 449\\nProofs of systems among the stars. 450\\nExemplified in the Pleiades, Nebula\\nof Hercules, Binary Stars, and Neb-\\nulas 450\\nUniformity of plan, in natural struc-\\ntures 450\\nAscending orders of systems de-\\nscribed 450\\nSupposed center of the universe 450\\nCentral sun where placed 450\\nReasons for believing that all the\\nheavenly bodies are united in one\\ngrand system 451", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0023.jp2"}, "24": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0024.jp2"}, "25": {"fulltext": "INTRODUCTION TO ASTRONOMY.\\nPreliminary Observations.\\n1. Astronomy is that science which treats of the heavenly\\nbodies.\\nMore particularly, its object is to teach what is known\\nrespecting the Sun, Moon, Planets, Comets, and Fixed Stars\\nand also to explain the methods by which this knowledge is\\nacquired. Astronomy is sometimes divided into Descriptive,\\nPhysical, and Practical. Descriptive Astronomy respects\\nfacts Physical Astronomy, causes Practical Astronomy,\\nthe means of investigating the facts, whether by instruments,\\nor by calculation. It is the province of Descriptive Astron\\nomy to observe, classify, and record all the phenomena of the\\nheavenly bodies, whether pertaining to those bodies individu-\\nally, or resulting from their motions and mutual relations. It\\nis the part of Physical Astronomy to explain the causes of\\nthese phenomena, by investigating and applying the general\\nlaws on which they depend especially by tracing out all the\\nconsequences 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\\nChaldea, in China, and in India. Such knowledge of the\\nheavenly bodies as could be acquired by close and long-con-\\ntinued observation, without the aid of instruments, was dili-\\ngently amassed; and tables of the celestial motions were\\nconstructed, which could be used in predicting eclipses, and\\nother astronomical phenomena.\\nAbout 500 years before the Christian era, Pythagoras, of\\nGreece, taught astronomy at the celebrated school at Crotona,\\nand exhibited more correct views of the nature of the celestial\\nmotions than were entertained by any other astronomer of the\\nl", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0025.jp2"}, "26": {"fulltext": "2 PRELIMINARY OBSERVATIONS.\\nancient world. His views, however, were not generally adopt-\\ned, but lay neglected for nearly 2000 years, when they were\\nrevived and established by Copernicus and Galileo. The most\\ncelebrated astronomical school of antiquity was at Alexandria,\\nin Egypt, which was established and sustained by the Ptole-\\nmies (Egyptian princes), about 300 years before the Christian\\nera. The employment of instruments for measuring angles,\\nand the introduction of trigonometrical calculations to aid the\\nnaked powers of observation, gave to the Alexandrian astrono-\\nmers great advantages over all their predecessors. The most\\nable astronomer of the Alexandrian school was Hipparchus,\\nwho was distinguished above all the ancients for the accuracy\\nof his astronomical measurements and determinations. The\\nknowledge of astronomy possessed by the Alexandrian school,\\nand recorded in the Almagest, or great work of Ptolemy, con-\\nstituted the chief of what was known of our science during the\\nmiddle ages, until the fifteenth and sixteenth centuries, when\\nthe labors of Copernicus of Prussia, Tycho Brake of Denmark,\\nKepler of Germany, and Galileo of Italy, laid the solid foun-\\ndations of modern astronomy. Copernicus expounded the true\\ntheory of the celestial motions Tycho Brahe carried the use\\nof instruments and the art of astronomical observation to a far\\nhigher degree of accuracy than had ever been done before;\\nKepler discovered the great laws of the planetary motions;\\nand Galileo, having first enjoyed the aid of the telescope, made\\ninnumerable discoveries in the solar system. ]STear the begin-\\nning of the eighteenth century, Sir Isaac Newton discovered,\\nin the law of universal gravitation, the great principle that\\ngoverns the celestial motions; and recently, La Place has\\nmore fully completed what Newton began, having followed\\nout all the consequences of the law of universal gravitation, in\\nhis great work, the Mecanique Celeste.\\n3. Among the ancients, astronomy was studied chiefly as\\nsubsidiary to astrology. Astrology was the art of divining\\nfuture events by the stars. It was of two kinds, natural and\\njudicial. Natural Astrology aimed at predicting remarkable\\noccurrences in the natural world, as earthquakes, volcanoes,\\ntempests, and pestilential diseases. Judicial Astrology aimed\\nat foretelling the fates of individuals or of empires.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0026.jp2"}, "27": {"fulltext": "PRELIMINARY OBSERVATIONS. 6\\n4. Astronomers of every age have been distinguished for\\ntheir persevering industry, and their great love of accuracy.\\nThey have uniformly aspired to an exactness in their inquiries\\nfar beyond what is aimed at in most geographical investiga-\\ntions, satisfied with nothing short of numerical accuracy,\\nwherever this is attainable and years of toilsome observation,\\nor laborious calculation, have been spent with the hope of at-\\ntaining a few seconds nearer to the truth. Moreover, a severe\\nbut delightful labor is imposed on all who would arrive at a\\nclear and satisfactory knowledge of the subject of astronomy.\\nDiagrams, artificial globes, orreries, and familiar comparisons\\nand illustrations, proposed by the author or the instructor, may\\nafford essential aid to the learner, but nothing can convey to\\nhim a perfect comprehension of the celestial motions, without\\nmuch diligent study and reflection.\\n5. In expounding the doctrines of astronomy, we do not, as\\nin geometry, claim that every thing shall be proved as soon as\\nasserted. We may first put the learner in possession of the\\nleading facts of the science, and afterwards explain to him the\\nmethods by which those facts were discovered, and by which\\nthey may be verified we may assume the principles of the\\ntrue system of the world, and employ those principles in the\\nexplanation of many subordinate phenomena, while we reserve\\nthe discussion of the merits of the system itself, until the\\nlearner is extensively acquainted with astronomical facts, and\\ntherefore better able to appreciate the evidence by which the\\nsystem is established.\\n6. The Copernican System is that which is held to be the\\ntrue system of the world. It maintains (1), That the apparent\\ndiurnal revolution of the heavenly bodies, from east to west, is\\nowing to the real revolution of the earth on its own axis from\\nwest to east, in the same time and (2), That the sun is the\\ncenter around which the earth and planets all revolve from\\nwest to east, contrary to the opinion that the earth is the center\\nof motion of the sun and planets.\\n7. We shall treat, first, of the Earth in its astronomical\\nrelations secondly, of the Solar System and, thirdly, of the\\nFixed Stars.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0027.jp2"}, "28": {"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\\nof the water fourthly, by the depression or dip of the horizon\\nwhen the spectator is on an eminence and, finally, by actual\\nobservations and measurements, made for the express purpose\\nof ascertaining the figure of the earth, by means of which\\nastronomers are enabled to compute\\nthe distances from the center of the\\nearth of various places on its surface,\\nwhich distances are found to be nearly\\nequal.\\n9. The Dip of the Horizon, is the\\napparent angular depression of the\\nhorizon, to a spectator elevated above\\nthe general level of the earth. The\\neye thus situated takes in more than a\\ncelestial hemisphere, the excess being\\nthe measure of the dip.\\nThus, in Fig. 1, let AO represent\\nFig. 1.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0028.jp2"}, "29": {"fulltext": "FIGURE AND DIMENSIONS. O\\nthe height of a mountain, ZO the direction of the plumb-line,\\nHOB, a line passing through the station O, and at right angles\\nto the plumb-line, C the center of the earth, DAE the portion\\nof the earth s surface seen from O OD, OE, lines drawn from\\nthe place of the spectator to the most distant parts of the\\nhorizon, and CD a radius of the earth. The dip of the horizon\\nis the angle HOD or ROE. Now the angle made between\\nthe direction of the plumb-line and that of the extreme line of\\nthe horizon or the surface of the sea, namely, the angle ZOD,\\ncan be easily measured and subtracting the right angle ZOH\\nfrom ZOD, the remainder is the dip of the horizon, from which\\nthe length of the line OD may be calculated (see Art. 10), the\\nheight of the spectator, that is, the line OA, being known.\\nThis length, to whatever point of the horizon the line is drawn,\\nis always found to be the same and hence it is inferred, that\\nthe boundary which limits the view on all sides is a circle.\\nMoreover, at whatever elevation the dip of the horizon is taken,\\nin any part of the earth, the space seen by the spectator is\\nalways circular. Hence the surface of the earth is spherical.\\n1 0. The earth being a sphere, the dip of the horizon HOD\\nOCD. Therefore, to find the dip of the horizon correspond-\\ning to any given height AO* (the diameter of the earth being\\nknown), .we have in the triangle OCD, the right angle at D,\\nand the two sides CD, CO, to find the angle OCD. Therefore,\\nCO rad. CD cos. OCD.\\nLearning the dip corresponding to different altitudes, by\\ngiving to the line AO different values, we may arrange the\\nresults in a table.\\nThe learner wiil remark that the line AO, as drawn in the figure, is much\\nlarger in proportion to CA than is actually the case, and that the angle HOD is\\nmuch too great for the reality. Such disproportions are very frequent in astro-\\nnomical diagrams, especially when some of the parts are exceedingly small com-\\npared with others and hence the diagrams employed in astronomy are not to be\\nregarded as true pictures of the magnitudes concerned, but merely as representing\\ntheir abstract geometrical relations.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0029.jp2"}, "30": {"fulltext": "6\\nTable\\nTHK EARTH.\\nthe Dip of the Horizon at different elevations,\\nfrom 1 foot to 100 feet.*\\nFeet.\\nFeet.\\nFeet.\\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\\n2.41\\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 HOE, but the angle taken\\nis that above the visible horizon OD. The dip, therefore, or\\nthe angle HOD, corresponding to the height of the point O,\\nmust be subtracted, to obtain the true altitude. On the Peak\\nof Teneriffe, a mountain 13,000 feet high, Humboldt observed\\nthe surface of the sea to be depressed on all sides nearly 2\\ndegrees. The sun arose to him 12 minutes sooner than to an\\ninhabitant of the plain and from the plain, the top of the\\nmountain appeared enlightened 12 minutes before the rising or\\nafter the setting of the sun.\\n1 1 The foregoing considerations show that the form of the\\nearth is spherical but more exact determinations prove that\\nthe earth, though nearly globular, is not exactly so its diame-\\nter from the north to the south pole is about 26 miles less than\\nthrough the equator, giving to the earth the form of an oblate\\nspheroid,t or a flattened sphere resembling an orange. We\\nThis table includes the allowance for refraction.\\nf An oblate spheroid is the solid described by the revolution of an ellipse about\\nits shorter axis.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0030.jp2"}, "31": {"fulltext": "FIG UK K AND DIMENSIONS. 7\\nshall reserve the explanations of the methods by which this\\nfact is established, until the learner is better prepared than at\\npresent to understand them.\\n1 2. The mean or average diameter of the earth is 7912.4\\nmiles, a measure which the learner should fix in his memory as a\\nstandard of comparison in astronomy, and of which he should\\nendeavor to form the most adequate conception in his power.\\nThe circumference of the earth is about 25,000 miles (24857.5).*\\nAlthough the surface of the earth is uneven, sometimes rising\\nIn high mountains, and sometimes descending in deep valleys,\\nyet these elevations and depressions are so small in comparison\\nwith the immense volume of the globe, as hardly to occasion\\nany sensible deviation from a surface uniformly curvilinear.\\nThe irregularities of the earth s surface in this view are no\\ngreater than the rough points on the rind of an orange, which\\ndo not perceptibly interrupt its continuity; for the highest\\nmountain on the globe is only about five miles above the\\ngeneral level and the deepest mine hitherto opened is only\\n5 1\\nabout half a mile.f Now t^j, or about one-sixteen-\\nhundredth part of the whole diameter, an inequality which, in\\nan artificial globe of eighteen inches diameter, amounts to only\\nthe eighty-eighth part of an inch.\\n1 3. 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, h miles from it.\\nLet x denote the radius of the earth.\\nThen x 2 h 2 (x a) 2 x 2 +2ax+a 2\\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 re-\\nquired, and it is therefore inserted.\\nf Sir John HerscheL", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0031.jp2"}, "32": {"fulltext": "8 THE EARTH.\\nb 2 a 2\\nHence, 2ax=o 2 \u00e2\u0080\u0094a 2 and a?=\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\\n89 miles=5. Hence, ^=2?^==!?^=?=3960=radiuB\\n2a 2 2\\nof the earth, and 7920=the earth s diameter.\\n1 4. Another method, and the most ancient, is to ascertain\\nthe distance on the surface of the earth, corresponding to a\\ndegree of latitude. Let us select two convenient places, one\\nlying directly north of the other, whose difference of latitude\\nis known. Suppose this difference to be 1\u00c2\u00b0 30 and the dis-\\ntance between the two places, as measured by a chain, to\\nbe 104 miles. Then, since there are 360 degrees of latitude\\nin the entire circumference, 1\u00c2\u00b0 30 104 360\u00c2\u00b0 21960. And\\n24960 -7944\\n3l416~\\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": "3825", "width": "2201", "jp2-path": "introductionto00olms_0032.jp2"}, "33": {"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\\none part of space as naturally up and another down, and\\nview himself as subject to a force which binds him to the earth\\nas truly as though he were fastened to it by some invisible\\ncords or wires, as the needle attaches itself to all sides of a\\nspherical loadstone. He should dwell on this point until it\\nappears to him as truly up in the direction of BB, CC, DD\\n(Fig. 3), when he is at B, C, and D, respectively, as in the\\ndirection of A A 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\\nupon them, compose the Doctrine of the Sphere*\\n17. A section of a sphere by a plane cutting it in any man-\\nner, is a circle. Great circles are those which pass through the\\ncenter of the sphere, and divide it into two equal hemispheres\\nSmall circles are such as do not pass through the center, but\\ndivide the sphere into two unequal parts. The circumference\\nof every circle, whether great or small, is divided into 360\\nequal parts called degrees. Hence, a degree is not a particular\\nlength of arc, but only a certain part of any whole circumference.\\n1 8. The Axis of a circle is a straight line passing through\\nits center at right angles to its plane.\\n1 9. 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 everywhere 90\u00c2\u00b0 from the great circle.\\nFor, the measure of an angle at the center of a sphere is the arc\\nof 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\\ns It is presumed that many of those who read this work will have studied\\nSpherical Geometry but it is so important to the. student of astronomy to have\\na clear idea of the circles of the sphere, that it is thought best to introduce\\nthem here.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0033.jp2"}, "34": {"fulltext": "10 THE EARTH.\\nthe sphere, namely, the distance from the pole to the circum-\\nference 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\\npoints diametrically opposite, and consequently their points of\\nsection are 180\u00c2\u00b0 apart. For the line of common section is a\\ndiameter in 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\\npasses through the pole and the center of the circle, it must\\npass through the axis; which being at right angles to the\\nplane of the circle, every plane which passes through it is at\\nright angles to the same plane.\\nThe great circle which passes through the pole of another\\ngreat circle, and is at right angles to it, is called a secondary\\nto 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\\nsurface of the earth or in the heavens, both the earth and the\\nheavens are conceived to be divided into separate portions by\\ncircles, which are imagined to cut through them in various ways.\\nThe earth, thus intersected, is called the terrestrial, and the\\nheavens, the celestial sphere. The learner will remark that these\\ncircles have no existence in nature, but are mere landmarks,\\nartificially contrived, for convenience of reference. On account\\nof the immense distance of the heavenly bodies, they appear to\\nus, wherever we are placed, to be fixed in the same concave", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0034.jp2"}, "35": {"fulltext": "DOCTRINE OF THE SPHERE. 11\\nsurface, or celestial vault. The great circles of the globe, ex-\\ntended every way to meet the concave surface of the heavens,\\nbecome circles of the celestial sphere.\\n24. The Horizon is the great circle which divides the earth\\ninto upper and lower hemispheres, and separates the visible\\nheavens from the invisible. This is the rational horizon. The\\nsensible horizon is a circle touching the earth at the place of the\\nspectator, and is bounded by the line in which the earth and\\nskies seem to meet. The sensible horizon is parallel to the\\nrational, but is distant from it by the semi-diameter of the earth,\\nor nearly 4,000 miles. Still, so vast isthe distance of the starry\\nsphere, that both these planes appear to cut that sphere in the\\nsame line so that we see the same hemisphere of stars that we\\nshould see if the upper half of the earth were removed, and we\\nstood on the rational 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\\ndirectly under our feet. The plumb line is in the axis of the\\nhorizon, 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 ex-\\ntending 90 degrees from his zenith in all directions.\\n20. Vertical circles are those which pass through the poles\\nof the horizon, perpendicular to it.\\nThe Meridian is that vertical circle which passes through\\nthe north and south points.\\nThe Prime Vertical is that vertical circle which passes\\nthrough the east and west points.\\n27. As in geometry we determine the position of any point\\nby means of rectangular co-ordinates, or perpendiculars drawn\\nfrom the point to planes at right angles to each other, so in\\nastronomy we ascertain the place of a body, as a fixed star, by\\ntaking its angular distance from two great circles, one of which\\nis perpendicular to the other. Thus the horizon and the\\nmeridian, or the horizon and the prime vertical, are co-ordinate\\ncircles used for such measurements.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0035.jp2"}, "36": {"fulltext": "12 THE EARTH.\\nThe Altitude of a body is its elevation above the horizon\\nmeasured on a vertical circle.\\nThe Azimuth of a body is its distance measured on the horizon\\nfrom 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\\na point is on the horizon it is only necessary to count the num-\\nber of degrees of the horizon between that point and the\\nmeridian, in order to find its azimuth but if the point is above\\nthe horizon, then its azimuth is estimated by passing a vertical\\ncircle through it, and reckoning the azimuth from the point\\nwhere this circle cuts the horizon.\\nThe Zenith Distance of a body is measured on a vertical cir-\\ncle passing through that body. It is the complement of the\\naltitude.\\n28. The Axis of the Earth is the diameter on which the\\nearth is conceived to turn in its diurnal revolution. The same\\nline continued until it meets the starry concave, constitutes the\\naxis of the celestial 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 inter-\\nsection of the plane of the equator with the surface of the earth,\\nconstitutes the terrestrial, and with the concave sphere of\\nthe heavens, the celestial equator. The latter, by way of dis-\\ntinction, is sometimes denominated the equinoctial.\\n30. The secondaries to the equator, that is, the great circles\\npassing through the poles of the equator, are called Merid-\\nians, because that secondary which passes through the zenith\\nof any place is the meridian of that place, and is at right angles\\nboth to the equator and the horizon, passing as it does through\\nthe poles of both. (Art. 21.) These secondaries are also called", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0036.jp2"}, "37": {"fulltext": "DOCTRINE OF THE SPHERE. 13\\nHour Circles, because the arcs of trie equator intercepted be-\\ntween them are used as measures of time.\\n3 1 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.\\nThe meridian usually taken as the standard, is that of the Ob-\\nservatory of Greenwich, near London. If a place is directly on\\nthe equator, we have only to inquire how many degrees of the\\nequator there are between that place and the point where the\\nmeridian of Greenwich cuts the equator. If the place is north\\nor south of the equator, then its longitude is the arc of the\\nequator intercepted between the meridian which passes through\\nthe place, and the meridian of Greenwich.\\n33. The Ecliptic is a great circle in which the earth performs\\nits annual revolution around the sun. It passes through the\\ncenter of the earth and the center of the sun. It is found by\\nobservation that the earth does not lie with its axis at right\\nangles to the plane of the ecliptic, but that it is turned about\\n23-J- degrees out of a perpendicular direction, making an angle\\nwith the plane itself of 66$\u00c2\u00b0. The equator, therefore, must be\\nturned the same distance out of a coincidence with the ecliptic,\\nthe two circles making an angle with each other of 23-J-\\n(23\u00c2\u00b0 27 40 It is particularly important for the learner to\\nform correct ideas of the ecliptic, and of its relations to the\\nequator, since to these two circles a great number of astro-\\nnomical measurements and phenomena are referred.\\n34. The Equinoctial Points, or Equinoxes,* are the inter-\\nsections of the ecliptic and equator. The time when the sun\\ncrosses the equator in returning northward is called the vernal,\\nand in going southward the autumnal equinox. The vernal\\nequinox occurs about the 21st of March, and the autumnal the\\n22d of September.\\nThe term Equinoxes strictly denotes the times when the sun arrives at the\\nequinoctial points, but it is also frequently used to denote those points themselves.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0037.jp2"}, "38": {"fulltext": "14: THE EARTH.\\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 22cl of June, and the winter solstice about the 22d of\\nDecember.\\nThe ecliptic is divided into twelve equal parts of 30\u00c2\u00b0 each,\\ncalled signs, which, beginning at the vernal equinox, succeed\\neach other in the following order\\nNorthern. Southern.\\n1. Aries T 7. Libra\\n2. Taurus 8 8. Scorpio *n\\n3. Gemini II 9. Sagittarius t\\n4. Cancer S 10. Capricornus V3\\n5. Leo 11. Aquarius\\n6. Yirgo \u00c2\u00abK 12. 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 Coheres. The Equinoctial Cohere is the meridian which\\npasses through the equinoctial points. The Solstitial Cohere 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\\nright angles, or a secondary to both the ecliptic and equator.\\nFor, like every other meridian, it is of course perpendicular to\\nthe equator, passing through its poles. Moreover, the equinox,\\nbeing a point both in the equator and in the ecliptic, is 90\u00c2\u00b0\\nfrom the solstice, from the pole of the equator, and from the\\npole of the ecliptic. Hence the solstitial colure, which passes\\nthrough the solstice and the pole of the equator, passes also\\nthrough the pole of the ecliptic, being the great circle of which\\nthe equinox itself is the pole. Consequently the solstitial\\ncolure is a secondary to both the equator and the ecliptic.\\n(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", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0038.jp2"}, "39": {"fulltext": "DOCTRINE OF THE SPHERE.\\n15\\nAscension is the angular distance from the vernal equinox, meas-\\nured on the equator. If a star is situated on the equator, then\\nits right ascension is the number of degrees of the equator be-\\ntween the star and the vernal equinox. But if the star is north\\nor south of the equator, then its right ascension is the arc of\\nthe equator intercepted between the vernal equinox and that\\nsecondary to the equator which passes through the star.\\nDeclination is the distance of a body from the equator, meas-\\nured on a secondary to the latter. Therefore, right ascension\\nand declination correspond to terrestrial longitude and latitude\\nright ascension being reckoned from the equinoctial colure, in\\nthe same manner as longitude is reckoned from the meridian\\nof Greenwich. On the other hand, celestial longitude and lati-\\ntude are referred, not to the equator, but to the ecliptic.\\nCelestial Longitude, is the distance of a body from the vernal\\nequinox reckoned on the ecliptic. Celestial Latitude, is the\\ndistance from the ecliptic measured on a secondary to the lat-\\nter. Or, more briefly, Longitude is distance on the ecliptic\\nLatitude, distance from the ecliptic. The North Polar Dis-\\ntance of a star, is the complement of its declination.\\nFig. 4.\\n38. Parallels of Latitude are z\\nsmall circles parallel to the equator.\\nThey constantly diminish in size as\\nwe go from the equator to the pole,\\nthe radius being always equal to the\\ncosine of the latitude. In fig. 4, let\\nHO be the horizon, EQ the equator,\\nPP the axis of the earth, Z1ST the\\nprime vertical, and ZL a parallel of\\nlatitude of any place Z. Then ZE is\\nthe latitude (Art. 31), and ZP the complement of the latitude;\\nbut Zrc, the radius of the parallel of latitude ZL, is the sine of\\nZP, and therefore the cosine of the latitude.\\n39. The Tropics are the parallels of latitude that pass\\nthrough the solstices. The northern tropic is called the tropic\\nof Cancer the southern, the tropic of Capricorn.\\n40. The Polar Circles are the parallels of latitude that pass", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0039.jp2"}, "40": {"fulltext": "16 THE EARTH.\\nthrough the poles of the ecliptic, at the distance of 23J degrees\\nfrom the pole of the earth. (Art. 33.)\\n41. The earth is divided into five zones. That portion of\\nthe earth which lies between the tropics, is called the Torrid\\nZone that between the tropics and the polar circles, the\\nTemperate Zones and that between the polar circles and the\\npoles, the Frigid Zones.\\n42. The Zodiac is the part of the celestial sphere which lies\\nabout 8 degrees on* each side of the ecliptic. This portion of\\nthe heavens is thus marked off by itself, because the planets\\nare never seen further from the ecliptic than this limit.\\n43. The elevation of the pole is equal to the latitude of the\\nplace.\\nThe arc PE (Fig. 4.)=ZO PO=ZE, which equals the lati-\\ntude.\\n44. The elevation of the equator is equal to the complement\\nof the latitude.\\nZH=90\u00c2\u00b0. But ZE=Lat. EH=90-Lat.=colatitude.\\n45. The distance of any place from the pole {or the polar\\ndistance) equals the complement of the latitude.\\nEP=90\u00c2\u00b0. But EZ=Lat. ZP=90-Lat.=colatitude.\\n1\\nCHAPTEE 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\\nearth on its own axis from west to east. If we conceive of a\\nradius of the earth s equator extended until it meets the con-\\ncave sphere of the heavens, then, as the earth revolves, the ex-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0040.jp2"}, "41": {"fulltext": "DIURNAL REVOLUTION. Vj\\ntremity of this line would trace out a curve on the face of the\\nsky, namely, the celestial equator. In curves parallel to this,\\ncalled the circles of diurnal revolution, the heavenly bodies\\nactually appear to move, every star having its own peculiar\\ncircle. After the learner has first rendered familiar the real\\nmotions of the earth from west to east, he may then, without\\ndanger of misconception, adopt the common language, that all\\nthe heavenly bodies revolve around the earth once a day from\\neast to west, in circles parallel to the equator and to each\\nother.\\n47. The time occupied by a star in passing from any point\\nin the meridian until it comes round to the same point again,\\nis called a sidereal day, and measures the period of the earth s\\nrevolution on its axis. If we watch the returns of the same\\nstar from day to day, we shall find the intervals exactly equal\\nto one another that is, the sidereal days are all equal*\\nWhatever star we select for the observation, the same result\\nwill be obtained. The stars, therefore, always keep the same\\nrelative position, and have a common movement round the\\nearth, a consequence that naturally flows from,the hypothesis\\nthat their apparent motion is all produced by a single real\\nmotion, namely, that of the earth. The sun, moon, and\\nplanets, revolve in like manner, but their returns to the merid-\\nian are not, like those of the fixed stars, at exactly equal in-\\ntervals.\\n48. The appearances of the diurnal motions of the heavenly\\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 dif-\\nferent positions on the earth.\\n49. If he is on the equator, his horizon passes through both\\npoles for the horizon cuts the celestial vault at 90 degrees in\\nevery direction from the zenith of the spectator but the pole\\nis likewise 90 degrees from his zenith, and consequently, the\\nAllowance is here supposed to be made for the effects of precession, c.\\n2", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0041.jp2"}, "42": {"fulltext": "18 THE EARTH.\\npole must be in his horizon. The celestial equator coincides\\nwith his prime vertical, being a great circle passing through\\nthe east and west points. Since all the diurnal circles are par-\\nallel to the equator, they are all, like the equator, perpendicu-\\nlar to his horizon. Such a view of the heavenly bodies is\\ncalled a right sphere or,\\nA Eight 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 situ-\\nated in the celestial equator, would appear to rise directly in\\nthe east, to pass the meridian in the zenith of the spectator,\\nand to set directly in the west. In proportion as stars are at a\\ngreater distance from the equator towards the pole, they de-\\nscribe smaller and smaller circles, until, near the pole, their\\nmotion is hardly perceptible. In a right sphere every star re-\\nmains an equal time above and below the horizon and since\\nthe times of their revolutions are equal, the velocities are as\\nthe lengths of the circles they describe. Consequently, as the\\nstars are more remote from the equator towards the pole, their\\nmotions become slower, until, at the pole, if a star were there,\\nit would appear stationary.\\n50. If the spectator advances one degree towards the north\\npole, his horizon reaches one degree beyond the pole of the\\nearth, and cuts the starry sphere one degree below the pole of\\nthe heavens, or below the north star if that be taken as the\\nplace of the pole. As he moves onward towards the pole, his\\nhorizon continually reaches further and further beyond it, until,\\nwhen he comes to the pole of the earth, and under the pole of\\nthe heavens, his horizon reaches on all sides to the equator, and\\ncoincides with it. Moreover, since all the circles of daily mo-\\ntion are parallel to the equator, they become, to the spectator\\n-at the pole, parallel to the horizon. This is what constitutes a\\nparallel sphere. Or,\\nA Parallel Sphere is that in which all the circles of daily\\nmotion are parallel to the horizon.\\n5 1 To render this view of the heavens familiar, the learner\\nshould follow round in his mind a number of separate stars,\\none near the horizon, one a few degrees above it, and a third", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0042.jp2"}, "43": {"fulltext": "DIURNAL REVOLUTION.\\n19\\nnear the zenith. To one who stood upon the north pole, the\\nstars of the northern hemisphere would all be perpetually in\\nview when not obscured by clouds or lost in the sun s light,\\nand none of those of the southern hemisphere would ever be\\nseen. The sun would be constantly above the horizon for six\\nmonths in the year, and the remaining six constantly out of\\nsight. That is, at the pole, the days and nights are each six\\nmonths long. The phenomena at the south pole are similar to\\nthose at the north.\\n52. A perfect parallel sphere can never be seen except at\\none of the poles, a point which has never been actually\\nreached by man; yet the British disco very -ships penetrated\\nwithin a few degrees of the north pole, and of course enjoyed\\nthe view of a sphere nearly parallel.\\n53. As the circles of daily motion are parallel to the horizon\\nof the pole, and perpendicular to that of the equator, so at all\\nplaces between the two, the diurnal motions are oblique to the\\nhorizon. This aspect of the heavens constitutes an oblique\\nsphere, which is thus defined\\nAn Oblique Sphere is that in which the circles of daily\\nmotion are oblique to the horizon.\\nSuppose for example the spectator is at the latitude of fifty\\ndegrees. His horizon reaches 50\u00c2\u00b0 beyond the pole of the\\nearth, and gives the same apparent elevation to the pole of the\\nheavens. It cuts the equator, and all the circles of daily mo-\\ntion, at an angle of 40\u00c2\u00b0, being\\nalways equal to the co-altitude\\nof the pole. Thus, let HO (Fig.\\n5), represent the horizon, EQ the\\nequator, and PP the axis of the\\nearth. Also, 11, mm, c, par-\\nallels of latitude. Then the ho-\\nrizon of a spectator at Z, in lati-\\ntude 50\u00c2\u00b0 reaches to 50\u00c2\u00b0 beyond\\nthe pole (Art. 50) and the angle\\nECH, is 40\u00c2\u00b0. As we advance\\nstill further north, the elevation\\nof the diurnal circles grows less", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0043.jp2"}, "44": {"fulltext": "THE EARTH.\\nand less, and consequently the motions of the heavenly bodies\\nmore and more oblique, until finally, at the pole, where the lati-\\ntude is 90\u00c2\u00b0, the angle of elevation of the equator vanishes, and\\nthe horizon and the equator coincide with each other, as before\\nstated.\\n54. The ciecle of perpetual apparition, is the boundary\\nof that 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\\nstar whose polar distance is just equal to the latitude, will,\\nwhen at its lowest point, only just reach the horizon and all\\nthe stars nearer the pole than this will evidently not descend\\nso 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\\ndistance from the pole OP is evidently equal to the elevation\\nof the pole, 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 occtjltation, is the boundary of\\nthat space around the depressed pole, within which the stars\\nnever rise. Thus, m m! (Fig. 5), is the circle of perpetual oc-\\ncultation, between which and the south pole the stars never\\nrise.\\n56. In an oblique sphere, the horizon cuts the circles of\\ndaily motion unequally. Towards the elevated pole, more\\nthan half the circle is above the horizon, and a greater and\\ngreater portion as the distance from the equator is increased,\\nuntil finally, within the circle of perpetual apparition, the\\nwhole circle is above the horizon. Just the opposite takes\\nplace in the hemisphere next the depressed pole. Accordingly,\\nwhen the sun is in the equator, as the equator and horizon, like\\nall other great circles of the sphere, bisect each other, the days\\nand nights are equal all over the globe. But when the sun is\\nnorth of the equator, our days become longer than our nights,\\nbut shorter when the sun is south of the equator. Moreover,\\nthe higher the latitude, the greater is the inequality in the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0044.jp2"}, "45": {"fulltext": "DIURNAL REVOLUTION. 21\\nlengths of the days and nights. All these points will be read-\\nily 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\\nactually all turns around the earth once in 24 hours, or that\\nthis motion of the heavens is merely apparent, arising from\\nthe revolution of the earth on its axis in the opposite direc-\\ntion, a motion of which we are insensible, as we sometimes\\nlose the consciousness of our own motion in a ship or a steam-\\nboat, and observe all external objects to be receding from us\\nwith a common motion. Proofs entirely conclusive and sat-\\nisfactory, establish the fact, that it is the earth and not the\\ncelestial sphere that turns but these proofs are drawn from\\nvarious sources, and the student is not prepared to appreciate\\ntheir value, or even to understand some of them, until he has\\nmade considerable proficiency in the study of astronomy, and\\nbecome familiar with a great variety of astronomical phenom-\\nena. To such a period of our course of instruction we there-\\nfore postpone the discussion of the hypothesis of the earth s\\nrotation on its axis.\\n58. While we retain the same place on the earth, the diur-\\nnal revolution occasions no change in our horizon, but our\\nhorizon goes round as well as ourselves. Let us first take our\\nstation on the equator at sunrise; our horizon now passes\\nthrough both the poles, and through the sun, which we are to\\nconceive of as at a great distance from the earth, and there-\\nfore as cut, not by the terrestrial but by the celestial horizon.\\nAs the earth turns, the horizon dips more and more below the\\nsun, at the rate of 15 degrees for every hour; and, as in the\\ncase of the polar star (Art. 50), the sun appears to rise at the\\nsame rate. In six hours, therefore, it is depressed 90 degrees\\nbelow the sun, which brings us directly under the sun, which,\\nfor our present purpose, we may consider as having all the\\nwhile maintained the same fixed position in space. The earth\\ncontinues to turn, and in six hours more, it completely reverses\\nthe position of our horizon, so that the western part of the\\nhorizon which at sunrise was diametrically opposite to the sun\\nnow cuts the sun, and soon afterwards it rises above the level", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0045.jp2"}, "46": {"fulltext": "22 THE EARTH.\\nof the sun, and the sun sets. During the next twelve hours,\\nthe sun continues on the invisible side of the sphere, until the\\nhorizon returns to the position from which it started, and a\\nnew day begins.\\n59. Let us next contemplate the similar phenomena at the\\npoles. Here the horizon, coinciding as it does with the equa-\\ntor, would cut the sun through its center, and the sun would\\nappear to revolve along the surface of the sea, one half above\\nand the other half below the horizon. This supposes the sun\\nin its annual revolution to be at one of the equinoxes. When\\nthe sun is north of the equator, it revolves continually round\\nin a path which, during a single revolution, appears parallel\\nto the horizon, and it is constantly day and when the sun is\\nsouth of the equator, it is, for the same reason, continual night.\\n60. We have endeavored to conceive of the manner in\\nwhich the apparent diurnal movements of the sun are really\\nproduced at two stations, namely, in the right sphere, and in\\nthe parallel sphere. These two cases being clearly understood,\\nthere will be little difficulty in applying a similar explanation\\nto an oblique sphere.\\nARTIFICIAL GLOBES.\\n6 1 Artificial globes are of two kinds, terrestrial and celes-\\ntial. The first exhibits a miniature representation of the\\nearth the second, of the visible heavens and both show the\\nvarious circles by which the two spheres are respectively trav-\\nersed. Since all globes are similar solid figures, a small\\nglobe, imagined to be situated at the center of the earth or of\\nthe celestial vault, may represent all the visible objects and\\nartificial divisions of either sphere, and with great accuracy\\nand just proportions, though on a scale greatly reduced. The\\nstudy of artificial globes, therefore, cannot be too strongly\\nrecommended to the student of astronomy.*\\nIt were desirable, indeed, that every student of the science should have the\\ncelestial globe at least, constantly before him. One of a small size, as eight or\\nnine inches, will answer the purpose, although globes of these dimensions cannot\\nusually be relied on for nice measurements.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0046.jp2"}, "47": {"fulltext": "ARTIFICIAL GLOBES. 23\\n62. An artificial globe is encompassed from north to south\\nby a strong brass ring, to represent the meridian of the place.\\nThis ring is made fast to the two poles, and thus supports the\\nglobe, while it is itself supported in a vertical position by\\nmeans of a frame, the ring being usually let into a socket in\\nwhich it may be easily slid, so as to give any required eleva-\\ntion to the pole. The brass meridian is graduated each way\\nfrom the equator to the pole 90\u00c2\u00b0, to measure degrees of latitude\\nor declination, according as the distance from the equator\\nrefers to a point on the earth or in the heavens. The horizon\\nis represented by a broad zone, made broad for the convenience\\nof carrying on it a circle of azimuth, another of amplitude, and\\na wide space on which are delineated the signs of the ecliptic,\\nand the sun s place for every day in the year; not because\\nthese points have any special connection with the horizon, but\\nbecause this broad surface furnishes a convenient place for\\nrecording them.\\n63. Hour Circles are represented on the terrestrial globe\\nby great circles drawn through the pole of the equator but,\\non the celestial globe, corresponding circles pass through the\\npoles of the ecliptic, constituting circles of celestial latitude\\n(Art. 37), while the brass meridian, being a secondary to the\\nequinoctial, becomes an hour circle of any star which, by\\nturning the globe, is brought under it.\\n64. The Sour Index is a small circle described around the\\npole of the equator, on which are marked the hours of the day.\\nAs this circle turns along with the globe, it makes a complete\\nrevolution in the same time with the equator or, for any less\\nperiod, the same number of degrees of this circle and of the\\nequator pass under the meridian. Hence the hour index\\nmeasures arcs of right ascension. (Art. 37.)\\n65. The Quadrant of Altitude is a flexible strip of brass,\\ngraduated into ninety equal parts, corresponding in length to\\ndegrees on the globe, so that when applied to the globe and\\nbent so as closely to fit its surface, it measures the angular\\ndistance between any two points. When the zero, or the\\npoint where the graduation begins, is laid on the pole of any", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0047.jp2"}, "48": {"fulltext": "24: THE EARTH.\\ngreat circle, the 90th degree will reach to the circumference of\\nthat circle, and being therefore a great circle passing through\\nthe pole of another great circle, it becomes a secondary to the\\nlatter. (Art. 21.) Thus the quadrant of altitude may be used\\nas a secondary to any great circle on the sphere but it is used\\nchiefly as a secondary to the horizon, the point marked 90\u00c2\u00b0\\nbeing screwed fast to the pole of the horizon, that is, the\\nzenith, and the other end, marked 0, being slid along between\\nthe surface of the sphere and the wooden horizon. It thus\\nbecomes a vertical circle, on which to measure the altitude of\\nany star through which it passes, or from which to measure\\nthe azimuth of the star, which is the arc of the horizon inter-\\ncepted between the meridian and the quadrant of altitude\\npassing through the star. (Art. 27.)\\n66. To rectify the globe for any place, the north pole must\\nbe elevated to the latitude of the place (Art. 43) then the\\nequator and all the diurnal circles will have their due inclina-\\ntion in respect to the horizon and, on turning the globe (the\\ncelestial globe west and the terrestrial east), every point on\\neither globe will revolve as the same point does in nature and\\nthe relative situations of all places will be the same as on the\\nrespective native spheres.\\nPROBLEMS ON THE TERRESTRIAL GLOBE.\\n67. To find the Latitude and Longitude of a place: Turn\\nthe globe so as to bring the place to the brass meridian; then\\nthe degree and minute on the meridian directly over the place\\nwill indicate its latitude, and the point of the equator under\\nthe meridian, will show its longitude.\\nEx. What are the Latitude and Longitude of the citv of JSTew\\nYork?\\n68. To find a place having its latitude and longitude given\\nBring to the brass meridian the point of the equator correspond-\\ning to the longitude, and then at the degree of the meridian\\ndenoting the latitude, the place will be found.\\nEx. What place on the globe is in Latitude 39 1ST. and Lon-\\ngitude 77 W.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0048.jp2"}, "49": {"fulltext": "PROBLEMS ON THE TERRESTRIAL GLOBE. 25\\n69. To find the hearing and distance of two places: Rectify\\nthe globe for one of the places (Art. 66) screw the quadrant\\nof altitude to the zenith,* and let it pass through the other\\nplace. Then the azimuth will give the bearing of the second\\nplace from the first, and the number of degrees on the quadrant\\nof altitude, multiplied by 69i (the number of miles in a degree),\\nwill give the distance between the two places.\\nEx. What is the bearing of New Orleans from New York,\\nand what is the distance between these places\\n7 O. 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 show\\nthe hour at the second place when it is noon at the first.\\nEx. When it is noon at New York, what time is it at London\\n7 1 The hour being given at any place, to tell what hour it\\nis in any other part of the world Find the difference of time\\nbetween the two places (Art. 70), and, if the place whose time\\nis required is eastward of the other, add this difference to the\\ngiven time, but if 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 antoeci,\\\\ the perioeci,% and the antipodes^ of\\nany place Bring the given place to the meridian then, under\\nthe meridian, in the opposite hemisphere, in the same degree\\nof latitude, will be found the antoeci. The same place remain-\\ning under the meridian, set the index to XII, and turn the globe\\nuntil the other XII is under the index then the perioeci will\\nbe on the meridian, under the same degree of latitude with the\\ngiven place, and the antipodes will be under the meridian, in\\nthe same latitude, in the opposite hemisphere.\\nEx. Find the antoeci, the perioeci, and the antipodes of the\\ncitizens of New York.\\nThe antoeci have the same hour of the day, but different\\nThe zenith will of course be the point of the rnevidaan over the place.\\navn oiKog. Kept qikos. avn ttsj.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0049.jp2"}, "50": {"fulltext": "26 THE EARTH.\\nseasons of the year the periceci have the same seasons, but\\nopposite hours; and the antipodes have both opposite hours\\nand opposite seasons.\\n73. To rectify the globe for the sun s place On the wooden,\\nhorizon, find the day of the month, and against it is given the\\nsun s place in the ecliptic, expressed by signs and degrees.*\\nLook for the same sign and degree on the ecliptic, bring that\\npoint to the meridian, and set the hour index to XII. To all\\nplaces under the meridian it will then be noon.\\nEx. Rectify the globe for the sun s place on the 1st of Sep-\\ntember.\\n7 4. The latitude of the place being given, to find the time of\\nthe sun s rising and setting on any given day at that place\\nHaving rectified the globe for the latitude (Art. 66), bring the\\nsun s place in the ecliptic to the graduated edge of the meridian,\\nand set the hour index to XII then turn the globe so as to\\nbring the sun to the eastern and then to the western horizon,\\nand the hour index will show the times of rising and setting\\nrespectively.\\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.\\n7 5. To find the Declination and Right Ascension of a heav-\\nenly body Bring the place of the body (whether the sun or a\\nstar) to the meridian. Then the degree and minute standing\\nover it will show its declination, and the point of the equinoc-\\ntial under the meridian will give its right ascension. It will\\nbe remarked, that the declination and right ascension are found\\nin the same manner as latitude and longitude on the terrestrial\\nglobe. Right ascension is expressed either in degrees or in\\nhours both being reckoned 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\\nThe larger globes have the day of the month marked against the correspond-\\ning sign on the ecliptic itself.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0050.jp2"}, "51": {"fulltext": "PROBLEMS ON THE CELESTIAL GLOBE. 27\\n76. 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\\nturn the globe westward until the index points to the given\\nhour, and the constellations would then have the same appear-\\nance to an eye situated at the center of the globe, as they have\\nat that moment in the sky.\\nEx. Required the aspect of the stars at New Haven, Lat.\\n41\u00c2\u00b0 18 at 10 o clock, on the evening of December 5th.\\n77. To find the altitude and azimuth of any star Rectify\\nthe globe for the latitude and the sun s place, and let the quad-\\nrant of altitude be screwed to the zenith, and be made to pass\\nthrough the star. The arc on the quadrant, from the horizon\\nto the star, will denote its altitude, and the arc of the horizon\\nfrom the meridian to the quadrant, will be its azimuth.\\nEx. What are the altitude and azimuth of Sirius (the bright-\\nest of the fixed stars) on the 25th of December at 10 o clock\\nin the evening, in Lat. 41\u00c2\u00b0\\n78. To find the angular distance of two stars from each\\nother Apply the zero mark of the quadrant of altitude to one\\nof the stars, and the point of the quadrant which falls on the\\nother star, will show the angular distance between the two.\\nEx. What is the distance between the two largest stars of\\nthe Great Bear?*\\n79. To find the sun s 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\\nmeridian, and count the number of degrees and minutes be-\\ntween that point of the meridian and the zenith. The comple-\\nment of this arc will be the sun s meridian altitude.\\nEx. What is the sun s meridian altitude at noon on the 1st\\nof August, in Lat. 41\u00c2\u00b0 18\\nThese two stars are sometimes called the Pointers, from the line which\\npasses through them being always nearly in the direction of the north star. The\\nangular distance between them is about 5\u00c2\u00b0, and may be learned as a standard\\nfor reference in estimating, by the eye, the distance between any two points on\\nthe celestial vault.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0051.jp2"}, "52": {"fulltext": "CHAPTEK III.\\nOF PARALLAX, REFRACTION, AND TWILIGHT.\\n80. Parallax is the apparent change of place which bodies\\nundergo by being viewed from different points. This change is\\ncalled diurnal parallax, when one point is at the surface of the\\nearth, and the other at the center. Thus (Fig. 6), an observer\\non the surface at A would see the moon F at p on the sky, while\\nfrom the center C, it would appear at P or, if the moon were\\nat E, H would be its apparent place as seen from the center,\\nand h from the surface. The angle AEC, or AFC, is the diur-\\nnal parallax and HA or Yp is the parallactic arc. It appears,\\ntherefore, that the diurnal parallax of a body is the angle at\\nthat body, subtended by the earth s radius.\\n81. Since then a heavenly body is liable to be referred to\\ndifferent points on the celestial vault, when seen from different\\nparts of the earth, and thus some confusion occasioned in the\\ndetermination of points on the celestial sphere, astronomers\\nhave agreed to consider the true place of a celestial object to\\nbe that where it would appear if seen from the center of the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0052.jp2"}, "53": {"fulltext": "PARALLAX.\\n29\\nearth. The doctrine of parallax teaches how to reduce obser-\\nvations made at any place on the surface of the earth, to such\\nas they would be if made from the center.\\n82. The angle AEC is called the horizontal parallax, which\\nmay be thus denned. Horizontal parallax is the change of\\nposition which a celestial body, appearing in the horizon as\\nseen from the surface of the earth, would assume if viewed\\nfrom the earth s center. It is the angle subtended by the\\nearth s radius, when viewed perpendicularly from the body.\\nIf we consider any one of the triangles represented in the\\nfigure, ACG for example,\\nSin AGO Sin GAZ Sin GAC) AC CG\\na n Sin GAZ x AC Sin GAZ\\nbin Parallax oo\\nHence the sine of the angle of parallax, or (since the angle\\nof parallax is always very small)* the parallax itself varies as\\nthe .sine of the zenith distance of the hody directly, and the dis-\\ntance of the body from the center of the earth inversely. Par-\\nallax, therefore, increases as a body approaches the horizon\\n(but increasing with the sines, it increases much slower than\\nin the simple ratio of the distance from the zenith), and dimin-\\nishes, as the distance from the spectator increases. Again,\\nsince the parallax AGC is as the sine of the zenith distance,\\nlet P represent the horizontal parallax, and P 7 the parallax\\nat any altitude then,\\nP\\nP P sin zenith dist. sin 90V. P=-\\nsin zen. dist.\\nHence, the horizontal parallax of a body equals its parallax\\nat any altitude, divided by the sine of its -distance from the\\nzenith.\\n83. From observations, therefore, on the parallax of a body\\nat any elevation, we are enabled to find the angle subtended\\nThe moon, on account of its nearness to the earth, has the greatest horizon-\\ntal parallax of any of the heavenly bodies yet this is less than 1\u00c2\u00b0 (being 57\\nwhile the greatest parallax of any of the planets does not exceed 30 The dif-\\nference in an arc of 1\u00c2\u00b0, between the length of the arc and the sine, is only 0 .18.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0053.jp2"}, "54": {"fulltext": "30\\nTHE EARTH.\\nby the semi-diameter of the earth as seen perpendicularly from\\nthe body. Or if the horizontal parallax is given, the parallax\\nat any altitude may be found, for\\nP =Px sin zenith distance.\\nHence, in the zenith the parallax is nothing, and is at its\\nmaximum 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\\nconsequence of parallax, E is depressed by the arc HA F by\\nthe arc ~Pp G by the arc Rr while O sustains no change.\\nHence, in all calculations respecting the altitude of the sun,\\nmoon, or planets, the amount of parallax is to be added the\\nstars, as we shall see hereafter, have no sensible parallax. As\\nthe depression which arises from parallax is in the direction of\\na vertical circle, a body, when on the meridian, has only a\\nparallax in declination but in other situations, there is at the\\nsame time a parallax in declination and right ascension for\\nits direction being oblique to the equinoctial, it can be resolved\\ninto two parts, one of which (the declination) is perpendicular,\\nand the other (the right ascension) is parallel to the equinoc-\\ntial.\\n85. The mode of determining the horizontal parallax, is as\\nfollows\\nLet O, O (Fig. 7), be two places on the earth, situated un-\\nder the same meridian, at a\\ngreat distance from each oth-\\ner one place, for example, at\\nthe Cape of Good Hope, and\\nthe other in the north of Eu-\\nrope. The latitude of each\\nplace being known, the arc of\\nthe meridian 00 is known,\\nand the angle OCO also is\\nknown. Let the celestial\\nbody M (the moon for exam-\\nple), be observed simultane-\\nously at O and O and its\\nzenith distance at each place\\nFig. 7.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0054.jp2"}, "55": {"fulltext": "PARALLAX. 31\\naccurately taken, namely, ZY and Z Y then the angles ZOM\\nand Z O M, and of course their supplements COM, C0 7 M are\\nfound. Join 00 and then in the isosceles triangle OCO 7\\ndetermine the angles O, O and the side 00 subtract O OC\\nfrom MOC, and OO C from MO C, and then in the triangle\\nMOO we can calculate MO and MO 7 Finally, in the trian-\\ngle MOC, two known sides and their contained angle will\\nfurnish the angle OMC (which is the parallax at the station\\nO), and the distance MC. To obtain the horizontal parallax\\nP, we have (Art. 82),\\nOMC\\nSin ZOY\\nOn this principle, the horizontal parallax of the moon was\\ndetermined by La Caille and La Lande, two French astrono-\\nmers, one stationed at the Cape of Good Hope, the other at\\nBerlin and in a similar way the parallax of Mars was ascer-\\ntained, by observations made simultaneously at the Cape of\\nGood Hope and at Stockholm.\\n86. On account of the great distance of the sun, his hori-\\nzontal parallax, which is only 8 6, cannot be accurately as-\\ncertained by this method. It can, however, be determined by\\nmeans of the transits of Yenus, a process to be described here-\\nafter.\\n87. The determination of the horizontal parallax of a celes-\\ntial body is an element of great importance, since it furnishes\\nthe means of estimating the distance of the body from the\\ncenter of the earth. Thus, if the angle AEC (Fig. 6) be\\nfound, the radius of the earth AC being known, we have in\\nthe triangle AEC, right-angled at A, the side AC and all the\\nangles, to find the hypotenuse CE, which is the distance of\\nthe moon from the center of the earth.\\nREFRACTION.\\n88. While parallax depresses the celestial bodies subject to\\nit, refraction elevates them and it affects alike the most dis-\\ntant as well as nearer bodies, being occasioned by the change", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0055.jp2"}, "56": {"fulltext": "OZ THE EARTH.\\nof direction which light undergoes in passing through the\\natmosphere. Let us conceive of the atmosphere as made up of\\na great number of concentric strata, as AA, BB, CC, and DD\\n(Fig. 8), increasing rapidly in density (as is known to be the\\nFig. 8.\\nfact) in approaching near to the surface of the earth. Let S\\nbe a star, from which a ray of light 8a enters the atmosphere\\nat a, where, being turned towards the radius of the convex\\nsurface, it would change its direction into the line ab, and\\nagain into he, and ?0, reaching the eye at O. Now, since an\\nobject always appears in the direction in which the light\\nfinally strikes the eye, the star would be seen in the direction\\nof the last ray cO, and the star would apparently change its\\nplace, in consequence of refraction, from S to S being\\nelevated out of its true position. Moreover, since on account\\nof the constant increase of density in descending through the\\natmosphere, the light would be continually turned out of its\\ncourse more and more it would therefore move, not in the\\npolygon 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\\nit enters the atmosphere at right angles to the refracting me-\\ndium, it suffers no refraction. Consequently, the position of\\nthe heavenly bodies, when in the zenith, is not changed by\\nrefraction while, near the horizon, where a ray of light strikes\\nthe medium very obliquely, and traverses the atmosphere", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0056.jp2"}, "57": {"fulltext": "PARALLAX.\\nS3\\nthrough its densest part, the refraction is greatest. The fol-\\nlowing numbers, taken at different altitudes, will show how\\nrapidly refraction diminishes from the horizon upward. The\\namount of refraction at the horizon is 34/ 00 At different\\nelevations it is as follows.\\nElevation.\\nRefraction.\\nElevation.\\nRefraction.\\n0\u00c2\u00b0 10\\n32 00\\n30\u00c2\u00b0\\n1 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\\nfrom the elevation of 30\u00c2\u00b0 to the zenith. From the horizon to\\n1\u00c2\u00b0 above, the refraction is diminished nearly 10 minutes. The\\namount at the horizon, at 45\u00c2\u00b0, and at 90\u00c2\u00b0 respectively, is 34/, 58\\nand 0. In finding the altitude of a heavenly body, the effect\\nof parallax must be added, but that of refraction subtracted.\\n90. Let us now learn the method by which the amount of\\nrefraction at different elevations is ascertained. To take the\\nsimplest case, we will suppose ourselves in a high latitude,\\nwhere some of the stars within the circle of perpetual apparition\\npass through the zenith of the place. We measure the distance\\nof such a star from the pole when on the meridian above the\\npole, that is, in the zenith, where it is not at all affected by\\nrefraction, and again its distance from the pole in its lower\\nculmination. Were it not for refraction, these two polar dis-\\ntances would be equal, since, in the diurnal revolution of a\\nstar, it is in fact always at the same distance from the pole\\nbut, on account of refraction, the lower distance will be less\\nthan the upper, and the difference between the two will show\\nthe amount of refraction at the lower culmination, the latitude\\nof the place being known.\\nExample. At Paris, latitude 48\u00c2\u00b0 50 a star was observed to\\npass the meridian 6 north of the zenith, and consequently\\n3", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0057.jp2"}, "58": {"fulltext": "34\\nTHE EARTH.\\n41\u00c2\u00b0 4/ from the pole.* It should have passed the meridian at\\nthe same distance below the pole, but the distance was found to\\nbe only 40\u00c2\u00b0 57 35 Hence, 41\u00c2\u00b0 4 ~40\u00c2\u00b0 57 35 =6 25 is the\\nrefraction due to that altitude, that is, at the altitude of\\n7\u00c2\u00b0 46 =(48\u00c2\u00b0 50 -41\u00c2\u00b0 4 By taking similar observations in\\nvarious places situated in high latitudes, the amount of refrac-\\ntion might be ascertained for a number of different altitudes,\\nand thus the law of increase in refraction, as we proceed from\\nthe zenith towards the horizon, might be ascertained.\\n9 1 Another method of finding the refraction at different\\naltitudes, is as follows. Take the altitude of the sun or a star,\\nwhose right ascension and declination are known, and note the\\ntime by the clock. Observe also when it crosses the meridian,\\nand the difference of time between the two observations will\\ngive the hour angle ZPa? (Fig. 9). In this triangle ZPa? we\\nalso know PZ the co-latitude and Pa? the co-declination. Hence\\nwe can find the co-altitude Zx, and of course the true altitude.\\nCompare the altitude thus found with that before determined\\nby observation, and the difference will be the refraction due\\nto the apparent altitude.\\nEx. On May 1, 1738, at 5h. 20m. in the morning, Oassini\\nFor the polar distance of the place=90-48 8 50 =41\u00c2\u00b0 10 and 41\u00c2\u00b0 10-6\\n=41\u00c2\u00b0 4", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0058.jp2"}, "59": {"fulltext": "REFE4CTI0N. 35\\nobserved the altitude of the sun s center at Paris to be 5\u00c2\u00b0 0 14\\nThe latitude of Paris being 48\u00c2\u00b0 50 10 and the sun s declina-\\ntion at that 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\\n5\u00c2\u00b0 0 14 the apparent altitude, 9 must be added for parallax,\\nand we have 5\u00c2\u00b0 0 23 the apparent altitude corrected for\\nparallax. Hence, 5\u00c2\u00b0 0 23 -4\u00c2\u00b0 49 52 =10 31 the refraction\\nat the apparent altitude 5\u00c2\u00b0 0 14\\n92. By these and similar methods, we could easily deter-\\nmine the refraction due to any elevation above the horizon,\\nprovided the refracting medium (the atmosphere) were always\\nuniform. But this is not the fact the refracting power of the\\natmosphere is altered by changes in density and temperature, f\\nHence, in delicate observations, it is necessary to take into the\\naccount the state of the barometer and of the thermometer, the\\ninfluence of the variations of each having been very carefully\\ninvestigated, and rules having been given accordingly. With\\nevery precaution to insure accuracy, on account of the variable\\ncharacter of the refracting medium, the tables are not con-\\nsidered as entirely accurate to a greater distance from the\\nzenith than 74\u00c2\u00b0 but almost all astronomical observations are\\nmade at a greater altitude than this.\\n93. Since the whole amount of refraction near the horizon\\nexceeds 33 and the diameters of the sun and moon are severally\\nless than this, these luminaries are in view both before they\\nhave actually risen and after they have set,\\n94. The rapid increase of refraction near the horizon is\\nstrikingly evinced by the oval figure which the sun assumes\\nwhen near the horizon, and which is seen to the greatest ad-\\nvantage when light clouds enable us to view the solar disk.\\nWere all parts of the sun equally raised by refraction, there\\nGregory s Ast., p. 65.\\nf 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, iii., 762.)", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0059.jp2"}, "60": {"fulltext": "36 THE EARTH.\\nwould be no change of figure but since the lower side is more\\nrefracted than the upper, the effect is to shorten the vertical\\ndiameter, and thus to give the disk an oval form. This effect\\nis particularly remarkable when the sun, at its rising or setting,\\nis observed from the top of a mountain, or at an elevation near\\nthe sea-shore for in such situations the rays of light make a\\ngreater angle than ordinary with a perpendicular to the re-\\nfracting medium, and the amount of refraction is proportion-\\nally greater. In some cases of this kind, the shortening of the\\nvertical diameter of the sun has been observed to amount to 6\\nor about one-fifth of the whole.\\n95. The apparent enlargement of the sun and moon in the\\nhorizon, arises from an optical illusion. These bodies in fact\\nare not seen under so great an angle when in the horizon, as\\nwhen on the meridian, for they are nearer to us in the latter\\ncase than in the former. The distance of the sun is indeed so\\ngreat that it makes very little difference in his apparent diam-\\neter, whether he is viewed in the horizon or on the meridian\\nbut with the moon the case is otherwise its angular diameter,\\nwhen measured with instruments, is perceptibly larger at the\\ntime of its culmination. Why then do the sun and moon\\nappear so much larger when near the horizon It is owing to\\nthat general law, explained in optics, by which we judge of\\nthe magnitudes of distant objects, not merely by the angle\\nthey subtend at the eye, but also by our impressions respecting\\ntheir distance, allowing, under a given angle, a greater mag-\\nnitude as we imagine the distance of a body to be greater.\\nNow, on account of the numerous objects usually in sight\\nbetween us and the sun, when on the horizon, he appears much\\nfurther removed from us than when on the meridian, and we\\nassign to him a proportionally greater magnitude. If we view\\nthe sun, in the two positions, through smoked glass, no such\\ndifference of size is observed, for here no objects are seen but\\nthe sun himself.\\nIn extreme cold weather, this shortening of the sun s vertical diameter\\nsometimes exceeds this amount.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0060.jp2"}, "61": {"fulltext": "TWILIGHT.\\n37\\nTWILIGHT.\\n96. Twilight also is another phenomenon depending upon\\nthe agency of the earth s atmosphere. It is due partly to re-\\nfraction and partly to reflection, but mostly the latter. While\\nthe sun is within 18\u00c2\u00b0 of the horizon, before it rises or after it\\nsets, some portion of its light is conveyed to us by means of nu-\\nmerous reflections from the atmosphere. Let AB (Fig. 10) be\\nFig. 10.\\nthe horizon of the spectator at A, and let SS be a ray of light\\nfrom the sun when it is two or three degrees below the horizon.\\nThen to the observer at A, the segment of the atmosphere ABS\\nwould be illuminated. To a spectator at C, whose horizon was\\nCD, the small segment SDa? would be the twilight while, at\\nE, the twilight would disappear altogether.\\n97. At the equator, where the circles of daily motion are\\nperpendicular to the horizon, the sun descends through 18\u00c2\u00b0 in\\nan hour and twelve minutes (f|=l|-h.), and the light of day\\ntherefore declines rapidly, and as rapidly advances after day-\\nbreak in the morning. At the pole, a constant twilight is en-\\njoyed while the sun is within 18\u00c2\u00b0 of the horizon, occupying\\nnearly two-thirds of the half year when the direct light of the\\nsun is withdrawn, so that the progress from continual day to\\nconstant night is exceedingly gradual. To the inhabitants of\\nan oblique sphere, the twilight is longer in proportion as the\\nplace is nearer the elevated pole.\\n98. Were it not for the power the atmosphere has of dis-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0061.jp2"}, "62": {"fulltext": "38 THE EARTH.\\npersing the solar light, and scattering it in various directions,\\nno objects would be visible to us out of direct sunshine every\\nshadow of a passing cloud would be pitchy darkness the stars\\nwould be visible all day, and every apartment into which the\\nsun had not direct admission, would be involved in the obscu-\\nrity of night. This scattering action of the atmosphere on the\\nsolar light, is greatly increased by the irregularity of tempera-\\nture caused by the sun, which throws the atmosphere into a\\nconstant state of undulation, and by thus bringing together\\nmasses of air of different temperatures, produces partial reflec-\\ntions and refractions at their common boundaries, by which\\nmeans much light is turned aside from the direct course, and\\ndiverted to the purposes of general illumination.* In the up-\\nper regions of the atmosphere, as on the tops of very high\\nmountains, where the air is too much rarefied to reflect much\\nlight, the sky assumes a black appearance, and stars become\\nvisible in the day-time.\\nCHAPTER IT.\\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\\nfrom one vessel into another, as in the hour-glass.\\n100. The great standard of time is the period of the revolu-\\ntion of the earth on its axis, which, by the most exact observa-\\ntions, is found to be always the same. The time of the earth s\\nrevolution on its axis is called a sidereal day, and is determined\\nby the revolution of a star from the instant it crosses the me-\\nridian, until it comes round to the meridian again. This inter-\\nval being called a sidereal day, it is divided into 24 sidereal\\nhours. Observations taken upon numerous stars, in different\\n8 Herschel.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0062.jp2"}, "63": {"fulltext": "TIME. 39\\nages of the world, show that they all perform their diurnal\\nrevolutions in the same time, and that their motion during any\\npart of the revolution is perfectly uniform.\\n101. Solar time is reckoned by the apparent revolution of\\nthe sun, from the meridian round to the same meridian again.\\nWere the sun stationary in the heavens, like a fixed star, the\\ntime of its apparent revolution would be equal to the revolu-\\ntion of the earth on its axis, and the solar and the sidereal days\\nwould be equal. But since the sun passes from west to east,\\nthrough 360\u00c2\u00b0 in 365J days, it moves eastward nearly 1\u00c2\u00b0 a day\\n(59 8 .3). While, therefore, the earth is turning round on its\\naxis, the sun is moving in the same direction, so that when we\\nhave come round under the same celestial meridian from which\\nwe started, we do not find the sun there, but he has moved\\neastward nearly a degree, and the earth must perform so much\\nmore than one complete revolution, in order to come under\\nthe sun again. ISTow since a place on the earth gains 360\u00c2\u00b0 in\\n24 hours, how long will it take to gain 1\u00c2\u00b0\\n24\\n360 24 1 WnQ=^ m nearly.\\nHence the solar day is about 4 minutes longer than the side-\\nreal and if we were to reckon the sidereal day 24 hours, we\\nshould reckon the solar day 24h. 4m. To suit the purposes of\\nsociety at large, however, it is found most convenient to reckon\\nthe solar day 24 hours, and to throw the fraction into the side-\\nreal day. Then,\\n24h. 4m. 24 24 23h. 56m. (23h. 56 m 4 s .09)=the length of\\na sidereal day.\\n102. The solar days, however, do not always differ from\\nthe sidereal by precisely the same fraction, since the increments\\nof right ascension (Art. 37), which measure the difference be-\\ntween a sidereal and a solar day, are not equal to each other.\\nApparent time is time reckoned by the revolutions of the sun\\nfrom the meridian to the meridian again. These intervals\\nbeing unequal, of course the apparent solar days are unequal\\nto each other.\\n103. Mean time is time reckoned by the average length of", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0063.jp2"}, "64": {"fulltext": "40 THE EARTH.\\nall the solar days throughout the year. This is the period\\nwhich constitutes the civil day of 24 hours, beginning when\\nthe sun is on the lower meridian, namely, at 12 o clock at\\nnight, and counted by 12 hours from the lower to the upper\\nculmination, and from the upper to the lower. The astronom-\\nical day is the apparent solar day counted through the whole\\n24 hours, instead of by periods of 12 hours each, and begins at\\nnoon. Thus 10th day and 14th hour of astronomical timej\\nwould be 11th day and 2d hour of civil time.\\n104. Clocks are usually regulated so as to indicate mean\\nsolar time yet as this is an artificial period, not marked off,\\nlike the sidereal day, by any natural event, it is necessary to\\nknow how much is to be added to or subtracted from the ap-\\nparent solar time, in order to give the corresponding mean\\ntime. The interval by which apparent time differs from mean\\ntime, is called the equation of time. If a clock were con-\\nstructed (as it may be) so as to keep exactly with the sun, going\\nfaster or slower according as the increments of right ascension\\nwere greater or smaller, and another clock were regulated to\\nmean time, then the difference of the two clocks at any period,\\nwould be the equation of time for that moment. If the ap-\\nparent clock were faster than the mean, then the equation of\\ntime must be subtracted but if the apparent clock were slower\\nthan the mean, then the equation of time must be added, to\\ngive the mean time. The two clocks- would differ most about\\nthe 3d of November, when the apparent time is 16-} ra greater\\nthan the mean (16 m 17 s But, since apparent time is some-\\ntimes greater and sometimes less than mean time, the two,\\nmust obviously be sometimes equal to each other. This is in\\nfact the case four times a year, namely, April 15th, June 15th,\\nSeptember 1st, and December 22d. These epochs, however,\\ndo not remain constant for, on account of the change in the\\nposition of the perihelion, or the point where the earth is near-\\nest the sun (which shifts its place from west to east about 12\\na year), the period when the sun s motions are most rapid, as\\nwell as that when they are slowest, will occur at different parts\\nof the year. The change is indeed exceedingly small in a sin-\\ngle year; but in the progress of ages, the time of year when the\\nsun s motion in its orbit is most accelerated, will not be, as", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0064.jp2"}, "65": {"fulltext": "TIME.\\n41\\nat present, on the first of January, but may fall on the first of\\nMarch, June, or any other day of the year, and the amount of\\nthe equation of time is obviously affected by the sun s distance\\nfrom its perihelion, since the sun moves most rapidly when\\nnearest the perihelion, and slowest when furthest from that point.\\n105. The inequality of the solar days depends on two\\ncauses, the unequal motion of the earth in its orbit, and the\\ninclination of the equator 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\\nequinox, than from the vernal to the autumnal, the difference\\nof the two periods being about eight days (Td. 17h. 17m.)\\nFig. 11.\\nThus, let AEB (Fig. 11) represent the earth s orbit, S being\\nthe place of the sun, A the perihelion, or nearest distance of\\nthe earth from the sun, B the aphelion, or greatest distance,\\nand E, E E positions of the earth in different points of its\\norbit. The place of the earth among the signs is the part of\\nThe exact figure of the earth s orbit will be more particularly shown here-\\nafter. All that the student requires to know, in order to understand the present\\nsubject, is, that the earth s orbit is an ellipse, and that the earth s real motion,\\nand consequently the sun s apparent motion, is greater in proportion as the earth\\nis nearer the sun.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0065.jp2"}, "66": {"fulltext": "42 THE EARTH.\\nthe heavens to which it would be referred if seen from the\\nsun and the place of the sun is the part of the heavens to\\nwhich it is referred as seen from the earth. Thus, when the\\nearth is at E, it is said to be in Aries and as it moves from E\\nthrough E to A, its path in the heavens is through Aries,\\nTaurus, Gemini, c. Meanwhile the sun takes its place suc-\\ncessively in Libra, Scorpio, Sagittarius, c. JSTow, as will be\\nshown more fully hereafter, the earth moves faster when\\nproceeding from Aries through its perihelion to Libra, than\\nfrom Libra through its aphelion to Aries, and, consequently,\\ndescribes the half of its apparent orbit in the heavens, T, S\\nsooner than the half V3. 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\\nthe vernal equinox. The earth passes through it about the\\nfirst of January, and then its velocity is the greatest in the\\nwhole year, being always greater as the distance is less, the\\nangular velocity being inversely as the square of the distance,\\nas will be shown by and by.\\n106. But differences of time are not reckoned on the eclip-\\ntic, but on the equinoctial for the ecliptic being oblique to\\nthe meridian in the diurnal motion, and cutting it at different\\nangles at different times, equal portions will not pass under\\nthe meridian in equal times, and therefore such portions could\\nnot be employed, as they are in the equinoctial, as measures\\nof time. If, therefore, the sun moved uniformly in his orbit, so\\nas to make the daily increments of longitude equal, still the\\ncorresponding arcs of right ascension, which determine the\\nlengths of the solar day, would be unequal. Let us start from\\nthe equinox, from which both longitude and right ascension\\nare reckoned, the former on the ecliptic, the latter on the\\nequinoctial. Suppose the sun has described 70\u00c2\u00b0 of longitude\\nthen to ascertain the corresponding arc of right ascension, we\\nlet a meridian pass through the sun the point where it cuts\\nthe equator gives the sun s right ascension. Now since the\\necliptic makes an acute angle with the meridian, while the\\nequinoctial makes a right angle with it, consequently the arc\\nof longitude is greater than the arc of right ascension. The\\ndifference, however, grows constantly less and less as we", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0066.jp2"}, "67": {"fulltext": "TIME.\\n43\\napproach the tropic, as the angle made between the ecliptic\\nand the meridian constantly increases, until, when we reach\\nthe tropic, the meridian is at right angles to both circles, and\\nthe longitude and right ascension each equals 90\u00c2\u00b0, and they\\nare of course equal to each other. Beyond this, from the\\ntropic to the other equinox, the arc of the ecliptic intercepted\\nbetween the meridian and the autumnal equinox being greater\\nthan the corresponding arc of the equinoctial, of course its\\nsupplement, which measures the longitude, is less than the\\nsupplement of the corresponding arc of the equator which\\nmeasures the right ascension. At the autumnal equinox again,\\nthe right ascension and longitude become equal. In a similar\\nmanner we might show that the daily increments of longitude\\nand right ascension are unequal.\\nIn order to illustrate the foregoing points, let T (Fig. 12)\\nFig. 12.\\nrepresent the equator, T T the ecliptic, and PSE, PS E\\ntwo meridians meeting the sun in S and S Then in the\\ntriangle TES, the arc of longitude TS, is greater than tE, the\\ncorresponding arc of right ascension but towards the tropic\\nthe difference between the two arcs evidently grows less and\\nless, until at T the arcs become equal, being each 90\u00c2\u00b0. But,\\nbeyond the tropic, since TE =a=, TS are equal to each other,\\neach being equal to 180\u00c2\u00b0, and since S is greater than E\\ntherefore TS must be less than TE", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0067.jp2"}, "68": {"fulltext": "44 THE EARTH.\\n107. As the whole arc of right ascension reckoned from the\\nfirst of Aries, does not keep uniform pace with the correspond-\\ning arc of longitude, so the daily increments of right ascension\\ndiffer from those of longitude. If we suppose in the quadrant\\nifT, points taken to mark the progress of the sun from day to\\nday, and let meridians like PSE pass through these points, the\\narcs of the ecliptic embraced between the meridians will be the\\ndaily increments of longitude, while the corresponding parts\\nof the equinoctial will be the daily increments of right ascen-\\nsion. Near T, the oblique direction in which the ecliptic cuts\\nthe meridian, will make the daily increments of longitude\\nexceed those of right ascension but this advantage is dimin-\\nished as we approach the tropic, where the ecliptic becomes\\nless oblique, and finally parallel to the equinoctial while the\\nconvergence of the meridians contributes still further to lessen\\nthe ratios of the daily increments of longitude to those of right\\nascension. Hence, at first, the diurnal arcs of right ascension\\nare less than those of longitude, but afterward greater and\\nthey continue greater for a similar distance beyond the 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\\naccount both of the unequal motion of the sun in his orbit,\\nand of the inclination of his orbit to the equinoctial.\\n109. As astronomical time commences when the sun is on\\nthe meridian, so sidereal time commences when the vernal\\nequinox is on the meridian, and is also counted from to 24\\nhours. By 3 o clock, for instance, of sidereal time, we mean\\nthat it is three hours since the vernal equinox crossed the\\nmeridian as we say it is 3 o clock of astronomical or of civil\\ntime, when it is three hours since the sun crossed the meridian.\\nTHE CALENDAR.\\nHO. The astronomical year is the time in which the sun\\nmakes one revolution in the ecliptic, and consists of 365d. 5h.\\n48m. 51\\\\60. The civil year consists of 365 days. The differ-\\nence is nearly 6 hours, making one day in four years.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0068.jp2"}, "69": {"fulltext": "THE CALENDAR. 45\\n111. The most ancient nations determined the number of\\ndays in the year by means of the stylus, a perpendicular rod\\nwhich cast its shadow on a smooth plane, bearing a meridian\\nline. The time when the shadow was shortest, would indicate\\nthe day of the summer solstice; and the number of days\\nwhich elapsed until the shadow returned to the same length\\nagain, would show the number of days in the year. This was\\nfound to be 365 whole days, and accordingly this period was\\nadopted for the civil year. Such a difference, however, be-\\ntween the civil and astronomical years, at length threw all\\ndates into confusion. For, if at first the summer solstice hap-\\npened on the 21st of June, at the end of four years, the sun\\nwould not have reached the solstice until the 22d of June,\\nthat is, it would have been behind its time. At the end of\\nthe next four years the solstice would fall on the 23d and in\\nprocess of time it would fall successively on every day of the\\nyear. The same would be true of any other fixed date.\\nJulius Caesar made the first correction of the calendar, by in-\\ntroducing an intercalary day every fourth year, making Feb-\\nruary to consist of 29 instead of 28 days, and of course the\\nwhole year to consist of 366 days. This fourth year was de-\\nnominated Bissextile.* It is also called Leap Year.\\n112. But the true correction was not 6 hours, but 5h.\\n49m. hence the intercalation was too great by 11 minutes.\\nThis small fraction would amount in 100 years to f of a day,\\nand in 1000 years to more than 7 days. From the year 325 to\\n1582, it had -in fact amounted to about 10 days; for it was\\nknown that in 325, the vernal equinox fell on the 21st of\\nMarch, whereas, in 1582 it fell on the 11th. In order to re-\\nstore the equinox to the same date, Pope Gregory XIII.\\ndecreed that the year should be brought forward ten days, by\\nreckoning the 5th of October the 15th. In order to prevent\\nthe calendar from falling into confusion afterward, the fol-\\nlowing 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,\\nbut is not divisible by 100, of 366 every year divisible, by 100\\nThe sextus dies ante Kalendas being reckoned twice (Bis).", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0069.jp2"}, "70": {"fulltext": "46 THE EARTH.\\nbut not by 400, again of 365 and every year divisible by 400,\\nof 366.\\nThus the year 1838, not being divisible by four, contains 365\\ndays, while 1836 and 1840 are leap years. Yet to make every\\nfourth year consist of 366 days would increase it too much by\\nabout of a day in 100 years therefore every hundredth year\\nhas only 365 days. Thus 1800, although divisible by 4, was\\nnot a leap year, but a common year. But we have allowed a\\nwhole day in a hundred years, whereas we ought to have al-\\nlowed only three-fourths of a day. Hence, in 400 years we\\nshould allow a day too much, and therefore we let the 400th\\nyear remain a leap year. This rule involves an error of less\\nthan a day in 4237 years.* If the rule were extended by\\nmaking every year divisible by 4,000 (which would now con-\\nsist of 366 days) to consist of 365 days, the error would not be\\nmore than one day in 100,000 years.f\\n113. This reformation of the calendar was not adopted in\\nEngland until 1752, by which time the error in the Julian\\ncalendar amounted to about 11 days. The year was brought\\nforward, by reckoning the 3d of September the 14th. Pre-\\nvious to that time the year began the 25th of March but it was\\nnow made to begin on the 1st of January, thus shortening the\\npreceding year, 1751, one quarter 4\\n114. As in the year 1582, the error in the Julian calendar\\namounted to 10 days, and increased by f of a day in a cen-\\ntury, at present the correction is 12 days and the number of\\nthe year will differ by one with respect to dates between the\\n1st of January and the 25th of March.\\nExamples. General Washington was born Feb. 11, 1731,\\nold style to what date does this correspond in new style\\nAs the date is the earlier part of the 18th century, the cor-\\nrection is 11 days, which makes the birthday fall on the 22d\\nWoodhouse, p. 874. f Herschel s Ast., p. 384.\\nRussia, and the Greek Church generally, adhere to the old style. In order\\nto make the Russian dates correspond to ours, we must add to them 12 days.\\nFrance and other Catholic countries, adopted the Gregorian calendar soon after\\nit was promulgated.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0070.jp2"}, "71": {"fulltext": "THE CALENDAR. 47\\nof February and since the year 1731 closed the 25th of\\nMarch, while according to new style 1732 would have com-\\nmenced on the preceding 1st of January therefore, the time\\nrequired is Feb. 22d, 1732. It is usual, in such cases, to write\\nboth years, thus: Feb. 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 week than it\\nbegan.\\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\\nyear would begin on Wednesday. Hence, generally, any day\\nof the month is one day later in the week than the same day\\nof the preceding year. Thus, July 4th, 1861, falls on Thursday\\n1862, on Friday 1863, on Saturday. But, in leap-year, this\\nrule applies only till the end of February. From that time to\\nthe same date in the year following, every day of a month\\nfalls two days later in the week than during the previous year.\\nThus, July 4th, 1871, is Tuesday; 1872, Thursday; and Feb-\\nruary 2d, 1872, is Friday 1873, Sunday.\\n116. Fortunately for astronomy, the confusion of dates in-\\nvolved in different calendars affects recorded observations but\\nlittle. Kemarkable eclipses, for example, can be calculated\\nback for several thousand years, without any danger of mis-\\ntaking the day of their occurrence and whenever any such\\neclipse is so interwoven with the account given by an ancient\\nauthor of some historical event, as to indicate precisely the\\ninterval of time between the eclipse and the event, and at the\\nsame time completely to identify the eclipse, that date is re-\\ncovered and fixed forever.*\\nAn elaborate view of the Calendar may be found in Delambre s Astronomy,\\nt. III. A useful table for finding the day of the week of any given date, is in-\\nserted in the American Almanac for 1832, p. 72.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0071.jp2"}, "72": {"fulltext": "CHAPTER V\\nOF ASTRONOMICAL INSTRUMENTS AND PROBLEMS FIGURE AND\\nDENSITY OF THE EARTH.\\n117. The most ancient astronomers employed no instru-\\nments for measuring angles, but acquired their knowledge of\\nthe heavenly bodies by long-continued and most attentive in-\\nspection with the naked eye. In the Alexandrian school,\\nabout 300 years before the Christian era, instruments began\\nto be freely used, and thenceforward trigonometry lent a pow-\\nerful aid to the science of astronomy. Tycho Brahe, in the\\n16th century, formed a new era in practical astronomy, and\\ncarried the measurement of angles to 10 a degree of accu-\\nracy truly wonderful, considering that he had not the advan-\\ntage of the telescope. By the application of the telescope to\\nastronomical instruments, a far better denned view of objects\\nwas acquired, and a far greater degree of refinement was at-\\ntainable. The astronomers royal of Great Britain perfected\\nthe art of observation, bringing the measurement of angles to\\n1 and the estimation of differences of time to -fo of a second.\\nBeyond this degree of refinement it is supposed that we can-\\nnot advance, since unavoidable errors arising from the uncer-\\ntainties of refraction, and the necessary imperfection of instru-\\nments, forbid us to hope for a more accurate determination\\nthan this. But a little reflection will show us, that 1 on the\\nlimb of an astronomical instrument, must be a space exceed-\\ningly small. Suppose the circle, on which the angle is meas-\\nx 12x3.14159\\nurea, be one loot in diameter. Then T V mch=\\nooO\\nspace occupied by 1\u00c2\u00b0. Hence =space of 1 and\\nspace of 1 Such minute angles can be measured\\nonly by large circles. If, for example, a circle is 20 feet in\\ndiameter, a degree on its periphery would occupy a space 20", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0072.jp2"}, "73": {"fulltext": "THE CALENDAR. 49\\ntimes as large as a degree on a circle of 1 foot. A degree\\ntherefore of the limb of such an instrument would occupy a\\nspace of 2 inches one minute, of an inch and one second,\\nxsV o of an inch.\\n118, But the actual divisions on the limb of an astronomi-\\ncal instrument never extend to seconds in the smaller instru-\\nments they reach only to 10 and on the largest rarely lower\\nthan V. The subdivision of these spaces is carried on by\\nmeans of the Yernier, which may be thus defined\\nA Yernier is a contrivance attached to the graduated limb\\nof an instrument, for the purpose of measuring aliquot parts\\nof the smallest spaces into which the instrument is divided.\\nThe vernier is usually a narrow zone of metal, which is\\nmade to slide on the graduated limb. Its divisions correspond\\nto those on the limb, except that they are a little larger,* one-\\ntenth, for example, so that ten divisions on the vernier would\\nequal eleven on the limb. Suppose now that our instrument\\nis graduated to degrees only, but the altitude of a certain star\\nis found to be 40\u00c2\u00b0 and a fraction, or 40\u00c2\u00b0 -fee. In order to\\nestimate the amount of this fraction, we bring the zero-point\\nof the vernier to coincide with the point which indicates the\\nexact altitude, or 40\u00c2\u00b0-f-\u00c2\u00bb. We then look along the vernier\\nuntil we find where one of its divisions coincides with one of\\nthe divisions of the limb. Let this be at the fourth division of\\nthe vernier. In four divisions, therefore, the vernier has\\ngained upon the divisions of the limb, a space equal to x and\\nsince, in the. case supposed, it gains of a degree, or 6 at\\neach division, the entire gain is 24 and the arc in question is\\n40\u00c2\u00b0 24\\n119. As the vernier is used in the barometer, where its\\napplication is more easily seen than in astronomical instru-\\nments, while the principle is the same in both cases, let us see\\nhow it is applied to measure the exact height of a column of\\nmercury. Let AB (Fig. 13) represent the upper part of a\\nbarometer, the level of the mercury being at 0, namely, at 30.3\\ninches, and nearly another tenth. The vernier being brought\\nIn the more modern instruments the divisions of the vernier are smaller\\nthan those of the limb.\\n4", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0073.jp2"}, "74": {"fulltext": "50\\nTHE EARTH.\\n(by a screw which is usually attached to it) to coincide with the\\nsurface of the mercury, we look along Fig. 13.\\ndown the scale, until we find that the\\ncoincidence is at the 8th division of\\nthe vernier. Now as the vernier gains\\nts \u00c2\u00b0f To iio \u00c2\u00b0f an i ncn at eacn ^ivi-\\nsi on upward, it of course gains r f in\\neight divisions. The fractional quan-\\ntity, therefore, is .08 of an inch, and\\nthe height of the mercury is 30.38. If\\nthe divisions of the vernier were such,\\nthat each gained (when 60 on the\\nvernier would equal 61 on the limb)\\non a limb divided into degrees, we\\ncould at once take off minutes and\\nwere the limb graduated to minutes,\\nwe could in a similar way read off seconds.\\nA\\nC\\nB\\nr\u00e2\u0080\u0094 31\\n30\\n\u00e2\u0080\u009429\\n1\\n1\\n2\\n3\\n4:\\n5\\nG\\n7\\n8\\n8\\n11)\\n11\\n1 20. The instruments most used for astronomical observa-\\ntions, are the Transit Instrument, the Astronomical Clock, the\\nMural Circle, and the Sextant. A large portion of all the\\nobseiwations made in an astronomical observatory, are taken\\non the meridian. When a heavenly body is on the meridian,\\nbeing at its highest point above the horizon, it is then least\\naffected by refraction and parallax its zenith distance (from\\nwhich its altitude and declination are easily derived) is readily\\nestimated and its right ascension may be very conveniently\\nand accurately determined by means of the astronomical clock.\\nHaving the right ascension and declination of a heavenly\\nbody, various other particulars resj)ecting its position may be\\nfound, as we shall see hereafter, by the aid of spherical trigo-\\nnometry. Let us then first turn our attention to the instru-\\nments employed for determining the right ascension and decli-\\nnation. They are the Transit Instrument, the Astronomical\\nClock, and the Mural Circle.\\n121. The Transit Instrument is a telescope, which is fixed\\npermanently in the meridian, and moves only in that plane.\\nIt rests on a horizontal axis, which consists of two hollow\\ncones applied base to base, a form uniting lightness and", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0074.jp2"}, "75": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n51\\nstrength. The two ends of the axis rest on two firm supports,\\nas pillars of stone, for example, usually built up from the\\nground, and so related to the building as to be as free as possible\\nfrom all agitation. In figure 14, AD represents the telescope,\\nE, W, massive stone pillars supporting the horizontal axis,\\nbeneath which is seen a spirit-level (which is used to bring\\nthe axis to a horizontal position), and n a vertical circle grad-\\nuated into degrees and minutes. This circle serves the pur-\\npose of placing the instrument at any required altitude or dis-\\ntance from the zenith, and of course for determining altitudes\\nand zenith distances.\\n122. Various methods are described in works on practical\\nastronomy, 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\\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 lat-\\nter above it, the instrument will be nearly in the plane of the\\nmeridian. To adjust it more exactly, compare the time oeeu", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0075.jp2"}, "76": {"fulltext": "52\\nTHE EARTH.\\npied by the pole-star in passing from its upper to its lower\\nculmination, with the time of passing from its lower to its upper\\nculmination. These two intervals ought to be precisely equal\\nand if they are so, the instrument is truly placed in the merid-\\nian but if they are not equal, the position of the instrument\\nmust be shifted until they become exactly equal.\\n1 23. The line of collimation of a telescope, is a line joining\\nthe center of the object-glass with the center of the eye-glass.\\nWhen the transit instrument is properly adjusted, this line, as\\nthe instrument is turned on its axis, moves in the plane of the\\nmeridian. Having, by means of the vertical circle w, set the\\ninstrument at the known altitude or zenith distance of any star,\\nupon which we wish to make observations, we wait until the\\nstar enters the field of the tel-\\nescope, and note the exact in-\\nstant when it crosses the ver-\\ntical wire in the center of the\\nfield, which wire marks the\\ntrue plane of the meridian.\\nUsually, however, there are\\nplaced in the focus of the eye-\\nglass five parallel wires or\\nthreads, two on each side of\\nthe central wire, and all at\\nequal distances from each oth-\\ner, as is represented in the\\nfollowing diagram. The time of arriving at each of the wires\\nbeing noted, and all the times added together and divided by\\nthe number of observations, the result gives the instant of\\ncrossing the central wire.\\n124. The astronomical clock is the constant companion of\\nthe transit instrument. It is regulated to keep exact pace with\\nthe stars, and of course with the earth s diurnal rotation that\\nis, it denotes sidereal time, measuring off one hour for every 15\u00c2\u00b0\\nof diurnal motion in a star. The sidereal day begins at the\\nmoment when the vernal equinox crosses the meridian but as\\nthe culmination of the equinox occurs about 4 minutes later\\nfrom day to day through the year the sidereal time may differ", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0076.jp2"}, "77": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 53\\nfrom the solar time by any quantity whatever. The sidereal\\nclock may point to 3h. 20m., in the morning, at noon, or any\\nother time of day, because it merely shows that 3h. 20m. have\\nelapsed since the equinox was on the meridian. Hence, when\\na star is on the meridian, the sidereal clock shows its right as-\\ncension.\\nAn astronomical clock must have a compensation pendulum,\\nand be made as perfect as possible. Its uniformity of move-\\nment can be tested by the transit instrument, and a list of right\\nascensions of stars. It is not so important that it should point\\nto Oh. 0m. 0s. when the equinox is on the meridian, or that it\\nshould not gain or lose compared with the revolution of the\\nstars, as that it should move uniformly through the day, and\\nfrom day to day. It is not customary, therefore, to alter the\\nclock, after it is once set, but to note from day to day how much\\nit is out of the way, and how fast it gains or loses. The first is\\ncalled the error, the last the rate. If these are known, then\\nthe exact time of an observation can be obtained.\\n125. To observe the transit of a star, the eye must discern\\nthe instant of its bisection by the wire, and the ear attend to\\nthe beat of the clock, the seconds being counted from the last\\ncompleted minute before the observation began. If the bi-\\nsection occurs between two beats, as it commonly does, the ob-\\nserver needs much practice to be able to divide the second\\naccurately into tenths, and decide at which of them the transit\\ntakes place. What is now known as the American method of\\nobserving transits, and recording them by electro-magnetism,\\ngives great facility and accuracy to this most difficult and im-\\nportant part of the work.\\nThe pendulum of the observatory clock is arranged to close\\nthe circuit of a battery, and break it again at the beginning of\\nevery beat. The closing of the circuit gives a small lateral\\nmotion to the registering pen, under which the paper is ad-\\nvancing about an inch per second. Thus the seconds are all\\npermanently recorded by notches one inch asunder in a straight\\nFig. 15\\nline, as a, h, c, c. (Fig. 15 The mark at the beginning of\\neach minute has some peculiarity by which it may be distin-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0077.jp2"}, "78": {"fulltext": "54 THE EARTH.\\nguished from the rest. The observer has under his hand a key,\\nwhich by a quick touch will also close and break the circuit.\\nWhenever a star is on one of the wires of the transit telescope,\\nhe touches the key, the pen is moved aside and indents the\\nline, as at A, and the observation is thus recorded and the\\nplace where this motion commenced between the second-marks\\ncan afterwards be carefully examined. Thus, without the dis-\\ntraction of attending to the clock, he can record the transits of\\nall the wires and if he only notices within what minute the\\nwork begins, he can read the entire record with accuracy to\\nthe T V or even the t ^q of a second. Since the general adoption\\nof this method, the number of wires in the focus of the eye-\\nglass has been increased from 5 to 30 or 40, in order to secure\\na more perfect result.\\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.\\nThe Mural Circle is a graduated circle, usually of very large\\nsize, fixed permanently in the plane of the meridian, and at-\\ntached firmly to a perpendicular wall. It is made of large size,\\nsometimes 11 feet in diameter, in order that very small angles\\nmay be measured on its limb and it is attached to a massive\\nwall of solid masonry in order to insure perfect steadiness, a\\npoint the more difficult to attain in proportion as the instru-\\nment is heavier. The annexed diagram represents a Mural\\nCircle ~B.xed to its wall and ready for observations. It will be\\nseen that every expedient is employed to give the instrument\\nfirmness of parts and steadiness of position. Its radii are com-\\nposed of hollow cones, uniting lightness and strength, and its\\ntelescope revolves on a large horizontal axis, fixed as firmly as\\npossible in a solid wall. The graduations are made on the\\nouter rim of the instrument, and are read off by six microscopes\\n(called reading microscopes), attached to the wall, one of which\\nis represented at A, and the places of the five others are marked\\nby the letters B, C, D, E, F. Six are used, in order that by\\ntaking the mean of such a number of readings, a higher de-\\ngree of accuracy may be insured, than could be obtained by a", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0078.jp2"}, "79": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\nFig. 16.\\n55\\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\\nthe principle of the micrometer. This is effected by placing\\nin the focus a delicate wire, which may be moved by means of\\na screw in a direction parallel to the divisions of the limb, and\\nwhich is so adjusted to the screw as to move over the whole\\nmagnified space of five minutes by five revolutions of the screw.\\nOf course one revolution of the screw measures one minute.\\nMoreover, if the screw itself is made to carry an index attached\\nto its axis and revolving with it over a disk graduated into\\nsixty equal parts, then the space measured by moving the in-\\ndex over one of these parts will be one second.\\n127. We have before shown (Art. 124), the method of find-\\ning the right ascension of a star by means of the Transit In-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0079.jp2"}, "80": {"fulltext": "56\\nTHE EARTH.\\nThen its meridian\\nstrument and the clock. The declination may be obtained by-\\nmeans of the mural circle in several different ways, our object\\nbeing always to find the distance of the star, when on the\\nmeridian, from the equator (Art. 37). First, the declination\\nmay be found from the meridian altitude. Let S (Fig. 17) be\\nthe place of a star when on the meridian,\\naltitude will be SH, which will best\\nbe found by taking its zenith distance\\nZS, of which it is the complement.\\nFrom SH subtract EH, the elevation\\nof the equator, which equals the co-\\nlatitude of the place of observation\\n(Art. 44), and the remainder, SE, is the\\ndeclination. Or, if the star is nearer\\nthe horizon than the equator is, as at\\nS subtract its meridian altitude from\\nthe co-latitude, for the declination.\\nSecondly, the declination may be found from the north polar\\ndistance, of which it is the complement. Thus from P to E is\\n90\u00c2\u00b0. Therefore, PE-PS=90\u00c2\u00b0-PS=SE=the declination. The\\nheight of the pole P is always known when the latitude of the\\nplace is known, being equal to the latitude.\\n12S. The astronomical instruments already described are\\nadapted to taking observations on the meridian only, but we\\nsometimes require to know the altitude of a celestial body\\nwhen it is not on the meridian, and its azimuth, or distance\\nfrom the meridian measured on the horizon and also the\\nangular distance between two points on any part of the celes-\\ntial sphere. An instrument especially designed to measure\\naltitudes and azimuths, is called an Altitude and Azimuth\\nInstrument, whatever may be its particular form. When a\\npoint is on the horizon, its distance from the meridian, or its\\nazimuth, may be taken by the common surveyor s compass,\\nthe direction of the meridian being determined by the needle\\nbut when the object, as a star, is not on the horizon, its azimuth,\\nit must be remembered, is the arc of the horizon from the\\nmeridian to a vertical circle passing through the star (Art. 27)\\nat whatever different altitudes, therefore, two stars may be,\\nand however the plane which passes through them may be", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0080.jp2"}, "81": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 57\\ninclined to the horizon, still it is their angular distance meas-\\nured on the horizon which determines their difference of\\nazimuth. Figure 18 represents an Altitude and Azimuth In-\\nstrument, several of the usual appendages and subordinate\\ncontrivances being omitted for the sake of distinctness and\\nsimplicity. Here abc is the vertical or altitude circle, and EFG\\nthe horizontal or azimuth circle AB is a telescope mounted\\nFig. 18.\\non a horizontal axis and capable of two motions, one in alti-\\ntude parallel to the circle abc, and the other in azimuth parallel\\nto EFG. Hence it can be easily brought to bear upon any\\nobject. At m, under the eye-glass of the telescope, is a small\\nmirror placed at an angle of 45\u00c2\u00b0 with the axis of the telescope,\\nby means of which the image of the object is reflected up-\\nward, so as to be conveniently presented to the eye of the ob-\\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, eacli foot being\\nfurnished with a screw for leveling.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0081.jp2"}, "82": {"fulltext": "58\\nTHE EARTH.\\n1 29. 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, I and H are two small\\nmirrors, and T a small telescope. ID represents a movable\\narm, or radius, which carries an index at D. The radius turns\\non a pivot at I, and the index moves on a graduated arc EF.\\nFig, 19.\\nI is called the Index Glass and H the Horizon Glass. The\\nunder part only of the horizon glass is coated with quicksilver,\\nthe upper part being left transparent so that while one object\\nis seen through the upper part by direct vision, another may\\nbe seen through the lower part by reflection from the two\\nmirrors. The instrument is so contrived, that when the index is\\nmoved up to F, where the zero-point is placed, or the gradu-\\nation begins, the two reflectors I and H are exactly parallel to\\neach other. If we now look through the telescope, T, so point-\\ned as to see the star S through the transparent part of the\\nhorizon glass, we shall see the same star, in the same place,\\nreflected from the silvered part for the star (or any similar\\nobject) is at such a distance that the rays of light which strike\\nupon the index glass I, are parallel to those which enter the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0082.jp2"}, "83": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 59\\neye directly, and will exhibit the object at the same place.\\nNow, suppose we wish to measure the angular distance be-\\ntween two bodies, as the moon and a star, and let the star be\\nat S and the moon at M. The telescope being still directed\\nto S, turn the index arm ID from F toward E until the image\\nof the moon is brought down to S, its lower limb just touching\\nS. By a principle in optics, the angular distance between the\\nmoon and its image, is twice the angle between the mirrors.\\nBut the mirror has passed over the graduated arc FD there-\\nfore double that arc is the angular distance between the star\\nand the moon s lower limb. If we then bring the upper limb\\ninto contact with the star, the sum of both observations, divided\\nby 2, will give the angular distance between the star and the\\nmoon s center. As each degree on the limb EF measures two\\ndegrees of angular distance, hence the divisions for single\\ndegrees 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,\\none of the objects, and the point in the horizon directly be-\\nneath, the other, we thus obtain the altitude of the object. In\\nthis observation, the horizon is viewed through the transparent\\npart of the horizon-glass. At sea, where the horizon is usually\\nwell defined, the horizon itself may be used for taking altitudes\\nbut on land, inequalities of the earth s surface oblige us to have\\nrecourse to an artificial horizon. This, in its simple state, is a\\nbasin of either water or quicksilver. By this means we see\\nthe image of the sun (or other body) just as far below the\\nhorizon as it is in reality above it. Hence, if we turn the\\nindex-glass until the limb of the sun, as reflected from it, is\\nbrought into contact with the image seen in the artificial\\nhorizon, we obtain double the altitude.*\\nWoodhouse s Ast., p. 774.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0083.jp2"}, "84": {"fulltext": "n\\n60 THE EARTH.\\nThe sextant must be held in such a manner that its plane\\nshall pass through the plane of the two objects. It must be\\nheld, therefore, in a vertical plane in taking altitudes, and in a\\nhorizontal plane in taking the horizontal diameters of the sun\\nand moon. Holding the instrument in the true plane of the\\ntwo bodies, whose angular distance is measured, is indeed the\\nmost difficult part of the operation.\\nThe peculiar value of the sextant consists in this, that the\\nobservations taken with it are not affected by any motion in\\nthe observer hence it is the chief instrument used for angular\\nmeasurements at sea.\\n131. Examples illustrating the use of the Sextant.\\nEx. 1. Alt. O s lower limb, 49\u00c2\u00b0 10 00\\nO 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 s upper limb above the image in the artificial\\nhorizon, 100\u00c2\u00b0 2 47\\nTrue altitude, 50\u00c2\u00b0 01 23 .5\\nO s semi-diameter, 00 15 50.\\n49\u00c2\u00b0 45 33 .5\\nEefraction, 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\\n132. Given the surfs Right Ascension and Declination, to\\nfind his Longitude and the Obliquity of the Ecliptic.\\n49\u00c2\u00b0\\n25\\n51\\n00\\n00\\n49\\n49\u00c2\u00b0\\n25\\n02\\n00\\n00\\n06\\nYoung s Spherical Trigonometry, p. 136. Vince s Complete System, vol. i.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0084.jp2"}, "85": {"fulltext": "ASTRONOMICAL PROBLEMS. 61\\nLet POP (Fig. 20) represent the celestial meridian that\\npasses through the first of Cancer and Capricorn (the solstitial\\ncolure), PP the axis of the sphere, EQ the equator, E C the\\necliptic, and PSP the declination\\ncircle (Art. 37) passing through the, Fl s- 20\\nsun S then ARS is a right angle,\\nand in the right-angled spherical\\ntriangle AKS, are given the right\\nascension AK (Art. 37), and the dec-\\nlination KS, to find the longitude\\nAS and the obliquity SAK.\\nAs longitude and right ascension\\nare measured from A, the first point\\nof Aries, in the direction AS of the\\nsigns, quite round the globe, when, of the four quantities men-\\ntioned in the problem, the obliquity and the declination are\\ngiven to find the others, we must know whether the sun is\\nnorth, or whether it is south of the equator, the longitude\\nbeing in the one case AS, and in the other, instead of AS it\\nis 360\u00e2\u0080\u0094 AS when near the same equinox, A. We must also\\nknow on which side of the tropic the sun is, for the sun in\\npassing from one of the tropics to the equinox, passes through\\nthe same degrees of declination as it had gone through in as-\\ncending from the other equinox to the tropic, although its\\nlongitude and right ascension go on continually increasing.\\nFrom the 21st of March to the 21st of June, while describing\\nthe firbt quadrant from the vernal equinox, the declination is\\nnorth and increasing; north, but decreasing, in the second\\nquadrant, until the 23d of September; south and increasing\\nin the third quadrant, until the 21st of December and finally,\\nin the fourth quadrant, south but decreasing until the 21st of\\nMarch.\\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.\\nApplying Napie^s Mule* to the right-angled triangle APS,\\nwe have\\nThe student is supposed to be acquainted with Spherical Trigonometry; but\\nto refresh his memory, we may insert a remark or two.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0085.jp2"}, "86": {"fulltext": "62\\nTHE EARTH.\\n1. Rad cos AS cos AR cos RS.\\n2. Rad sin AE=tan RS cot A.-, cot A= _ rad m AR\\ntan RS\\nHence the computation for AS and A is as follows\\nFor the Longitude AS.\\ncos AR 53\u00c2\u00b0 38 00 9.7730185\\ncosRS 19 15 57 9.9749710\\ncos AS 55 57 43 9.7479895\\nFor the Obliquity A.\\nsinAR 9.9059247\\ntan RS, ar. com. 0.4565209\\ncot A 23\u00c2\u00b0 27 50i\\n10.3624456\\nFie. 21.\\nIt will be recollected that in Napier s rule for the solution of a right-angled\\nspherical triangle, 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\\nthree sides and the two oblique angles. If we take any one of these as a middle\\npart, the two which lie next to it on each side will be adjacent parts. Thus (in\\nFig. 21), taking A for a middle part, b and c will be the adjacent parts if we\\ntake c for the middle part, A and B will\\nbe the adjacent parts if we take B for\\nthe middle part, c and a will be the ad-\\njacent parts but if we take a for the\\nmiddle part, then as the angle C is not\\nconsidered as one of the circular parts, B\\nand b are the adjacent parts and, lastly,\\nif b is the middle part, then the adjacent\\nparts are A and a. The two parts immediately beyond the adjacent parts on\\neach side, still disregarding the right angle, are called the opposite parts thus,\\nif A is the middle part, the opposite parts are a and B. Napier s rule is as\\nfollows\\nRadius into the sine of the middle part, equals the product of the tangents of the adjacent\\nparts, or of the cosines of Ike opposite parts.\\n(The corresponding vowels are marked to aid the memory In the use of this\\nrule, it must be understood that the complements of the angles and the hypote-\\nnuse are used, instead of those parts themselves. Thus, if A is middle part, we\\nsay rad X cos A, not rad X sin A, and sc of B or, if A B is adjacent part, we use\\ncot AB, not tan AB if opposite, sin AB, not cos AB, c\\nExamples. 1. In the right-angled triangle ABC, are given the two perpen-\\ndicular sides, viz., a=48\u00c2\u00b0 24 10 6=59\u00c2\u00b0 88 27 to find the hypotenuse c. The\\nhypotenuse being made the middle part, the other sides become the opposite\\nparts, being separated from the middle part by the angles A and B. Hence,\\ncos a cos b\\nRad cos c=cos a cos b cos c= =70 28 40\\nrad\\n2. In the spherical triangle, right-angled at C, are given two perpendicular\\nsides, viz., a\u00e2\u0080\u0094 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., b, which make\\nthe middle part. Then,\\nRadXsin 6=cot A tan a\\nradXsm b\\ncot A=\u00e2\u0080\u0094 6\\ntan a\\n13", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0086.jp2"}, "87": {"fulltext": "ASTRONOMICAL PROBLEMS. 63\\nEx. 2. On the 31st of March, 1816, the sun s Declination was\\nobserved at Greenwich to be 4\u00c2\u00b0 13 31-J- 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-\\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 8 s 7\u00c2\u00b0 40 56 and the\\nObliquity 23\u00c2\u00b0 27 42^ what was the Right Ascension in\\ntime? Ans. 16h. 23m. 34s.\\n133. Given the sun s Declination to find the time of his\\nRising and 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 ap-\\nparent path of the sun on the pro-\\nposed day, cutting the horizon in S.\\nThen the arc EZ will be the latitude\\nof the place, and consequently EH,\\nor its equal QO, will be the co-lati-\\ntude, and this measures the angle\\nOAQ also RS will be the sun s dec-\\nlination, and AR expressed in time\\nwill be the time of rising before 6\\no clock. For it is evident that it\\nwill be sunrise when the sun arrives at the horizon at S but\\nPP being an hour circle whose plane is perpendicular to the\\nmeridian (and of course projected into a straight line on the\\nplane of projection), the time the sun is passing from S to S\\ntaken from the time of describing S L, which is six hours, must\\nbe the time from midnight to sunrise. But the time of de-\\nscribing SS is measured on the corresponding arc of the equi-\\nnoctial AR.\\nIn the right-angled triangle ARS, we have the declination\\nRS, and the angle A to find AR. Therefore,\\nRadxsin AR=cot Ax tan RS.\\nEx. 1. Required the time of sunrise at latitude 52\u00c2\u00b0 13 N.\\nwhen the sun s declination is 23\u00c2\u00b0 28", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0087.jp2"}, "88": {"fulltext": "64\\nTHE EARTH.\\nRad\\nCot A or tan 52\u00c2\u00b0 13\\nTan KS= 23\u00c2\u00b0 28\\nSin 34\u00c2\u00b0 03 21 J\\n4*\\n10.\\n10.1105786\\n9.6376106\\n9.7481892\\n2h. 16 13 25\\n6\\n3h. 43 46 35 the time after midnight, and of\\ncourse the time of rising.\\nEx. 2, Kequired 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\u00c2\u00b0\\n12 K when his declination is 18\u00c2\u00b0 40 S.\\nAns. 7h. 35m. 52s.\\n134. Given the Latitude of the place, and the Declination\\nof a heavenly body, to determine its Altitude and Azimuth\\nwhen on the six o clock hour circle.\\nLet HZO (Fig. 23) fee the meridian of the place/Z the zenith,\\nHO the horizon, S the place of the object on the 6 o clock hour\\nFig. 23.\\ncircle PSP which of course\\ncuts the equator in the east and\\nwest points, and ZSB the verti-\\ncal circle passing through the\\nbody. Then in the right-angled\\ntriangle SB A, the given quan-\\ntities are AS, which is the dec-\\nlination, and the arc OP or\\nangle SAB, the latitude of the\\nplace, to find the altitude BS,\\nand the azimuth BO, or the\\namplitude AB, which is its\\ncomplement.\\nEx. 1. What were the altitude and azimuth of Arcturus,\\nwhen upon the six o clock hour circle of Greenwich, lat. 51\u00c2\u00b0\\nDegrees are converted into hours by multiplying by 4 and dividing by 60.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0088.jp2"}, "89": {"fulltext": "ASTRONOMICAL PROBLEMS.\\n65\\n28 40 N. on the first of April, 1822 its declination being\\n20\u00c2\u00b0 6 50 1ST.\\nFor the Altitude.\\nBad 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\\nFor the Azimuth.\\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\\n9.3581067\\nEx. 2. At latitude 62\u00c2\u00b0 12 K the altitude of the sun at 6\\no clock in the morning was found to be 18\u00c2\u00b0 20 23 required\\nhis declination and azimuth.\\nAns. Dec. 20\u00c2\u00b0 50 12 1ST. Az. 79\u00c2\u00b0 56 4\\n135. The Latitudes and Longitudes of two celestial objects\\nbeing given, to find their Distance ajpavt.\\nLet P (Fig. 24) represent the pole of the ecliptic, and PS,\\nPS two arcs of celestial latitude (Art. 37) drawn to the two\\nFig. 24.\\nobjects SS then will these arcs rep-\\nresent the co-latitudes, the angle P\\nwill be the difference of longitude,\\nand the arc SS will be the distance\\nsought. Here we have the two sides\\nand the included angle given to find\\nthe third side. By Napier s Rules\\nfor the solution of oblique-angled spherical triangles (see\\nSpherical Trigonometry), the sum and difference of the two\\nangles opposite the given sides may be found, and thence the\\nangles themselves. The required side may then be found by\\nthe theorem, that the sines of the sides are as the sines of their\\nopposite angles.* The computation is omitted here on account\\nof its great length. If P be the pole of the equator instead of\\nthe ecliptic, then PS and PS will represent arcs of co-declina-\\ntion, and the angle P will denote difference of right ascension.\\nFrom these data, also, we may therefore derive the distance\\nbetween any two stars. Or, finally, if P be the pole of the\\nhorizon, the angle at P will denote difference of azimuth, and\\ns More concise formulas for the solution of this case may be found in Young s\\nTrigonometry, p. 99 Francceur s Uranography, Art. 830 Dr. Bowditch s\\nPractical Navigator, p. 436.\\n5", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0089.jp2"}, "90": {"fulltext": "Ob THE EARTH.\\nthe sides PS, PS zenith distances, from which the side SS\\nmay 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\\nearth is taken as the base line in determining the parallax of\\nthe heavenly bodies, and lies, therefore, at the foundation of\\nall astronomical measurements, it is very important that it\\nshould be ascertained with the greatest possible exactness.\\nHaving now learned the use of astronomical instruments, and\\nthe method of measuring arcs on the celestial sphere, we are\\nprepared to understand the methods employed to determine\\nthe exact figure of the earth. This element is indeed ascer-\\ntained in five different wavs, each of which is independent of\\nall the rest, namely, by investigating the effects of the centrifu-\\ngal force arising from the revolution of the earth on its axis\\nby measuring arcs of the meridian by experiments with the\\npendulum by the unequal action of the earth on the moon,\\narising from the redundance of matter about the equatorial\\nregions and by the precession of the equinoxes. We will\\nbriefly consider each of these methods.\\n137. First, the known effects of the centrifugal force would\\ngive to the earth a spheroidal figure, elevated in the equatorial,\\nand flattened 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\\nto them a greater centrifugal force, and cause the body to\\nswell out into the form of an oblate spheroid.* Even had the\\nsolid part of the earth consisted of unyielding materials and\\nbeen created a perfect sphere, still the waters that covered it\\nwould have receded from the polar and have been accumulated\\nSee a good explanation of this subject in the Edinburgh Encyclopaedia, ii., 665.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0090.jp2"}, "91": {"fulltext": "FIGURE OF THE EARTH.\\n67\\nin the equatorial regions, leaving bare extensive regions on the\\none side, and ascending 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\\nin different latitudes, and the figure of equilibrium which would\\nresult, Newton inferred that the earth must have the form of\\nan oblate spheroid before the fact had been established by ob-\\nservation and he assigned nearly the true ratio of the polar\\nand equatorial diameters.\\n138. Secondly, the spheroidal figure of the earth is proved\\nby actually measuring the length of a degree on the meridian in\\ndifferent 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\\nperfect circle, whose curvature would be equal in all parts\\nbut if we find by actual observation that the curvature of the\\nsection is not uniform, we infer a corresponding departure in\\nthe earth from the figure of a perfect sphere. This task of\\nmeasuring portions of the meridian has been executed in dif-\\nferent countries by means of a system of triangles with aston-\\nishing accuracy.* The result is, that the length of a degree\\nincreases as we proceed from the equator toward the pole, as\\nmay be seen from the following table\\nPlaces of observation.\\nLatitude.\\nLength of a degree\\nin miles.\\nPeru\\n00\u00c2\u00b0 00 f 00\\n39 12 00\\n43 01 00\\n46 12 00\\n51 29 54|\\nQQ 20 10\\n68/732\\n68.896\\n68.998\\n69.054\\n69.146\\n69.292\\nPennsylvania\\nItaly\\nFrance\\nEngland\\nSweden\\nCombining the results of various measurements, the dimen-\\nsions of the terrestrial spheroid are found to be as follows f\\nEquatorial diameter, 7925.308\\nPolar diameter, 7898.952\\nMean diameter, 7912.1 30\\nSee Day s Trigonometry.\\nf Bessel.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0091.jp2"}, "92": {"fulltext": "68 THE EARTH.\\nThe difference between the greatest and least, is 26.356 3^\\nof the greatest. This fraction (3-^7) is denominated the ellip-\\nticity of the earth, being the excess of the transverse over the\\nconjugate axis, on the supposition that the section of the earth\\ncoinciding with the meridian is an ellipse and that such is\\nthe case, is proved by the fact that calculations on this hypoth-\\nesis, of the lengths of arcs of the meridian in different latitudes,\\nagree nearly with the lengths obtained by actual measurement.\\n139. Thirdly, the figure of the earth is shown to he spheroidal\\nby observations 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 dif-\\nferent forces, varies as the square root of the forces* Hence,\\nby carrying a pendulum to different parts of the earth, and\\ncounting the number of vibrations it performs in a given time,\\nwe obtain the relative forces of gravity at those places and\\nthis leads to a knowledge of the relative distance of each place\\nfrom the center of the earth, and finally, to the ratio between\\nthe equatorial and the polar diameters,\\n1 40. Fourthly, that the earth is of a spheroidal figure is\\nmf erred 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\\nlunar motions, the amount of which becomes a measure of the\\nexcess itself, and hence affords the means of determining the\\nearth s ellipticity. This calculation has been made by the most\\nprofound mathematicians, and the figure deduced from this\\nsource corresponds very nearly to that derived from the several\\nother independent methods.\\n141. Fifthly, the spheroidal farm of the earth accounts for\\nthe precession of the equinoxes.\\nIt will be shown in Chap. IT., Part II., that the slow back-\\nward motion of the equinoctial points on the ecliptic is due to\\nthe attraction of the sun and moon upon the belt of matter on\\nMechanics, Art. 161.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0092.jp2"}, "93": {"fulltext": ".DENSITY OF THE EARTH.\\n69\\nthe equator, combined with the inertia of the earth in its rota-\\ntion on its axis.\\nWe thus have the shape of the earth established upon the\\nmost satisfactory evidence, and are furnished with a starting\\npoint from which to determine various measurements among\\nthe heavenly bodies.\\nFig. 25.\\n1\\n141 The density of the earth compared with water, that\\nis, its specific gravity, is 5^.* The density was first estimated\\nby Dr. Hutton, from observations made by Dr. Maskelyne,\\nAstronomer Royal, on Sehehallien, a mountain of Scotland, in\\nthe year 177-1. Thus, let M\\n(Fig. 25) represent the moun-\\ntain, D, B, two stations on op-\\nposite sides of the mountain,\\nand I a star; and let IE and\\nIG be the zenith distances as\\ndetermined by the differences\\nof latitudes of the two stations.\\nBut the apparent zenith dis-\\ntances as determined by the\\nplumb-line are IE and IG\\nThe deviation toward the moun-\\ntain on each side exceeded 7 .f\\nThe attraction of the mountain\\nbeing observed on both sides\\nof it, and its mass being computed from the number of sec-\\ntions taken -in all directions, these data, when compared with\\nthe known attraction and magnitude of the earth, led to a\\nknowledge of its mean density. According to Dr. Hutton,\\nthis is to that of water as 9 to 2 but later and more accurate\\nestimates have made the specific gravity of the earth as stated\\nabove. But this density is nearly double the average density\\nof the materials that compose the exterior crust of the earth,\\nshowing a great increase of density toward 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\\nthe other members of the solar system.\\nBaily, Ast. Tables, p. 21.\\nf Eobison s Phys. Ast.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0093.jp2"}, "94": {"fulltext": "PART II.\u00e2\u0080\u0094 OF THE SOLAR SYSTEM\\n142. Haying- considered the Earth, in its astronomical re-\\nlations, and the Doctrine of the Sphere, we proceed now to a\\nsurvey of the Solar System, and shall treat successively of the\\nSun, Moon, Planets, and Comets.\\nCHAPTEE I.\\nOF THE SUN SOLAK SPOTS ZODIACAL LIGHT.\\n143. The figure which the sun presents to us is that of a\\nperfect circle, whereas most of the planets exhibit a disk more\\nor less elliptical, indicating that the true shape of the body is\\nan oblate spheroid. So great, however, is the distance of the\\nsun, that a line 400 miles long would subtend an angle of only\\n1 at the eye, and would, therefore, be the least space that\\ncould be measured. Hence, were the difference between two\\nconjugate diameters of the sun any quantity less than this, we\\ncould not determine by actual measurement that it existed at\\nall. Still we learn from theoretical considerations, founded\\nupon the known effects of centrifugal force, arising from the\\nsun s revolution on his axis, that his figure is not a perfect\\nsphere, but is slightly spheroidal.*\\n144. The distance of the sun from, the earth is nearly\\n95,000,000 miles. For, its horizontal parallax being 8 .6\\n(Art. 86), and the semi-diameter of the earth 3956 miles,\\nSin 8 .6 3956 Rad 95,000,000 nearly.\\nIn order to form some faint conception at least of this vast\\ndistance, let us reflect that a railway car, moving at the rate of\\n20 miles per hour, would require more than 500 years to reach\\nthe sun.\\ns See Me canique Celeste, iii., p. 165. Delambre, t. i., p. 483.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0094.jp2"}, "95": {"fulltext": "SOLAR SPOTS.\\n71\\n145. The apparent diameter of the sun may be found either\\nby the Sextant (Art. 129), by an instrument called the Heli-\\nometer, specially designed for measuring its angular breadth,\\nor by the time it occupies in crossing the meridian.\\nThe last is the most accurate. If the sun, when on the\\nequator, March 21 or September 22, is found to cross the me-\\nridian in 2m. 10s., sidereal time* then 24h. 2m. 10s. 360\u00c2\u00b0 32\\n30 the angular breadth of the sun. But if the sun ha s a dec-\\nlination north or south, the degrees of the diurnal circle on\\nwhich he moves are shorter than those on the equator, in the\\nratio of the cosine of declination to radius and therefore the\\ntime of crossing is lengthened; hence the calculated breadth\\nmust be diminished in the same ratio. Having the distance\\nand angular diameter, we can easily find its\\nlinear diameter. Let E (Fig. 26) be the\\nearth, S the sun, ES a line drawn to the\\ncenter of the disk, and EC a line drawn\\ntouching the disk at C. Join SG then\\nKad ES sin 16 1 .5 (the sun s mean\\napparent semidiameter) SC =442,840 miles.\\n2x442840\\n112 nearly that is,\\nFig. 26.\\nAnd\\n7912\\nit\\nwould require one hundred and twelve bodies\\nlike the earth, if laid side by side, to reach\\nacross the diameter of the sun. Since spheres\\nare to each other as the cubes of their diam-\\neters, I s 112 3 1 1,400,000 nearly that\\nis, the sun is- about 1,400,000 times as large as the earth.\\n146. In density the sun is only one-fourth that of the\\nearth, being but a little heavier than water (Art. 141 and\\nsince the quantity of matter, or mass of a body, is proportion-\\ned to its magnitude and density, hence 1,400,000x^=350,000;\\nthat is, the quantity of matter in the sun is three hundred and\\nfifty thousand (or, more accurately, 354,936) times as great as\\nin the earth. Now the weight of bodies (which is a measure\\nof the force of gravity) varies directly as the quantity of mat-\\nter, and inversely as the square of the distance. A body,\\ntherefore, would weigh 350,000 times as much on the surface\\nof the sun as on the earth, if the distance of the center of force", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0095.jp2"}, "96": {"fulltext": "72\\nTHE SUN.\\nwere the same in both cases; but since the attraction of a\\nsphere is the same as though all the matter were collected in\\nthe center, consequently, the weight of a body, so far as it de-\\npends on its distance from the center of force, would be the\\nsquare of 112 times less at the sun than at the earth. Or, put-\\nting W for the weight at the .earth, and W for the weight at\\nthe sun, then\\nHence a body would weigh nearly 28 times as much at the\\nsun as at the earth. A man weighing 200 lbs. would, if trans-\\nported to the surface of the sun, weigh 5,580 lbs., or nearly 2J-\\ntons. To lift one s limbs would, in such a case, be beyond the\\nordinary power of the muscles. At the surface of the earth a\\nbody falls through 16 T feet in a second and since the spaces\\nare as the velocities, the times being equal, and the velocities\\nas the forces, therefore a body would fall at the sun in one\\nsecond through 16 T 1 2x27 T 9 o =448.7 feet.\\nSOLAR SPOTS.\\n147. The surface of the sun, when viewed with a tele-\\nscope, often shows dark spots, which vary much, at different\\ntimes, in number, figure, and extent. One hundred or more,\\nassembled in several distinct groups, are sometimes visible at\\nonce on the solar disk. The solar spots are commonly very\\nsmall, but occasionally a spot of enormous size is seen occupy-\\ning an extent of 50,000 miles or more in diameter. They are\\nsometimes even visible to the naked eye, when the sun is\\nviewed through colored glass, or when near the horizon, it is\\nseen through light clouds or vapors. When it is recollected\\nthat 1 of the solar disk implies an extent of 400 miles (Art.\\n143), it is evident that a space large enough to be seen by the\\nnaked eye, must cover a very large extent.\\nFig. 27 exhibits the appearance of solar spots, though much\\ntoo large compared with the disk. Whenever a spot is seen near\\nthe edge of the disk, it appears foreshortened by perspective,\\nas in the figure. A solar spot usually consists of two parts,\\nthe nucleus and the umhra. The nucleus is black, of a very\\nirregular shape, and is subject to great and sudden changes", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0096.jp2"}, "97": {"fulltext": "SOLAR SPOTS.\\n73\\nboth in form and size. A Fi S- 27-\\nspot sometimes divides into\\nmany smaller ones, and again\\na group may be united into a\\nsingle spot. The umbra is a\\nwide margin of lighter shade,\\nand is commonly of greater\\nextent than the nucleus. The\\nspots are usually confined to\\na zone extending across the\\ncentral regions of the sun, not\\nexceeding 60\u00c2\u00b0 in breadth. When the spots are observed from\\nday to day, they are seen to move across the disk of the sun,\\noccupying about two weeks in passing from one limb to the\\nother. After an absence of about the same period, the spot\\nreturns, having taken 27d. 7h. 37m. in the entire revolution.\\n148. Besides the fact of foreshortening already mentioned,\\nthere is another proof that the spots are at the surface of the\\nsun. Were they bodies at a distance\\nfrom it, the time during which they\\nwould be seen on the solar disk would\\nbe less than that occupied in the re-\\nmainder of the revolution. Thus, let S\\n(Fig. 28) be the sun, E the earth, and\\ndbc the path of the body revolving\\nabout the sun. Unless the spot were\\nnearly or quite in contact with the\\nbody of the sun, being projected upon\\nhis disk only while passing from o to\\nc, and being invisible while describing\\nthe arc cab, it would of course be out\\nof sight longer than in sight, whereas\\nthe two periods are found to be equal.\\nMoreover, the lines which all the solar\\nspots describe on the disk of the sun\\nare found to be parallel to each other,\\nlike the circles of diurnal revolution\\naround the earth and hence it is in-\\nferred that they arise from a similar cause, namely, the rcrohi-\\nFig. 28.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0097.jp2"}, "98": {"fulltext": "74: THE SUN.\\ntion of the sun on his axis, a fact which is thus made known\\nto us.\\nBut although the spots occupy about 27i days in passing\\nfrom one limb of the sun around to the same limb again, yet\\nthis is not the period of the sun s revolution on his axis, but\\nexceeds it by nearly two days. For, let AA B (Fig. 29) repre-\\nsent the sun, and EE M the orbit of the earth. When the\\nearth is at E, the visible disk of the\\nsun will be AA B and if the earth\\nremained stationary at E, the time oc-\\ncupied by a spot after leaving A until\\nit returned to A, would be just equal\\nto the time of the sun s revolution on\\nhis axis. But during the 27^ days in\\nwhich the spot has been performing\\nits apparent revolution, the earth has\\nbeen advancing in her orbit from E to\\nE where the visible disk of the sun is\\nA B Consequently, before the spot\\ncan appear again on the limb from which it set out, it must\\ndescribe so much more than an entire revolution as equals the\\narc AA which equals the arc EE Hence,\\n365d. 5h. 4Sm. 27d. 7h. 37m. 365d. 5h. 48m. 27d. Yh.\\n37m. 25d. 9h. 59m.=the time of the sun s revolution on\\nhis axis.\\n1 49. If the path which the spots appear to describe by the\\nrevolution of the sun on his axis left each a visible trace on his\\nsurface, they would form, like the circles of diurnal revolution\\non the earth, so many parallel rings, of which that which\\npassed through the center would constitute the solar equator,\\nwhile those on each side of this great circle would be small\\ncircles, corresponding to parallels of latitude on the earth. Let\\nus conceive of an artificial sphere to represent the sun, having\\nsuch rings plainly marked on its surface. Let this sphere be\\nplaced at some distance from the eye, with its axis perpendicu-\\nlar to the axis of vision, in which case the equator would coin-\\ncide with the line of vision, and its edge be presented to the\\neye. It would therefore be projected into a straight line. The\\nsame would be the case with all the smaller rings, the distance", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0098.jp2"}, "99": {"fulltext": "SOLAR SPOTS. 75\\nbeing supposed such that the rays of light come from them all\\nto the eye nearly parallel. Now let the axis, instead of being\\nperpendicular to the line of vision, be inclined to that line,\\nthen all the rings being seen obliquely, would be projected\\ninto ellipses. If, however, while the sphere remained in a\\nfixed position, the eye were carried around it (being always in\\nthe same plane) twice during the circuit, it would be in the\\nplane of the equator, and project this and all the smaller\\ncircles into straight lines and twice, at points 90\u00c2\u00b0 distant from\\nthe foregoing positions, the eye would be at a distance from\\nthe planes of the rings equal to the inclination of the equator\\nof the sphere to the line of vision. Here it would project the\\nrings into wider ellipses than at other points and the ellipses\\nwould become more and more eccentric as the eye departed\\nfrom either of these points, until they vanished again into\\nstraight lines.\\n150. It is in a similar manner that the eye views the paths\\ndescribed by the spots on the sun. If the sun revolved on an\\naxis perpendicular to the plane of the earth s orbit, the eye be-\\ning situated in the plane of revolution, and at such a distance\\nfrom the sun that the light comes to the eye from all parts of\\nthe solar disk nearly parallel, the paths described by the spots\\nwould be projected into straight lines, and each would describe\\na straight line across the solar disk, parallel to the plane of\\nrevolution. But the axis of the sun is inclined to the ecliptic\\nabout Yi\u00c2\u00b0 from a perpendicular, so that usually all the circles\\ndescribed by the spots are projected into ellipses. The breadth\\nof these, however, will vary as the eye, in the annual revolu-\\ntion, is carried around the sun, and when the eye comes into\\nthe plane of the rings, as it does twice a year, they are pro-\\njected into straight lines, and for a short time a spot seems\\nmoving in a straight line inclined to the plane of the ecliptic\\n7i\u00c2\u00b0. The two points where the sun s equator cuts the ecliptic\\nare called the sun s nodes. The longitudes of the nodes are\\n80\u00c2\u00b0 V 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\\ntimes that the spots appear to describe straight lines. We\\nhave mentioned the various changes in the apparent paths of\\nthe solar spots, which arise from the inclination of the sun s", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0099.jp2"}, "100": {"fulltext": "76\\nTHE SUN.\\naxis to the plane of the ecliptic but it was in fact by first ob-\\nserving these changes, and proceeding in the reverse order\\nfrom that which we have pursued, that astronomers ascer-\\ntained that the sun revolves on his axis, and that this axis is\\ninclined to the ecliptic 82f\u00c2\u00b0.\\n151. Besides the spots already described, there are faint\\ninequalities of light over the general surface, in delicate lines\\nand freckles, which are also perpetually changing. These are\\ncalled faculcB.\\nThe theory, which is generally received, regards the visible\\nsurface of the sun as an incandescent, gaseous substance,\\nalways in violent commotion, and sometimes rent here and\\nthere by a broad opening, which reveals a lower stratum of\\nless illumination. This is the umbra of a spot and a smaller\\nrupture in that shows a still lower stratum, or else the solid\\nbody of the sun, as the nucleus of the same. These apertures\\nin the luminous strata may be caused, as some think, by vol-\\ncanic action below, or according to others, by storms or tor-\\nnadoes in the solar atmosphere.\\nZODIACAL LIGHT.\\n152. The Zodiacal Light is\\na faint light resembling the tail\\nof a comet, and is seen at cer-\\ntain seasons of the year following\\nthe course of the sun after even-\\ning twilight, or preceding his\\napproach in the morning sky.\\nFigure 30 represents its appear-\\nance as seen in the evening, in\\nMarch, 1836. The following are\\nthe leading facts respecting it.\\n1. Its form is that of a lumi-\\nnous triangle, having its base\\ntoward the sun. It reaches to\\nan immense distance from the\\nsun, sometimes even beyond the\\nFig. 30.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0100.jp2"}, "101": {"fulltext": "ZODIACAL LIGHT. 77\\norbit of the earth. It is brighter in the parts nearer the sun\\nthan in those that are more remote, and terminates in an ob-\\ntuse apex, its light fading away by insensible gradations, until\\nit becomes too feeble for distinct vision. Hence its limits are, at\\nthe same time, fixed at different distances from the sun by dif-\\nferent observers, according to their respective powers of 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\\n18 it becomes visible before the dawn of day, rising along\\nnorth of the ecliptic, and terminating above the nebula of\\nCancer. About the middle of November, its vertex is in the\\nconstellation Leo. At this time no traces of it are seen in the\\nwest after sunset, but about the first of December it becomes\\nfaintly visible in the west, crossing the Milky Way near the\\nhorizon, and reaching from the sun to the head of Capri-\\ncornus, forming, as its brightness increases, a counterpart to\\nthe Milky Way, between which on the right, and the Zodiacal\\nLight on the left, lies a triangular space embracing the Dol-\\nphin. Through the month of December, the Zodiacal Light is\\nseen on both sides of the sun, namely, before the morning\\nand after the evening twilight, sometimes extending 50\u00c2\u00b0 west-\\nward, and 70\u00c2\u00b0 eastward of the sun at the same time. After it\\nbegins to appear in the western sky, it increases rapidly\\nfrom night to night, both in length and brightness, and with-\\ndraws itself from the morning sky, where it is scarcely seen\\nafter the month of December, until the next October.\\n3. The Zodiacal Light moves through the heavens in the\\norder of the signs. It moves with unequal velocity, being\\nsometimes stationary and sometimes retrograde, while at other\\ntimes it advances much faster than the sun. In February and\\nMarch, it is very conspicuous in the west, reaching to the\\nPleiades and beyond but in April it becomes more faint, and\\nnearly or quite disappears during the month of May. It is\\nscarcely seen in this latitude during the summer months.\\n4. It is remarkably conspicuous at \u00e2\u0096\u00a0certain periods of a few\\nyears, and then for a long interval almost disappears.\\n5. The Zodiacal Light toas formerly held to he the atmos-\\nphere of the sun.* But La Place has shown that the solar\\nMairan, Memoirs French Academy, for 1783.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0101.jp2"}, "102": {"fulltext": "78 THE STTN.\\natmosphere could never reach so far from the sun as this light\\nis seen to extend.* It has been supposed by others to be a\\nnebulous body revolving around the sun. From recent obser-\\nvations, made with care in various parts of tropical America,\\nthere appears to be strong evidence that the Zodiacal Light is\\na belt which entirely surrounds the earth.f\\nCHAPTEK II.\\nOF THE APPAEENT ANNUAL MOTION OF THE SUN SEASONS\u00e2\u0080\u0094 FIG-\\n153. The revolution of the earth around the sun once a\\nyear, produces an apparent motion of the sun around the earth\\nin the same period. When bodies are at such a distance from\\neach other as the earth and the sun, a spectator on either\\nwould project the other body upon the concave sphere of the\\nheavens, always seeing it on the opposite side of a great circle,\\n180\u00c2\u00b0 from himself. Thus, when the earth arrives at Libra\\n(Fig. 11), we see the sun in the opposite sign Aries. When\\nthe earth moves from Libra to Scorpio, as we are unconscious\\nof our own motion, the sun it is that appears to move from\\nAries to Taurus, being always seen in the heavens, where a\\nline drawn from the eye of the spectator through the body\\nmeets the concave sphere of the heavens. Hence the line of\\nprojection carries the sun forward on one side of the ecliptic,\\nat the same rate as the earth moves on the opposite side and\\ntherefore, although we are unconscious of our own motion, we\\ncan read it from day to day in the motions of the sun. If we\\ncould see the stars at the same time with the sun, we could\\nactually observe from day to day the sun s progress through\\nthem, as we observe the progress of the moon at night only\\nthe sun s rate of motion would be nearly fourteen times slower\\nthan that of the moon. Although we do not see the stars\\nMec. Celeste, iii., 525.\\nf See a paper by Rev. Geo. Jones, U. S. Navj Proc. Amer. Assoc, 1859, p.\\n172.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0102.jp2"}, "103": {"fulltext": "ANNUAL MOTION. i\\nwhen the sun is present, yet after the sun is set, we can ob-\\nserve that it makes daily progress eastward, as is apparent\\nfrom the constellations of the Zodiac occupying, successively,\\nthe western sky after sunset, proving that either all the stars\\nhave a common motion westward independent of their diurnal\\nmotion, or that the sun has a motion past them, from west to\\neast. TTe shall see hereafter abundant evidence to prove that\\nthis change in the relative position of the sun and stars, is\\nowing to a parallactic change in the place of the sun, and not\\nto any change in the stars.\\n154. Although the apparent revolution of the sun is in a\\ndirection opposite to the real motion of the earth, as regards\\nabsolute space, yet both are nevertheless from west to east,\\nsince these terms do not refer to any directions in absolute\\nspace, but to the order in which certain constellations (the con-\\nstellations of the Zodiac) succeed one another. The earth itself,\\non opposite sides of its orbit, does, in fact, move toward di-\\nrectly opposite points of space but it is all the while pursuing\\nits course in the order of the signs. In the same manner,\\nalthough the earth turns on its axis from west to east, yet any\\nplace on the surface of the earth is moving in a direction in\\nspace exactly opposite to its direction twelve hours before. If\\nthe sun left a visible trace on the face of the sky, the ecliptic\\nwould, of course, be distinctly marked on the celestial sphere\\nas it js, on an artificial globe and were the equator delineated\\nin a similar manner (by any method like that supposed in Art.\\n46), we should then see at a glance the relative position of\\nthese two circles the points where they intersect one another\\nconstituting the equinoxes, the points where they are at the\\ngreatest 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\\nwill even aid the learner to have constantly before his mental\\nvision, an imaginary delineation of these two important circles\\non the face of the sky.\\n155. The 7nethod of ascertaining the nature and position of\\nthe earth s orbit is by observations on the sun s Declination and\\nRight Ascension.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0103.jp2"}, "104": {"fulltext": "80 THE SUN.\\nThe exact declination of the sun at any time is determined\\nfrom his meridian altitude or zenith distance, the latitude of\\nthe place of observation being known (Art. 37). The instant\\nthe center of the sun is on the meridian (which instant is given\\nby the transit instrument), we take the distance of his upper\\nand that of his lower limb from the zenith half the sum of the\\ntwo observations corrected for refraction, gives the zenith dis-\\ntance of the center. This result is diminished for parallax\\n(Art. 84), and we obtain the zenith distance as it would be if\\nseen from the center of the earth. The zenith distance being\\nknown, the declination is readily found by subtracting that\\ndistance from the latitude. By thus taking the sun s declina-\\ntion for every day of the year at noon, and comparing the\\nresults, we learn its motion to and from the equator.\\n156. To obtain the motion in right ascension, we observe,\\nwith a transit instrument, the instant when the center of the\\nsun is on the meridian. Our sidereal clock gives us the right\\nascension in time (Art. 124), which we may easily, if we\\nchoose, convert into degrees and minutes, although it is more\\ncommon to express right ascension by hours, minutes, and\\nseconds. The differences of right ascension from day to day\\nthroughout the year, give us the sun s annual motion parallel\\nto the equator. From the daily records of these two motions,\\nat right angles to each other, arranged in a table,* it is easy to\\ntrace out the path of the sun on the artificial globe or to cal-\\nculate it with the greatest precision by means of spherical tri-\\nangles, since the declination and right ascension constitute two\\nsides of a right-angled spherical triangle, the corresponding arc\\nof the ecliptic, that is, the longitude, being the third side (Art.\\n132). By inspecting a table of observations, we shall find that\\nthe declination attains its greatest value on the 22d of Decem-\\nber, when it is 23\u00c2\u00b0 27 51 south that from this period it di-\\nminishes daily and becomes nothing on the 21st of March;\\nthat it then increases toward the north, and reaches a similar\\nmaximum at the northern tropic about the 22d of June and,\\nfinally, that it returns again to the southern tropic by grada-\\nSuch a table may be found in Biot s Astronomy, in Delambre, and in most\\ncollections of Astronomical Tables.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0104.jp2"}, "105": {"fulltext": "ANNUAL MOTION. 81\\ntions similar to those which marked its northward progress.\\nA table of observations, also, would show us that the daily\\ndifferences of declination are very unequal that, for several\\ndays, when the sun is near either tropic, its declination scarcely\\nvaries at all while near the equator, the variations from day\\nto day are very rapid a fact which is easily understood, when\\nwe reflect, that at the solstices the equator and the ecliptic are\\nparallel to each other,* both being at right angles to the\\nmeridian while at the equinoxes, the ecliptic departs most\\nrapidly from the direction of the equator.\\nOn examining, in like manner, a table of observations of\\nthe right ascension, we And that the daily differences of right\\nascension are likewise unequal that the mean of them all is\\n3 m 56 s or 236 s but that they have varied between 215 s and\\n266\\\\ On examining, moreover, the right ascension at each of\\nthe equinoxes, we find that the two records differ by 180\u00c2\u00b0;\\nwhich proves that the path of the sun is a great circle, since\\nno other would bisect the equinoctial as this does.\\n157. The obliquity of the ecliptic is equal to the surfs great-\\nest declination. For, by article 22, the inclination of any two\\ngreat circles is equal to their greatest distance asunder, as\\nmeasured on the sphere. The obliquity of the ecliptic may be\\ndetermined from the sun s meridian altitude, or zenith distance,\\non the day of the solstice. The exact instant of the solstice,\\nhowever, is not likely to occur when the sun is on the merid-\\nian, but may happen at some other meridian still, the changes\\nof declination near the solstice are so exceedingly small that\\nbut a slight error can result from this source. The obliquity\\nmay also be found, without knowing the latitude, by observing\\nthe greatest and least meridian altitudes of the sun, and taking\\nhalf the difference. This is the method practiced in ancient\\ntimes by Hipparchus. (Art. 2.) On comparing observations\\nmade at different periods for more than two thousand years, it\\nis found that the obliquity of the ecliptic is not constant, but\\nthat it undergoes a slight diminution from age to age, amount-\\ning to 52 in a century, or about half a second annually. We\\nOr, move properly, the tangents of the two circles (which denote the direc-\\ntions of the curves at those points) are parallel.\\n6", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0105.jp2"}, "106": {"fulltext": "82\\nTHE SUN.\\nmight apprehend that by successive approaches to each other\\nthe equator and ecliptic would finally coincide but astrono-\\nmers have ascertained by an investigation, founded on the\\nprinciples of universal gravitation, that this variation is con-\\nfined within certain narrow limits, and that the obliquity,\\nafter diminishing for some thousands of years, will then in-\\ncrease for a similar period, and will thus vibrate forever about\\na mean value.\\n158. The dimensions of the earth s orbit, when compared\\nwith its own magnitude are immense.\\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\\nmiles, it will be found, on calculation, that the earth moves\\n1,640,000 miles per day, 68,000 miles per hour, 1,100 miles per\\nminute, and nearly 19 miles every second, a velocity nearly\\nfifty times as great as the maximum velocity of a cannon-ball.\\nA place on the earth s equator turns, in the diurnal revolution,\\nat the rate of about 1,000 miles an hour, and T 5 g of a mile per\\nsecond. The motion around the sun, therefore, is nearly 70\\ntimes as swift as the greatest motion around the axis.\\nTHE SEASONS.\\n159. The change of seasons depends on two causes, (1) the\\nobliquity of the ecliptic, and (2) the earth s axis always remain-\\ning parallel to itself. Had the earth s axis been perpendicular\\nto the plane of its orbit, the equator would have coincided\\nwith the ecliptic, and the sun would have constantly appeared\\nin the equator. To the inhabitants of the equatorial regions,\\nthe sun would always have appeared to move in the prime\\nvertical and to the inhabitants of either pole, he would always\\nhave been in the horizon. But the axis being turned out of a\\nperpendicular direction 23\u00c2\u00b0 28 the equator is turned the same\\ndistance out of the ecliptic and since the equator and ecliptic\\nare two great circles which cut each other in two opposite\\npoints, the sun, while performing his circuit in the ecliptic,\\nmust, evidently, be once a year in each of those points, and\\nmust depart from the equator of the heavens to a distance on\\neither side equal to the inclination of the two circles that is,\\n23\u00c2\u00b0 28 (Art. 22.)", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0106.jp2"}, "107": {"fulltext": "THE SEASONS.\\n83\\n160. The earth being a globe, the sun constantly enlightens\\nthe half next to him,* while the other half is in darkness.\\nThe boundary between the enlightened and the unenlightened\\npart is called the circle of illumination. When the earth is at\\none of the equinoxes, the sun is at the other, and the circle of\\nillumination passes through both the poles. When the earth\\nreaches one of the tropics, the sun being at the other, the circle\\nof illumination cuts the earth so as to pass 23\u00c2\u00b0 28 beyond the\\nnearer, and the same distance short of the remoter pole. These\\nresults would not be uniform, were not the earth s axis always\\nto remain parallel to itself. The following figure will illustrate\\nthe foregoing statements.\\nFig. 31.\\nIn fact, the sun enlightens a little more than half the earth, since, on ac-\\ncount of his vast magnitude, the tangents drawn from the sides of the sun to\\ncorresponding sides of th\u00c2\u00ab earth, converge to a point behind the earth, as will be\\nseen by and by, in the representation of eclipses. The amount of illumination,\\nalso, is increased by refraction.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0107.jp2"}, "108": {"fulltext": "8i THE SUN.\\nLet ABCD represent the earth s place in different parts of\\nits orbit, having the snn in the center. Let A, C, be the po-\\nsition of the earth at the equinoxes, and B, D, its positions at\\nthe tropics, the axis ns being always parallel to itself.* At A\\nand C the snn shines on both n and s and now let the globe\\nbe turned round on its axis, and the learner will easily con-\\nceive that the snn will appear to describe the equator, which\\nbeing bisected by the horizon of every place, of course the day\\nand night will be equal in all parts of the globe. f Again, at\\nB, when the earth is at the southern tropic, the sun shines 23^- a\\nbeyond the north pole n 9 and falls the same distance short of\\nthe south pole s. The case is exactly reversed when the earth\\nis at the northern tropic and the sun at the southern. While\\nthe earth is at one of the tropics, at B for example, let us con-\\nceive of it as turning on its axis, and we shall readily see that\\nall that part of the earth which lies within the north polar\\ncircle will enjoy continual day, while that within the south\\npolar circle will have continual night, and that all other places\\nwill have their days longer as they are nearer to the enlight-\\nened pole, and shorter as they are nearer to the unenlightened\\npole. This figure likewise shows the successive positions of\\nthe earth at different periods of the year, with respect to the\\nsigns, and what months correspond to particular signs. Thus\\nthe earth enters Libra and the sun Aries, on the 21st of March,\\nand on the 21st of June the earth is just entering Capricorn\\nand the sun Cancer.\\n161. Had the axis of the earth been perpendicular to the\\nplane of the ecliptic, then the sun would always have appeared\\nto move in the equator, the days would everywhere have been\\nequal to the nights, and there could have been no change of\\nseasons. On the other hand, had the inclination of the eclip-\\ntic to the equator been much greater than it is, the vicissitudes\\nof the seasons would have been proportionally greater than at\\npresent. Suppose, for instance, the equator had been at right\\nThe learner will remark that the hemisphere toward n is above, and that\\ntoward s is below the plane of the paper. It is important to form a just con-\\nception of the position of the axis with respect to the plane of its orbit.\\nf At the pole, the solar disk, at the time of the equinox, appears bisected by\\nthe horizon.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0108.jp2"}, "109": {"fulltext": "85\\nangles to the ecliptic, in which case, the poles of the earth\\nwould have been situated in the ecliptic itself; then in differ-\\nent parts of the earth the appearances would have been as\\nfollows To a spectator on the equator, the sun, as he left the\\nvernal equinox would every day perform his diurnal revolution\\nin a smaller and smaller circle, until he reached the north pole,\\nwhen he would halt for a moment and then wheel about and\\nreturn to the equator in the reverse order. The progress of\\nthe sun through the southern signs, to the south pole, would\\nbe similar to that already described. Such would be the ap-\\npearances to an inhabitant of the equatorial regions. To a\\nspectator living in an oblique sphere, in our own latitude for\\nexample, the sun, while north of the equator, would advance\\ncontinually northward, making his diurnal circuits in parallels\\nfurther and further distant from the equator, until he reached\\nthe circle of perpetual apparition, after which he would climb\\nby a spiral course to the north star, and then as rapidly return\\nto the equator. By a similar progress southward, the sun\\nwould at length pass the circle of perpetual occultation, and\\nfor some time (which would be longer or shorter, according to\\nthe latitude of the place of observation) there would be contin-\\nual night.\\nThe great vicissitudes of heat and cold which would attend\\nsuch a motion of the sun, would be wholly incompatible with\\nthe existence of either the animal or the vegetable kingdoms,\\nand all terrestrial nature would be doomed to perpetual steril-\\nity and desolation. The happy provision which the Creator\\nhas made against such extreme vicissitudes, by confining the\\nchanges of the seasons within such narrow bounds, conspires\\nwith many other express arrangements in the economy of\\nnature to secure the safety and comfort of the human race.\\nFIG-URE OF THE EARTH S ORBIT.\\n162. Thus far we have taken the earth s orbit as a great\\ncircle, such being the projection of it on the celestial sphere\\nbut we now proceed to investigate its actual figure.\\nWere the earth s path a circle, having the sun in the center,\\nthe sun would always be at the same distance from us; that is,\\nthe radius vector (the name given to a line drawn from the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0109.jp2"}, "110": {"fulltext": "86\\nTHE SUN.\\ncenter of the sun to the orbit of any planet) would always be\\nof the same length. But the earth s distance from the sun is\\nconstantly varying, which shows that its orbit is not a circle,\\nhaving the sun at the center. We learn the true figure of the\\norbit, by ascertaining the relative distances of the earth from the\\nsun at various periods of the year. When these are laid down\\naccording to their relative length, and making angles with\\neach other equal to the changes in the sun s angular motions,\\na curve joining the extremities of these lines gives us our first\\nidea of the shape of the orbit, which is found to be an ellipse.\\nThus (considering the earth E, for the present, as fixed, and\\nthe sun as the moving body), let E\u00c2\u00ab, E Ec, c. (Fig. 32), be\\nthe successive distances of the sun, laid down as just described\\nthen will the dotted line qfmt, which passes through their ex-\\ntremities, show the form of the apparent solar orbit, with the\\nearth in one of its foci.\\nFig. 32.\\n163. These relative distances may be found by observing\\nthe changes in the sun s apparent diameter. Were the varia-\\ntions in the sun s horizontal parallax considerable, as is the\\ncase with the moon s, this might be made the measure of the\\nrelative distances, for the parallax varies inversely as the dis-\\ntance (Art. 82) but the whole horizontal parallax of the sun\\nis only 9 and its variations are too slight and delicate, and\\ntoo difficult to be found, to serve as a criterion of the changes\\nin the sun s distance from the earth. But the changes in the\\nsurfs apparent diameter are much more sensible, and furnish", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0110.jp2"}, "111": {"fulltext": "FIGURE OF THE KARTll s ORBIT\\n87\\na better method of measuring the relative distances of the\\nearth from the sun. By a principle in optics, the apparent\\ndiameter of an object, at different distances from the spectator,\\nis inversely as the distance.* Hence, the lines E\u00c2\u00ab, E c.\\n(Fig. 32), are to be drawn proportional to the reciprocals of the\\napparent diameters of the sun.\\n164. The point where the earth, or any planet, in its rev-\\nolution, is nearest the sun, is called its perihelion the point\\nwhere it is furthest from the sun, its aphelion. The place of\\nthe earth s perihelion is known, since there the apparent mag-\\nnitude of the sun is greatest and when the sun s magnitude is\\nleast, the earth is known to be at its aphelion. The sun s ap-\\nparent diameter when greatest is 32 35 6 and when least,\\n31 31 hence the radius vector at the aphelion rad vector\\nat the perihelion 32.5933 31.5167 1.034 1. Half of the\\ndifference of the two is equal to the distance of the focus of the\\nellipse from the center, a quantity which is always taken as\\nthe measure of the eccentricity of a planetary orbit. From\\ntwenty-four observations made with the greatest care by Dr.\\nMaskelyne, at the Royal Observatory of Greenwich, the fol-\\nlowing distances of the earth from the sun are determined for\\neach 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\\n165. Having determined the form of the solar orbit, we\\nare prepared to see what relation exists between the sun s\\nangular velocity in this orbit, and the length of the radius\\nvector. It has been already noticed (Art. 105), that the sun s\\nprogress in the ecliptic is fastest near the perihelion, and slow-\\nest near the aphelion. For instance, the sun at perihelion ad-\\ns More exactly, the* tangent of the apparent diameter is inversely as the dis-\\ntance but in small angles like those concerned in the present inquiry, the angle\\nand its tangent vary alike.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0111.jp2"}, "112": {"fulltext": "SS THE SUN.\\nvances about 61 in 2\u00c2\u00b1 hours, and at aphelion only about 57\\nNow 1.07, which is the square of 1.034, the ratio of ap-\\no i\\nparent diameters at the same points. Indeed, a careful com-\\nparison of the sun s angular velocities, in all parts of the orbit,\\nshows that they vary inversely as the squares of the distances.\\nIf changes in angular (i. apparent) velocity were caused\\nwholly by difference of distance, then it would vary inversely\\nonly as the first power of the distance, just as the apparent\\ndiameter does. But since the angular velocity varies inversely\\nas the square, instead of the first power of the distance, the\\nabsolute velocity must also be greater as the distance is less,\\nand vice versa. Thus we perceive, that when the sun is near-\\nest to us, he appears to move fastest for two reasons, first, be-\\ncause the same rate of motion would appear greater, if nearer\\nto us, and secondly, because the actual motion is then greater;\\nand each of these is in the inverse ratio of the distance.\\n166. It must be remembered, that this reasoning proceeds\\non the ground that the line of motion is everywhere at right\\nangles to the radius vector. That this is true without sensible\\ndeviation, appears from the fact that the solar orbit is very\\nnearly circular, with the earth at its center. If truly repre-\\nsented on paper, it could not be distinguished by the eye from\\na circle.\\nThis relation between distances and apparent velocities\\nhaving been once established, advantage may be taken of the\\nrapid rate of change in the latter, to determine the variations\\nin the radius vector more accurate-\\nly than can be done by the appar-\\nent diameter.\\n167. The angular velocity being\\ninversely as the square of the dis-\\ntance in all parts of the solar orbit,\\nit follows that the product of the\\nangle described in any given time,\\nby the square of the distance, is\\nalways the same constant quantity.\\nFor if of two factors, A xB, A is in-\\nFig. sa.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0112.jp2"}, "113": {"fulltext": "89\\ncreased as B is diminished, the product of A and B is always\\nthe same. If, therefore, from the sun S (Fig. 33), two radii be\\ndrawn to T, B, the extremities of any. small arc, as that de-\\nscribed in one day, and the angle between them be called S,\\nthen SB 2 xS gives the same constant product in all parts of the\\norbit.\\n168. The radius vector of the solar orbit describes equal\\nareas in equal times j and in unequal times, areas proportional\\nto the times.\\nThe solar orbit is so nearly a circle, that TB may everywhere\\nbe regarded as perpendicular to the radius SB or ST. Hence,\\nthe sector described in a given time, as one day, TSB oo SB x\\nTB. But a circular arc varies both as the angle which it sub-\\ntends, and also as the radius by which it is described there-\\nfore TB oo SBxS. Hence, TSB oo SB 2 xS. But (Art. 167)\\nthis is a constant product; therefore, the area TSB is also con-\\nstant, and the radius vector describes equal areas in equal\\ntimes.\\nThe sun s orbit may be accurately represented by taking\\nsome point, as the perihelion, drawing the radius vector to that\\npoint, and, considering this line as unity, drawing other radii\\nmaking angles with each other such that the included areas\\nshall be proportional to the times, and of a length required by\\nthe distance of each point as given in the table (Art. 164). On\\nconnecting these radii, we shall thus see at once how little the\\nearth s orbit departs from a perfect circle. Small as the differ-\\nence appears between the greatest and least distances, yet it\\namounts to nearly Jg of the perihelion distance, a quantity no\\nless than 3,000,000 of miles.\\n169. The foregoing method of determining the iigure of\\nthe earth s orbit is founded on observation but this figure is\\nsubject to numerous irregularities, the nature of which cannot\\nbe clearly understood without a knowledge of the leading-\\nprinciples of Universal Gravitation. An acquaintance with\\nthese will also be indispensable to our understanding the cause*\\nof the numerous irregularities, which (as will hereafter appear)\\nattend the motions of the moon and planets. To the laws of\\nuniversal gravitation, therefore, let us next apply our attention.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0113.jp2"}, "114": {"fulltext": "CHAPTEE III.\\nOF CENTRAL FORCES GRAVITATION.\\n170. When a body moves in a curve of any kind, we rec-\\nognize the effect of two forces: one, an impulse, which acting\\nalone would have caused a uniform motion in a straight line,\\nand whose influence is always retained in the curve-motion\\nthe other, an accelerating force, which continually urges the\\nbody toward some point out of the original line of motion.\\nThe first is called the projectile force, the other the centripetal\\nforce. If the action of the latter were to cease at any moment,\\nthe body by its inertia would from that moment continue uni-\\nformly in the direction in which it was then moving. Such\\nmotion in the tangent may be regarded as the effect of an im-\\npulse first given in the direction of that tangent. This supposed\\nimpulse is the projectile force for the moment in question but\\nit is in truth the resultant of the original impulse, and the infi-\\nnite series of actions already produced by the centripetal force.\\nThe centripetal force is of necessity infinitely small compared\\nwith the projectile force. For, if not, the curve would depart\\nby a finite angle from the tangent whereas, by the very\\nnature of the relation of a curve to its tangent, the angle is in-\\nfinitely small therefore, the deflecting force is infinitely small.\\nBut it produces finite deflection after a time, because its action\\nis incessantly repeated.\\n171. From a long and laborious examination of the record-\\ned observations of Tycho Brahe, Kepler deduced three laws\\nrelating to the movements of the planets, which are therefore\\ncalled Kepler s laws.\\n1. The orbit of every planet is an ellipse, having the sun in\\none focus.\\n2. The radius vector of each orbit describes equal areas in\\nequal times.\\n3. The squares of the periodic times of the several planets\\nvary as the cubes of their mean distances.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0114.jp2"}, "115": {"fulltext": "CENTRAL FORCES. 91\\nThese were thus ascertained as facts, many years before\\nNewton demonstrated, by mathematical reasoning, that they\\nare necessarily involved in the laws of inertia and gravitation.\\nThe fundamental principles of all mechanical action, per-\\ntaining alike to terrestrial bodies and to the worlds scattered\\nthroughout space, are the following\\n1. Matter, until acted on by extraneous force, will remain\\nperpetually in its present condition, whether of rest or straight\\nuniform motion.\\n2. All motions communicated to a body coexist in the mo-\\ntion of the body.\\n3. To every action there is an equal and opposite reaction.\\n4. All masses tend toward each other, with a force varying\\ndirectly as the quantity of matter, and inversely as the square\\nof the distance.\\nThe three first, the laws of inertia, of coexistent motions, and\\nof equal action and reactio?i, were seen to be the true first\\nprinciples in the Mechanics of terrestrial bodies. But they are\\nequally essential in Astronomy the celestial Mechanics and\\nnot only does no fact in this science militate against them, but,\\non the contrary, they form the basis of all correct reasoning on\\nthe motions of the heavenly bodies. The fourth, usually called\\nthe law of gravity, is far more prominent in Astronomy than\\nin Mechanics, but harmonizes with all the facts of both. We\\nproceed to show that Kepler s laws and other laws of central\\nforces, are the necessary consequences of the above-named me-\\nchanical principles.\\n172. Whatever path a body describes under the influence\\nof a projectile and a centripetal force, the radius vector of that\\npath passes over equal spaces in equal times.\\nLet S (Fig. 34) be the center of attraction, and suppose the\\nprojectile force in the line YK. to be such as to cause the body\\nto pass over the equal spaces PQ, QE,, c, each in a certain\\nunit of time. When the body reaches Q, let the action toward\\nS be sufficient to move it over QY in the same time in which\\nby the original impulse it would describe QK. Then it will\\nin the same time describe the diagonal QC of the parallelo-\\ngram. Join ES and CS. The triangles QSC and QSXv are\\nequal; but QSR=QSP; QSC=QSP. That is, the areas do-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0115.jp2"}, "116": {"fulltext": "92\\nUNIVERSAL GRAVITATION.\\nFig. 34.\\nscribed in the first and second units of time are equal. In like\\nmanner, by supposing a second action toward S to occur at C,\\na third at D, c, it is proved that QCS, CDS, DES, c,\\nwhich are described in equal times, are equal. This is true,\\nhowever small the unit of time between the successive actions\\ntoward S, and is therefore true, wdien the central force acts in-\\ncessantly^ and causes curvilinear motion. As the diagonal of\\neach parallelogram is in the same plane with its two sides, it\\nis obvious that the whole orbit lies in one and the same plane.\\n173. Conversely, if equal areas be described about a point\\nin equal times, by the radius vector, the deflecting force acts\\ntoward that point. For PSQ=QSR, as before (Fig. 34);\\nand by supposition, PSQ=QSC QSC=QSR; hence CR is\\nparallel to QS, and QC is the diagonal of a parallelogram,\\nwhose side QV, in which the deflecting force acts, is directed\\ntoward S.\\nIt has been shown (Art. 168) that, from observations on the\\nangular velocity of the earth about the sun, equal areas are in\\nfact described by the radius vector in equal times. It is there-\\nfore inferred that there is an accelerating force urging the\\nearth toward the sun.\\n174. The velocity at any point of an orbit, varies inversely", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0116.jp2"}, "117": {"fulltext": "CENTRAL FORCES. 93\\nas the perpendicular from the center of force to the tangent at\\nthat point.\\nLet SY (Fig. 31) be perpendicular to PQ then the area\\nSPQ=iPQxSY, which varies as PQxSY PQ oo -?Q.\\nb X\\nBut PQ oo Y, the velocity at P and the area SPQ is constant\\nToo 3 or the velocity varies inversely as the perpen-\\ndicular from S upon the line in which the body is moving\\nin other words, upon the tangent of its path, if it describes\\na curve.\\nIn the orbits of the planets, since they are very nearly cir-\\ncular, SY meets the path almost at the point where the body\\nis moving, and therefore is about equal to the radius vector\\nso that in the planetary orbits, the absolute velocity varies in-\\nversely as the radius vector very nearly. We have already\\nnoticed this to be sensibly true in the case of the earth s orbit.\\n(Arts. 165, 166.) It follows from the above reasoning, that in\\na circular orbit, where the radius vector is constant, the ve-\\nlocity of the body is uniform.\\n175. When a body moves in a curve, since by its inertia it\\ntends at each point to proceed in the tangent at that point,\\nthere is a continual outward pressure directed from the center\\nof force; this is called the centrifugal force. It may be regard-\\ned as that infinitesimal component of the projectile force, which\\nopposes the action of the centripetal, the motion along the curve\\nbeing the other component. If the body is maintained at the\\nsame distance from the center (that is, in the circumference of a\\ncircle), the centrifugal force equals the centripetal but in orbits\\nof other forms, it is sometimes greater and sometimes less than\\nthe centripetal.\\n17G. In a circular orbit, the central force (either centripe-\\ntal or centrifugal) varies as the square of the velocity divided by\\nthe, radius.\\nIf v~ the uniform velocity in the orbit, and \u00c2\u00a3=the infin-\\nitely small portion of time of describing the minute arc Ab,\\nand r=the radius of the circle, then Ab~vt. But A5, or its", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0117.jp2"}, "118": {"fulltext": "94: UNIVERSAL GRAVITATION.\\nchord, is a mean proportional between its\\nversed sine Aa, and the diameter 2r or\\n~KF 2 vH 2\\nAa=\u00e2\u0080\u0094 which, in a given time, varies\\nv 2\\nas that is (since the central forced is meas-\\nv 2\\nnred by Act), f\\nHence, in a given circle, where r is constant, the central\\nforce varies as the square of the velocity. In whirling a ball,\\nfor instance, with a string of given length, if the velocity is\\ndoubled, the strain upon the string (the centrifugal force) is\\nfour times as great, and the strength of the string (the centrip-\\netal force) needs also to be four times as great. If a train of\\ncars goes round a curve with a velocity 1\u00c2\u00a3 times that which is\\nintended, its tendency to be thrown from the track is increased\\n2\u00c2\u00a3 times.\\n177. In a circular orbit, the central force (centripetal or\\ncentrifugal) varies as the radius of the circle divided by the\\nsquare of the time of revolution.\\nLet \u00c2\u00a3=the time of describing the whole circumference 2nr\\nQTcr r r 2\\n2-rrr=vt, and which varies as--; v oo But (Art.\\nt to\\nv 2 r 2 r r\\n176) fa oo -i-rroo^; .-.fee\u00e2\u0080\u0094. Hence, if the periodic time\\nr z t t\\nls the same, the attraction to the center must be increased in\\nthe same ratio as the radius of the orbit, for then fco r. If a\\nstring is twice as long, it must have twice the strength, in order\\nto whirl a ball at the same rate of revolution.\\n178. If a body describes an elliptical orbit by a centripetal\\nforce which acts toward the focus, that force varies inversely\\njts the square of the distance.\\nLet the body be at M (Fig. 36), and MF the radius vector\\nat that point. Let MO be the radius of curvature at M, and\\ntherefore perpendicular to the tangent and suppose MN to\\nbe an infinitely small arc described in a given small portion of\\ntime. Draw FP perpendicular to the tangent MP, NK to", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0118.jp2"}, "119": {"fulltext": "CENTRAL FORCES.\\n95\\nFM, and IH to MO then PFM, MHI, KOT, are similar tri-\\nangles. MJST, considered as a straight line, is described by the\\njoint action of the centripetal force MI, and the projectile\\nforce, which is equal and parallel to IN. The motion in MJ\\nFig. 36.\\nmay be regarded as uniformly accelerated, because in the in-\\nfinitely small time of describing it, the centripetal force may\\nbe considered constant. Hence, 2MI may be taken as the\\nmeasure of the centripetal force f.* Therefore fee ML It is\\nto be proved that MI go ^-r\\nr FM 2\\n179. By similar triangles, MI MH 1STI NK\\n,.mi^mh|I.\\nNow, the chord MN is a mean proportional between the\\nME 2\\nversed sine MH, and the diameter 2MO or IH=- TF7\\n2MO\\nNH 2\\nbut, as the arc is infinitely small, KH=MN MH=-^.\\nJ J* 2MO\\nAgain, the versed sine MH, and therefore HI, is infinitely\\nsmall compared with E H, and NI may be substituted for\\nNH;\\nKI 2\\nMH =iMO\\nNat. Phil., Art. 28.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0119.jp2"}, "120": {"fulltext": "UNIVERSAL GRAVITATK N.\\nNow, it is shown in conic sections, that MO= v^p J by\\n/NI 3\\nsimilar triangles, MO=M ^p J Substituting this for MO\\nNK 3\\nin the equation for MH above, we have MH Hence,\\nin the equation for MI, we have\\nNK 3 NI l x _,\\nMI= TT x -NK\\nJ9 NI NK\\nNow the sector FMN is measured bv fFM.NK; NK=\\n2FMN ATir2 4FMN 2 _- T 4FMN 2 _\\n~fm and TiF~ ml= J7fW as equal\\nareas are described by the radius vector in equal times, FMN\\nis constant. Therefore\\nm (=/)\u00c2\u00bb.j5p;\\nthat is the centripetal force varies inversely as the square of\\nthe distance.\\n180. It is thus proved, that in any elliptical orbit de-\\nscribed about the focus as the center of attraction, the inten-\\nsity of that attraction varies inversely as the square of the ra-\\ndius vector. As there is nothing in the foregoing demonstra-\\ntion to limit the conclusion to the orbits which are nearly cir-\\ncular, like those of the planets, we are at liberty to apply it to\\norbits of extreme eccentricity, as those of the comets. And it\\nis proved by Newton in his Principia, that the same law of\\nforce is necessary, in order that a body may describe any one\\nof the conic sections about its focus as the center of attraction.\\n181. And not only does this law prevail in all parts of any\\nJackson s Conic Sections. The same may be derived from Coffin s Con.\\n(FM MV) 3\\nSec. Pr. V., Curvature. E 2 or M0 2 -r; a and b being the semi-axes\\na?b\\n1 1 A 1\\nM0= X(FM.MV) 2 Multiply by (6 2 2 and divide by its equal (FP.yL) 2\\nab\\n6 2 /FM MV\\\\^ fi 2 /FM \\\\l\\nthen M0= l 2 =-f ~\u00e2\u0080\u009eg l 2 since FMP and VML, are similar. But\\n3 P 1 *u J\u00c2\u00b0/FM 2 \u00c2\u00bb/FM\\\\3\\np being the parameter M0 2 I J", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0120.jp2"}, "121": {"fulltext": "CENTRAL FORCES. 97\\none orbit, but it is true also, that all the different bodies of a\\nsystem, describing orbits about the same center of force, are\\nurged toward that center by attractions which vary, from one\\norbit to another, inversely as the square of the distance.\\nLet a be the semi-major, and b the semi-minor axis of any\\nelliptic orbit. Then a is the mean distance of all points of the\\norbit from the focus. By a rule of mensuration, the area of\\nthe ellipse =7rah. Ifs=the area described by the radius vec-\\ntor in a unit of time, as one second, and \u00c2\u00a3=the number of sec-\\nonds in the whole period of revolution, then the ellipse also= 9.\\nTherefore nab~ts and t\u00e2\u0080\u0094 and t 2 j\u00e2\u0080\u0094. By Kepler s\\na 2 b 2 b 2\\nthird law (Art. 171), t 2 ooa s r ooa 3 -aos 2 But, be-\\nS\\ncause the semi-parameter is a third proportional to the\\nh 2 7) 7) 7)\\nsemi-axes a and b, x s 2 Hence, substituting\\nfor s\\\\ that is, FMN 2 in the equation for MI (Art. 179), we\\n4FMN 2 2\u00c2\u00bb 2 1\\nndm ^^\u00c2\u00a5W=^W FW -^YW 0r the force\\nvaries inversely as the square of the distance, in different or-\\nbits, as well as in different parts of the same orbit.\\nThe satellites which revolve about the planets, are found to\\nconform to Kepler s laws, and therefore the force which urges\\nthem toward their respective primaries, varies in each case in-\\nversely as the square of the distance.\\n182. But the inquiry still remains, does the law of gravity,\\nas demonstrated in the foregoing articles, hold good at the\\nsmallest distances also For example, do the tendencies of\\nbodies resting on the earth, and of those elevated in the air,\\nand of the moon, toward the earth s center, come under the\\nsame general law This is the very question which presented\\nitself to the mind of Newton, after he had discovered that the\\nforce which deflects the planets from their lines of motion\\ntoward the sun, varies inversely as the square of their distance\\nfrom it. As he noticed the fall of an apple, the inquiry arose,\\nmay not this/M be of the same nature as the bending of the\\n7", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0121.jp2"}, "122": {"fulltext": "98\\nUNIVERSAL GRAVITATION\\nmoon s path toward the earth, and may not the force in the\\ntwo cases be as the squares of the distances inversely\\nLet us then find what is the distance through which the\\nmoon actually descends in a second of time. Let the earth be\\nat E (Fig. 37), and Ah the arc described by the moon in one\\nsecond. As she was going toward B\\nat the point A, she would have gone\\nover the line AB in one second, if\\nsome influence had not turned her\\naside. This influence must be direct-\\ned toioard the earth E, because it is\\naround E that the radius vector de-\\nscribes equal areas in equal times\\n(Art, 173). Therefore B6, or the\\nversed sine Act (which may be con-\\nsidered equal to it), is the distance\\nfallen through in one second. Now\\nthe distance of the moon from the\\nearth s center is 238,545 miles (Art.\\n201). Hence, the circumference is known. The time of rev-\\nolution is 27.32 days. (Art. 213.) Therefore Ah, the distance\\ntraveled in one second is obtained. This is so small, that its\\nversed sine Aa can not be calculated by ordinary trigonomet-\\nrical tables but is easily and accurately determined by ge-\\nometry thus, 2AE Ah Ah Ad since the arc Ah and the\\nchord Ah may be considered identical. A a, thus calculated,\\nis found to be 0.0535 of an inch. At the surface of the earth,\\na body falls about 16^2 feet in the first second. In order to\\ndiminish this for the moon s distance, we make the proportion,\\n(238.515) 2 (3956) 2 16 T2 ft, 0.05S6, agreeing very accu-\\nrately with the distance which the moon actually falls from a\\ntangent in a second of time. When Newton, however, first\\nmade the comparison just described, the result was quite un-\\nsatisfactory. The tendency of the moon was about too\\ngreat, Near 20 years afterward, when a new measurement of\\na degree of the meridian had been made, and thus a corrected\\nmagnitude of the earth, he repeated the process, and found\\nthe law of attraction in this case to be the same as elsewhere\\nin the solar system.\\nAgain, the numerous disturbances which the bodies of the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0122.jp2"}, "123": {"fulltext": "CENTRAL. FORCES. 99\\nsolar system produce in each other s motions, are all accounted\\nfor by applying the same law. If a planet moves for a time\\ntoward another, it is accelerated and its acceleration is\\ngreater, as the square of the distance is less, and it is retarded\\naccording to the same law, when departing from it.\\nSince all bodies manifest a tendency toward each other, it\\nis natural to suppose that the tendency should vary as the\\nquantity of matter, other things being equal. Both observa-\\ntion and calculation confirm, without any exceptions, such a\\nsupposition; and therefore a full statement of the law of\\ngravity includes the fact, that it varies directly as the quanti-\\nty of matter.\\n183. Since, as we have seen, gravity just at the earth s\\nsurface is governed by the same law of distance as it is further\\noff, therefore the curved paths of projectiles are of the same\\nnature as the orbits of planets and satellites that is, they are\\nellipses, one of whose foci is at the earth s center. And there\\nis no real discrepancy between this statement and that proved\\nin Mechanics,* that the path of a projectile is a parabola* In\\nthat demonstration, it was assumed that the lines in which the\\ngravitating force acts at each point of the path, are parallel to\\neach other, and that the force is constant, neither of which is\\nstrictly true since the verticals all meet at the center of at-\\ntraction, and the intensity of gravity slightly increases as the\\nbody descends. Knowing the distance and period of the\\nmoon, it is easy to find by Kepler s third law the period of\\nrevolution in case of a given projectile, if its orbit could be\\ncompleted in accordance with the law. Any force, which man\\ncould apply, would carry the perigee so little beyond the cen-\\nter of the earth, that the mean distance -might be called one-\\nhalf the radius of the earth. Therefore, calling the moon s\\ndistance 60 radii, and her period 27} days, we should have\\n(60) 3 (if (27J-) 2 x\\\\ the square root of which would be\\nabout 30 minutes. Every projectile, then, if it were free to\\ncomplete its orbit, unobstructed, and according to the law of\\ngravity which prevails outside of the earth, would make an\\nentire revolution, and return to its place in half an hour. Ae\\nNat. Phil., Art. 49.\\ntoffc", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0123.jp2"}, "124": {"fulltext": "100\\nUNIVERSAL GRAVITATION.\\ncording to Art, 174, the velocity at the perihelion would be as\\nmuch greater than that of projection as its distance from the\\ncenter is less.\\nFig. 38.\\n184. In Fig. 38, let AC be the vertical, and AB, at right\\nangles to it, the line of projection; then, according to the\\nvelocity given, AD, AE, or AF might be the commencement\\nof the orbit; from the point A the velocity would increase\\ncontinually till the moment of nearest approach to the center,\\nfrom which point it would decrease all the way back to A. In\\nall these orbits, the center of the earth will occupy the focus\\nmost remote from the point of projection in other words, the\\nplace of projection is the apogee of the orbit. Now suppose\\ntnat the velocity should be greatly augmented, as in Fig. 39,\\nso that, in one case, the curve should strike the earth at D, in\\nanother at E, and so on, until finally a force should be given\\nsufficient to carry the body round in a circle. This last case", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0124.jp2"}, "125": {"fulltext": "CENTRAL -FORCES. 101\\nwill happen when the centrifugal force has been increased so\\nas to just equal gravity (Art. 175). As the mean distance\\nnow equals the radius of the earth, the time of revolution is\\neasily found to be lh. 24m. 39s. Any increase of projectile\\nforce beyond this will again produce an ellipse as PK, whose\\nperigee is at P and we can imagine the velocity of projection\\nincreased until the ellipse becomes one of extreme eccentricity,\\nand then changes into a parabola, and then into an hyperbola,\\nin which last cases the body will never return, or even reach\\nthe point of apogee.\\n185. If we suppose the projectile motion of the earth or\\nany other planet, to have been produced by a single impulse,\\nthat impulse may also have caused the diurnal rotation of the\\nbody. If it had been directed in a line passing through the\\ncenter of gravity of the planet, then it would have caused a\\nprogressive motion, without rotation on the axis. But if the\\nline of the impulse did not pass through the center of gravity,\\nthen besides the motion forward, there would also be a rota-\\ntion whose velocity would depend on the distance of the line\\nfrom the center. According to the calculation made by Ber-\\nnouilli, the earth s progressive and rotary motions might have\\nboth been produced by the application of a force in a line\\npassing twenty-four miles from the center of the earth, on the\\nside most remote from the sun.*\\nHad it been directed through a point lying on the side near-\\nest the sun, the diurnal rotation would obviously have been\\nretrograde.\\n186. But if a force were applied to a planet as we have\\nbeen supposing, what effect would be produced on the system\\nas a whole To simplify the case, suppose the sun and one\\nplanet at rest, and at a given distance apart. Let them begin\\nto attract each other, and at the same instant let an impulse be\\napplied to the planet at right angles to the line joining the two,\\nand of sufficient intensity to cause revolution in a circle will\\nthat circle be described about the sun as a stationary body\\nIt will not, but around the common center of gravity as a mov-\\n8 Francceur, Uian,, p. 49.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0125.jp2"}, "126": {"fulltext": "102\\nTJNIVEKSAL GRAVITATION.\\ning point, while the sun will do the same in consequence of the\\nmutual attraction between them. Figure 40 will illustrate the\\ncase. It is proved (Nat. Phil., Art. 89) that a force applied to\\none body of a system will produce the same effect on the cen-\\nter of gravity of that system, as if the force were applied to\\nFig. 40\\nA g\\nr^Os\\nthe entire system collected at that center. Therefore, let S be\\nthe sun, E the earth, and C their center of gravity and let the\\nimpulse be such as to move the sum of both bodies over Ca,\\nah, he, c, in any equal times, while in each unit of time it\\ncarries E over a given arc, say 45\u00c2\u00b0 of its circle, then, when the\\ncenter is at a, E is at 1, 45\u00c2\u00b0 from a perpendicular at a. But S\\nmust be on the opposite side of a, and at the same distance from\\nit as from C before, because E s distance from the center re-\\nmains unaltered. Therefore, by the impulse given to E, and\\nthe mutual attraction between E and S, the latter has been\\ndrawn along from S to 1 Drawing again two circles from\\nthe center b, one for E, the other for S, the next positions for\\nthe bodies are 2 and 2 While E was on the upper side of Cd,\\nS was drawn toward that line, and now crosses it, and by its\\nown inertia continues upward, although E is now below the\\nline. In this manner the two bodies revolve about a moving\\ncenter, describing circles relatively to that, but curves of a to-\\ntally different character in space. These curves are always\\nsome variety or other of the curve called an epicycloid. In the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0126.jp2"}, "127": {"fulltext": "CENTRAL FORCES.\\n103\\ncase represented in the figure, the smaller body describes an\\nepicycloid which forms a series of loops, intersecting its own\\npath at every revolution, while the path of the heavier body is\\nof a waving form. The body E retrogrades on the lower part\\nof the loop, from 3 to 5, while S advances continually, but\\nwith unequal velocities, each body being alternately drawn\\nforward and held back by the other.\\nThe only way in which two separate bodies could be made\\nto rotate about a fixed center of gravity, would be to give an\\nequal impulse to each body, and in opposite directions. Two\\nsuch forces would constitute a couple \u00c2\u00a3N at. Phil., Art. 57),\\nwhose effect is to produce rotation merely.\\n187. The learner may find some difficulty in understanding\\nwhy a planet, when it reaches its aphelion C (Fig. 41), where\\ngravity is more feeble than it had\\npreviously been, should begin from\\nthat point to approach the sun and\\nagain, why, at the perihelion G,\\nwhere gravity is greatest, it should\\nbegin to depart, instead of approach-\\ning nearer and nearer in a spiral, till R\\nit falls upon the sun. This is owing\\nto the change in velocity, and conse-\\nquently in centrifugal force. As the\\nplanet ascends through H, K, and\\nA, the action is partly against its\\nmotion, and consequently retards it,\\ntill the projectile force is too small to maintain it at that dis-\\ntance, and it begins from C to approach. In approaching, the\\nattraction of the sun partly conspires with its own inertia, to\\naccelerate it, through D, E, and F its velocity is thus increased,\\ntill the centrifugal force becomes so great at G, precisely op-\\nposite to C, that it commences once more to depart in its former\\npath. Of course these effects could not take place unless the\\ncentrifugal force varied more rapidly than the centripetal,\\nwhich is true for it is proved that the centrifugal force in an\\norbit varies inversely as the cube of the distance, while the cen-\\ntripetal varies only as the square inversely.*\\nM. Stewart s Phys. and Math. Tracts, Prop. 8.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0127.jp2"}, "128": {"fulltext": "CHAPTEE IT.\\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 out con-\\ntinual shifting of the equinoctial points from east to west.\\nSuppose that we mark the exact place in the heavens where\\nthe sun crosses the equator, the present year in March, and\\nthat this point is close to a certain star next year the sun will\\ncross the equator a little way westward of that star, and so\\nevery year a little further westward, until, in a long course of\\nages, the place of the equinox will occupy successively every\\npart of the ecliptic, until we come round to the same star\\nagain. As, therefore, the sun, revolving from west to east in\\nhis apparent orbit, comes round toward the point where it\\nleft the equinox, it meets the equinox before it reaches that\\npoint. As the time of crossing, in every instance, precedes the\\ntime on the previous year, the phenomenon is called the Pre-\\ncession of the Equinoxes, and the fact is expressed by saying\\nthat the equinoxes retrograde on the ecliptic, until the line of\\nthe equinoxes makes a complete revolution from east to west.\\nThe equator is conceived as sliding westward on the ecliptic,\\nalways preserving the same inclination to it, as a ring placed\\nat a small angle with another of nearly the same size, which\\nremains fixed, may be slid quite around it, giving a corre-\\nsponding motion to the two points of intersection. It must be\\nobserved, however, that this mode of conceiving of the pre-\\ncession of the equinoxes is purely imaginary, and is employed\\nmerely for the convenience of representation.\\n189. The amount of precession annually is 50 .l whence,\\nsince there are 3600 in a degree, and 360\u00c2\u00b0 in the w T hole cir-\\ncumference, and consequently, 1 296000 this sum divided by\\n50.1 gives 25868 years for the period of a complete revolution\\nof the equinoxes.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0128.jp2"}, "129": {"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\\nto the axis of the ecliptic, the other to that of the equator, the\\nextremity of each being the pole of its circle. As the ring de-\\nnoting the equator turns round on the ecliptic, which with its\\naxis remains fixed, it is easy to conceive that the axis of the\\nequator revolves around that of the ecliptic, and the pole of\\nthe equator around the pole of the ecliptic, and constantly at a\\ndistance equal to the inclination of the two circles. To trans-\\nfer our conceptions to the celestial sphere, we may easily see\\nthat the axis of the diurnal sphere (that of the earth produced,\\nArt. 28) would not have its pole constantly in the same place\\namong the stars, but that this pole would perform a slow rev-\\nolution around the pole of the ecliptic from east to west, com-\\npleting the circuit in about 26,000 years. Hence the star\\nwhich we now call the pole-star, has not always enjoyed that\\ndistinction, nor will it always enjoy it hereafter. When the\\nearliest catalogues of the stars were made, this star was 12\u00c2\u00b0\\nfrom the pole. It is now 1\u00c2\u00b0 24/, and will approach still near-\\ner or, to speak more accurately, the pole will come still near-\\ner 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\\npole-star, will be within 5\u00c2\u00b0 of the pole, and will constitute the\\nPole-star. As Lyra now passes near our zenith, the learner\\nmight suppose that the change of position of the pole among\\nthe stars, would be attended with a change of altitude of the\\nnorth pole above the horizon. This mistaken idea is one of\\nthe many misapprehensions which result from the habit of\\nconsidering the horizon as a fixed circle in space. However\\nthe pole might shift its position in space, we should still be at\\nthe same distance from it, and our horizon would always reach\\nthe same distance beyond it.\\n191. The precession of the equinoxes is an effect of the\\nspheroidal figure of the earth, and arises from the attraction of\\nthe sun and moon upon the excess of matter about the earth s\\nequator.\\nWere the earth a perfect sphere, the attractions of the sun\\nand moon upon the earth would be in equilibrium among", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0129.jp2"}, "130": {"fulltext": "106 THE SUN.\\nthemselves. But if a globe were cut out of the earth (taking\\nhalf the polar diameter for radius), it would leave a protuber-\\nant mass of matter in the equatorial regions, which may be\\nconsidered as all collected into a ring resting on the earth.\\nThe sun being in the ecliptic, while the plane of this ring is\\ninclined to the ecliptic 23\u00c2\u00b0 28 of course the action of the sun is\\noblique to the ring, and may be resolved into two forces, one\\nin the plane of the equator, and the other perpendicular to it.\\nThe latter only can act as a disturbing force, and tending as\\nit does to draw down the ring to the ecliptic, the ring would\\nturn upon the line of the equinoxes as upon a hinge, and\\ndragging the earth along with it, the equator would ultimately\\ncoincide with the ecliptic were it not for the revolution of the\\nFig. 42.\\nearth upon its axis. Let EC (Fig. 42) be the ecliptic, and QE.\\nthe equator. Any particle A, of the ring, by its inertia of\\nrotation, tends to move toward T in the plane QB. Let AB\\nrepresent this force, and AF the pressure toward EC produced\\nby the sun; then the resultant will be AD; shifting the\\nequinox backward from T to T Each particle is subjected\\nto this influence, except at the moment (each day) of crossing\\nT and so long as the sun is not himself in the line T =s= pro-\\nduced, which occurs in March and September. The effect is\\nthen interrupted for a short time.\\n192. The moon conspires with the sun in producing the\\nprecession of the equinoxes, its effect, on account of its nearness\\nto the earth, being more than double that of the sun, or as 7\\nto 3. The planets likewise, by their attraction, produce a", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0130.jp2"}, "131": {"fulltext": "PRECESSION OF THE EQUINOXES. 107\\nsmall effect upon the equatorial ring, but the result is slightly\\nto diminish the amount of precession. The whole effect of the\\nsun and moon being 50 .41, that of the planets is 0 .31, leaving\\nthe actual amount of precession 50 1.\\nThe law of compositions of motion in rotation is analogous\\nto that for the composition of rectilinear motions (Nat. Phil.,\\nArt. 12), and may be stated thus if two forces are applied to\\na body, which, separately, would cause it to rotate on two dif-\\nferent axes, their joint action will produce rotation on an axis\\nlying between the others, at angles whose sines are inversely as\\nthe forces. In the precession of equinoxes, the earth rotates on\\nthe diurnal axis by one force, and the sun tends to revolve it\\non an axis passing through the equinoxes. As the latter force\\nis minute, compared with the other, the new axis is shifted by\\na very small angle each year from the axis of rotation toward\\nthe line of equinoxes. And as this line slides along by the\\nsame quantity, the two axes remain perpetually at right angles\\nwith each other.*\\n193. The time occupied by the sun in passing from an\\nequinox or solstice round to the same point again, is called the\\ntropical year. As the sun does not perform a complete rev-\\nolution in this interval, but falls short of it 50 1, the tropical\\nyear is shorter than the sidereal by 20m. 20s. in mean solar\\ntime, this being the time of describing an arc of 50 1 in the\\nannual revolution. The changes produced by the precession\\nof the equinoxes in the apparent places of the circumpolar\\nstars, have led to some interesting results in chronology. In\\nconsequence of the retrograde motion of the equinoctial points,\\nthe signs of the ecliptic (Art. 35) do not correspond at present\\nto the constellations which bear the same names, but lie about\\none whole sign, or 30\u00c2\u00b0, westward of them. Thus, that division\\nof the ecliptic which is called the sign Taurus, lies in the con-\\nstellation Aries, and the sign Gemini in the constellation\\nTaurus. Undoubtedly, however, when the ecliptic was thus\\nfirst divided, and the divisions named, the several constella-\\nf The precession of equinoxes, and other cases of compound rotations, are\\nfinely illustrated by the gyroscope of Foucault, and still better by Johnson s\\nrotascope.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0131.jp2"}, "132": {"fulltext": "108 THE SUN.\\ntions lay in the respective divisions which bear their names.\\nHow long is it, then, since our zodiac was formed\\n50 .l 1 year 30\u00c2\u00b0 10S000 2155.6 years.\\nThe result indicates that the present divisions of the zodiac\\nwere made soon after the establishment of the Alexandrian\\nschool of astronomy. (Art. 2.)\\nNUTATION.\\n104. Nutation is a vibratoiy motion of the earth s axis,\\narising from periodical fluctuations in the obliquity of the\\necliptic.\\nIf the sun and moon moved in the plane of the equator,\\nthere would be no precession, and the effect of their action in\\nproducing it varies with their distance from that plane. Twice\\na year, therefore, namely, at the equinoxes, the effect of the\\nsun is nothing; while at the solstices the effect of the sun is a\\nmaximum. On this account the obliquity of the ecliptic is\\nsubject to a semi-annual variation, since the sun s force, which\\ntends to produce a change in the obliquity, is variable, while\\nthe diurnal motion of the earth, which prevents the change\\nfrom taking place, is constant. Hence the plane of the equa-\\ntor is subject to an irregular motion, which is called the Solar\\nNidation. The name is derived from the oscillatory motion\\ncommunicated by it to the earth s axis, while the pole of the\\nequator is performing its revolution around the pole of the\\necliptic (Art. 190). The effect of the sun, however, is less than\\nthat of the moon, in the ratio of 2 to 5. By the nutation\\nalone, the pole of the earth would perforin a revolution in a\\nvery small ellipse, only 18 in diameter, the center being in\\nthe circle which the pole describes around the pole of the\\necliptic but the combined effects of precession and nutation\\nconvert the circumference of this circle into a wavy line. The\\nmotion of the equator occasioned by nutation, causes it alter-\\nnately to approach to and recede from the stars, and thus to\\nchange their declinations The solar nutation, depending on\\nthe position of the sun with respect to the equinoxes, passes\\nthrough all its variations annually; but the lunar nutation,\\ndepending on the position of the moon, with respect to her\\nnodes, varies through a period of about 18^- years.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0132.jp2"}, "133": {"fulltext": "ABERRATION. 109\\nABERRATION.\\n195. Aberration is an apparent change of place in the\\nstars, occasioned by the joint effects of the motion of the earth\\nin its orbit, and the progressive motion of light.\\nSuppose the earth to move from C to E, while the light from\\nS describes the line DE. If they arrive together at the point\\nE, the impression on the eye will not be\\nthe same as if the observer had been at\\nrest, but it will appear to come in the di-\\nrection of S E, the star being apparently\\nthrown forward from S to S\\\\ For, make\\nEA DE, and complete the parallelogram\\nC A and suppose, according to the princi-\\nple of equal action and reaction, that the\\nlight has a motion EC given to it, in place\\nof the earth s motion CE then the two\\nmotions EA and EC will produce the re-\\nsultant EB, as though the light had come\\nfrom S instead of S.\\nSince the earth moves 19 miles, and light 192,000 per second,\\nif S is in a direction perpendicular to the line of the earth s\\nmotion, the right-angled triangle ECB gives about 20 .5 for\\nthe displacement of the star. In fact, however, it was the ob-\\nserved displacement of 20 5 in all stars situated 90\u00c2\u00b0 from the\\ndirection in which the earth is moving at any time, which led\\nto the knowledge of the velocity of light thus,\\ntan 20 .5 K 19 192,000.\\nIf there were no change in the aberration of a star, the fact\\nof such aberration could never have been discovered. When\\nwe move directly toward or from a star, it plainly has no ab-\\nerration but three months before that time our motion crosses\\nthe line of the rays at right angles, and also three months after,\\nbut in a contrary direction. Hence any star in the plane of\\nthe ecliptic apparently moves back and forth over an arc of\\n41 (2 x 20 5) in a year. Those out of the ecliptic seem to\\ndescribe elliptic orbits, whose major axis is ll and of various\\neccentricity, the minor axis increasing with their latitude.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0133.jp2"}, "134": {"fulltext": "110 THE SUN.\\nMOTION OF THE APSIDES.\\n196. The two points of the ecliptic, where the earth is at\\nthe greatest and least distances from the sun respectively, do\\nnot always maintain the same places among the signs, but\\ngradually shift their positions from west to east. If we accu-\\nrately observe the place among the stars, where the earth is at\\nthe time of its perihelion the present year, we shall find that\\nit will not be precisely at that point the next year when it\\narrives at its perihelion, but about 12 (11 66) to the east of\\nit. And since the equinox itself, from which longitude is reck-\\noned, moves in the opposite direction 50 1 annually, the lon-\\ngitude of the perihelion increases every year 61 .76, or a little\\nmore than one minute. This fact is expressed by saying that\\nthe line of the apsides of the earth s orbit has a slow motion\\nfrom west to east. Tt completes one entire revolution in its\\nown plane in about 100,000 years (111,119).\\nThe mean longitude of the perihelion at the commencement\\nof the present century was 99\u00c2\u00b0 30 5 and of course in the\\nninth degree of Cancer, a little past the winter solstice. In\\nthe year 1248, the perihelion was at the place of this solstice.\\nThe advance of apsides is caused by the attraction of the\\nother planets. As their weight is mostly outside of the earth s\\norbit, their effect is to diminish the earth s tendency toward\\nthe sun. But this influence is, on the whole, greater when\\nthe earth is most distant; that is, at aphelion. Consequently\\nthe earth passes a little further onward than at the preceding\\nrevolution, before turning to approach the perihelion. Thus\\nthe aphelion advances, and the law of revolution requires that\\nthe perihelion be opposite to it hence that advances also.\\n197. The angular distance of a body from its perihelion is\\ncalled its Anomaly and the interval between the sun s pass-\\ning the point of the ecliptic corresponding to the earth s peri-\\nhelion, and returning to the same point again, is called the\\nanomalistic year. This period must be a little longer than\\nthe sidereal year, since, in order to complete the anomalistic\\nrevolution, the sun must traverse an arc of 11 .66 in addition\\nto 360\u00c2\u00b0. Now 360\u00c2\u00b0 365.256 11 .66 4m. 44s.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0134.jp2"}, "135": {"fulltext": "MEAN AND TRUE PLACES OF THE SUN. Ill\\n198. Since the points of the annual orbit, where the sun is\\nat the greatest and least distances from the earth, change their\\nposition with respect to the solstices, a slow change is occa-\\nsioned in the duration of the respective seasons. For, let the\\nperihelion correspond to the place of the winter solstice, as\\nwas the case in the year 1248 then as the sun moves more\\nrapidly in that part of his orbit, the winter season will be\\nshorter than the summer. But, again, let the perihelion be at\\nthe summer solstice, as it will be in the year 11740,* then the\\nsun will move most rapidly through the summer months, and\\nthe winters will be longer than the summers. At present the\\nperihelion is so near the winter solstice, that, the year being\\ndivided into summer and winter by the equinoxes, the six\\nwinter months are passed over between seven and eight days\\nsooner than the summer months.\\nMEAN AND TRUE PLACES OF THE SUN.\\n199. The Mean Motion of any body revolving in an orbit,\\nis that which it would have if, in the same time, it revolved\\nuniformly in a circle.\\nIn surveying an irregular field, it is common first to strike\\nout some regular figure, as a square or a parallelogram, by run-\\nning long lines, and disregarding many small irregularities in\\nthe boundaries of the field. By this process, we obtain an ap-\\nproximation to the contents of the field, although we have per-\\nhaps thrown out several small portions which belong to it, and\\nincluded a number of others which do not belong to it. These\\nbeing separately estimated and added to or subtracted from\\nour first computation, we obtain the true area of the field. In\\na similar manner, we proceed in finding the place of a heaven-\\nly body, which moves in an orbit more or less irregular. Thus\\nwe estimate the sun s distance from the vernal equinox for every\\nday of the year at noon, on the supposition that he moves uni-\\nformly in a circular orbit This is the sun s mean longitude.\\nWe then apply to this result various corrections for the irregu-\\nlarity of the sun s motions, and thus obtain the true longitude.\\n200. The corrections applied to the mean motions of a heav-\\nBiot.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0135.jp2"}, "136": {"fulltext": "112 THE SUN.\\nenly body, in order to obtain its true place, are called Equations.\\nTims the elliptical form of the earth s orbit, the precession of\\nthe equinoxes, and the nutation of the earth s axis, severally\\naffect the place of the sun in his apparent orbit, for which\\nequations are applied. In a collection of Astronomical Tables,\\na large part of the whole are devoted to this object. They give\\nus the amount of the corrections to be applied under all the\\ncircumstances and constantly varying relations in which the\\nsun, moon, and earth are situated with respect to each other.\\nThe angular distance, of the earth or any planet from its peri-\\nhelion, on the supposition that it moves uniformly in a circle,\\nis called its Mean Anomaly its actual distance at the same\\nmoment in its orbit is called its True Anomaly.\\nThus in figure 44, let AEP represent the orbit of the earth\\nhaving the sun in one of the foci at S. Upon AP describe the\\ncircle AMP. Let E be the place of the earth in its orbit, and\\nM the corresponding place in the circle Fj? 44\\nthen the angle MCP is the mean, and\\nESP the true anomaly. The difference\\nbetween the mean and true anomaly,\\nESP MCP, is called the Equation of\\nthe Center, being that correction which\\ndepends on the elliptical form of the or-\\nbit, or on the distance of the center of\\nattraction from the center of the figure,\\nthat is, on the eccentricity of the orbit. It is much the great-\\nest of all the corrections used in finding the sun s true longi-\\ntnde, amounting, at its maximum, to nearly two degrees (1\u00c2\u00b0\\n55 26 .8).\\nConsidering the mean and true anomaly as agreeing at P,\\nthe true place of the earth E is in advance of the mean place\\nM, because the velocity near the perihelion is greater than the\\nmean velocity. This difference between the mean and true\\nplaces (equation of the center), increases till the earth has ad-\\nvanced about 90\u00c2\u00b0 to D, when the velocity has reached its mean\\nvalue from D to A, the true place moves slower than the mean,\\nuntil at A the gain and loss are balanced, and the true and\\nmean again coincide. But, as the earth s motion is now slower\\nthan the average, the true place falls behind the mean, and the\\nequation is negative, till the earth returns to the perihelion.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0136.jp2"}, "137": {"fulltext": "CHAPTEE V.\\n-PHASES OF THE MOON HER\\nREVOLUTIONS.\\n201. Next to the Sun, the Moon naturally claims our atten\\ntion.\\nThe Moon is an attendant or satellite to the earth, around\\nwhich she revolves at the distance of nearly 240,000 miles.\\nHer mean horizontal parallax being 57 09 f consequently,\\nsin 57 09 semi-diameter of the earth (3956.2) rad 238,545.\\n(Art. 87.)\\nThe moon s apparent diameter is 31/ 7 and her real diameter\\n2160 miles. For,\\nEad 238,545 sin 15 33^ 1079.6. =moon s semi-diam-\\neter. (See Fig. 26, p. 71.)\\nAnd, since spheres are as the cubes of the diameters, the\\nvolume of the moon is that of the earth. Her density is\\nnearly f (.615) the density of the earth, and her mass x\\n.615) is about gV\\n202. The moon shines by reflected light borrowed from the\\nsun, and, when full, exhibits a disk of silvery brightness, di-\\nversified by extensive portions partially shaded. By the aid\\nof the telescope, we see undoubted signs of a varied surface,\\ncomposed of extensive tracts of level country, and numerous\\nmountains and valleys.\\n203. The line which separates the enlightened from the\\ndark portions of the moon s disk, is called the Terminator.\\n(See Fig. 2, Frontispiece.) As the terminator traverses the\\ndisk from new to full moon, it appears through the telescope\\nexceedingly broken in some parts, but smooth in others, indi-\\ncating that some portions of the lunar surface are uneven while\\nSelenography is a word more appropriate to a description of the moon, but is\\nnot perhaps sufficiently familiarized by use.\\nBaily s Astronomical Tables.\\n8", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0137.jp2"}, "138": {"fulltext": "114 THE MOON.\\nothers are level. The broken regions appear brighter than the\\nsmooth tracts. The latter were formerly taken for seas, and\\nreceived names accordingly; as A (Fig. 2, Fr.), mare humorum\\nB, mare nubium, c. But improved telescopes have shown\\nthat they are extensive plains, having inequalities which,\\nthough comparatively low, are permanent. That there are\\nmountains, is known by the following indications. As the ter-\\nminator advances over the disk, the light strikes the highest\\npeaks, which appear as bright points a little way upon the dark\\npart of the moon. After the terminator has passed over them,\\nthey project shadows away from the sun, corresponding to the\\napparent shape of the mountain, and growing shorter, as the\\nrays fall more nearly vertical. And again, in the waning of\\nthe moon, the shadows are cast in the opposite direction, length-\\nening until the dark part of the disk reaches them, and the\\nsummits once more become isolated bright points, and then dis-\\nappear. A view with a good telescope, continued for fifteen\\nminutes, will often show perceptible changes in the position of\\nthe shadows, and the shape of illuminated peaks.\\n204. The valleys very generally have a circular form, vary-\\ning in diameter from a mile or two up to sixty miles; the\\nmountain ridge, which surrounds them, being of a ring form,\\ngenerally much more precipitous on the inner side than the\\nouter. The heights surrounding these valleys are called ring-\\nmountains. One or more conical mountains frequently occu-\\npy the center of the area inclosed within the ring. Some of\\nthe principal are, !N~o. 1. Tycho 2. Kepler 3. Copernicus/\\n4. Aristarchus, c. (Fig. 1, Fr.) There are also larger and\\nless regular areas, surrounded by mountains, called bulwark\\nplains. The diameter of some is 130 miles and they gener-\\nally have small mountains, both of the conical and ring form,\\nscattered over the plain. The largest are Clavius, Walther,\\nRegiomontanus, Parbueh, Alphonse, Ptolemosus. Besides the\\npeculiar forms now mentioned, there are chains and spurs of\\nmountains, resembling terrestrial ranges.*\\nThe lunar map of Beer and Madler, 2\u00c2\u00a3 feet in diameter, contains a very per-\\nfect delineation of the mountains and valleys of the moon, accompanied by their\\nnames.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0138.jp2"}, "139": {"fulltext": "LUNAR GEOGRAPHY. 115\\n205. The appearances described in the foregoing articles\\nare obviously due to differences of elevation, since they are re-\\nvealed by the sun-light falling on them at considerable ob-\\nliquity. They come into view in succession, as the sun rises\\nupon them, during the first two quarters, or sets and leaves\\nthem in shade in the last two. At the full moon, the sun s\\nrays and our line of vision coincide in direction, and no shad-\\nows appear, and the features of mountain and valley are only\\nimperfectly seen. But a peculiarity of another kind presents\\nitself at the time of full moon. There are luminous stripes ex-\\ntending from several of the ring-mountains in straight lines to\\nthe distance of hundreds of miles. They are not ridges, since\\nthey cast no shadows as the terminator passes them and the\\ndifference of illumination must result from difference of reflect-\\nive power. But perhaps no satisfactory reason can be given\\nfor their remarkable arrangement. They are sometimes termed\\nlava lines. The most extensive systems of this kind occur\\naround Tycho, Copernicus, Kepler, and Anaxagoras.\\nThere is no appearance of fluidity on the lunar surface, nor\\nany such condition as we might expect to result from the flow\\nof a liquid. All inequalities are angular and rigid, instead of\\nbeing softened down by the action of water. There are no\\nchanges which might be ascribed to the growth and decay of\\nvegetation. No spot is ever concealed by a cloud, or dimmed\\nby an impure atmosphere. The cold is probably too intense\\nfor the existence of a liquid substance, just as the earth would\\nbe, if it were destitute of an atmosphere, and thus exposed to\\nthe low temperature of the space through which it travels.*\\n2G6. The method of estimating the height of lunar moun-\\ntains is as follows\\nLet ABO (Fig. 45) be the illuminated hemisphere of the\\nmoon, SO a solar ray touching the moon in O, a point in the\\ncircle which separates the enlightened from the dark part of\\nthe moon. All the part ODxA will be in darkness but if this\\npart contains a mountain MF, so elevated that its summit a[\\nreaches to the solar ray SOM, the point M will be enlightened.\\nFor a fuller description of the moon s surface, seeLardner s Hand-book on\\nMeteorology and Astronomy, pp. 208-212.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0139.jp2"}, "140": {"fulltext": "116\\nTHE MOON.\\nLet E be the place of an observer on the earth, and suppose a\\nline ES to be drawn to the sun then MES is the elongation\\nof the point M from the sun, which is determined by observa-\\ntion. The angle EMS can never differ so much as 9 from the\\nFig. 45.\\nsupplement of MES, on account of the great distance of the\\nsun compared with EM, which is about 400 to 1. But to ob-\\ntain EMS accurately, 400 1 sin MES sin ESM, which\\nangle subtracted from the supplement of MES, leaves EMS.\\nLet MEO, the visual angle between the mountain top and the\\nterminator, be measured by a micrometer. Then, as the dis-\\ntance from the earth to the moon is known, the isosceles trian-\\ngle NEO gives the length of ON. As E is very small, the\\nangles at N may be considered right angles hence, the right-\\nangled triangle OMN, in which ON and M are known, gives\\nOM. Finally, from the known sides- OC and OM, in the right-\\nangled triangle OMC, CM is obtained and OC being sub-\\ntracted from it, we find MF, the height of the mountain.\\n207. As OM is very small compared with OC, FM is both\\nmore easily and more accurately found by taking the third\\nproportional to 20 C and OM. For, suppose a perpendicular\\ndrawn from F to OC then OM may be called equal to FO,\\nand FM to the versed sine; hence 20C MO MO FM.\\nThe whole work may be finished by logarithms, without taking", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0140.jp2"}, "141": {"fulltext": "LUNAR GEOGRAPHY. U 7\\nfrom the tables any natural number, except FM the quantity\\nsought. The heights of some mountains, determined in this\\nway, have been found between three and four miles.\\nWhen the moon is exactly at quadrature, EMS is a right\\nangle, and OM (being coincident with ON) is obtained direct-\\nly from the micrometrical measurement of the angle E from\\nwhich FM is derived as before.\\n208. Schroeter, a German astronomer, estimated the heights\\nof the lunar mountains by observations on their shadows. He\\nmade them in some cases as high as -^tt \u00c2\u00b0f ne semi-diameter\\nof the moon, that is, about 5 miles. The same astronomer\\nalso estimates the depths of some of the lunar valleys at more\\nthan four miles. Hence it is inferred that the moon s surface\\nis more broken and irregular than that of the earth, its moun-\\ntains being higher and its valleys deeper in proportion to the\\nsize of the moon than those of the earth.\\n209. It has sometimes been supposed that there are slight\\nindications of an atmosphere about the moon. This is proba-\\nbly an error. The severest test of a perceptible atmosphere\\nwould be the effect on a star, at the beginning and end of its\\noccultation by the moon. The star would appear to be detain-\\ned a little in its diurnal motion, just before disappearing, and\\njust after reappearing, in consequence of the bending of the\\nrays which come from it, as they pass the edge of the moon s\\ndisk, and probably some loss of light would in that case be\\nperceptible at the same moments. But the most careful ob-\\nservations have failed to show any such detention and as to\\nloss of light, the star, on coming up to the edge of the moon\\ndisappears all at once, with a suddenness which is startling.\\nIf there is an atmosphere, it cannot have a thousandth part of\\nthe density of the earth s.*\\n210. The improbability of our ever identifying artificial\\nstructures in the moon may be inferred from the fact that a\\nline one mile in length in the moon subtends an angle at the\\neye of only about one second. If, therefore, works of art were\\nc Lardner.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0141.jp2"}, "142": {"fulltext": "IIS THE MOON\\nto have a sufficient horizontal extent to become visible, they\\ncan hardly be supposed to attain the necessary elevation, when\\nwe reflect that the height of the great pyramid of Egypt is less\\nthan the sixth part of a mile.\\nPHASES OF THE MOON.\\n211. The changes of the moon, commonly called her\\nPhases, arise from different portions of her illuminated side\\nbeing turned toward the earth at different times. When the\\nmoon is first seen after the setting sun, her form is that of a\\nbright crescent, on the side of the disk next to the sun, while\\nthe other portions of the disk shine with a feeble light, reflect-\\ned to the moon from the earth. Every night we observe the\\nmoon to be further and further eastward of the sun, and at the\\nsame time the crescent enlarges, until, when it has reached an\\nelongation from the sun of nearly 90\u00c2\u00b0, half her visible disk is\\nenlightened, and she is said to be in her first quarter. The\\nterminator, or line which separates the illuminated from the\\ndark part of the moon, is convex toward the sun from the\\nnew moon to the first quarter, and the moon is said to be\\nhorned. The extremities of the crescent are called cusps. At\\nthe first quarter, the terminator becomes a straight line, coin-\\nciding with a diameter of the disk but after passing this\\npoint, the terminator becomes concave toward the sun, bound-\\ning that side of the moon by an elliptical curve, when the\\nmoon 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,\\nrising about the time the sun sets. For a week after the full, the\\nmoon appears gibbous again, until, at a little less than 90\u00c2\u00b0\\nfrom the sun, she resumes the same form as at the first quarter,\\nbeing then at her third quarter. From this time until new\\nmoon, she exhibits again the form of a crescent before the\\nrising sun, until approaching her conjunction with the sun,\\nher narrow thread of light is lost in the solar blaze; and final-\\nly, at the moment of passing the sun, the dark side is wholly\\nturned toward us and for some time we lose sight of the moon.\\nThe two points in the orbit corresponding to new and full\\nmoon respectively, are called by the common name of syzygies", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0142.jp2"}, "143": {"fulltext": "PHASES. 119\\nthose which are 90\u00c2\u00b0 degrees from the sun are called quadra-\\ntures j and the points half way between the syzygies and quad-\\nratures are called octants. The circle which divides the en-\\nlightened from the unenlightened hemisphere of the moon, is\\ncalled the circle of illumination that which divides the hem-\\nisphere that is turned toward us from the opposite one is called\\nthe circle of the disk. The degree of each phase depends on\\nthe angle between these circles.\\n212. As the moon is an opaque body of a spherical figure,\\nand borrows her light from the sun, it is obvious that that\\nhalf only which is toward the sun can be illuminated. More\\nor less of this side is turned toward the earth, according as\\nthe moon is at a greater or less elongation from the sun. The\\nreason of the different phases will be best understood from a\\nFig. 46.\\ndiagram. Therefore, let T (Fig. 46) represent the earth, and\\nS the sun. Let A, B, C, c, be successive positions of the\\nmoon. At A the entire dark side of the moon being turned\\ntoward the earth, the disk would be wholly invisible. At B,\\nthe circle of the disk cuts off a small part of the enlightened\\nhemisphere, which appears in the heavens at 5, under the form\\nof a crescent. At C, the first quarter, the circle of the disk\\ncuts off half the enlightened hemisphere, and the moon appears\\ndichotomized at c. In like manner it will be seen that the\\nappearances presented at D, E, F, c, must be those repre-\\nsented at d, e,f.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0143.jp2"}, "144": {"fulltext": "120 THE MOON.\\nREVOLUTIONS OF THE MOON.\\n213. The moon revolves around the earth from west to east,\\nmaking the entire circuit of the heavens in about 27 days.\\nThe precise law of the moon s motions in her revolution\\naround the earth is ascertained, as in the case of the sun (Art.\\n155), by daily observations on her meridian altitude and right\\nascension. Thence are deduced by calculation her latitude\\nand longitude, from which we find, that the moon describes\\non the celestial sphere a great circle of which the earth is the\\ncenter.\\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 sy nodical month* is\\nthe time from one conjunction or new moon to another. The\\nsynodical month is about 29} 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. ll s .5= 27.32 days. As the sun\\nand moon are both revolving in the same direction, and the\\nsun is moving nearly a degree a day, during the 27 days of the\\nmoon s revolution, the sun must have moved 27\u00c2\u00b0. Now since\\nthe moon passes over 360\u00c2\u00b0 in 27.32 days, her daily motion\\nmust be 13\u00c2\u00b0 17 It must therefore evidently take about two\\ndays for the moon to overtake the sun. The difference between\\nthese two periods may, however, be determined with great\\nexactness. The middle of an eclipse of the sun marks the\\ntime of conjunction or new moon and by dividing the inter-\\nval between any two distant solar eclipses by the number of\\nrevolutions of the moon, or lunations, we obtain the precise\\nperiod of the synodical month. Suppose, for example, two\\neclipses occur at an interval of 1,000 lunations then the whole\\nnumber of days and parts of a day that compose the interval\\ndivided by 1,000 will give the exact time of one lunation. f\\nThe time of the synodical month being ascertained, the exact\\nperiod of the sidereal month may be derived from it. For the\\naw and o 5os, implying that the two bodies come together.\\nf It might at first view seem necessary to know the period of one lunation be-\\nfore we could know the number of lunations in any given interval. This period\\nis known very nearly from the interval between one new moon and another.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0144.jp2"}, "145": {"fulltext": "REVOLUTIONS. 1 21\\narc which the moon describes in order to come into conjunc-\\ntion with the sun, exceeds 360\u00c2\u00b0 by the space which the sun has\\npassed over since the preceding conjunction, that is, in 29.53\\ndays. Therefore,\\n365.24 360\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, as\\nthe whole distance the moon must move from the sun to reach\\nit again, is to one revolution of the moon, so is the time of ac-\\ncomplishing the former, to the time of a revolution; i. e.,\\n360\u00c2\u00b0+29\u00c2\u00b0.l 360\u00c2\u00b0 29.53d. 27.32d.\\n214.. The moon s orbit is inclined to the ecliptic at an angle\\nof about 5\u00c2\u00b0 (5\u00c2\u00b0 8 48 The intersections are called the ascend-\\ning and descending nodes through the ascending, the moon\\npasses from south to north through the descending, from\\nnorth to south. The angle is found by measuring the moon s\\ngreatest latitude, which is, of course, equal to the inclination\\nof the circles.\\n215. The moon, at the same age, crosses the meridian at\\ndifferent altitudes at different seasons of the year. The full\\nmoon, for example, will appear much further in the south\\nwhen on the meridian at one period of the year than at anoth-\\ner. This is owing to the fact that the moon s path is different-\\nly situated with respect to the horizon, at a given time of\\nnight, at different seasons of the year. By taking the ecliptic\\non an. artificial globe to represent the moon s path (which is\\nalways near it, Art. 214), and recollecting that the new moon\\nis seen in the same part of the heavens with the sun, and the\\nfull moon in the opposite part of the heavens from the sun, we\\nshall readily see that in the winter the new moons must run\\nlow because the sun does, and for a similar reason the full\\nmoons mast run high. It is equally apparent that, in summer,\\nwhen the sun runs high, the new moons must cross the merid-\\nian at a high, and the full moons at a low altitude. This\\narrangement gives us a great advantage in respect to the\\namount of light received from the moon since the full moon\\nis longest above the horizon during the long nights of winter.\\nwhen her presence is most needed. This circumstance is es-\\npecially favorable to the inhabitants of the polar regions, the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0145.jp2"}, "146": {"fulltext": "122 THE MOON.\\nmoon, when full, traversing that part of her orbit which lies\\nnorth of the equator, and of course above the horizon of the\\nnorth pole, and traversing the portion that lies south of the\\nequator, and below the polar horizon, when new. During the\\npolar winter, therefore, the moon, from the first to the last\\nquarter, is commonly above the horizon, while the sun is ab-\\nsent whereas, during summer, while the sun is present, the\\nmoon is above the horizon while describing her first and last\\nquadrants.\\n216. About the time of the autumnal equinox, the moon\\nwhen near the full, rises about sunset for a number of nights\\nin succession; and as this is, in England, the period of har-\\nvest, the phenomenon is called the Harvest Moon. To un-\\nderstand the reason of this, since the moon is never far from\\nthe ecliptic, we will suppose her progress to be in the ecliptic.\\nIf the moon moved in the equator, then, since this great circle\\nis at right angles to the axis of the earth, all parts of it, as the\\nearth revolves, would cut the horizon at the same constant angle.\\nBut the moon s orbit, or the ecliptic, which is here taken to\\nrepresent it, being oblique to the equator, cuts the horizon at\\ndifferent angles in different parts, as will easily be seen by\\nreference to an artificial globe. When the first of Aries, or\\nvernal equinox, is in the eastern horizon, it will be seen that\\nthe ecliptic (and consequently the moon s orbit) makes its\\nleast angle with the horizon. Now at the autumnal equinox,\\nthe sun being in Libra, the moon at the full is in Aries, and\\nrises when the sun sets. On the following evening, although\\nshe has advanced in her orbit about 13\u00c2\u00b0 (Art. 213), yet her\\nprogress being oblique to the horizon, and at a small angle\\nwith it, she will be found at this time but a little way below\\nthe horizon, compared with the point where she was at sunset\\nthe preceding evening. She therefore rises but a little later\\neach evening than she did on the evening previous, but her\\nplace of rising moves rapidly northward. It should be ob-\\nserved, that in making her revolution round the earth, the\\nmoon must pass the first of Aries, and therefore make these\\nsmall differences in the time of rising, every month. But as\\nthe moon is not full at the same time, except in autumn, the\\ncircumstance attracts no attention.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0146.jp2"}, "147": {"fulltext": "REVOLUTIONS. 123\\nWhen the ascending node is at the vernal equinox, the\\nangle of the moon s path with the horizon at the time of rising,\\nis 10\u00c2\u00b0 smaller than when the descending node is there and the\\nintervals vary accordingly. This occurs once in about 18 years.\\n217. The moon is about }q nearer to us when near the zenith\\nthan when in the horizon.\\nThe horizontal distance CD (Fig 47) is Fig. 47.\\nnearly equal to AD=AD which is great-\\ner than CD by AC, the semi-diameter of\\nthe earth =6 J o the distance of the moon.\\nAccordingly, the apparent diameter of the\\nmoon, when actually measured, is about D\\n30 (which equals about of the whole) greater when in the\\nzenith than in the horizon. The apparent enlargement of the\\nfull moon when rising, is owing to the same causes as that of\\nthe sun, as explained in article 96.\\n218. The moon turns on its axis in the same time in which\\nit revolves around the earth.\\nThis is knowm by the moon s always keeping nearly the\\nsame face toward us, as is indicated by the telescope, which\\ncould not happen unless her revolution on her axis kept pace\\nwith her motion in her orbit. Thus, it will be seen by in-\\nspecting figure 31, that the earth turns different faces toward\\nthe sun at different times and if a ball having one hemi-\\nsphere white and the other black be carried around a lamp, it\\nwill easily be seen that it cannot present the same face con-\\nstantly toward the lamp unless it turns once on its axis while\\nperforming its revolution. But though the same side of the\\nmoon on the whole is always toward the earth, yet there are\\nsmall apparent oscillations, by which narrow portions of the\\nremote side are presented alternately to view. These are\\ncalled Vibrations.\\n219. One is the libralion in longitude, because it brings\\ninto view portions of the equator on one side and then on the\\nother. It is owing to the fact that the moon revolves uni-\\nformly on its axis, and with unequal angular motion around\\nthe earth. Near the apogee, where she advances slowest, she", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0147.jp2"}, "148": {"fulltext": "12\u00c2\u00b1 THE MOON.\\ndescribes less than 90\u00c2\u00b0 of her orbit while she turns just one-\\nfourth round upon her axis consequently showing us a little\\nof the further side on the east limb. But in the perigeal part\\nof her orbit, she advances faster than the mean, and therefore\\nin one-fourth of her diurnal rotation she moves forward more\\nthan 90\u00c2\u00b0 in her orbit, and presents some surface beyond the\\nwest limb.\\nThe libration in latitude, by which she alternately presents\\nto our view the space about her poles, is caused by the obliqui-\\nty of her equator to her orbit. Her equator is inclined about\\n1^\u00c2\u00b0 (1\u00c2\u00b0 30 il to the ecliptic, and remains parallel to itself.\\nBut the angle between her equator and orbit varies from about\\n3^-\u00c2\u00b0 to 6-J\u00c2\u00b0, on account of the morion of the nodes. Each pole\\nof the moon is presented toward the earth every 27 days, just\\nas the earth s poles are turned toward the sun every year,\\nthough in a much less degree. (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 toward the center of the\\nearth only, whereas we view her from the surface. When she\\nis on the meridian, we see her disk nearly as though we\\nviewed it from the center of the earth, and hence in this situa-\\ntion it is subject to little change but when near the horizon,\\nour circle of vision takes in more of the upper limb than\\nwould be presented to a spectator at the center of the earth.\\nHence, from this cause, we see a portion of one limb while the\\nmoon is rising, which is gradually lost sight of, and we see a\\nportion of the opposite limb as the moon declines toward the\\nwest. It will be remarked that neither of the foregoing\\nchanges implies any actual motion in the moon, but that each\\narises from a change of position in the spectator relative to the\\nmoon.\\n220. An inhabitant of the moon would have but one day\\nand one night during the whole lunar month of 29|- days.\\nOne of its days, therefore, is equal to nearly 30 of ours. So\\nprotracted an exposure to the sun s rays, if the moon had an\\natmosphere like that of the earth, would occasion an excessive\\naccumulation of heat and so long an absence of the sun must\\noccasion a corresponding degree of cold. Each day would be", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0148.jp2"}, "149": {"fulltext": "REVOLUTION-. 125\\na wearisome summer each night a severe winter.* A spec-\\ntator on the side of the moon which is opposite to us would\\nnever see the earth but one on the side next to us would see\\nthe earth presenting a gradual succession of changes during\\nhis long night of 360 hours. Soon after the earth s conjunc-\\ntion with the sun, he would have the light of the earth re-\\nflected to him, presenting at first a crescent, but enlarging, as\\nthe earth approaches its opposition, to a great orb, 13 times as\\nlarge as the full moon appears to us, and affording nearly 13\\ntimes as much light. Our seas, plains, mountains, and clouds,\\nwould present a great diversity of appearance, as the earth\\nperformed its diurnal rotation though the distinctness would\\nbe much impaired by the strong light reflected by our atmos-\\nphere. The earth to his view would remain always in the\\nsame part of the sky, having only small monthly oscillations,\\nnorth and south, by means of the libration in latitude, also\\neast and west, by the libration in longitude. For, being un-\\nconscious of his own motion around the earth, it would seem\\nto revolve about his planet from west to east; but, meanwhile,\\nhis own diurnal rotation would give the earth an apparent\\nmotion to the west at the same mean rate, and the two would\\nbalance each other, except so far as the librations would affect\\nthem. An observer on the center of the moon s disk, would\\nsee the earth always over head one at the edge of the disk,\\nwould see it at the horizon. The earth is full to the moon\\nwhen the latter is new to us and universally the two phases\\nare complementary to each other.\\n221. If the ecliptic (the earth s path about the sun), and\\nthe moon s path about the earth, were visible lines in the sky,\\nsince we are in the plane of each, they would both appear as\\ngreat circles intersecting each other in opposite points, and in-\\nclined about 5\u00c2\u00b0 to each other. But if we could take a view of\\nthese orbits from a distant position out of their planes, they\\nwould appear as two very unequal circles, one having a diam-\\neter 400 times greater than the other, and the small circle\\nmoving around with its center upon the circumference of the\\nlarge one, once in a year.\\nFrancoeur, Uranog., p. 91.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0149.jp2"}, "150": {"fulltext": "126 THE MOON,\\nBut again, if we confine our attention to the moon s patli in\\nits relations to the sun, instead of the earth, and trace it as a\\nvisible line in the solar system, we shall see that it loses en-\\ntirely its character of a small circle on the circumference of a\\nlarge one. On the other hand, it can hardly be distinguished\\nfrom the earth s orbit itself, making 25 slight undulations al-\\nternately inside and outside of it, and never deviating from it\\nmore than one 400th part of its radius, as represented in\\nFig. 4:7\\nFig. 47*.\\nIf we regard now the forces to which the moon is subjected\\nin describing this path, it is clear, that since it differs so little\\nfrom that of the earth, the moon must be controlled by nearly\\nthe same forces as those which keep the earth in its orbit so\\nthat, if the earth were annihilated, the moon would still pre-\\nserve its course round the sun, with so little change from its\\npresent orbit, that it would hardly be noticed by an observer\\nwho could take the whole into view at once. According to\\nthe second law of motion (Nat. Phil., Art. 12), the moon s mo-\\ntion round the earth simply co-exists with its motion round the\\nsun and the joint effect is a curve of that species called an\\nepicycloid.\\n,222. The relative attraction exerted by the sun and earth\\nupon the moon, is found by applying the formula (Art. 177)\\nfco Calling the radius of the moon s orbit=l, that of the\\nearth s is about 400 and the times are 27.32 and 365.25.\\nHence, attraction to the sun that to the earth /ft _^ 5\\n(36o.2o)\\n2.2 1, So that the sun, though so very far from\\n(27.32)\\nthe moon, exerts upon it 2J times more attraction than the\\nearth does. The moon, therefore, is much more under the in-\\nfluence of the sun than of the earth the latter only causing it", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0150.jp2"}, "151": {"fulltext": "LUNAR IRREGULARITIES. 127\\nto oscillate on her own path as already shown. When the\\nmoon is in conjunction, the attraction of the earth diminishes\\nits tendency to the sun, and therefore its distance increases, till\\nit comes to the opposition and while thus ascending, being\\nin the rear of the earth, it is accelerated by it, and goes past it\\nat the moment of opposition. But now the attraction of the\\nearth conspires with that of the sun, so that the moon can not\\nkeep in a circular orbit at that distance, and therefore descends\\nagain toward the conjunction. While descending, being now\\nin advance of the earth, it is retarded by it, and loses so much\\nof its velocity, that on reaching the conjunction, the earth\\npasses it again as before. Thus the moon, by the earth s\\ninfluence, approaches the sun, and then recedes from it, and\\nalso gains velocity, and then loses it, suffering these changes\\nas slight disturbances in its great annual revolution about the\\nsun.\\nThe earth is also affected in precisely the same manner,\\nthough in a far less degree*, by the moon it is the center of\\ngravity of the two, which describes the annual elliptical orbit.\\n223. If a chord be supposed drawn in the earth s orbit\\n(Fig. 47 between successive points of quadrature, it is found\\nthat this chord, at its middle point, falls about 600,000 miles\\nwithin the orbit, while the moon is only 238,000 miles within\\nit at the conjunction. Her path is, therefore, so near that of\\nthe earth as to be always concave toward the sun.\\nCHAPTER VI.\\nLUNAR IRREGULARITIES.\\n224. Considering the moon s motion simply in its relation\\nto the earth, we have thus far spoken of its path as an ellipse,\\nwith the earth in one focus. But careful observations have\\nproved that this elliptical revolution is subject to numerous\\nirregularities. The law of universal gravitation has been ap-\\nplied with wonderful success to their investigation, and its", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0151.jp2"}, "152": {"fulltext": "128 THE MOON.\\nresults have conspired, with those of long-continued observa-\\ntion, to furnish the means of ascertaining, with great exactness,\\nthe place of the moon in the heavens at any given instant of\\ntime, past or future, and thus to enable astronomers to deter-\\nmine longitudes, to calculate eclipses, and to solve various other\\nproblems of the highest interest. A complete understanding\\nof all the irregularities of the moon s motions must be sought\\nfor in more extensive treatises of astronomy than the present\\nbut some general acquaintance with the subject, clear and in-\\ntelligible, as far as it goes, may be acquired by first gaining a\\ndistinct idea of the mutual actions of the sun, the moon, and\\nthe earth.\\n225. The irregularities of the moon s motions are due chiefly\\nto the disturbing influence of the sun, which operates in two\\nways first, by acting unequally on the earth and moon, and,\\nsecondly, by acting obliquely on the moon.\\nIf the sun acted equally on the earth and moon, and always\\nin parallel lines, this action would serve only to restrain them\\nin their annual motions round the sun, and would not affect\\ntheir actions on each other, or their motions about their com-\\nmon center of gravity. In that case, if they were allowed to\\nfall directly toward the sun, they would fall equally, and their\\nrespective situations would not be affected by their descending\\nequally toward it. We might then conceive them as in a\\nplane, every part of which being equally acted on by the sun,\\nthe whole plane would descend toward the sun, but the re-\\nspective motions of the earth and the moon in this plane w T ould\\nbe .the same as if it were quiescent. Supposing, then, this\\nplane and all in it to have an annual motion imprinted on it,\\nit would move regularly round the sun, while the earth and\\nmoon would move in it, with respect to each other, as if the\\nplane were at rest, without any irregularities. But because\\nthe moon is nearer the sun in one half of her orbit than the\\nearth is, and in the other half of her orbit is at a greater dis-\\ntance than the earth from the sun, while the power of gravity\\nis always greater at a less distance, it follows, that in one-half\\nof her orbit the moon is more attracted than the earth toward\\nthe sun, and in the other half less attracted than the earth.\\nThe excess of the attraction, in the first case, and the defect in", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0152.jp2"}, "153": {"fulltext": "LUNAR IRREGULARITIES. 129\\nthe second, constitutes a disturbing force; to which we may\\nadd another, namely, that arising- from the oblique action of\\nthe solar force, since this action is not directed in parallel\\nlines, but in lines that meet in the center of the sun and one\\npart of this oblique action is in the orbit of the moon, being\\nnow east of the earth, and then west of it and the other part\\nis from the orbit toward the plane of the ecliptic.\\n226. To see the effects of this process, let us suppose that\\nthe projectile motions of the earth and moon were destroyed,\\nand that they were allowed to fall freely toward the sun. If\\nthe moon was in conjunction with the sun, or in that part of\\nher orbit which is nearest to him, the moon would be more\\nattracted than the earth, and fall with greater velocity toward\\nthe sun so that the distance of the moon from the earth would\\nbe increased in the fall. If the moon was in opposition, or in\\nthe part of her orbit which is farthest from the sun, she would\\nbe less attracted than the earth by the sun, and would fall\\nwith a less velocity toward the sun, and would be left behind\\nso that the distance of the moon from the earth would be in-\\ncreased in this case also. If the moon was in one of the quar-\\nters, then the earth and moon being both attracted toward the\\ncenter of the sun, they would both descend directly toward\\nthat center, and by approaching it, they would necessarily, at\\nthe same time, approach each other, and in this case their\\ndistance from each other would be diminished. Now when-\\never the action of the sun would increase their distance, if\\nthey were allowed to fall toward the sun, then the sun s action,\\nby endeavoring to separate them, diminishes their gravity to\\neach other whenever the sun s action would diminish the\\ndistance, then it increases their mutual gravitation. Hence,\\nin the conjunction and opposition, that is, in the syzygies,\\ntheir gravity toward each other is diminished by the action of\\nthe sun, while in the quadratures it is increased. But it must\\nbe remembered that it is not the total action of the sun on\\nthem that disturbs their motions, but only that part of it\\nwhich tends at one time to separate them, and at another time\\nto bring them nearer together. The other and far greater part,\\nhas no other effect than to retain them in their annual course\\naround the sun.\\n9", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0153.jp2"}, "154": {"fulltext": "130\\nTHE MOON.\\n227. Suppose the moon setting out from the quarter that\\nprecedes the conjunction with a velocity that would make her\\ndescribe an exact circle round the earth, if the sun s action had\\nno effect on her since her gravity is increased by that action,\\nshe must descend toward the earth and move within that cir-\\ncle. Her orbit then would be more curved than it otherwise\\nwould have been because the addition to her gravity will\\nmake her fall further at the end of an arc below the tangent\\ndrawn at the other end of it. Her motion will be thus accel-\\nerated, and it will continue to be accelerated until she arrives\\nat the ensuing conjunction, because the direction of the sun s\\naction upon her, during that time, makes an acute angle with\\nthe direction of her motion. (See Fig. 41.) At the conjunc-\\ntion, her gravity toward the earth being diminished by the\\naction of the sun, her orbit will then be less curved, and she\\nwill be carried further from the earth as she moves to the next\\nquarter; and because the action of the sun makes there an\\nobtuse angle with the direction .of\\nher motion, she will be retarded in Flg 48\\nthe same degree as she was acceler-\\nated before.\\n228. After this general explana-\\ntion of the mode in which the sun\\nacts as a disturbing force on the mo-\\ntions of the moon, the learner will\\nbe prepared to understand the math-\\nematical development of the same\\ndoctrine.\\nTherefore, let ADBC (Fig. 48) be\\nthe orbit, nearly circular, in which\\nthe moon M revolves in the direc-\\ntion CADB, round the earth E.\\nLet S be the sun, and let SE, the\\nradius of the earth s orbit, be taken\\nto represent the force with which\\nthe earth gravitates to the sun.\\nThen (Art. 181) SE the force by which\\nthe sun draws the moon in the direction MS. Take MG", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0154.jp2"}, "155": {"fulltext": "LUNAR IRREGULARITIES. 131\\nSE 3\\nQ^ 23 and let the parallelogram KF be described, having MG\\nfor its diagonal* and having its sides parallel to EM and ES.\\nThe force MG may be resolved into two, MF and MK, of\\nwhich MF, directed toward E, the center of the earth, in-\\ncreases the gravity of the moon to the earth, and does not\\nhinder the areas described by the radius vector from being\\nproportional to the times. The other force MK draws the\\nmoon in the direction of the line joining the centers of the\\nsun and earth. It is, however, only the excess of this force\\nabove the force represented by SE, or that which draws the\\nearth to the sun, which disturbs the relative position of the\\nmoon and earth. This is evident, for if KM were just equal to\\nES, no disturbance of the moon, relative to the earth, could\\narise from it. If, then, ES be taken from MK, the difference\\nHK is the whole force in the direction parallel to SE, by which\\nthe sun disturbs the relative position of the moon and earth.\\nNow, if in MK, MN be taken equal to HK, and if NO be\\ndrawn perpendicular to the radius vector EM produced, the\\nforce MIST may be resolved into two, MO and ON, the first\\nlessening the gravity of the moon to the earth and the second,\\nbeing parallel to the tangent of the moon s orbit in M, accel-\\nerates the moon s motion from C to A, and retards it from A\\nto D, and so alternately in the other two quadrants. Thus the\\nwhole solar force directed to the center of the earth, is com-\\nposed of the two parts MF and MO, which are sometimes op-\\nposed to one -another, but which never affect the uniform\\ndescription of the areas about E. Near the quadratures the\\nforce MO vanishes, and the force MF, which increases the\\ngravity of the moon to the earth, coincides with CE or DE.\\nAs the moon approaches the conjunction at A, the force MO\\nprevails over MF, and lessens the gravity of the moon to the\\nearth. In the opposite point of the orbit, when the moon is in\\nopposition at B, the force with which the sun draws the moon\\nis less than that with which the sun draws the earth, so that\\nthe effect of the solar force is to separate the moon and earth,\\nor to increase their distance that is, it is the same as if, con-\\nceiving the earth not to be acted on, the sun s force drew the\\nmoon in the direction from E to B. This force is negative,\\ntherefore, in respect to the force at A, and the effect in both", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0155.jp2"}, "156": {"fulltext": "132 THE MOON.\\ncases is to draw the moon from the earth in a direction perpen-\\ndicular to the line of the quadratures. Hence, the general\\nresult is, that by the disturbing force of the sun, the gravity to\\nthe earth is increased at the quadratures, and diminished at\\nthe syzygies. It is found by calculation that the average\\namount of this disturbing force is 5^ of the moon s gravity to\\nthe earth.*\\n229. With, these general principles in view, we may now\\nproceed to investigate the figure of the moon s orbit, and the\\nirregularities to which the motions of this body are subject.\\n230. The figure of the moon s orbit is an ellipse r having the\\nearth in one of the foci.\\nThe elliptical figure of the moon s orbit, is revealed to us by\\nobservations on her changes in apparent diameter, and in her\\nhorizontal parallax. First, we may measure from day to day\\nthe apparent diameter of the moon. Its variations being in-\\nversely as the distances (Art. 163), they give us at once the\\nrelative distance of each point of observation from the focus.\\nSecondly, the variations on the moon s horizontal parallax,\\nwhich also are inversely as the distances (Art. 82),, lead to the\\nsame results. Observations on the angular velocities, com-\\nbined with the changes in the lengths of the radius vector, af-\\nford the means of laying down a plot of the lunar orbit, as in\\nthe case of the sun, represented in figure 32. The orbit is\\nshown to be nearly an ellipse, because it is found to have the\\nproperties of an ellipse.\\nThe moon s greatest and least apparent diameters are respect-\\nively 33 518 and 29 365, while her corresponding changes of\\nparallax are 61 .4 and 53 8. The two ratios ought to be equal,\\nand we shall find such to be the fact very nearly, as expressed\\nby the foregoing 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.\\nHence, taking the arithmetical mean, which is 59.879, we find\\nPlay fair.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0156.jp2"}, "157": {"fulltext": "LUNAR IRREGULARITIES. 133\\nthat the mean distance of the moon from the earth is very\\nnearly 60 times the radius of the earth. The point in the\\nmoon s orbit nearest the earth, is called her perigee the point\\nfurthest from the earth, her apogee.\\nThe greatest and least apparent diameters of the sun are re-\\nspectively 32.583, and 31.517, which numbers express also the\\nratio of the greatest and least distances of the earth from the\\nsun. By comparing this ratio with that of the distances of the\\nmoon, it will be seen that the latter vary much more than the\\nformer, and consequently that the lunar orbit is much more ec-\\ncentric than the solar. The eccentricity of the moon s orbit is\\nin fact 0.0548 (the semi-major axis being as usual taken for\\nunity)= T 1 of its mean distance from the earth, while that of\\nthe earth is only .01685 of its mean distance from the sum\\n231. The moorHs nodes constantly shift their positions in\\nthe eeliptic from east to west, at the rate of 19\u00c2\u00b0 S^ per annum^\\nreturning io the same points in 18.6 years.\\nSuppose the great circle of the ecliptic marked out on the\\nface of the sky in a distinct line, and let us observe, at any\\ngiven time, the exact point where the moon crosses this line,\\nwhich we will suppose to be close to a certain star then, on\\nits next return to that part of the heavens, we shall find that\\nit crosses the ecliptic sensibly to the westward of that star, and\\nso on, further and further to the westward every time it crosses\\nthe ecliptic at either node. This fact is expressed by saying\\nthat the nodes retrograde on the ecliptic, and that the line which\\njoins them, or the line of the nodes, revolves from east to west.\\n232. This shifting of the moon s nodes implies that the lu-\\nnar orbit is not a curve returning into itself, but that it more\\nresembles a spiral like the curve represented in figure 49, where\\nabc represents the ecliptic, and ABC Flg 49\\nthe lunar orbit, having its nodes at b\\nC and E, instead of A and a\\\\ con- /^^^^^^s.\\nsequently, the nodes shift backward v Y\\\\\\nthrough the arcs aG and AE. The J) e\\nmanner in which this effect is pro- V W..\\nduced may be thus explained. That ^f^zrr^\\npart oi the solar force which is parallel to the line joining the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0157.jp2"}, "158": {"fulltext": "134: THE MOON.\\ncenters of the sun and earth (see Fig. 4S), is not in the plane\\nof the moon s orbit (since this is inclined to the ecliptic about\\n5\u00c2\u00b0), except when the sun itself is in that plane, or when the\\nline of the nodes being produced passes through the sun. In\\nall other cases it is oblique to the plane of the orbit, and may\\nbe resolved into two forces, one of which is at right angles to\\nthat plane, and is directed toward the ecliptic. This force of\\ncourse draws the moon continually toward the ecliptic, or pro-\\nduces a continual deflection of the moon from the plane of her\\nown orbit toward that of the earth. Hence the moon meets\\nthe plane of the ecliptic sooner than it would have done if that\\nforce had not acted. At every half revolution, therefore, the\\npoint in which the moon meets the ecliptic shifts in a direction\\ncontrary to that of the moon s motion, or contrary to the order\\nof the signs. If the earth and sun were at rest, the effect\\nof the deflecting force just described would be to produce a\\nretrograde motion of the line of the nodes till that line was\\nbrought to pass through the sun, and, of consequence, the plane\\nof the moon s orbit to do the same, after which they would\\nboth remain in their position, there being no longer any force\\ntending to produce change in either. But the motion of the\\nearth carries the line of the nodes out of this position, and pro-\\nduces, by that means, its continual retrogradation. The same\\nforce produces a small variation in the inclination of the moon s\\norbit, giving it an alternate increase and decrease within very\\nnarrow limits.* These points will be easily understood by the\\naid of a diagram. Therefore, let MN (Fig. 50) be the ecliptic,\\nAE B the orbit of the moon, the moon being in L, and N its\\ndescending node. Let the disturbing force of the sun which\\ntends to bring it down to the ecliptic be represented by L5, and\\nits velocity in its orbit by ~La. Under the action of these two\\nforces, the moon will describe the diagonal Lc of the parallelo-\\ngram ba, and its orbit will be changed from AN to ~LN the\\nnode N passes to N and the exterior angle at W of the tri-\\nangle LNJSP being greater than the interior and opposite angle\\nat N, the inclination of the orbit is increased at the node.\\nAfter the moon has passed the ecliptic to the south side to I,\\nthe disturbing force Id produces a new change of the orbit N le\\nPlayfair.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0158.jp2"}, "159": {"fulltext": "LUNAR IRREGULARITIES.\\nFig. 50.\\n135\\nto Wlf, and the inclination is diminished as at W r In general,\\nwhile the moon is receding from one of the nodes, its inclina-\\ntion is diminishing while it is approaching a node, the incli-\\nnation is increasing.*\\n233. The period occupied by the sun in passing from one\\nof the moon s nodes until it comes round to the same node\\nagain, is called the synodical revolution of the node. This\\nperiod is shorter than the sidereal year, being only about 346^-\\ndays. For since the node shifts its place to the westward 19\u00c2\u00b0\\n35 per annum, the sun, in his annual revolution, comes to it\\nso much before he completes his entire circuit and since the\\nsun moves about a degree a day, the synodical revolution of\\nthe node is 365\u00e2\u0080\u009419 346, or more exactly, 346.619851. The\\ntime from one new moon, or from one full moon, to another,\\nis 29.5305887 days. Now 19 synodical revolutions of the nodes\\ncontain very nearly 223 of these periods.\\nFor 346.619851 xl9=6585.78,\\nAnd 29.5305887x223=6585.32.\\nHence, if the sun and moon were to leave the moon s node\\ntogether, after the sun had been round to the same node 19\\ntimes, the moon would have performed very nearly 223 synod-\\nical revolutions, and would, therefore, at the end of this period\\nmeet at the same node, to repeat the same circuit. And since\\neclipses of the sun and moon depend upon the relative position\\nof the sun, the moon, and node, these phenomena are repeated\\nin nearly the same order, in each of those periods. Hence,\\nFrancceur, Uianog., p. 158 Robison s Phys. Astronomy. Art. 204.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0159.jp2"}, "160": {"fulltext": "136 THE MOON.\\nthis period, consisting of about 18 years and 10 days, under\\nthe name of the Saros, was used by the Chaldeans and other\\nancient nations in predicting eclipses.\\n234. The Metonio Cycle is not the same with the Saros,\\nbut consists of 19 tropical years. During this period the moon\\nmakes very nearly 235 synodical revolutions, and hence the\\nnew and full moons if reckoned by periods of 19 years, recur\\nat the same dates. If, for example, a new moon fell on the\\nfiftieth day of one cycle, it would also fall on the fiftieth day\\nof each succeeding cycle; and, since the regulation of games,\\nfeasts, and fasts, has been made very extensively according to\\nnew or full moons, hence this lunar cycle has been much used\\nboth in ancient and modern times. The Athenians adopted it,\\n433 years before the Christian era, for the regulation of their\\ncalendar, and had it inscribed in letters of gold on the walls\\nof the temple of Minerva. Hence the term Golden Number,\\nwhich denotes the year of the lunar cycle.\\n235. The line of the apsides of the moon s orbit revolves\\nfrom west 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\\nbefore, and so on at every revolution, until, after 9 years, it\\nwould come to its perigee at nearly the same point as at first.\\nThis fact is expressed by saying that the perigee, and of course\\nthe apogee, revolves, and that the line which joins these two\\npoints, or the line of the apsides, also revolves.\\nThe place of the perigee may be found by observing when\\nthe moon has the greatest apparent diameter. But as the\\nmagnitude of the moon varies slowly at this point, a better\\nmethod of ascertaining the position of the apsides, is to take\\ntwo points in the orbit where the variations in apparent diam-\\neter are most rapid, and to find where they are equal on oppo-\\nsite sides of the orbit. The middle point between the two will\\ngive the place of the perigee.\\nThe angular distance of the moon from her perigee in any\\npart of her revolution, is called the Maoris Anomaly,", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0160.jp2"}, "161": {"fulltext": "LUNAR IRREGULARITIES. 137\\n236. The change of place in the apsides of the moon s\\norbit, like the shifting of the nodes, is caused by the disturbing\\ninfluence of the sun. If when the moon sets out from its peri-\\ngee, it were urged by no other force than that of projection,\\ncombined with its gravitation toward the earth, it would de-\\nscribe a symmetrical curve (Art. 187), coming to its apogee at\\nthe distance of 180\u00c2\u00b0 But as the mean disturbing force in the\\ndirection of the radius vector tends, on the whole, to diminish\\nthe gravitation of the moon to the earth, the portion of the\\npath described in an instant will be less deflected from her\\ntangent, or less curved, than if this force did not exist. Hence\\nthe path of the moon will not intersect the radius vector at\\nright angles, that is, she will not arrive at her apogee until after\\npassing more than 180\u00c2\u00b0 from her perigee, by which means\\nthese points will constantly shift their positions from west to\\neast.* The motion of the apsides is found to be 3\u00c2\u00b0 1 20 for\\nevery sidereal revolution of the moon.\\n237. On account of the greater eccentricity of the moon s\\norbit above that of the sun, the Equation of the Center, or that\\ncorrection which is applied to the moon s mean anomaly to find\\nher true anomaly (Art. 200), is much greater than that of the\\nsun, being when greatest more than six degrees (6\u00c2\u00b0 17 12 .7),\\nwhile that of the sun is less than two degrees (1\u00c2\u00b0 55 2 6 8).\\nThe irregularities in the motions of the moon may be com-\\npared to. those of the magnetic needle. As a first approxima-\\ntion, we say that the needle places itself in a north and south\\nline*. On closer examination, however, we find that, at differ-\\nent places, it deviates more or less from this line, and we in-\\ntroduce the first great correction under the name of the decli-\\nnation of the needle. But observation shows us that the\\ndeclination alternately increases and diminishes every day, and\\ntherefore we apply to the declination itself a second correction\\nfor the diurnal variation. Finally, we ascertain, from long-\\ncontinued observations, that the diurnal variation is affected\\nby the change of seasons, being greater in summer than in\\nwinter, and hence we apply to the diurnal variation a third\\ncorrection for the annual variation.\\nPlayfair.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0161.jp2"}, "162": {"fulltext": "138 THE MOON.\\nIn like manner, we shall find the greater inequalities of the\\nmoon s motions are themselves subject to subordinate inequal-\\nities which give rise to smaller equations, and these to smaller\\nstill, to the last degree of refinement.\\n238. Next to the equation of the center, the greatest cor-\\nrection to be applied to the moon s longitude, is that which\\nbelongs to the Ejection. The evection is a change of form in\\nthe lunar orbit, by which its eccentricity is sometimes increased,\\nand sometimes diminished. It depends on the position of the\\nline of the apsides with respect to the line of the syzygies.\\nThis irregularity, and its connection with the place of the\\nperigee with respect to the place of conjunction or opposition,\\nwas known as a fact to the ancient astronomers, Hipparchus\\nand Ptolemy but its cause was first explained by Newton in\\nconformity with the law of universal gravitation. It was\\nfound, by observation, that the equation of the center itself\\nwas subject to a periodical variation, being greater than its\\nmean, and greatest of all when the conjunction or opposition\\ntakes place at the perigee or apogee, and least of all when the\\nconjunction or opposition takes place at a point half way be-\\ntween the perigee and apogee or, in the more common lan-\\nguage of astronomers, the equation of the center is increased\\nwhen the line of the apsides is in syzygy, and diminished when\\nthat line is in quadrature. If, for example, when the line of\\nthe apsides is in syzygy, we compute the moon s place by de-\\nducting the equation of the center from the mean anomaly (see\\nArt. 200), seven days after conjunction, the computed longi-\\ntude will be greater than that determined by actual observa-\\ntion, by about 80 minutes but if the same estimate is made\\nwhen the line of the apsides is in quadrature, the computed\\nlongitude will be less than the observed, by the same quantity.\\nThese results plainly show a connection between the velocity\\nof the moon s motions and the position of the line of the apsides\\nwith respect to the line of the syzygies.\\n239. Now any cause which, at the perigee, should have\\nthe effect to increase the moon s gravitation toward the earth\\nbeyond its mean, and, at the apogee, to diminish the moon s\\ngravitation toward the earth, would augment the difference", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0162.jp2"}, "163": {"fulltext": "LUNAR IRREGULARITIES. 139\\nbetween the gravitation at the perigee and at the apogee, and\\nconsequently increase the eccentricity of the orbit. Again,\\nany cause which at the perigee should have the effect to lessen\\nthe moon s gravitation toward the earth, and at the apogee\\nto increase it, would lessen the difference between the two, and\\nconsequently diminish the eccentricity of the orbit, or bring it\\nnearer to a circle. Let us see if the disturbing force of the sun\\nproduces these effects. The sun s disturbing force, as we have\\nseen in article 228, admits of two resolutions, one in the direc-\\ntion of the radius vector (OM, Fig. 48), the other (OE in the\\ndirection of a tangent to the orbit. First, let AB be the line\\nof the apsides in syzygy, A being the place of the perigee. The\\nsun s disturbing force OM is greatest in the direction of the\\nline of the syzygies yet depending as it does on the unequal\\naction of the sun upon the earth and the moon, and being\\ngreater as their distance from each other is greater, it is at a\\nminimum when acting at the perigee, and at a maximum when\\nacting at the apogee. Hence its effect is to draw away the\\nmoon from the earth less than usual at the perigee, and of\\ncourse to make her gravitation toward the earth greater than\\nusual; while at the apogee its effect is to diminish the tendency\\nof the moon to the earth more than usual, and thus to increase\\nthe disproportion between the two distances of the moon from\\nthe focus at these two points, and of course to increase the\\neccentricity of the orbit. The moon, therefore, if moving\\ntoward the perigee, is brought to the line of the apsides in a\\npoint between its mean place and the earth or if moving to-\\nward the apogee, she reaches the line of the apsides in a point\\nmore remote from the earth than its mean place.\\nSecondly, let CD be the line of apsides in quadrature. The\\neffect of the sun s action is to increase the moon s tendency\\nto the earth, when in quadrature. If, however, the moon is\\nthen at perigee, such increase will be less than usual, because\\nthe sun s action is less oblique and if at apogee, it will be\\nmore than usual, because more oblique. Hence its effect will\\nbe to lessen the disproportion between the two distances of the\\nmoon from the focus at these two points and of course to di-\\nminish the eccentricity of the orbit, The moon, therefore, if\\nmoving toward the perigee, meets the line of the apsides in a\\npoint more remote from the earth than the mean place of the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0163.jp2"}, "164": {"fulltext": "140 THE MOON.\\nperigee and if moving toward the apogee, in a point between\\nthe earth and the mean place of the apogee.*\\n240. A third inequality in the lunar motions, is the Vari-\\nation. By comparing the moon s place as computed from her\\nmean motion corrected for the equation of the center and for\\nevection, with her place as determined by observation, Tycho\\nBrahe discovered that the computed and observed places did\\nnot always agree. They agreed only in the syzygies and quad-\\nratures, and disagreed most at a point half way between these,\\nthat is, at the octants. Here, at the maximum, it amounted to\\nmore than half a degree (35 41 .6). It appeared evident from\\nexamining the daily observations while the moon is perform-\\ning her revolution around the earth, that this inequality is\\nconnected with the angular distance of the moon from the sun,\\nand in every part of the orbit could be correctly expressed by\\nmultiplying the maximum value, as given above, into the sine\\nof twice the angular distance between the sun and the moon.\\nIt is, therefore, at the conjunctions and quadratures, and\\ngreatest at the octants. Tycho Brahe knew the fact: Newton\\ninvestigated the cause.\\nIt appears by article 228, that the sun s disturbing force can\\nbe resolved into two parts one in the direction of the radius\\nvector, the other at right angles to it in the direction of a tan-\\ngent to the moon s orbit. The former, as already explained,\\nproduces the Evection the latter produces the Variation.\\nThis latter force will accelerate the moon s velocity, in every\\npoint of the quadrant which the moon describes in moving\\nfrom quadrature to conjunction, or from C to A (Fig. 48), but\\nat an unequal rate, the acceleration being greatest at the\\noctant, and nothing at the quadrature and the conjunction\\nand when the moon is past conjunction, the tangential force\\nwill change its direction and retard the moon s motion. All\\nthese points will be understood by inspection of figure 48.\\n241. A fourth lunar inequality is the Annual Equation.\\nThis depends on the distance of the earth (and of course the\\nmoon) from the sun. Since the disturbing influence of the sun\\nWoodhonse s Ast., p. 680.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0164.jp2"}, "165": {"fulltext": "LUNAR IRREGULARITIES. 141\\nhas a greater effect in proportion as the sun is nearer,* conse-\\nquently all the inequalities depending on this influence must\\nvary at different seasons of the year. Hence, the amount of\\nthis effect due to any particular time of the year is called the\\nAnnual Equation.\\n242. The foregoing are the largest of the inequalities of the\\nmoon s motions, and may serve as specimens of the corrections\\nthat are to be applied to the mean place of the moon in order\\nto find her true place. These were first discovered by actual\\nobservation but a far greater number, though most of them\\nare exceedingly minute, have been made known by the inves-\\ntigations of Physical Astronomy, in following out all the con-\\nsequences of universal gravitation. In the best tables, about\\n30 equations are applied to the mean motions of the moon.\\nThat is, we first compute the place of the moon on the supposi-\\ntion that she moves uniformly in a circle. This gives us her\\nmean place. We then proceed, by the aid of the Lunar Ta-\\nbles, to apply the different corrections, such as the equation of\\nthe center, evection, variation, the annual equation, and so on,\\nto the number of 28. Numerous as these corrections appear,\\nyet La Place informs us, that the whole number belonging to\\nthe moon s longitude is no less than 60 and that to give the\\ntables all the requisite degree of precision, additional investi-\\ngations will be necessary, as extensive at least as those already\\nmade.f The best tables in use in the time of Tycho Brahe,\\ngave the moon s place only by a distant approximation. The\\ntables in use in the time of Newton (Halley s tables), approxi-\\nmated within 7 minutes. Tables at present in use give the\\nmoon s place to 5 seconds. These additional degrees of accu-\\nracy have been attained only by immense labor, and by the\\nunited efforts of Physical Astronomy and the most refined ob-\\nservations.\\n243. The inequalities of the moon s motions are divided\\ninto periodical and secular. Periodical inequalities are those\\nwhich are completed in comparatively short periods, like evec-\\nVarying reciprocally as the cube of the sun s distance from the earth,\\nf Syst. du Monde., 1. iv., c. 5.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0165.jp2"}, "166": {"fulltext": "142 THE MOON.\\ntion and variation Secular inequalities are those which are\\ncompleted only in very long periods, such as centuries or ages.\\nHence the corresponding terms periodical equations, and secu-\\nlar equations. As an example of a secular inequality, we may\\nmention the acceleration of the moon s mean motion. It is dis-\\ncovered that the moon actually revolves around the earth in\\nless time now than she did in ancient times. The difference,\\nhowever, is exceedingly small, being only about 10 in a cen-\\ntury, but increases from century to century as the square of\\nthe number of centuries from a given epoch. This remarkable\\nfact was discovered by Dr. Halley.* In a lunar eclipse the\\nmoon s longitude differs from that of the sun, at the middle of\\nthe eclipse, by exactly 180\u00c2\u00b0 and since the sun s longitude at\\nany given time of the year is known, if we can learn the day\\nand hour when an eclipse occurs, we shall of course know the\\nlongitude of the sun and moon. Eow in the year 721 before\\nthe Christian era, on a specified day and hour, Ptolemy records\\na lunar eclipse to have happened, and to have been observed\\nby the Chaldeans. The moon s longitude, therefore, for that\\ntime, is known and if we compute the place which the moon\\nwould now occupy, had she always maintained her present\\nperiod of revolution, we shall find that place to be about a\\ndegree and a half in advance of her actual place, showing that\\nthe period we have used is too short. Moreover, the same\\nconclusion is derived from a comparison of the Chaldean ob-\\nservations with those made by an Arabian astronomer of the\\ntenth century.\\nThis phenomenon at first led astronomers to apprehend that\\nthe moon encountered a resisting medium, which, by destroy-\\ning at every revolution a small portion of her projectile force,\\nwould have the effect to bring her nearer and nearer to the\\nearth, and thus to augment her velocity. But in 1TS6, La\\nPlace demonstrated that this acceleration is one of the legiti-\\nmate effects of the sun s disturbing force, and is so connected\\nwith changes in the eccentricity of the earth s orbit, that the\\nmoon will continue to be accelerated while that eccentricity\\ndiminishes but when the eccentricity has reached its minimum\\n(as it will do after many ages), and begins to increase, then\\nAstronomer Royal of Great Britain, and cotemporary with Sir Isaac Newton.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0166.jp2"}, "167": {"fulltext": "ECLIPSES. Ii3\\nthe moon s motion will begin to be retarded, and thus her\\nmean motions will oscillate forever about a mean value.\\n244. The lunar inequalities which have been considered\\nare such only as affect the moon s longitude but the sun s\\ndisturbing force also causes inequalities in the moon s latitude\\nand parallax. Those of latitude alone, require no less than\\ntwelve equations. Since the moon revolves in an orbit in-\\nclined to the ecliptic, it is easy to see that the oblique action\\nof the sun must admit of a resolution into two forces, one of\\nwhich being perpendicular to the moon s orbit, must effect\\nchanges in her latitude. Since, also, several of the inequalities\\nalready noticed, involve changes in the length of the radius\\nvector, it is obvious that the moon s parallax must be subject\\nto corresponding perturbations.\\nCHAPTER VII.\\nECLIPSES.\\n245. An eclipse of the moon happens when the moon, in its\\nrevolution about the earth, falls into the earth s shadow. An\\neclipse of the sun happens when the moon, coming between\\nthe earth and the sun, covers either a part or the whole of the\\nsolar disk. An eclipse of the sun can occur only at the time\\nof conjunction, or new moon and an eclipse of the moon only\\nat the time of opposition, or full moon. Were the moon s\\norbit in the same plane with that of the earth, or did it coin-\\ncide with the ecliptic, then an eclipse of the sun would take\\nplace at every conjunction, and an eclipse of the moon at every\\nopposition for as the sun and earth both lie in the ecliptic,\\nthe shadow of the earth must also extend in the same piano,\\nbeing, of course, always directly opposite to the sun and since,\\nas we shall soon see, the length of this shadow is much greater\\nthan the distance of the moon from the earth, the moon, if it\\nrevolved in the plane of the ecliptic, must pass through the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0167.jp2"}, "168": {"fulltext": "14:4 THE MOON.\\nshadow at every full moon. For similar reasons, the moon\\nwould occasion an eclipse of the sun, partial or total, in some\\nportions of the earth at every new moon. But the lunar orbit\\nis inclined to the ecliptic about 5\u00c2\u00b0, so that the center of the\\nmoon, when she is furthest from her node, is 5\u00c2\u00b0 from the axis\\nof the earth s shadow (which is always in the ecliptic) and, as\\nwe 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\\nit, is only about f of a degree, while the semi-diameter of the\\nmoon s disk is only about of a degree hence the two semi-\\ndiameters, namely, that of the moon and the earth s shadow,\\ncannot overlap one another, unless, at the time of new or full\\nmoon, the sun is at or very near the moon s node. In the\\ncourse of the sun s apparent revolution around the earth once\\na year, he is successively in every part of the ecliptic conse-\\nquently, the conjunctions and oppositions of .the sun and moon\\nma}^ occur at any part of the ecliptic, either when the sun is\\nat the moon s node (or when he is passing that point of the\\ncelestial vault on which the moon s node is projected as seen\\nfrom the earth), or they may occur when the sun is 90\u00c2\u00b0 from\\nthe moon s node, where the lunar and solar orbits are at the\\ngreatest distance from each other or, finally, they may occur\\nat any intermediate point. Now the sun, in his annual revo-\\nlution, passes each of the moon s nodes on opposite sides of the\\necliptic, and of course at opposite seasons of the year so that,\\nfor any given year, the eclipses commonly happen in two op-\\nposite months, as January and July, February and August,\\nMay and November. These are called Node Months, and\\nbecome earlier each year, because the nodes retrograde.\\n246. If the sun were of the same size with the earth, the\\nshadow of the earth would be cylindrical and infinite in length,\\nsince the tangents drawn from the sun to the earth (which\\nform the boundaries of the shadow) would be parallel to each\\nother but as the sun is a vastly larger body than the earth,\\nthe tangents converge and meet in a point at some distance\\nbehind the earth, forming a cone, of which the earth is the\\nbase, and whose vertex (and of course its axis) lies in the eclip-\\ntic. A little reflection will also show us that the form and", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0168.jp2"}, "169": {"fulltext": "ECLIPSES. 145\\ndimensions of the shadow must be affected by several circum-\\nstances that the shadow must be of the greatest length and\\nbreadth when the sun is furthest from the earth that its\\nfigure will be slightly modified by the spheroidal figure of the\\nearth and that the moon, being, at the time of its opposition,\\nsometimes nearer to the earth, and sometimes further from it,\\nwill accordingly traverse it at points where its breadth varies\\nmore or less,\\n247, The semi-angle of the cone of the earth s shadow is\\nequal to the sun s apparent semi-diameter, minus his horizontal\\nparallax.\\nLet AS (Fig. 51) be the semi-diameter of the sun, BE\\nthat of the earth, and EC the axis of the earth s shadow.\\nThen the semi-angle of the cone of the earth s shadow\\nFig. 51.\\nECB AES EAB, of which AES is the sun s semi-diame-\\nter, and EAB his horizontal parallax and as both these quan-\\ntities are known, hence the angle at the vertex of the shadow\\nbecomes known. Putting 6 for the sun s semi-diameter, and p\\nfor his horizontal parallax, we have the semi-angle of the earth s\\nshadow ECB 6\u00e2\u0080\u0094 p.\\n248. At the mean distance of the earth from the sun, the\\nlength of the earth s shadow is about 860,000 miles, or more\\nthan three times the distance of the moon from the earth.\\nIn the right-angled triangle ECB, right angled at B, the\\nangle ECB being known, and the side EB, we can find the side\\nEC. For sin (3 -p) EB B EC ^-=P This value\\nx sm (0 \u00e2\u0080\u0094p)\\nwill vary with the sun s semi-diameter, being greater as that\\nis less. Its mean value being 16 1 .5, and the sun s horizon-\\n1 10", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0169.jp2"}, "170": {"fulltext": "146 THE MOON.\\ntal parallax being 8 6, d p 15 5$, and EB 3956.2\\nHence,\\nSin 15 53 Kad 3956.2 856,275.\\nSince the distance of the moon from the earth is 238,545\\nmiles, the shadow extends about 3.6 times as far as the moon,\\nand consequently the moon passes the shadow toward its broad-\\nest part, where its breadth is much more than sufficient to\\ncover the moon s disk.\\n249. The average breadth of the earth s shadow, where it\\neclipses the 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\\ncircular section. Then the angle MEm will be the angular\\nbreadth of half the shadow. But,\\nME??z BwE BCE that is, since J$mE is the moon s hori-\\nzontal parallax (Art. 82), and BCE equals the sun s semi-\\ndiameter minus his horizontal parallax {6 p), therefore, put-\\nting P for the moon s horizontal parallax, we have\\nMEm P (d -p) V+p d that is, since P= 57 1 and\\nd-p 15 52 .9, therefore 57 1 15 52 .9 =41 8 .l, which\\nis nearly three times 15 33 the semi-diameter of the moon.\\nThus it is seen how, by the aid of geometry, we learn to esti-\\nmate various particulars respecting the earth s shadow, by\\nmeans of simple data derived from observation.\\n250. The distance from the node to the center of the earth s\\nshadow, when so situated that the moon would merely touch\\nit at opposition, is called the lunar ecliptic limit; and the solar\\necliptic limit is the distance from the node to the center of the\\nsun s disk, when the moon apparently touches it in passing the\\nconjunction. All eclipses of the moon and sun occur within\\nthese limits respectively.\\n251. The Lunar Ecliptic Limit is nearly 12 degrees.\\nLet CN (Fig. 52) be the sun s path, MN the moon s, and N\\nthe node. Let Qa be the semi-diameter of the earth s shadow,\\nand Ma the semi-diameter of the moon. Since Ca and Ma are\\nknown quantities, their sum CM is also known. The angle at\\n!N is known, being the inclination of the lunar orbit to the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0170.jp2"}, "171": {"fulltext": "ECLIPSES. 147\\necliptic. Hence, in the spherical triangle MCIST, right angled\\nat M,* by Xapier s theorem (Art. 132, Note),\\nEadXsin CM=sin CNxsin MNC.\\nFig. 52.\\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 gener-\\nally is in these circumstances) at 5\u00c2\u00b0 17 and we have Had x sin\\nr aM T Q \u00e2\u0084\u00a2t Radxsin 62 37 .5\\n62 37 .5=sm CNxsin 5\u00c2\u00b0 17 or sin CN= KQ\\nsin 5 17\\nand GN =11\u00c2\u00b0 25 40 f This is the greatest distance of the\\nmoon from her node at which an eclipse of the moon can take\\nplace. By varying the value of CM, corresponding to varia-\\ntions in the distances of the sun and moon from the earth, it is\\nfound that if NC is less than 9\u00c2\u00b0, there must be an eclipse but\\nbetween this and the limit, the case is doubtful.\\nWhen the moon s disk only comes in contact with the earth s\\nshadc.w, 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\\nshadow. The eclipse is called central when the moon s center\\ncoincides with the axis of the shadow, which happens when the\\nmoon at the moment of opposition is exactly at her node.\\n252. Before the moon enters the earth s shadow, the earth\\nbegins to intercept from it portions of the sun s light, gradu-\\nally increasing until the moon reaches the shadow. This par-\\ntial light is called the moon s Penumbra. Its limits are ascer-\\nThe line CM is to be regarded as the projection of the line which connects\\nthe centers of the moon and section of the earth s shadow, as seen from the\\nearth.\\nf Woodhouse s Astronomy, p. 718.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0171.jp2"}, "172": {"fulltext": "148 THE MOON.\\ntained by drawing the tangents AC B and A C B. (Fig. 51.)\\nThroughout the space included between these tangents, more\\nor less of the sun s light is intercepted from the moon by the\\ninterposition of the earth for it is evident, that as the moon\\nmoves toward the shadow, she would gradually lose the view\\nof the sun, until, on entering the shadow, the sun would be\\nentirely hidden from her.\\n253. The semi-angle of the Penumbra equals the sun s semi-\\ndiameicr and horizontal parallax, or d+p.\\nThe angle ACM (Fig. 51) AC S= AES+B AE. But AES\\nis the sun s semi-diameter, and B AE is the sun s horizontal\\nparallax, both of which quantities are known.\\n254. The semi-angle of a section of the Penumbra, where\\nthe moon crosses it, equals the moon s horizontal parallax, plus\\nthe sun s, plus the sun s semi-diameter.\\nThe angle AEM (Fig. 51) EAC +EC A. But EAC =P,\\nthe moon s horizontal parallax, and EG h=d-{-p (Art. 253),\\n7iEM=P-ri?+#, a which are likewise known quantities.\\nHence, by means of these few elements, which are known\\nfrom observation, we ascend to a complete knowledge of all the\\nparticulars necessary to be known respecting the moon T s pe-\\nnumbra.\\n255. In the preceding investigations, we have supposed that\\nthe cone of the earth s shadow is formed by lines drawn from\\nthe sun, and touching the earth s surface. But the apparent\\ndiameter of the shadow is found by observation to be somewhat\\ngreater than would result from this hypothesis. The fact is\\naccounted for by supposing that a portion of the solar rays\\nwhich graze the earth s surface are absorbed and extinguished\\nby the lower strata of the atmosphere. This amounts to the\\nsame thing as though the earth were larger than it is, in which\\ncase the moon s horizontal parallax would be increased and\\naccordingly, in order that theory and observation may coincide,\\nit is found necessary to increase the parallax by\\n256. In a total eclipse of the moon, its disk is still visible,\\nshining with a dull red light. This is due to the earth s at-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0172.jp2"}, "173": {"fulltext": "ECLIPSES.\\n149\\nmosphere, which acts as a convex lens, and converges the light\\ninto the shadow. The lower rays, if they could escape, would\\nbe bent twice 34 (Art 89), and reach the axis thousands of\\nmiles this side of the moon. As it is, only a little light emerges,\\nwhich is sufficiently bent to fall on the moon when centrally\\neclipsed. An observer at the moon, in witnessing a solar eclipse,\\nwould see the sun expanded into a dim narrow ring, having\\nnearly four times its usual diameter.\\n257. In calculating an eclipse of the moon, we first learn\\nfrom the tables in what month the sun, at the time of full\\nmoon in that month, is near the moon s node, or within the\\nlunar ecliptic limit. This it must evidently be easy to deter-\\nmine, since the tables enable us to find both the longitudes of\\nthe nodes, and the longitudes of the sun and moon, for every\\nday of the year. Consequently, we can find when the sun has\\nnearly the same longitude as one of the nodes, and also the\\nprecise moment when the longitude of the moon is 180\u00c2\u00b0 from\\nthat of the sun, for this is the time of opposition, from which\\nmay be derived the time of the middle of the eclipse. Having\\nthe time of the middle of the eclipse, and. the breadth of the\\nshadow (Art. 249), and knowing, from the tables, the rate at\\nwhich the moon moves per hour faster than the shadow, we\\nean find how long it will take her to traverse half the breadth\\nof the shadow and this time subtracted from the time of the\\nmiddle of the eclipse, will give the beginning, and added to the\\ntime of the middle will give the end of the eclipse. Or if in-\\nstead of the -breadth of the shadow, we employ the breadth of\\nthe penumbra {Art. 253), we may find, in the same manner,\\nwhen the moon enters and when she leaves the penumbra.\\nWe see, therefore, how, by having a few things known by ob-\\nservation, such as the sun and moon s semi-diameters, and their\\nhorizontal parallaxes, we rise, by the aid of trigonometry, to\\nthe knowledge of various particulars respecting the length and\\nbreadth of the shadow and of the penumbra. These being\\nknown, we next have recourse to the tables which contain all\\nthe necessary particulars respecting the motions of the sun and\\nmoon, together with equations or corrections, to be applied for\\nall their irregularities. Hence it is comparatively an easy task\\nto calculate with great accuracy an eclipse of the moon.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0173.jp2"}, "174": {"fulltext": "150 THE MOON.\\n258. Let us then see how we may find the exact time of the\\nbeginning, end, duration, and magnitude, of a lunar eclipse.\\nLet NG (Fig. 53) be the ecliptic, and ISag the moon s orbit,\\nthe sun being in A* when the moon is in opposition at a let\\nN be the ascending node, and Aa the moon s latitude at the\\nFig. 53.\\ninstant of opposition. An hour afterward the sun will have\\npassed to A and the moon to g, when the difference of longi-\\ntude of the two bodies will be GA Then gh is the moon s\\nhourly motion in latitude, and ah her hourly motion in longi-\\ntude. As the character and form of the eclipse will depend\\nsolely upon the distances between the centers of the sun and\\nmoon, that is, upon the line gA instead of considering the two\\nbodies as both in motion, we may suppose the sun at rest in A,\\nand the moon as advancing with a motion equal to the differ- r\\nence between its rate and that of the sun, a supposition that\\nwill simplify the calculation. Therefore, draw gd parallel and\\nequal to A 7 A, join dA, and this line being equal to gA\\\\ the\\ntwo bodies will be in the same relative situation as if the sun\\nwere at A and the moon at g. Join da and produce the line\\nda both ways, cutting the ecliptic in F then daF will be the\\nmoon s Relative Orbit. Hence ai ah\u00e2\u0080\u0094 AA =the difference\\nof the hourly motions of the sun and moon, that is, the moon s\\nrelative motion in longitude, and di=the moon s hourly motion\\nin latitude.\\nDraw CD (Fig. 54) to represent the ecliptic, and let A be\\nthe place of the sun. As the tables give the computation of\\nthe moon s latitude at every instant, consequently, we may\\ntake from them the latitude corresponding to the instant of op-\\nposition, and to one hour later and we may take also the sun s\\nand moon s hourly motions in longitude. Take AD, AB, each\\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\\nmotions of the sun, the latter are used in conformity with the language of the\\ntables.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0174.jp2"}, "175": {"fulltext": "ECLIPSES.\\n151\\nequal to the relative motion, and Aa\u00e2\u0080\u0094the latitude in opposition,\\nDd=th.e latitude one hour afterward join da and produce\\nthe line da both ways, and it will represent the moon s relative\\norbit. Draw Bb at right angles to CD, and it will be the lati-\\nFig. 54.\\nD F\\ntude an hour before opposition. At the time of the eclipse,\\nthe apparent distance of the center of the shadow from the\\nmoon is very small consequently, CD, cd, T d, c, may be\\nregarded as straight lines. During the short interval between\\nthe beginning and end of an eclipse, the motion of the sun, and\\nconsequently that of the center of the shadow, may likewise\\nbe regarded as uniform.\\n259. The various particulars that enter into the calculation\\nof an eclipse are called its Elements and as our object is\\nhere merely to explain the method of calculating an eclipse of\\nthe moon (referring to the Supplement for the actual compu-\\ntation), we may take the elements at their mean value. Thus,\\nwe will -consider cd as inclined to CD 5\u00c2\u00b0 9 the moon s hori-\\nzontal parallax as 58 its semi-diameter as 16 and that of the\\nearth s shadow as 42 The line Am, perpendicular to cd, gives,\\nthe point m for the place of the moon at the middle of the\\neclipse, for this line bisects the chord, which represents the\\npath of the moon through the shadow and mM, perpendicu-\\nlar to CD, gives AM for the time of the middle of the eclipse\\nbefore opposition, the number of minutes before opposition\\nbeing 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 semicircle BLF, and it will represent the\\nThe situation of the moon when at m is called orbit opposition and her situa-\\ntion when at a. ecliptic opposition.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0175.jp2"}, "176": {"fulltext": "152 THE MOON.\\nprojection of the shadow traversed by the moon. With a\\nradius equal to the semi-diameter of the shadow and that of\\nthe moon (=42 +16 =58 and with the center A, mark the\\ntwo points o and f on the relative orbit, and they will be the\\nplaces of the center of the moon at the beginning and end of\\nthe eclipse. The perpendiculars cG, f\u00c2\u00a5, give the times AC\\nand AF of the commencement and the end of the eclipse, and\\nCM or MF gives half the duration. From the centers e andy,\\nwith a radius equal to the semi-diameter of the moon (16 de-\\nscribe circles, and they will each touch the shadow (Euc, 3, 12),\\nindicating the position of the moon at the beginning and end\\nof the eclipse. If the same circle described from m is wholly\\nwithin the shadow, the eclipse will be total; if it is only partly\\nwithin the shadow, the eclipse will be partial. With the\\ncenter A, and radius equal to the semi-diameter of the shadow\\nminus that of the moon (42 16 =26 mark the two points e y\\nf\\\\ which will give the places of the center of the moon, at the\\nbeginning and end of total darkness, and MC, MF will give\\nthe corresponding times before and after the middle of the\\neclipse. Their sum will be the duration of total darkness.\\n260. If the foregoing projection be accurately made from\\na scale, the required particulars of the eclipse may be ascer-\\ntained by measuring, on the same scale, the lines which re-\\nspectively represent them and we should thus obtain a near\\napproximation to the elements of the eclipse. A more accu-\\nrate determination of these elements may however, be ob-\\ntained by actual calculation. The general principles of the\\ncalculation will be readily understood.\\nFirst, knowing ai (Fig. 53), the moon s relative longitude,\\nand di, her latitude, we find the angle dai, which is the in-\\nclination of the moon s relative orbit. But dai=aAm and,\\nin the triangle \u00c2\u00abAm, we have the angle at A, and the side A#,\\nbeing the moon s latitude at the time of opposition, which is\\ngiven by the tables. Hence we can find the side Am. In the\\ntriangle AmM (Fig. 54), having the side Am and the angle\\nAmM (=aAm), we can find AM=the arc of relative longitude\\ndescribed by the moon from the time of the middle of the\\neclipse to the time of opposition and knowing the moon s\\nhourly motion in longitude, we can convert AM into time, and", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0176.jp2"}, "177": {"fulltext": "ECLIPSES. 106\\nthis subtracted from the time of opposition gives us the time of\\nthe middle of the eclipse.\\nSecondly, joining Ac (Fig. 54), not represented in the fig-\\nure, we calculate mAc, in the triangle Acm then mAB\\nmaA)\u00e2\u0080\u0094 mAc=cAC. Hence, in the triangle AC we can de-\\ntermine AC, and therefore AC AM=MC, which, changed\\ninto time as before, gives us, when subtracted from the time\\nof the middle of the eclipse, the time of the beginning of the\\neclipse, or, when added to that of the middle, the time of the\\nend of the eclipse. The sum of the two equals the whole dura-\\ntion.\\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 dark-\\nness, or when added gives the end of total darkness. Their\\nsum is the duration of total darkness.\\nFourthly, the quantity of the eclipse is determined by sup-\\nposing the diameter of the moon divided into twelve equal\\nparts called Digits, and finding how many such parts lie\\nwithin the shadow, at the time when the centers of the moon\\nand the shadow are nearest to each other. Even when the\\nmoon lies wholly within the shadow, the quantity of the\\neclipse is still expressed by the number of digits contained in\\nthat part of the line which joins the center of the shadow and\\nthe center of the moon, which is intercepted between the edge\\nof the shadow and the inner edge of the moon. Thus in figure\\n54, the number of digits eclipsed, equals -j r\\nAo\u00e2\u0080\u0094(Am\u00e2\u0080\u0094nm)\\n7 an expression containing only known quan-\\ni^no\\ntities.\\n261. The foregoing will serve as an explanation of the gen-\\neral principles, on which proceeds the calculation of a lunar\\neclipse. The actual methods practiced employ many expedi-\\nents to facilitate the process, and to insure the greatest possible\\naccuracy, the nature of which are explained and exemplified\\nin Mason s Supplement to this work.\\n262. The leading particulars respecting an Eclipse of the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0177.jp2"}, "178": {"fulltext": "154: THE MOON.\\nSun, are ascertained very nearly like those of a lunar eclipse.\\nThe shadow of the moon travels over a portion of the earth, as\\nthe shadow of a small cloud, seen from an eminence in a clear\\nday, rides along over hills and plains. Let us imagine our-\\nselves standing on the moon then we shall see the earth par-\\ntially eclipsed by the shadow of the moon, in the same manner\\nas we now see the moon eclipsed by the earth s shadow and\\nwe might proceed to find the length of the shadow, its breadth\\nwhere it eclipses the earth, the breadth of the penumbra, and\\nits duration and quantity, in the same way as we have ascer-\\ntained these particulars for an eclipse of the moon.\\nBut, although the general characters of a solar eclipse might\\nbe investigated on these principles, so far as respects the earth\\nat large, yet as the appearances of the same eclipse of the sun\\nare very different at different places on the earth s surface, it\\nis necessary to calculate its peculiar aspects for each place sep-\\narately, a circumstance which makes the calculation of a solar\\neclipse much more complicated and tedious than of an eclipse\\nof the moon. The moon, when she enters the shadow of the\\nearth, is deprived of the light of the part immersed, and that\\npart appears black alike to all places where the moon is above\\nthe horizon. But it is not so with a solar eclipse. We do not\\nsee this by the shadow cast on the earth, as we should do if\\nwe stood on the moon, but by the interposition of the moon\\nbetween us and the sun and his edge may be hidden from one\\nobserver while he is in full view of another only a few miles\\ndistant. In strictness, the phenomenon should be called an\\noccultation, not an eclipse, of the sun the earth is eclipsed, or\\nobscured by a shadow cast upon it, while the sun, to those\\nwithin the shadow, is hidden by an intervening body.\\n263. We have compared the motion of the moon s shadow\\nover the surface of the earth to that of a cloud but its velocity\\nis incomparably greater. The mean motion of the moon\\naround the earth is about 33 per hour but 33 of the moon s\\norbit is 2280 miles, and the shadow moves of course at the\\nsame rate, or 2280 miles per hour, traversing the entire disk of\\nthe earth in less than four hours. This is the velocity of the\\nshadow when it passes perpendicularly over the earth when\\nthe direction of the axis of the shadow is oblique to the earth s", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0178.jp2"}, "179": {"fulltext": "ECLIPSES. 155\\nsurface, the velocity is increased in proportion of radius to the\\nsine of obliquity. Thus the shadows of evening have a far\\nmore rapid motion than those of noonday.\\nLet us endeavor to form a just conception of the manner in\\nwhich these three bodies the sun, the earth, and the moon are\\nsituated with respect to each other at the time of a solar\\neclipse. First, suppose the conjunction to take place at the\\nnode. Then the straight line which connects the centers of\\nthe sun and the earth, also passes through the center of the\\nmoon, and coincides with the axis of its shadow and, since\\nthe earth is bisected by the plane of the ecliptic, the shadow\\nwould traverse the earth in the direction of the terrestrial\\necliptic, from west to east, passing over the middle regions of\\nthe earth. Here the diurnal motion of the earth being in the\\nsame direction with the shadow, but with a less velocity, the\\nshadow will appear to move with a speed equal only to the\\ndifference between the two. Secondly, suppose the moon is\\non the north side of the ecliptic at the time of conjunction, and\\nmoving toward her descending node, and that the conjunction\\ntakes place just within the solar ecliptic limit, say 16\u00c2\u00b0 from\\nthe node. The shadow will now not fall in the plane of the\\necliptic, but a little northward of it, so as just to graze the\\nearth near the pole of the ecliptic. The nearer the conjunc-\\ntion comes to the node, the further the shadow will fall from\\nthe pole of the ecliptic toward the equatorial regions. In cer-\\ntain cases, the shadow strikes beyond the pole of the earth\\nand then its easterly motion being opposite to the diurnal mo-\\ntion of the places which it traverses, consequently its velocity\\nis greatly increased, being equal to the sum of both.\\n264. After these general considerations, we will now exam-\\nine more particularly the method of investigating the elements\\nof a solar eclipse.\\nThe length of the moon s shadow is the first object of in-\\nquiry. The moon, as well as the earth, is at different distan-\\nces from the sun at different times, and hence the length of\\nher shadow varies, being always greatest when she is furthest\\nfrom the sun. Also, since her distance from the earth varies,\\nthe section of the moon s shadow made by the earth, is greater\\nin proportion as the moon is nearer the earth. The greatest", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0179.jp2"}, "180": {"fulltext": "156\\nTHE MOON.\\neclipses of the sun, therefore, happen when the sun is in apo-\\ngee,* and the moon in perigee.\\n265. When the moon is at her mean distance from the\\nearth, and from the sun, her shadow nearly reaches the earth s\\nsurface.\\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,\\nFig.55\\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\\nseen from the moon, and DRK, is the sun s horizontal parallax\\nat the moon. Since, on account of the great distance of the\\nsun compared with that of the moon, the semi-diameter of the\\nsun as seen from the moon must evidently be very nearly the\\nsame as when seen from the earth, and since, on account of the\\nminuteness of the moon s semi-diameter when seen from the\\nsun, the sun s horizontal parallax at the moon must be very\\nsmall, we might, without much error, take the sun s apparent\\nsemi-diameter from the earth, as equal to the semi-angle of the\\ncone of the moon s shadow but, for the sake of greater accu-\\nracy, let us estimate the value of the sun s semi-diameter and\\nhorizontal parallax at the moon.\\nNow, SDR: STR:: ST SDf\\nSTR=1.0025\\n400 399 hence SDR=\\nSTR; and the sun s mean semi-diameter\\n16\\nSTR being 16.025, hence SDR=1.0025xl6.025 l6.065\\n3 .9.\\nAgain, since parallax is inversely as the distance, the sun s\\nThe sun is said to be in apogee, when the earth is in aphelion.\\nThe apparent magnitude of an object being reciprocally as its distance from\\nthe eye. See Note, p. 87.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0180.jp2"}, "181": {"fulltext": "ECLIPSES. 157\\nhorizontal parallax at the moon, is, since she is nearer to the\\nsnn, about greater than at the earth but on account of\\nher inferior size it is ^f-\u00c2\u00a3\u00c2\u00a7 less than at the earth. Hence, in-\\ncreasing the sun s horizontal parallax at the earth by the for-\\nmer fraction, and diminishing it by the latter, we have x\\nOut/\\nx9 =2 .5=the sun s horizontal parallax at the moon.\\nTherefore, the semi-angle of the cone of the moon s shadow,\\nwhich, as appears above, equals SDR\u00e2\u0080\u0094 DEK, equals 16 3 .9\\n2 .5 16 1 .4, which so nearly equals the sun s apparent\\nsemi-diameter, as seen from the earth, that we may adopt the\\nlatter as the value of the semi-angle of the shadow. Hence,\\nsin 16 1 .5 1080 (BD) Ead DK=231690. But the\\nmean distance of the moon from the surface of the earth is\\n238545-3956=234589, which exceeds a little the mean length\\nof the shadow as above.\\nBut when the moon is nearest the earth, her distance from\\nthe center of the earth is only 221,148 miles and when the\\nearth is furthest from the sun, the sun s apparent semi-diame-\\nter is only 15 45 5. By employing this number in the fore-\\ngoing estimate, we shall find the length of the shadow 235,630\\nmiles; and 235630-221148=14482, the distance which the\\nmoon s shadow may reach beyond the center of the earth.\\n266. The diameter of the rnoorCs shadow where it traverses\\nthe earth, i s y at its maximum, about 170 miles*\\nIn the triangle *TK, the angle at K=15 45 .5 (Art. 265),\\nthe side 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 27 ST\u00c2\u00ab, or the arc de.\\nAnd 2de=2\u00c2\u00b0 26 54 =m.\\nHence 360 2.45 (=2\u00c2\u00b0 26 54 24899f 170 (nearly).\\n26 7. The greatest portion of the earth s surface ever covered\\nby the moon s penumbra, is about 4393 miles.\\nc This supposes the conjunction to take place at the node, and the shadow to\\nstrike the earth perpendicularly to its surface where it strikes obliquely, the\\nsection may be greater than this.\\nf The equatorial circumference.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0181.jp2"}, "182": {"fulltext": "158\\nTHE MOON.\\nThe semi-angle of the penumbra BID=BSD-f-SBB, of\\nwhich BSD the sun s horizontal parallax at the moon =2 5,\\nand SBR the sun s apparent semi-diameter=16 3 9, and\\nhence BID is known. The moon s apparent semi-diameter\\nBGD=16 45 .5. Therefore GDT is known, as likewise DT\\nand TG-. Hence the angle GTd may be found, and the arc dG\\nand its double GH, which equals the angular breadth of the\\npenumbra. It may be converted into miles by stating a pro-\\nportion as in article 266. On making the calculation it will\\nbe found to be 4393 miles.\\n268. The apparent diameter of the moon is sometimes\\nlarger than that of the sun, sometimes smaller, and sometimes\\nexactly equal to it. Suppose an observer placed on the right\\nline which joins the centers of the sun and moon if the ap-\\nparent diameter of the moon is greater than that of the sun,\\nthe eclipse will be total. If the two diameters are equal, the\\nmoon s shadow just reaches the earth, and the sun is hidden\\nbut for a moment from the view of spectators situated in the\\nFig. 55\\nline which the vertex of the shadow describes on the surface of\\nthe earth. But if, as happens when the moon comes to her\\nconjunction in that part of her orbit which is toward her apo-\\ngee, the moon s diameter is less than the sun s, then the ob-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0182.jp2"}, "183": {"fulltext": "ECLIPSES, 159\\nserver will see a ring of the sun encircle the moon, constitu-\\nting an annular eclipse. (Fig. 55\\n269. Eclipses of the sun are modified by the elevation of\\nthe moon above the horizon, since its apparent diameter is\\naugmented as its altitude is increased (Art. 217). This effect,\\ncombined with that of parallax, may so increase or diminish\\nthe apparent distance between the centers of the sun and\\nmoon, that from this cause alone, of two observers at a dis-\\ntance from each other, one might see an eclipse which was not\\nvisible to the other. If the horizontal diameter of the moon\\ndiffers but little from the apparent diameter of the sun, the\\ncase might occur where the eclipse would be annular over the\\nplaces where it was observed morning and evening, but total\\nwhere it was observed at mid-day.\\nThe earth in its diurnal revolution and the moon s shadow\\nboth move from west to east, but the shadow moves faster\\nthan the earth hence the moon overtakes the sun on its\\nwestern limb and crosses it from west to east. The excess\\nof the apparent diameter of the moon above that of the\\nsun in a total eclipse is so small, that total darkness seldom\\ncontinues longer than four minutes, and can never continue\\nso long as eight minutes. An annular eclipse may last\\n12m. 24s.\\nSince the sun s ecliptic limits are more than 17\u00c2\u00b0 and the\\nmoon s less than 12\u00c2\u00b0, eclipses of the sun are more frequent than\\nthose of the moon. Yet lunar eclipses being visible to every\\npart of the terrestrial hemisphere opposite to the sun, while\\nthose of the sun are visible only to the small portion of the\\nhemisphere on which the moon s shadow falls, it happens that\\nfor any particular place on the earth, lunar eclipses are more\\nfrequently visible than solar. In any year, the number of\\neclipses of both luminaries can not be less than two nor more\\nthan seven the most usual number is four, and it is very rare\\nto have more than six. The sun does not remain long enough\\nnear a node for the moon to be in syzygy, within ecliptic\\nlimits, more than three times. Hence, only three eclipses can\\noccur successively while the sun is near a node. As he passes\\nboth nodes in the same year, there may therefore be six eclipses.\\nBut a seventh may possibly come just within 12 months,", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0183.jp2"}, "184": {"fulltext": "160 THE MOON.\\nreckoned from the first, in consequence of the backward mo-\\ntion of the nodes.\\n270. It has been observed already, that were the spectator\\non the moon instead of on the earth, he would see the earth\\neclipsed by the moon, and the calculation of the eclipse would\\nbe very similar to that of a lunar eclipse; but to an observer\\non the earth the eclipse does not of course begin when the\\nearth first enters the moon s shadow, and it is necessary to de-\\ntermine not only what portion of the earth s surface will be\\ncovered by the moon s shadow, but likewise the path described\\nby its center relative to various places on the surface of the\\nearth. This is known when the latitude and longitude of the\\ncenter of the shadow on the earth is determined for each\\ninstant, The latitude and longitude of the moon are found on\\nthe supposition that the spectator views it from the center of\\nthe earth, whereas his position on the surface changes, in con*\\nsequence of parallax, both the latitude and longitude, and the\\namount of these changes must be accurately estimated, before\\nthe appearance of the eclipse at any particular place can be\\nfully determined.\\nThe details of the method of calculating a solar eclipse can\\nnot be understood in any way so well as by actually perform-\\ning the process according to a given example. For such\\ndetails, therefore, the reader is referred to the Supplement.\\n271. In total eclipses there has sometimes been seen a\\nremarkable radiation of light around the moon, while the sun\\nis behind it. This is called a corona, and appears to be con-\\ncentric with the sun s disk, rather than with the moon s. It is\\nby some considered to indicate the existence of an extensive\\nsolar atmosphere.\\nAnother interesting phenomenon often attends the moment of\\nconcealment and reappearance of the sun s edge at the begin-\\nning and end of total darkness, as also the formation and rup-\\nture of the ring in annular eclipses. It is the dividing up of\\nthe fine thread of the sun s edge into a series of bright beads.\\nBeing first noticed by Mr. Francis Baily, they are known by\\nthe name of Baily* 8 Beads. The appearance is by some at-\\ntributed to the light of the sun s edge coming through between", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0184.jp2"}, "185": {"fulltext": "LONGITUDE. 161\\nthe mountain summits of the rough outline of the moon s disk.\\nThat they are not always seen may arise from the fact that the\\nedge may in some cases be much less serrated by mountains\\nthan in others.*\\nThere is another peculiarity for which no satisfactory ex-\\nplanation is yet offered. The moment succeeding the total\\noccupation of the sun, irregular projections start out from the\\nedge here and there, entirely detached from each other, either\\nof a flame or a rose color, sometimes short and wide, at others\\nnarrow, 2 or 3 long, and often bent at a considerable angle.\\nDuring the continuance of the eclipse, these change their forms,\\nor disappear, and new ones start up elsewhere. The instant\\nthat the thread-like edge of the sun appears, the white corona\\nand the flame-colored protuberances vanish.\\nA total eclipse of the sun. is one of the most sublime and\\nimpressive phenomena of nature. The darkness is such that\\nthe larger planets and stars appear, and a chill is felt like that\\nof night. Flowers shut up, and animals retire to rest. It is\\nnot strange that people of barbarous countries are filled with\\nconsternation and fear by the occurrence of a total eclipse.\\nCHAPTER YIIL\\nLONGITUDE TIDES.\\n27 2. As eclipses of the sun afford one of the most approved\\nmethods of finding the longitudes of places, our attention is\\nnaturally turned next toward that subject.\\nThe ancients studied astronomy in order that they might\\nread their destinies in the stars; the moderns, that they may\\nsecurely navigate the ocean. A large portion of the refined\\nlabors of modern astronomy has been directed toward perfect-\\ning the astronomical tables, with the view of finding the longi-\\ntude at sea an object manifestly worthy of the highest efforts\\nLardner.\\n11", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0185.jp2"}, "186": {"fulltext": "162 THE MOON.\\nof science, considering the vast amount of property and of\\nhuman life involved in navigation.\\n273. The difference of longitude between two places, may be\\nfound by any method by which we can ascertain the difference\\nof their local times at the same instant of absolute time.\\nAs the earth turns on its axis from west to east, any place\\nthat lies eastward of another will come sooner under the sun,\\nor will have the sun earlier on the meridian, and consequently,\\nin respect to the hour of the day, will be in advance of the\\nother at the rate of one hour for every 15\u00c2\u00b0, or four minutes of\\ntime for each degree. Thus, to a place 15\u00c2\u00b0 east of Greenwich,\\nit is 1 o clock, p. m., when it is noon at Greenwich and to a\\nplace 15\u00c2\u00b0 west of that meridian, it is 11 o clock, a. m. at the\\nsame instant. Hence, the difference of time at any two places\\nindicates their difference of longitude.\\n27 4. The easiest method of finding the longitude is by\\nmeans of an accurate timepiece, or chronometer. Let us set\\nout from London, with a chronometer accurately adjusted to\\nGreenwich time, and travel eastward to a certain place, where\\nthe time is accurately kept, or may be ascertained by observa-\\ntion. We find, for example, that it is 1 o clock by our chro-\\nnometer, when it is 2 o clock and 30 minutes at the place of\\nobservation. Hence, the longitude is 15 x 1.5 22J E. Had\\nwe traveled westward until our chronometer was an hour and\\na half in advance of the time at the place of observation (that\\nis, so much later in the day), our longitude would have been\\n22-^-\u00c2\u00b0 W. But it would not be necessary to repair to London in\\norder to set our chronometer to Greenwich time. This might\\nbe done at any observatory, or any place whose longitude had\\nbeen accurately determined. For example, the time at New\\nYork is 4-h. 56m. 4 s 5 behind that of Greenwich. If, therefore,\\nwe set our chronometer so much before the true time at New\\nYork, it will indicate the time at Greenwich. Moreover, on\\narriving at different places, anywhere on the earth, whose\\nlongitude is accurately known, we may learn whether our\\nchronometer keeps accurate time or not and if not, the\\namount of its error. Chronometers have been constructed of\\nsuch an astonishing degree of accuracy, as to deviate but a few", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0186.jp2"}, "187": {"fulltext": "LONGITUDE. 163\\nseconds in a- voyage from London to Baffin s Bay and back,\\nduring an absence of several years. But chronometers which\\nare sufficiently accurate to be depended on for long vo} T ages,\\nare too expensive for general use, and the means of verifying\\ntheir accuracy are not sufficiently easy. Moreover, chronom-\\neters, by being transported from one place to another, change\\ntheir daily rate, or depart from that mean rate which they\\npreserve at a fixed, station. A chronometer, therefore, can\\nnot be relied on for determining the longitudes of places\\nwhere the greatest degree of accuracy is required, especially\\nwhere the instrument is conveyed over land, although the\\nuncertainty attendant on one instrument may be nearly ob-\\nviated by employing several, and taking their mean results.*\\n275. Eclipses of the sun and moon are sometimes used for\\ndetermining the longitude. The exact instant of immersion or\\nof emersion, or any other definite moment of the eclipse which\\npresents itself to two distant observers, affords the means of\\ncomparing their difference of time, and hence of determining\\ntheir difference of longitude. Since the entrance of the moon\\ninto the earth s shadow, in a lunar eclipse, is seen at the same\\ninstant of absolute time at all places where the eclipse is visible\\n(Art. 262), this observation would be a very suitable one for\\nfinding the longitude, were it not that, on account of the in-\\ncreasing darkness of the penumbra near the boundaries of the\\nshadow, it is difficult to determine the precise instant when the\\nmoon enters the shadow. By taking observations on the im-\\nmersions of known spots on the lunar disk, a mean result may\\nbe obtained which will give the longitude with tolerable accu-\\nracy. In an eclipse of the sun, the instants of immersion and\\nemersion may be observed with greater accuracy, although,\\nsince these do not take place at the same instant of absolute\\ntime, the calculation of the longitude from observations on a\\nsolar eclipse is complicated and laborious.\\nA method very similar to the foregoing, by observations on\\neclipses of Jupiter s satellites, and on occupations of stars, will\\nbe mentioned hereafter.\\nWoodhouse, p. 838.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0187.jp2"}, "188": {"fulltext": "164 THE MOON.\\n276. The Lunar method of finding the longitude, at sea, is\\nin man j respects preferable to every other. It consists in\\nmeasuring (with a sextant) the angular distance between the\\nmoon and the sun, or between the moon and a star, and then\\nturning to the Nautical Almanac,* and finding what time it\\nwas at Greenwich when that distance was the same. The\\nmoon moves so rapidly, that this distance will not be the same\\nexcept at very nearly the same instant of absolute time. For\\nexample, at 9 o clock, a. m., at a certain place, we find the\\nangular distance of the moon and the sun to be 72\u00c2\u00b0 and on\\nlooking into the Nautical Almanac, we find that the time\\nwhen this distance was the same for the meridian of Greenwich\\nwas 1 o clock, p. m. hence we infer that the longitude of the\\nplace 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 (Yenus,\\nMars, Jupiter, and Saturn), and from nine bright fixed stars,\\nfor the beginning of every third hour of mean time for the\\nmeridian of Greenwich and the time corresponding to any\\nintermediate distance, may be found by proportional parts.f\\n277. It would be a very simple operation to determine the\\nlongitude by Lunar Distances, if the process, as described in\\nthe preceding article, were all that is necessary but the vari-\\nous circumstances of parallax, refraction, and dip of the hori-\\nzon, would differ more or less at the two places, even were the\\nbodies (whose distances were taken) in view from both, which is\\nnot necessarily the case. The observations, therefore, require\\nto be reduced to the center of the earth, being cleared of the\\neffects of parallax and refraction. Hence, three observers are\\nnecessary in order to take a lunar distance in the most exact\\nmanner, viz., two to measure the altitudes of the two bodies\\nrespectively, at the same time that the third takes the angular\\ndistance between them. The altitudes of the two luminaries\\nThe Nautical Almanac is published annually three or four years in advance,\\ncontaining all necessary tables and information, for the use of navigators. The\\nEnglish Board of Longitude have for a long series of years issued such a work.\\nThe American Ephemeris and Nautical Almanac, which possesses the same general\\ncharacter, was commenced but a few years since.\\nf See Bowditch s Navigator, tenth ed., p. 226.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0188.jp2"}, "189": {"fulltext": "tid.es. 165\\nat the time of observation must be known, in order to estimate\\nthe effects of parallax and refraction.\\n278. Since the invention of the magnetic telegraph, it has\\nbeen employed to determine the differences of longitude be-\\ntween fixed stations on land with a precision which was before\\naltogether unattainable. Suppose two stations to be connected\\nby the telegraphic line, and that there is at each a clock keeping\\nthe local time. The observers agree beforehand at what time\\nby his own clock the one at the most easterly station shall com-\\nmence giving signals and also at what time the other shall\\ncommence giving another series according to his clock. The\\ninterval between successive signals is also previously deter-\\nmined. When the moment arrives, the first observer strikes\\nthe telegraphic key at the exact beat of the clock, and the\\nseeond observer records the time of the signal as shown by his\\nown clock, and thus they continue to do till the full series is\\nrecorded. The second observer then commences sending sig-\\nnals, which are in like manner recorded by the first. The ve-\\nlocity of the electric current is so great that the absolute time\\nof making a signal at one station, and of perceiving it at the\\nother, may be considered identical, so that the difference which\\nis indicated by the two clocks in each case is wholly due to dif-\\nference of longitude. Still greater precision is attained by\\ncausing the signal key at each station to record its own move-\\nment on the line of second-marks made by the clock at the-\\nother station (Art. 125).\\nTIDES.\\n279. The tides are an alternate rising and falling of the\\nwaters of the ocean at regular intervals. They have a maxi-\\nmum and minimum twice a day and the daily maximum and\\nminimum reach their highest and lowef values twice in a sy-\\nnod ical revolution of the moon, or 29^ days. The maximum\\nof the daily tide is called high tide, and the minimum low tide.\\nThe maximum tide during a lunation is called the spring tid*\\nthe minimum, neap tide. The rising of the tide is called flood^\\nand the falling, ebb.\\nSimilar tides, whether high or low, occur on opposite sides", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0189.jp2"}, "190": {"fulltext": "1G6 THE MOON.\\nof the earth at once. Thus at the same time it is high tide at\\nany given place, it is also high tide on the inferior meridian\\nand the same 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 min-\\nutes later than it occurred on the preceding day. In this re-\\nspect, as well as in various others, it corresponds very nearly\\nto the motions of 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,\\nthe difference between the two diameters of the oval would be\\n5 feet, or more exactly 5 feet and 8 inches but its natural\\nheight at various places is very different, sometimes rising to 60\\nor TO feet, and sometimes being scarcely perceptible. At the\\nsame place, also, the phenomena of the tides are very different\\nat different times.\\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\\nand moon upon different parts of the earth.\\nSuppose the projectile force by which the earth is carried\\nforward in her orbit to be suspended, and the earth to fall\\ntoward one of these bodies, the moon for example, in conse-\\nquence of their mutual attraction. Then, if all parts of the\\nearth fell equally toward the moon, no derangement of its dif-\\nferent parts would result, any more than of the particles of a\\ndrop of water in its descent to the ground. But if one part\\nfell faster than another, the different portions would evidently\\nbe separated from each other. Now this is precisely what takes\\nplace with respect to the earth in its fall toward the moon.\\nThe portions of the earth in the hemisphere next to the moon,\\non account of being n arer to the center of attraction, fall faster\\nthan those in the opp( site hemisphere, and consequently leave\\nthem behind. The solid earth, on account of its cohesion, can\\nnot obey this impulse, since all its different portions constitute\\none mass, which is acted on in the same manner as though it\\nwere all collected in the center but the waters on the surface,\\nmoving freely under this impulse, endeavor to desert the solid", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0190.jp2"}, "191": {"fulltext": "TIDES*\\n167\\nmass arid fall toward the moon. For a similar reason the wa-\\nters in the opposite hemisphere falling less toward the moon\\nthan the solid earth, are left behind, or appear to rise from the\\ncenter of the earth.\\n281. Let DEFG (Fig. 56) represent the globe; and, for the\\nsake of illustrating the principle, we will suppose the waters\\nentirely to cover the globe at a uniform depth. Let defg repre-\\nsent the solid globe, and the circular\\nring exterior to it, the covering of wa-\\nters. Let C be the center of gravity\\nof the solid mass, A that of the hemi-\\nsphere next to the moon, and B that\\nof the remoter hemisphere. Now the\\nforce of attraction exerted by the\\nmoon acts in the same manner as\\nthough the solid mass were all concen-\\ntrated in C, and the waters of each\\nhemisphere at A and B respectively\\nand (the moon being supposed above E) it is evident that A\\nwill 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\\ndirection of that meridian which is under the moon, and flat-\\ntened in the intermediate parts, and most of all at points ninety\\ndegrees* distant from that meridian.\\nWere it not, therefore, for impediments which prevent the\\nforce from producing its full effects, we might expect to see\\nthe great tide-wave, as the elevated crest is called, always\\ndirectly beneath the moon, attending it regularly around the\\nglobe. But the inertia of the waters prevents their instantly\\nobeying the moon s attraction, and the friction of the waters on\\nthe bottom of the ocean, still further retards its progress. It is\\nnot therefore until several hours (differing at different places)\\nafter the moon has passed the meridian of a place, that it is\\nhigh tide at that place.\\n282. The sun has a similar action to the moon, but only\\none-third as great. On account of the great mass of the sun", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0191.jp2"}, "192": {"fulltext": "168 THE MOON.\\ncompared with that of the moon, we might suppose that his\\naction in raising the tides would be greater than the moon s\\nbut the nearness of the moon to the earth more than compen-\\nsates for the sun s greater quantity of matter. Let us, however,\\nform a just conception of the advantage which the moon de-\\nrives from her proximity. It is not that her actual amount of\\nattraction is thus rendered greater than that of the sun but it\\nis that her attraction for the different parts of the earth is very\\nunequal, while that of the sun is nearly uniform. It is the in-\\nequality of this action, and not the absolute force, that pro-\\nduces the tides. The diameter of the earth is of the distance\\nof the moon, while it is less than T o^o o \u00c2\u00b0f tne distance of the\\nsun.\\n283. Having now learned the general cause of the tides,\\nwe will 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 in\\na line and the Neap tides, or those which are unusually low\\ntwice a month, are produced by the sun and moon s acting 90\\ndegrees from each other. The Spring tides occur at the syzygies\\nthe J^eap tides at the quadratures. At the time of new moon,\\nthe sun and moon both being on the same side of the earth,\\nand acting upon it in the same line, their actions conspire, and\\nthe sun may be considered as adding so much to the force of\\nthe moon. We have already explained how the moon con-\\ntributes to raise a tide on the opposite side of the earth. But\\nthe sun as well as the moon raises its own tide-wave, which, at\\nnew moon, coincides with the lunar tide- wave. At full moon\\nalso, the two luminaries conspire in the same way to raise the\\ntide for we must recollect that each body contributes to raise\\nthe tide on the opposite side of the earth as well as on the side\\nnearest to it. At both the conjunctions and oppositions, there-\\nfore, that is, at thq syzygies, we have unusually high tides.\\nBut here also the maximum effect is not at the moment of the\\nsyzygies, but 36 hours afterward.\\nAt the quadratures, the solar wave is lowest where the lunar\\nwave is highest hence the low tide produced by the sun is\\nsubtracted from high water and produces the ]STeap tides.\\nMoreover, at the quadratures the solar wave is highest where", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0192.jp2"}, "193": {"fulltext": "TIDES.\\n169\\nthe lunar wave is lowest, and hence is to be added to the\\nheight of low water at the time of Neap tides. Hence the\\ndifference between high and low water is only about half as\\ngreat at Neap tide as at Spring tide.\\n284. The power of the moon or of the sun to raise the tide\\nis found by the doctrine of universal gravitation to be inversely\\nas the cube of the distance* The variations of distance in the\\nsun are not great enough to influence the tides very materially,\\nbut the variations in the moon s distances have a striking\\neffect. The tides which happen when the moon is in perigee,\\nare considerably greater than when she is in apogee and if\\nshe happens to be in perigee at the time of the syzygies, the\\nSpring tide is unusually high.\\n285. The declinations of the sun and moon cause the im\\nmediate tide, at a given latitude, to be greater than the opposite\\none, or the reverse, according as the declination and latitude\\nare alike or unlike. When the declination is nothing, both\\ntides are alike at every place. For if the moon is in the plane\\nof the equator (Fig. 57),f then the highest points of both tide-\\nwaves are also on the equator; and, at a given latitude, a place\\nby the earth s rotation is carried round through T2, T3, at\\nLa Place. Syst. du Monde, 1. iv., c. x.\\nf Diagrams like these are apt to mislead the learner, by exhibiting the pro-\\ntuberance occasioned by the tides as much greater than the reality. We must\\nrecollect that it amounts, at the highest, to only a very few. feet in eight thou-\\nsand miles. Were the diagram, therefore, drawn in just proportions, the altt ra-\\ntions of figure produced by the tides would be wholly insensible.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0193.jp2"}, "194": {"fulltext": "170 THE MOON.\\nequal distances from the highest points, and therefore the im-\\nmediate tide T3, and the opposite one T2, are equal both are\\nless, the higher the latitude, and at the poles there is no tide.\\nWhen the moon is on the north side of the equator, as in fig-\\nure 58, at her greatest northern declination, a place describing\\nthe parallel TT will have T 3 for the height of the tide when\\nthe moon is on the superior meridian, and T2 for the height\\nwhen the moon is on the inferior meridian. Therefore, all\\nplaces north of the equator will have the highest tide when the\\nmoon is above the horizon, and the lowest when she is below\\nit the difference of the tides diminishing toward the equator,\\nwhere thej are equal. At the same time, places south of the\\nequator have the highest tides w r hen the moon is below the\\nhorizon, and the lowest when she is above it. When the moon\\nis at her greatest declination, the highest tides will take place\\ntoward the tropics. The circumstances are all reversed when\\nthe moon is south of the equator.*\\n286. The motion of the tide-wave, it should be remarked,\\nis not a progressive motion, but a mere undulation, and is to\\nbe carefully distinguished from the currents to which it gives\\nrise. If the ocean enveloped the earth, and the sun and moon\\nwere at rest in the equator, the tide-wave would travel at the\\nsame rate as the earth on its axis. Indeed, the correct way of\\nconceiving of the tides, is first to regard the moon as at rest,\\nand the earth as revolving and bringing successive parts under\\nit, which parts are thus elevated in succession and then, to\\nconsider the moon and tides as moving east 13\u00c2\u00b0 per day; thus\\nmaking the time of the relative revolution of the tides west-\\nward, near 25 instead of 24 hours.\\n287. The tides of rivers, narrow bays, and shores far from\\nthe main body of the ocean, are not produced in those places\\nby the direct action of the sun and moon, but are subordinate\\nwaves propagated from the great tide- wave.\\nLines drawn through all the adjacent parts of any tract of\\nwater, which have high water at the same time, are called co-\\ntidal lines.f We may, for instance, draw a line through all\\nEdin Encyc Art. Astronomy, p. 623.\\nf Whewell, Phil. Transactions for 1833. p 148.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0194.jp2"}, "195": {"fulltext": "TIDES.\\n171\\nplaces in the Atlantic Ocean which have high tide on a given\\nday at 1 o clock, and another through all places which have\\nhigh tide at 2 o clock. The cotidal line for any hour may be\\nconsidered as representing the summit or ridge of the tide-\\nwave at that time and could the spectator, detached from the\\nearth, perceive the summit of the wave, he would see it trav-\\neling round the earth in the open ocean once in twenty-five\\nhours, followed by another in twelve and a half hours, both\\nsending branches into rivers, bays, and other openings into the\\nmain land. These latter are called Derivative tides, while\\nthose raised directly by the action of the sun and moon, are\\ncalled Primitive tides.\\n288. The velocity with which the wave moves will depend\\non various circumstances, but principally on the depth, and\\nprobably on the regularity of the channel. If the depth be\\nnearly uniform, the cotidal lines will be nearly straight and\\nparallel. But if some parts of the channel are deep, while\\nothers are shallow, the tide will be detained by the greater\\nfriction of the shallow places,\\nand the cotidal lines will be\\nirregular. The direction, also,\\nof the derivative tide may be\\ntotally different from that of\\nthe primitive. Thus (Fig. 59),\\nif the great tide- wave, moving\\nfrom east* to west, be repre-\\nsented by the lines 1, 2, 3, 4\\nthe derivative tide, which is\\npropagated up a river or bay,\\nwill be represented by the co-\\ntidal lines 3, 4, 5, 6, 7. Ad- f W\\nvancing faster in the channel f\\nthan next the banks, the tides will las: behind toward the\\nshores, and the cotidal lines w T ill take the form of curves, as\\nrepresented in the diagram.\\nFig. 59.\\nSt 3r\\n-289. On account of the retarding influence of shoals, and\\nan uneven, indented coast, the tide-wave travels more slowly\\nalong the shores of an island than in the neighboring sea,", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0195.jp2"}, "196": {"fulltext": "172 THE MOON.\\nassuming convex figures at a little distance from the island\\nand on opposite sides of it. These convex lines sometimes\\nmeet and become blended in such a manner as to create singu-\\nlar anomalies in a sea much broken by islands, as well as on\\ncoasts indented with numerous bays and rivers.* Peculiar\\nphenomena are also produced, when the tide flows in at oppo-\\nsite extremities of a reef or island, as into the two opposite\\nends of Long Island Sound. In certain cases a tide-wave is\\nforced into a narrow arm of the sea, and produces very re-\\nmarkable tides. The tides of the Bay of Fundy (the highest\\nin the world j sometimes rise to the height of 60 or 70 feet\\nand 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\\nabout 36 hours after the new or full moon. But as the\\namount of this tide would be affected by the distance of the\\nsun and moon from the earth (Art. 284), and by their declina-\\ntions (Art. 285), these distances are taken at their mean value,\\nand the luminaries are supposed to be in the equator the ob-\\nservations being so reduced as to conform to these circum-\\nstances. The unit of altitude can be ascertained by observa-\\ntion only. The actual rise of the tide depends much on the\\nstrength and direction of the wind. When high winds con-\\nspire with a high flood tide, as is frequently the case near the\\nequinoxes, the tide rises to a very unusual height. We sub-\\njoin, from the American Almanac, a few examples of the unit\\nof altitude for different places.\\nFeet.\\nCumberland, head of the Bay of Fundy, 71\\nBoston, 11|\\nNew Haven, 8\\nNew York, .5\\nCharleston, S. C, 6\\n291. The Establishment of any port is the mean interval\\nbetween noon and the time of high water, on the day of new\\nSee an excellent representation and description of these different phenomena\\nby Professor Whe well, Phil. Trans., 1833, p. 153.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0196.jp2"}, "197": {"fulltext": "TIDES. 173\\nor full moon. As the interval for any given place is always\\nnearly the same, it becomes a criterion of the retardation of\\nthe tides at that place. On account of the importance to\\nnavigation of a correct knowledge of the tides, the British\\nBoard of Admiralty, at the suggestion of the Eoyal Society,\\nrecently issued orders to their agents in various important\\nnaval stations, to have accurate observations made on the\\ntides, with the view of ascertaining the establishment and\\nvarious other particulars respecting each station and the\\ngovernment of the United States is prosecuting similar investi-\\ngations respecting our own ports.\\n292. According to Professor Tvnewell,t the tides on the\\ncoast of North America are derived from the great tide-wave\\nof the South Atlantic, which runs steadily northward along\\nthe coast to the mouth of the Bay of Fundy, where it meets\\nthe northern tide-wave flowing in the opposite direction.\\nHence he accounts for the 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\\nand Euxine, and the same is found to be true of the largest of\\nthe North American -Lakes, Lake Superior.^\\nAlthough these several tracts of water appear large, when\\ntaken by themselves, yet they occupy but small portions of\\nthe surface of the globe, as will appear evident from the delin-\\neation of them on an artificial globe. Now we must recollect\\nthat the primitive tides are produced by the unequal action of\\nthe sun and moon upon the different parts of the earth and\\nthat it is only at points whose distance from each other bears a\\nconsiderable ratio to the whole distance of the sun or the moon,\\nthat the inequality of action becomes manifest. The space re-\\nquired is larger than either of these tracts of water. It is\\nobvious, also, that they have no opportunity to be subject to a\\nderivative tide.\\n294. To apply the theory of universal gravitation to all\\nLubbock, Report on the Tides, 1833. f Phil. Trans., 1833, p. 172.\\nSee Experiments of Gov. Cass, Am. Jour. Science.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0197.jp2"}, "198": {"fulltext": "174: THE PLANETS.\\nthe varying circumstances that influence the tides, becomes a\\nmatter of such intricacy, that La Place pronounces the\\nproblem of the tides the most difficult problem of celestial\\nmechanics.\\n295. The Atmosphere that envelops the earth must evi-\\ndently be subject to the action of the same forces as the cov-\\nering of waters, and hence we might expect a rise and fall of\\nthe barometer, indicating an atmospheric tide corresponding\\nto the tide of the ocean. La Place has calculated the amount\\nof this aerial tide. It is too inconsiderable to be detected by\\nchanges in the barometer, unless by the most refined observa-\\ntions. Hence it is concluded that the fluctuations produced by\\nthis cause are too slight to affect meteorological phenomena in\\nany appreciable degree.*\\nCHAPTEE IX.\\nOF THE PLANETS\u00e2\u0080\u0094 INFERIOR PLANETS, MERCURY AND VENUS.\\n296. The name planet signifies a wanderer^ and is ap-\\nplied to this class of bodies because they shift their positions\\nin the heavens, whereas the fixed stars apparently always\\nmaintain the same places with respect to each other. The\\nplanets known from a high antiquity, are Mercury, Venus,\\nEarth, Mars, Jupiter, and Saturn. To these, in 1781, was added\\nUranus X (or H^rschel, as it was formerly called, from the name\\nof its discoverer), and, as late as 18-16, another large planet,\\nNeptune, was added to the list, making eight in all of those\\nbodies usually called planets. Besides these, there is, between\\nMars and Jupiter, a remarkable group of small planets, called\\nAsteroids, or more properly, Planetoids. Four of them were\\ndiscovered near the beginning of the present century. From\\nBowditch s La Place, ii., p. 797. f From the Greek. rAn^r^.\\nFrom Ovpavot.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0198.jp2"}, "199": {"fulltext": "PRIMARY AND SECONDARY PLANETS. 175\\nthat time till 1845, none were added but since 1845, scarce a\\nyear has passed in which one or more have not been discov-\\nered and sometimes five or six have been found in a single\\nyear. Though names have generally been given them, they\\nare more commonly designated by a number, in the order of\\ntheir discovery, the number being inclosed in a circle, which\\nis intended to represent the planetary disk.\\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\\nUranus, six and Neptune, one. These bodies, also, are\\nplanets, but in distinction from the others, they are called\\nsecondary planets. Grouping the planetoids together, and\\ngiving them the rank of one primary planet (though all united\\nwould make but a small one), there are nine primaries and\\ntwenty secondaries.\\n297. The primary planets all (with the exception of the\\nasteroids) have their orbits nearly in the same plane, and are\\nnever seen far from the ecliptic. Mercury, whose orbit is most\\ninclined of all, never departs further from the ecliptic than\\nabout 7\u00c2\u00b0, while most of the other planets pursue very nearly\\nthe same path with the earth, in their annual revolution\\naround the sun. The asteroids, however, make wider excur-\\nsions from the plane of the ecliptic, amounting, in the case of\\nPallas, to 34^\u00c2\u00b0.\\n298. Mercury and Yenus are called inferior planets, be-\\ncause their orbits are nearer to the sun than that of the earth\\nwhile all the others being more distant from the sun than the\\nearth, are called superior planets. The planets present great\\ndiversities among themselves in respect to distance from the\\nsun, magnitude, time of revolution, and density. They differ\\nalso in regard to satellites, of which, as we have seen, the\\nEarth and Neptune have each one, Jupiter has four, Saturn\\neight, and Uranus six while Mercury, Yenus, and Mars, have\\nRespecting the number of satellites belonging- to Uranus, there is some doubt,\\nwhich will be considered under the history of that planet.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0199.jp2"}, "200": {"fulltext": "176 THE PLANETS.\\nnone at all. It will aid the memory, and render our view of\\nthe, planetary system more clear and comprehensive, if we\\nclassify, as far as possible, the various particulars compre-\\nhended under the foregoing heads.\\n299. DISTANCES FROM THE SUN.*\\n1. Mercury, 37,000,000 0.38709S1\\n2. Yenus, 68,000,000 0.7233316\\n3. Earth, 95,000,000 1.0000000\\n4. Mars, 145,000,000 1.5236923\\n5. Planetoids, 250,000,000 2.6612SS5\\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, trav-\\neling night and day at the rate of 20 miles an hour, and of\\ncourse making 480 miles a day, would require about 50 days\\nto travel round the Earth on a great circle, and about 500 days\\nto reach the moon but it will give some idea of the vastness\\nof the planetary spaces to reflect, that setting out from the\\nsun, and traveling from planet to planet at the same rate, to\\nreach Mercury would require about 200 years; Yenus, nearly\\n400 the Earth, 542 Mars, more than 800 Jupiter, toward\\n3,000 Saturn, above 5,000 Uranus, 10,000 Neptune, more\\nthan 16,000 and to cross the entire orbit of Neptune would\\nrequire upward of 32,000 years.\\nIt may aid the memory to remark, that in regard to the\\nplanets nearest the sun, the distances increase in an arithmeti-\\ncal ratio, while those most remote increase in a geometrical\\nratio. Thus, if we add 30 to the distance of Mercury, it gives\\nus nearly that of Yenus 30 more gives that of the Earth\\nwhile Saturn is nearly twice the distance of Jupiter, and\\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\\nof the Earth being 1, from which a more exact determination may be made\\nwhen required, the Earth s distance being taken at. 95,298,260 miles.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0200.jp2"}, "201": {"fulltext": "DISTANCES- FROM THE SUN 177\\nUranus twice that of Saturn. If this, however, were a per-\\nfectly correct rule, Neptune would be twice as far from the\\nsun as Uranus, and therefore 3,600 millions of miles, whereas\\nits actual distance is short of 3,000 millions. Between the\\norbits of Mars and Jupiter a great chasm appeared, which\\nbroke the continuity but the discovery of the planetoids has\\nfilled the void. A more exact law of the series is that called\\nBode s. law. It is as follows if we represent the distance of\\nMercury by 4, and increase trie following terms by the prod-\\nuct of 3. into the ascending powers of 2, 4 we shall obtain the\\nrelative distances of the planets from the sun. Thus,\\nMercury, 4 =4\\nVenus, 4+3.2\u00c2\u00b0 7\\nEarth, 4+3.2 1 10\\nMars, 4+3.2* 16\\nPlanetoids, 4+3.2 3 28\\nJupiter, 4+3.2 4 52\\nSaturn, 4+3.2 5 =100\\nUranus, 4+3.2 6 =196\\nNeptune, 4+3.2 7 =388\\nBefore the discovery of Neptune, Bode s law rudely ex-\\npressed the relative distances from the sun; but it signally\\nfails of including the new planet, as it gives near 3,600 millions\\ninstead of the true distance, 2,800 millions.\\nBut the relative distances from the sun are accurately ob-\\ntained by Kepler s third law, that the squares of the periodic\\ntimes are as the cubes of the distances (Art. 171). 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,\\nas the square of the Earth s period (365.256 days) is to the\\nsquare of Jupiter s period (4332.586 days), so is the cube of the\\nEarth s distance to the cube of Jupiter s distance, the cube root\\nof which will be the distance itself. Or, to express the same\\ntruth more concisely, 365.256 2 4332.S86 2 l 3 5.202 3 Of\\ncourse, this method can as yet be used only approximately for\\nNeptune, which has described but a short portion of its orbit\\nsince its discovery.\\n12", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0201.jp2"}, "202": {"fulltext": "178 THE PLANETS.\\n300. MAGNITUDES.\\nDiameter Mean apparent\\nin Miles. Diameter. Mass. Volume.\\nMercury, 2,950* 8 8 A\\nYenus, 7,800 17 97 ft\\nEarth, 7,912 100 1\\nMars, 4,500 6 15 i\\nPlanetoids, 0 .5 uncertain.\\nJupiter, 89,000 37 37,171 1,400\\nSaturn, 79,000 16 11,121 1,000*\\nUranus, 35,000 4 1,564 86\\nNeptune, 31,000* 2 .5 672 60\\nDiagrams and orreries, as usually constructed, wholly fail of\\ngiving any just conceptions of the distances of the planets\\nfrom the sun and from each other. If we represent, for in-\\nstance, the distance of the earth by 1 foot, we shall require 30\\nfeet in order to reach the place of Neptune; and when we\\nhave constructed a diagram on so large a scale, we must still\\nbear in mind that each foot represents a space of nearly 100\\nmillions of miles.f\\nWe remark here a great diversity in regard to magnitude\\na diversity which does not appear to be subject to any definite\\nlaw. While Yenus, 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 several\\nof the planets, when nearest to us, appear brilliant and large\\nwhen compared with the fixed stars, yet the angle which they\\nsubtend is very small, that of Yenus, the greatest of all, never\\nexceeding about 1 or more exactly 61 2, and that of Jupiter,\\nwhen greatest, being only about f of a minute.\\nHind.\\nf For the purposes of illustration to a class or to a popular audience, the fol-\\nlowing plan of representation is recommended, not only for the entire solar sys-\\ntem, but for each of the subordinate systems, as that of Jupiter or Saturn.\\nStretch upon the wall a piece of black cambric, as long as the room will allow,\\nsay 30 ft. This length may be taken for the radius of Neptune s orbit. At one\\nend, attach a circle of white cloth, inch in diameter for the sun. From it as\\na center describe arcs across the cloth at proper distances for the several orbits,\\nand sew white tape on these arcs. We then have the planetary distances, and\\nthe size of the sun, upon one scale. The planets themselves can not be repre-\\nsented, since the largest of them would be almost invisibly small. The cloth\\nmay be conveniently rolled up, when not in use.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0202.jp2"}, "203": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 179\\nTlie 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\\nthe sun. (Art 145.)\\n301.\\nPERIODIC TIMES.\\nSidereal revolution.\\nMean daily motion.\\nMercury,\\n3 months.\\nor\\n88 days,\\n4\u00c2\u00b0 5 32 .6\\nVenus,\\nn\\na\\n224:\\n1\u00c2\u00b0 36 7 .8\\nEarth,\\n1 year,\\na\\n365\\n0\u00c2\u00b0 59 8 .3\\nMars,\\n2\\nu\\n687\\n0\u00c2\u00b0 31 26 .7\\nCeres,\\nH\\nu\\n1,681\\n0\u00c2\u00b0 12 50 .9\\nJupiter,\\n12\\na\\n4,332\\n0\u00c2\u00b0 4 59 .3\\nSaturn,\\n29\\nu\\n10,759\\n0\u00c2\u00b0 2 0 .6\\nUranus,\\n84:\\nu\\n30,686\\n0\u00c2\u00b0 0 42 .4\\nNeptune, 164+\\na\\n60,127\\n0\u00c2\u00b0 0 21 .5\\nFrom this view it appears that the planets nearest the sun\\nmove most rapidly. Thus Mercury performs nearly 350 revo-\\nlutions while Uranus performs one. This is evidently not\\nowing merely to the greater dimensions of the erbit of Uranus,\\nfor the length of its orbit is not 50 times that of the orbit of\\nMercury, while the time employed in describing it is 350\\ntimes that of Mercury. Indeed, this ought to follow from\\nKepler s law, that the squares of the periodic times are as the\\ncubes of the distances from which it is manifest that the times\\nof revolution increase faster than the dimensions of the orbit.\\nAccordingly, the apparent progress of the most distant planets\\nis exceedingly slow, the rate of Uranus being only 42 .4 per\\nday so that for weeks and months, and even years, this planet\\nbut slightly changes its place 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\\nearth and secondly, the superior, which have their orbits ex-\\nterior to the 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", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0203.jp2"}, "204": {"fulltext": "180\\nTHE PLANETS.\\nupon the sun. Mercury never appears further from the sun\\nthan 29\u00c2\u00b0 (28\u00c2\u00b0 48 and seldom so far and Yenus never more\\nthan about 47\u00c2\u00b0 (47\u00c2\u00b0 12 Both planets, therefore, appear either\\nin the west soon after sunset, or in the east a little before sun-\\nrise. In high latitudes, where the twilight is prolonged, Mer-\\ncury can seldom be seen with the naked eye, and then only at\\nthe periods of its greatest elongation.* The reason of this will\\nreadily appear from the following diagram.\\nLet S represent the sun, E the earth, and MK 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 con-\\ncave sphere of the heavens, we should see the sun at Z and\\nMercury at O, when at its greatest eastern elongation, and at P\\nwhen at its greatest western elongation and while passing\\nfrom M to 1ST through Q, it would appear to describe the arc\\nOP and while passing from N to M, through R, it would\\nappear to run back across the sun on the same arc. It is\\nfurther evident that it would be visible only when at or near\\none of its greatest elongations being at all other times so near\\nthe sun as to be lost in his light.\\n303. A planet is said to be in conjunction with the sun\\nwhen it is seen in the same part of the heavens with the sun,\\nCopernicus is said to have lamented, on his death-bed, that he had never\\nbeen able to obtain a sight of Mercury and Delambre, a great French astrono-\\nmer, sa-v^ it but twice.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0204.jp2"}, "205": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 181\\nor when it has the same longitude. Mercury and Yenus have\\neach two conjunctions, the inferior and the superior. The\\ninferior conjunction is its position when in conjunction on the\\nsame side of the sun with the earth, as at Q in the figure the\\nsuperior conjunction is its position when on the side of the sun\\nmost distant from the earth, as at R.\\n304. The period occupied by a planet between successive\\nconjunctions of the same kind is called its synodical revolution.\\nBoth the planet and the earth being in motion, the time of the\\nsynodical revolution exceeds that of the sidereal revolution of\\nMercury or Yenus 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 Mer-\\ncury come into its inferior conjunction at Q (Fig. 60). In\\nabout 88 days the planet will come round to the same point\\nagain but meanwhile the earth has moved forward through\\nnearly a fourth part of her revolution, and will continue to\\nmove onward while Mercury, with a swifter motion, is follow-\\ning on to overtake her, the case being analogous to the hour\\nand minute hand of a clock. Having the sidereal period of a\\nplanet, which may always be accurately determined by obser-\\nvation, we may ascertain its synodical period, as follows\\nBy the table in article 301, the mean daily motion of Mer-\\ncury is 4\u00c2\u00b0 5 32 .6 14732 .6, and that of the earth is 59\\n8 .3=354:8 .3. Therefore, 14r732 .6-3548.3=11184 .3, which\\nis the average gain of Mercury over the earth in a day. But\\nin order to overtake the earth, Mercury must complete one\\nrevolution and as much of another as the earth has performed,\\nnntil the planet overtakes it that is, the planet must gain an\\nentire revolution. Now,\\n11184 .3 1 day 360\u00c2\u00b0 115,8 days, the synodical period of\\nMercury. In like manner, the daily gain of Yenus is 2219 .5,\\nand\\n2219 .5 1 day 360\u00c2\u00b0 583.9 days, the synodical period of\\nYenus.\\n\u00e2\u0080\u00a2305. The motion of an inferior planet is direct in passing\\nthrough its superior conjunction, and retrograde in passing\\nthrough its inferior conjunction.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0205.jp2"}, "206": {"fulltext": "182\\nTHE PLANETS.\\nThus Yenus, while going from B through D to A (Fig. 61),\\nmoves in the order of the signs, or from west to east, and\\nwould appear to traverse the celestial vault B S A from right\\nto left but in passing from A through C to B, her course\\nwould be retrograde, returning on the same arc from left to\\nright. If the earth were at rest, therefore (and the sun, of\\ncourse, at rest), the inferior planets would appear to oscillate\\nbackward and forward across the sun. But it must be recol-\\nlected that the earth is moving in the same direction with the\\nplanet, as respects the signs, but with a slower motion. This\\nmodifies the apparent motions of the planet, accelerating it in\\nthe superior, and retarding it in the inferior conjunctions.\\nThus, in figure 61, Yenus, while moving through BDA, would\\nFig. 61.\\nseem to move in the heavens from B f to A were the earth at\\nrest but meanwhile the earth changes its position from E to\\nE by which means the planet is not seen at A but at A\\nbeing accelerated by the arc A A in consequence of the\\nearth s motion. On the other hand, when the planet is pass-\\ning through its inferior conjunction ACB, it would appear to\\nmove backward 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,\\nmoved from E to E being retarded by the arc B B Al-\\nthough the motions of the earth have the effect to accelerate", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0206.jp2"}, "207": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 183\\nthe planet in the superior, and to retard it in the inferior con-\\njunction, jet on account of the greater distance, the apparent\\nmotion of the planet is much slower in the superior than in\\nthe inferior conjunction.\\n306. In passing from either conjunction to the other, an\\ninferior planet is stationary at a point a little way from the\\ngreatest elongation toward the inferior conjunction.\\nIf the earth, were at rest the stationary points would be at\\nthe greatest elongations A and B for then the planet would\\nbe moving directly toward or from the earth, and would be\\nseen for some time in the same place in the heavens but the\\nearth itself is moving nearly at right angles to the line of the\\nplanet s motion, and therefore a direct apparent motion is\\ngiven to the planet. Hence we need to choose such a position\\nfor the planet that its retrograde movement shall be just suffi-\\ncient to counteract this. Of course it must be on the arc ACB.\\nBut, as the planet s angular velocity is much greater than the\\nearth s, it must be near A or B, where the motion is quite ob-\\nlique to our own, else the retrogradation will be too rapid to\\nneutralize the direct motion caused by the earth s progress.\\nThe stationary point for Mercury is at an elongation of 15\u00c2\u00b0 or\\n20\u00c2\u00b0 from the sun, that of Yenus at about 29\u00c2\u00b0.\\n307. Mercury and Yenus exhibit to the telescope phases\\nsimilar to. those of the moon.\\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 the side of\\ntheir superior conjunctions, as from B to A through D, they\\nappear gibbous. At the moment of superior conjunction, the\\nwhole enlightened orb of the planet is turned toward 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 positions of the\\nplanet with respect to the sun and earth, will be readily un-\\nderstood by inspecting the diagram (Fig. 61).\\nThe phases show that these bodies are not self-luminous, but\\nshine only as they reflect to us the light of the sun and all\\nthe planets in some way give evidence of the same fact.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0207.jp2"}, "208": {"fulltext": "184:\\nTHE PLANETS.\\nFie:. 62.\\n308. The distance of an inferior planet from the sun, may\\nhe found 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 SCE\\nwill be known, being a right angle. The angle SEC is the\\ngreatest elongation this is known by observation. Hence, if\\nES is considered to be known, Ead sin E SE SC, which\\nis the distance of the planet from the sun. But\\nif SE be not definitely known, then this pro-\\nportion gives only the ratio of the distances of\\nthe earth and the inferior planet from the sun.\\nIn finding the earth s distance from the sun by\\nmeans of the transit of Yenus (Art. 318), this\\nratio will be employed. If the orbits were\\nboth circles, this method would be very exact\\nbut being elliptical, we obtain the mean value\\nof the radius SC by observing its greatest elon-\\ngation in different parts of its orbit.*\\n309. The orbit of Mercury is more eccentric,\\nand more inclined to the ecliptic, than that of E\\nany other planet /f while that of Venus is nearly circular, and\\nbut little inclined to the ecliptic.\\nThe eccentricity of the orbit of Mercury is nearly J of its\\nsemi-major axis, while that of Yenus is T Js and that of the\\nearth only -\u00c2\u00a7q the inclination of Mercury s orbit is 7\u00c2\u00b0, while\\nthat of Yenus is only 3i\u00c2\u00b0.$ At the perihelion, Mercury is\\nonly 29 millions of miles from the sun, while at the aphelion\\nhis distance is 44 millions, a variation of 15 millions, and more\\nthan five times as great as in the case of the earth. On ac-\\ncount of his different distances from the earth, Mercury is also\\nsubject to much variation in his apparent diameter, which is\\n12 in perigee, but only 5 in apogee.\\n310. After the mean distance has been found (Art. 307),\\nthe periodic time is obtained, by applying Kepler s third law\\nto the orbit of the planet, and that of the earth. From this is\\ncalculated the synodical period (Art. 304).\\nHerschel s Outlines, p. 275.\\nBaily s Tables.\\nf The asteroids are of course excepted.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0208.jp2"}, "209": {"fulltext": "INFERIOR PLANETS MERCURY AND VENUS. 185\\nThe synodical period is also obtained very accurately from\\nthe interval between two transits across the sun s disk.\\n311. An inferior planet is brightest at a certain point be-\\ntween its greatest elongation and inferior conjunction.\\nAs to distance, the planet would give us most light when\\nnearest, i. e., at the inferior conjunction but so far as the\\nphase is concerned, it would give us most at the superior con-\\njunction, where the planet is at the full. Of course, the maxi-\\nmum is at some point between the two conjunctions; and by\\ncalculation it is found between the inferior conjunction and\\ngreatest elongation, within a few degrees of the latter. Yenus\\nappears most luminous when about 40\u00c2\u00b0 from the sun, and is\\nsometimes visible all day.\\n312. Mercury and Venus both revolve on their axes in\\nnearly the same time with the earth.\\nThe diurnal period of Mercury is a little greater than that of\\nthe earth, being 24h. 5m. 28s., and that of Venus is a little\\nless than the earth s, being 23h. 21m. 7s. The revolutions on\\ntheir axes have been determined by means of some spot or\\nmark seen by the telescope, as the revolution of the sun on his\\naxis is ascertained by means of his spots.\\n313. Yenus is regarded as the most beautiful of the plan-\\nets, and is well known as the morning and evening star. The\\nmost ancient nations did not indeed recognize the evening and\\nmorning star as one and the same body, but supposed they\\nwere different planets, and accordingly gave them different\\nnames, calling the morning star Lucifer, and the evening star\\nHesperus. At her period of greatest splendor, Yenus casts a\\nshadow, and is sometimes visible in broad daylight. This oc-\\ncurred in a very striking manner in September, 1852, Yenus\\nbeing on the meridian about 9 o clock, a. m., and her northern\\ndeclination nearly 15 degrees. Although not 15\u00c2\u00b0 from the in-\\nferior conjunction, and consequently exposing only a portion\\nof her disk, like that of the moon when three or four days old,\\nyet her light is then estimated as equal to that of twenty stars\\nof the first magnitude.* At her period of greatest elongation,\\nFrancoeur, Uranogrophy, p. 125.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0209.jp2"}, "210": {"fulltext": "186 THE PLANETS.\\nYenus is visible from three to four hours after the setting, or\\nbefore the rising of the sun.\\n314. Every eight years, Venus forms her conjunctions with\\nthe sun in the sam,e part of the heavens.\\nThe sidereal period of Yenus being 224.7 days, and that of\\nthe earth 365.256 days, thirteen revolutions of Yenus are ac-\\ncomplished in nearly the same time as eight revolutions of the\\nearth: for 224.7x13=2921, and 365.256x8=2922, At the\\nend, therefore, of 2922 days, or eight years, the two bodies will\\ncome round to the same point of the heavens, and be in the\\nsame situation in their respective orbits, as at the beginning.\\nConsequently, whatever appearances of this planet arise from\\nits positions with respect to the earth and the sun (as, for ex-\\nample, being visible in the daytime), they are repeated every\\neight years in nearly the same form.\\nTRANSITS OF THE INTERIOR PLANETS.\\n315. The transit of Mercury or Venus, is its passage across\\nthe sun s dish, 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\\nthese planets coincident with the earth s orbit, a transit would\\noccur at some part of the earth at every inferior conjunction,\\nas there would be an eclipse of the sun at every new moon,\\nwere the moon s revolution in the plane of the ecliptic. But\\nthe orbit of Yenus makes an angle of 3|-\u00c2\u00b0 with that of the\\nearth, and the orbit of Mercury an angle of 7\u00c2\u00b0 and, more-\\nover, the apparent diameter of each of these bodies is very\\nsmall, both of which circumstances conspire to render a transit\\na comparatively rare occurrence, since it can happen only\\nwhen the sun, at the time of an inferior conjunction, happens\\nto be at, or extremely near the planet s node. The nodes of\\nMercury lie in that part of the earth s orbit which it passes in\\nthe months of May and November. It is only in these months,\\ntherefore, that transits of Mercury can occur. For a similar", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0210.jp2"}, "211": {"fulltext": "TRANSITS OF THE INFERIOR PLANETS. 187\\nreason, those of Terms occur only in June and December.\\nSince the nodes of both planets have a small retrograde mo-\\ntion, the months in which transits occur, will change in the\\ncourse of ages but the months for transits will for a long\\ntime remain the same as at present, since the nodes of Mer-\\ncury change their places only 13 and those of Yenus only 31\\nin a century.*\\nThe first prediction of this phenomenon was made by Kepler,\\nand was that of a transit of Mercury, which occurred on the\\n7th of November, 1631. As early as 1629, Kepler announced\\nto astronomers that his tables gave the latitude of Mercury, at\\nthe conjunction which was to take place on that day, less than\\nthe sun s semi-diameter consequently, that the planet, in\\npassing by the sun, would be nearer the sun s center than the\\nlength of the sun s radius, and of course appear on his disk.\\nThe event corresponded to the prediction. The transit of\\nMercury, which occurred on the 8th of November, 1848, was\\nthe 25th since the one predicted by Kepler, averaging nearly\\none in 8 years, although they take place at very unequal in-\\ntervals.\\n316. The shortest interval between two successive transits\\nof Mercury is 3-j- years, and of Venus, 8 years: but sometimes\\nthey are separated by long intervals, especially those of Yenus.\\nThe only transits of Yenus in the 19th century, are in 1874\\nand 1882; and in the 20th, not a single one will occur; the\\nintervals being 8, 121i 8, 105^, 8, 1211, c years. The in-\\ntervals between the transits of Mercury, from 1848, through\\nthe century, are 13, 7, 9i, 3J, 9|, and 3J years. The shortest\\ninterval for Mercury at the same node is 7 years hence, at\\nopposite nodes, two transits may occur within 3^ years. More\\nof the transits of Mercury happen in November than in May,\\nbecause the orbit of this planet (w T hich has a great eccentricity,\\nArt. 308), is so situated that in November the planet is near its\\nperihelion, and is then more likely to be projected on the sun,\\nin passing its inferior conjunction, than in a part of its orbit\\nmore distant from the sun.\\n\u00e2\u0080\u00a2Let us see how the intervals between the transits of Mercury\\nHind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0211.jp2"}, "212": {"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\\n365.256, and since the number of times each will revolve in a\\ngiven period is inversely as the time of one revolution, there-\\nfore, in 224,700 revolutions of the earth, and 365,256 revolu-\\ntions of Yenus, the two bodies would meet exactly at the same\\nnode as before. But 224,700 365,256 8 13 nearly so that\\ntransits of Yenus are sometimes repeated at intervals of 8 years,\\nand if the ratio of 8 to 13 were exactly that of the two first\\nterms of the proportion, we should have a transit of Yenus\\nevery 8 years. The ratio of 227 to 369 is still nearer that of\\nthose terms and hence a transit after 227 years is still more\\nprobable but since there are two nodes, the chance is doubled,\\nso that a transit is highly probable after an interval of 113J\\nyears. The two transits of Yenus in the 18th century occurred\\nin June, 1761, and June, 1769, 8 years apart; the two transits\\nof the 19th century are in December, 1874, and December,\\n1882, the intervals being 105^ and 8 years. The average long\\ninterval is 113^ years, but it may be lengthened to 121J, or\\nshortened to 105J, according as the preceding transit took place\\nbefore or after passing the node.\\n317. The great interest attached by astronomers to a transit\\nof Yenus, arises from its furnishing the most accurate means\\nin our power of determining the surfs horizontal parallax- an\\nelement of great importance, since it leads to a knowledge of\\nthe distance of the earth from the sun, and consequently, by\\nthe application of Kepler s third law (Art. 183), of the dis-\\ntances of all the other planets. Hence, in 1769, great efforts\\nwere made throughout the civilized world, under the patron-\\nage of different governments, to observe this phenomenon\\nunder circumstances the most favorable for determining the\\nparallax of the sun. The method of finding the parallax of a\\nheavenly body, described in Art. 85, can not be relied on to a\\ngreater degree of accuracy than 4 In the case of the moon,\\nwhose greatest parallax amounts to about 1\u00c2\u00b0, this deviation\\nfrom absolute accuracy is not material, but it amounts to\\nnearly half the entire parallax of the sun and since the dis-\\ntance is inversely as the horizontal parallax, such an error\\nwould make the distance of the sun either twice as great, or", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0212.jp2"}, "213": {"fulltext": "TRANSITS OF THE INFERIOR PLANETS. 189\\nonly two-thirds as great as the true distance, according as the\\nparallax was 4 below or 4 above the truth.\\n318. If the sun and Yenus were equally distant from us,\\nthey would be equally affected by parallax as viewed by spec-\\ntators in different parts of the earth, and consequently their\\nrelative situation would not be altered by such a difference in\\nthe points of view but since Yenus, at the inferior conjunc-\\ntion, is only about one-third as far off as the sun, her parallax\\nis proportionally greater, and therefore spectators, at distant\\npoints, will see Yenus projected on different parts of the solar\\ndisk and as the planet traverses the disk, she will appear to\\ndescribe chords of different lengths, by means of which the\\nduration of the transit may be estimated at different places.\\nThe difference in the duration of the transit, as viewed from\\nopposite parts of the earth, does not amount to many minutes\\nbut to make it as large as possible, places very distant from\\neach other are selected for observation. Thus, in the transit\\nof 1769, among the places selected, two of the most favorable\\nwere Wardhus, in Lapland, and Otaheite (now written Tahiti),\\none of the Society Islands, in the South Pacific Ocean, to which\\nplace the celebrated Captain Cook was dispatched by the\\nBritish government for the express purpose of observing the\\ntransit.\\nAlthough the exact determination of the sun s horizontal\\nparallax by this method is a very complicated and difficult\\nproblem, yet the principle on which the process depends ad-\\nmits of an easy illustration. Let E (Fig. 63) be the earth, Y\\nYenus, and S the center of the sun. Suppose A and B two\\nFig. 63.\\nB\\n3E\\nobservers at the extremities of that diameter of the earth which\\nis perpendicular to the orbit of Yenus. At a certain moment\\nthe spectator A will see Yenus on the sun s disk at a, and the\\nspectator B will see it at b and since AY and BY may be\\nconsidered as equal to each other, as also Yb and Ya there-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0213.jp2"}, "214": {"fulltext": "190 THE PLANETS.\\nfore the triangles YAB and Yah are similar and AY aV\\nAB ah. But AB is known also the ratio of AY aV (Art.\\n308) hence ah, the distance between the points at which the two\\nobservers see Y projected on the sun s disk, is known in miles.\\nWe need now to obtain the angular value of ah. The observers\\ncarefully note the instant when Yenus touches the disk, at the\\nbeginning of the transit, and also at the end. Thus the time\\nof making the transit, as seen by each observer, is accurately\\nobtained. But since the angular motion per hour, both of the\\nplanet and of the sun, is known, this time of crossing the disk\\ncan be changed into an arc and we thus have the number of\\nminutes of a degree in the chord cd, and also the number in ef y\\nand of course in their halves ca and eh. But cS and eS, the\\nangular semi-diameter of the sun at the same time is known\\nhence, in the right-angled triangles cSa, eSb, we readily find\\nthe minutes in S#, S5, the difference between which is the\\nangular value of ah. We have, therefore, ascertained what\\nangle is subtended by a line of given length, when placed at\\nthe sun and viewed from the earth or, which is the same\\nthing, placed at the earth and viewed from the sun and\\ntherefore we know what angle at the sun is subtended by the\\nearth s semi-diameter, which is the sun s horizontal parallax.\\nThe observers can not, probably, be at points diametrically\\nopposite, nor can they remain stationary during the transit, on\\naccount of diurnal motion therefore allowance must be made\\nfor these circumstances. The line ah will be more accurately\\nmeasured, according as the transit occurs nearer to the edge of\\nthe sun s disk, because of the greater inequality in the length\\nof the chords. The solar parallax is so small that several sta-\\ntions should be occupied, so as to obtain a number of inde-\\npendent results. The parallax of the sun, as measured in 1769,\\nis 8 .5776\\nYenus when on the side of her inferior conjunction, and\\nMars when near his opposition, each comes comparatively near\\nto the earth, and at these times exhibits a large horizontal\\nparallax. That of Yenus, especially, may be obtained with\\ngreat accuracy when she is near her greatest elongation and\\nDelambre, t. ii Vince, Complete Syst., vol. i. Woodhouse, p. 754; Her-\\nschel s Outlines, p. 255.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0214.jp2"}, "215": {"fulltext": "TRANSITS OF THE INFERIOR PLANETS. 191\\nsince it is easy, by article 308, to determine, at that time, the\\nratio of her distance from the sun to the earth s distance, it is\\na matter of great interest to astronomy to have the parallax of\\nYenns, when thus situated, accurately found. For this pur-\\npose, the government of the United States, in 1849, sent an\\nexpedition, under Lieutenant Gilliss, to Chili, in order to take\\nobservations on Mars and Yenus, especially the latter, during\\n1850, 1851, and 1852, in concert with the Observatory at\\nWashington. These observations seem to indicate that the\\nsolar parallax is a little less than stated above, probably near-\\ner 8 .5 than 8 .6.*\\n319. During the transits of Yenus over the sun s disk in\\n1761 and 1769, a sort of penumbral light was observed around\\nthe planet by several astronomers, which was thought to indi-\\ncate an atmosphere. This appearance was particularly observ-\\nable while the planet was coming on and going off the solar\\ndisk. The total immersion and emersion were not instanta-\\nneous but as two drops of water when about to separate form\\na ligament between them, so there was a dark shade stretched\\nout between Yenus and the sun, and when the ligament broke,\\nthe planet seemed to have got about an eighth part of her\\ndiameter from the limb of the sun.f The presence of an at-\\nmosphere is also indicated by appearances of twilight and\\nindications of a horizontal refraction.^\\nAlthough no satellite has hitherto been discovered attending\\neither Mercury or Yenus, yet suspicions have, at different\\ntimes, been entertained of a satellite belonging to Yenus.\\nNone has been seen in any of the transits of Yenus and al-\\nthough the distance of the satellite (if one exists) from the\\nprimary might have been too great to be projected with the\\nprimary on the sun, yet its absence on each of these occasions\\nhas strengthened the belief of astronomers that no such satel-\\nlite exists.\\nSee Astron. Journ., Oct., 1858. f Edin. Encyc, Art. Astronomy. Hind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0215.jp2"}, "216": {"fulltext": "CHAPTER X.\\nOF THE STTPEEIOE PLANETS MAES, THE PLANETOIDS, JUPITEE,\\nSATTJEN, TJEANUS, AND NEPTTJNE.\\n320. The Superior planets are distinguished from the In-\\nferior, by being seen at all distances from the sun from 0\u00c2\u00b0 to\\n180\u00c2\u00b0. Having their orbits exterior to that of the earth, they\\nof course never come between us and the sun, that is, they\\nhave never any inferior conjunction like Mercury and Venus,\\nbut they are seen in superior conjunction and in opposition.\\nNor do they, like the inferior planets, exhibit to the telescope\\ndifferent phases; but, with a single exception, they always\\npresent the side that is turned toward the earth fully enlight-\\nened. This is owing to their great distance from the earth\\nfor were the spectator to stand upon the sun, he would, of\\ncourse, always have the illuminated side of each of the planets\\nturned toward him but so distant are all the superior plan-\\nets except Mars, that they are viewed by us very nearly as\\nthey would be if we actually stood on the sun.\\n321. Maes 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\\ndistance is 145,200,000 miles; but in consequence of the eccen-\\ntricity of his orbit, the distance varies greatly, the difference\\nbetween the perihelion and aphelion distances being 27,000,000\\nmiles. Mars is always near the ecliptic, never varying from it\\n2\u00c2\u00b0. He is distinguished from all the other planets by his deep\\nred color and fiery aspect but his brightness and apparent\\nmagnitude vary much at different times, being sometimes\\nnearer to us than at others by the whole diameter of the\\nearth s orbit, that is, by about 190,000,000 miles. When Mars\\nis on the same side of the sun with the earth, or at his opposi-\\ntion, he comes within 50,000,000 miles of the earth, and, rising\\nHind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0216.jp2"}, "217": {"fulltext": "MAES. 193\\nabout the time the sun sets, surprises us by his magnitude and\\nsplendor but when he passes to the other side of the sun to\\nhis superior conjunction, he dwindles to the appearance of a\\nsmall star, being then 240,000,000 miles from us. Thus, let M\\n(Fig. 64) represent Mars in opposition, and M in superior\\nconjunction, it is obvious that the planet must be nearer to us\\nin the former situation than in the latter by the whole diame-\\nter of the earth s orbit.\\n322. Mars is the only one of the superior planets which\\nexhibits phases. When he is toward the quadratures at Q or\\nQ it is evident from the figure that only a part of the circle\\nof illumination is turned toward the earth, such a portion of\\nthe remoter part of it being concealed from our view as to\\nrender the form more or less gibbous.\\n323. When viewed with a powerful telescope, the surface\\nof Mars appears diversified with numerous varieties of light\\nand shade. The region around the poles is marked by white\\nspots, which vary their appearance with the changes of the\\nseasons in the planet. Hence Dr. Herschel conjectured that\\nthey are owing to ice or snow which occasionally accumulates\\nand melts, according to the position of each pole with respect\\n13", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0217.jp2"}, "218": {"fulltext": "194- THE PLANETS.\\nto the sun.* It has been common to ascribe the ruddy light\\nof this planet to an extensive and dense atmosphere, which was\\nsupposed to be distinctly indicated by the gradual diminution\\nof light observed in a star as it approached very near to the\\nplanet in undergoing an occultation but more recent observa-\\ntions afford no such evidence of an atmosphere.f By observa-\\ntions on the spots, we learn that Mars revolves on his axis in\\nvery nearly the same time with the earth (24h, 39m. 21 s .3);\\nand that the angle between his equator and the plane of his\\norbit is also nearly the same as between the earth s equator r.nd\\nthe ecliptic, the former being 28\u00c2\u00b0 42 the latter 23\u00c2\u00b0 28 so that\\nthe changes of seasons on Mars must resemble our own.\\nNo satellite has ever been discovered belonging to Mars,\\nalthough being situated at a greater distance from the sun than\\nour 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,:): while the earth s ellipticity is one three-\\nhundreth. 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\\nsame side of the sun with the earth, and the ratio of his dis-\\ntance from the sun to that of the earth being easily obtained,\\nastronomers have sought by means of his parallax, as by that\\nof Venus, to find the sun s horizontal parallax. But the meth-\\nod by observations on Yenus, as described in Art. 318, is more\\nto be relied on.\\n325. The Asteroids or Planetoids compose a group of very\\nsmall planets, indefinite in number, whose orbits lie beyond\\nthat of Mars, at the distance of about 250,000,000 miles from\\nthe sun. The discovery of them commenced with the begin-\\nning of the present century. Kepler had long before noticed\\na large interval between Mars and Jupiter, which seemed to\\nPhil. Trans., 1784. Sir James South, Phil. Trans., 1833. Hind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0218.jp2"}, "219": {"fulltext": "NEW PLANETS, OR ASTEROIDS. 195\\nbreak the continuity of the series and about the close of the\\nlast century, Bode, of Berlin, showed that a series of numbers\\nfollowing a certain law (Art. 299) would express quite accu-\\nrately the distances from the sun, even to Uranus, which had\\njust been discovered, if only the vacancy between Mars and\\nJupiter were supplied. 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\\nformed on the continent of Europe of twenty-four observers,\\nwho divided the sky into as many zones, one of which was\\nallotted to each member of the association. The discovery of\\nthe first of these bodies was, however, made accidentally by\\nPiazza, an astronomer of Palermo, on the 1st of January, 1801.\\nIt was shortly afterward lost sight of, on account of its prox-\\nimity to the sun, and was not seen again until the close of the\\nyear, when it was rediscovered in Germany. Piazza called it\\nCeres, in honor of the tutelary goddess of Sicily, and her em-\\nblem, the sickle has been adopted as the appropriate sym-\\nbol. The difficulty of finding Ceres induced Dr. Olbers, of\\nBremen, to examine, with particular care, all the small stars\\nthat lie near her path, as seen from the earth and, while pros-\\necuting these observations, in March, 1802, he discovered\\nanother similar body, very nearly at the same distance from\\nthe sun, and resembling the former in many other particulars.\\nThe discoverer gave to this second planet the name of Pallas,\\nchoosing- for its symbol the lance the characteristic of\\nMinerva.\\n326. 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 com-\\nmon node a circumstance that indicated an identity of origin.\\nOn account of this singularity, Dr. Olbers was led to conjecture\\nthat Ceres and Pallas are only fragments of a larger planet\\nwhich had formerly circulated around the sun at this distance,\\nand been shattered 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 was adopted for its symbol, representing the starry scep-\\nter of the goddess. In 1807, a fourth planet, Vesta, was dis-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0219.jp2"}, "220": {"fulltext": "1 6 THE PLANETS.\\ncovered, and for its symbol the character fi was chosen an\\naltar surmounted with a censer holding the sacred fire. It is\\none of the largest of the asteroids, and has sometimes been seen\\nby the naked eye.\\n327. From 1807 to 1845, a period of nearly forty years, no\\nmore of these small planets were discovered, and, up to this\\ntime, by the asteroids were meant the fonr little planets already\\nenumerated Ceres, Pallas, Juno, and Yesta. Meanwhile,\\nvery accurate maps of the stars, including all up to the tenth\\nmagnitude, had been published, especially in the region of the\\nzodiac, and astronomers scrutinized these with such extreme\\ncloseness, that any wanderer appearing among them was likely\\nto be immediately detected. Since 1845, new ones have been\\nadded to the list nearly every year. At the beginning of 1850,\\nthe whole number known was 10 of 1855, 23 of 1860, 57.\\nThough feminine mythological names have been applied to\\nnearly all of them, yet they are better designated by a small\\ncircle inclosing a number which expresses the order of their\\ndiscovery thus Ceres is Q Thetis, Pandora, 0, c.\\nThey vary somewhat in their mean distances, and of course\\nin their periods. Some of them have orbits more eccentric,\\nand others more inclined to the ecliptic, than any of the larger\\nplanets. They are too small to be measured with any certainty\\nthe largest, Ceres, is not estimated to be more than 160 miles in\\ndiameter. It is probable that all of them united would form\\nbut an inconsiderable planet. Some of them are attended by a\\nnebulosity, which indicates that they have an extensive atmos-\\nphere. The different planetoids have been first discovered by\\nobservers of many countries England, Prance, Germany, Italy,\\nand America.\\n328. 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 ex-\\nceeding the polar diameter in the ratio of 107 to 100,* which\\nis 21 times as great as the earth s ellipticity. This flattening\\nHerschel.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0220.jp2"}, "221": {"fulltext": "JUPITER. 197\\nof the poles is indeed quite perceptible by the telescope, and\\nis obvious to the eye in a correct drawing of the planet. (See\\nFrontispiece.) Such a figure might naturally be expected from\\nthe rapidity of his diurnal revolution, which is accomplished\\nin about 10 hours (9k. 55m. 21 s .3).*\\nA place on tke equator of Jupiter must revolve 450 miles\\nper minute, or 27 times as fast as a place on the terrestrial\\nequator. The distance of Jupiter from the sun is 495,000,000\\nmiles (495,817,000).f His plane of rotation is but slightly in-\\nclined to the plane of his orbit (only about 3\u00c2\u00b0), and consequent-\\nly his climate experiences but a slight change of seasons.\\n329. The view of Jupiter through a good telescope is one\\nof the most magnificent and interesting spectacles among the\\nheavenly bodies. The disk expands into a large and bright\\norb like the full moon the spheroidal figure which theory as-\\nsigns to revolving worlds is here palpably exhibited to the eye;\\nacross the disk, arranged in parallel stripes, are discerned sev-\\neral dusky bands, called belts; and four bright satellites, always\\nIn attendance, but ever varying their positions, compose a\\nsplendid retinue. Indeed, astronomers gaze with peculiar in-\\nterest on Jupiter and his moons, as affording a miniature rep-\\nresentation of the whole solar system repeating, on a smaller\\nscale, the same revolutions, and exemplifying, in a manner\\nmore within the compass of our observation, the same laws as\\nregulate the entire assemblage of sun and planets.\\n330. 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\\ndisk. Occasionally these belts retain nearly the same form and\\npositions 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\\nover the whole face of the planet. The prevailing opinion\\namong astronomers in reference to the nature of these belts is,\\nthat they are produced by disturbances in the planet s atmos-\\nAiry. f Hind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0221.jp2"}, "222": {"fulltext": "198 THE PLANETS.\\npliere, which occasionally render its dark body visible and,\\nas the belts are found to traverse the disk in lines uniformly\\nparallel to Jupiter s equator, they are inferred to be connected\\nwith the rotation of the planet upon its axis, the great rapidity\\nof which would naturally produce peculiarities in its atmos-\\npheric phenomena.\\n331. The Satellites of Jupiter may be seen with a telescope\\nof very moderate powers. Even a common spy-glass will\\nenable us to discern them. Indeed, being nearly equal in bril-\\nliancy to the smallest stars visible to the naked eye, a slight\\nincrease of optical power brings them into view and some few\\npersons, endowed with extraordinary powers of vision, have\\nsupposed that they saw one of these little bodies without the\\naid of instruments but on applying the telescope it has been\\nfound that three of the satellites have approached so near to-\\ngether as to appear like one.* In the largest telescopes, they\\nseverally appear as bright as Sirius does to the naked eye.\\nWith such an instrument, the view of Jupiter with his moons\\nand belts is truly a magnificent spectacle a world within it-\\nself. As the orbits of the satellites do not deviate far from the\\nplane of the ecliptic, and but little from the equator of the\\nplanet (which nearly coincides with the ecliptic), they are\\nusually seen almost in a straight line extending across the cen-\\ntral part of the disk. (See Frontispiece.)\\n332. Jupiter s satellites are distinguished from one another\\nby the denominations of first, second, third, and fourth, accord-\\ning to their relative distances from the primary, the first being\\nthat which is nearest to him.f Their apparent motion is os-\\ncillatory, like that of a pendulum, going alternately from their\\ngreatest elongation on one side to their greatest elongation on\\nthe other, sometimes in a straight line, and sometimes in an\\nelliptical curve, according to the different points of view in\\ns Hind. Rev. Mr. Stoddard, a graduate of Yale College, missionary to the\\nNestorians, has repeatedly seen one of these bodies with the naked eye, from\\nMount Seir, near Oroomiah. Mr. Stoddard is known to the author as an excel-\\nlent observer, and his testimony on this point may be fully relied on.\\nf Mythological names were long since proposed for the satellites of Jupiter,\\nviz., Io, Europa, Ganymede, Calisto but the mode of designating them by num-\\nbers generally prevails.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0222.jp2"}, "223": {"fulltext": "JUPITER.\\n199\\nwhich, we observe them from the earth. Their motion is al-\\nternately direct and retrograde they are sometimes stationary\\nand, in short, they exhibit in miniature all the phenomena of\\nthe planetary system. Yarious particulars of the system are\\nexhibited in the following table, the diameters being in miles,\\nand the distances being taken from the center of the primary.*\\nSatellite.\\nDiameter.\\nDistances.\\nSidereal Revolution.\\n1\\n2\\n3\\n4\\n2,440 i\\n2,190\\n3,580\\n3,060\\n278,500\\n443,300\\n707,000\\n1,243,500\\nId. 18h. 28m.\\n3 13 15\\n7 3 43\\n16 16 32\\nFrom this table we see that Jupiter s satellites are all larger\\nthan the moon, the second exceeding it by only 30 miles in di-\\nameter, the third by 1420 miles. 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,\\nreduces their apparent size and light as seen from Jupiter.\\nThus the largest of them would exhibit to a spectator on the\\nequator of the planet, a diameter of only 36 which is only a\\nlittle greater than that of the moon, while the smallest would\\nappear only one-fourth as large. It is noticeable, that the\\nsatellites of Jupiter make very quick revolutions, when com-\\npared with the earth s moon, although they are all at greater\\ndistances from the primary than the moon from the earth the\\nfurthest revolving in about of the moon s period, and the\\nnearest more than 16 times as quick. This is because they are\\nso powerfully attracted by the planet. To prevent their being\\ndrawn in from their circular orbits, a great projectile velocity is\\nnecessary.\\n333. The orbits of the satellites are nearly or quite circu-\\nlar, and deviate but little from the plane of the planet s\\nequator, and of course are but slightly inclined to the plane of\\nhis orbit. They are, therefore, in a similar situation with\\nrespect to Jupiter as the moon would be with respect to the\\nearth, if her orbit nearly coincided with the ecliptic, in which\\nHind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0223.jp2"}, "224": {"fulltext": "200 THE PLANETS.\\ncase she would eclipse the sun every new moon, and be herself\\neclipsed every full moon.\\n334. The eclipses of Jupiter s satellites, in their general\\nconception, are perfectly analogous to those of the moon, but\\nin their details they differ in several particulars. Owing to\\nthe much greater distance of Jupiter from the sun, and its\\ngreater magnitude, the cone of its shadow is more than sixty\\ntimes that of the earth, stretching off into space more than\\n55,000,000 miles. On this account, as well as on account of\\nthe little inclination of their orbits to that of their primary, the\\nthree inner satellites of Jupiter pass through the shadow and\\nare totally eclipsed at every revolution. The fourth satellite,\\nowing to the greater inclination of its orbit, sometimes, though\\nrarely, escapes eclipse, and sometimes merely grazes the limits\\nof the shadow, or suffers a partial eclipse.* These eclipses,\\nmoreover, are not seen by us, as is the case with those of the\\nmoon, from the center of their motion, but from a remote\\nstation, and one whose situation, with respect to the line of the\\nshadow, is variable. This of course makes no difference in the\\ntimes of the eclipses, but a very great difference in their visi-\\nbility, and in their apparent situations with respect to the\\nplanet at the moment of their entering or quitting the shadow.\\n335. The eclipses of Jupiter s satellites present some curious\\nphenomena, which will be best understood from a diagram.\\nLet A, B, C (Fig. 65) represent the earth in different parts of\\nits orbit, revolving from A, through D, to C and B. If a line,\\njoining S and A, be produced to meet the concave sphere of\\nof the heavens xy, it marks the place of opposition, while the\\nearth is at A. Hence, Jupiter, in the figure, is represented\\neast of the opposition. When the earth arrives at D, Jupiter\\nis in opposition; and when at C, he is west of opposition.\\nRemembering now, that the satellites revolve .in the same\\ndirection as the earth, it is obvious that when Jupiter is east of\\nopposition, the immersions are seen, but the emersions generally\\ntake place behind the planet and are not seen so that the\\neclipse, in this position of the bodies, always precedes the\\nHerschel s Ast., p. 285.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0224.jp2"}, "225": {"fulltext": "JUPITER. 201\\noccultation. But if the earth passes beyond D, to C, then\\nJupiter is west of opposition for the place of opposition would\\nbe in SC produced. And now, each satellite passes behind the\\nplanet, and thus suffers occultation before it reaches the\\nFig. 65.\\nshadow, and is eclipsed; and, in entering the shadow, the\\nsatellites are generally behind the planet, while in leaving it,\\nthey are in sight so that occupations precede eclipses. The\\nfourth satellite often enters and leaves the shadow on the same\\nside of the planet, and sometimes the third, and possibly the\\nsecond, but this is never true of the first.\\n336. When one of the satellites is passing between Jupiter\\nand the sun, it casts its shadow upon its primary, as the moon\\ndoes on the earth in a solar eclipse, which is seen, by the tele-\\nscope, traveling across the disk of Jupiter, as the shadow of the\\nmoon would be seen to traverse the earth by a spectator favor-\\nably situated in space. When Jupiter is east of opposition,\\nthe earth being at A (Fig. 65), the shadow strikes the disk of\\nthe planet, before the satellite itself is seen upon it, because\\nthe satellite will evidently come between S and Jupiter\\nsooner than it does between A and Jupiter. Just the re-\\nverse of this takes place, when the earth is at C, that is,\\nwhen Jupiter is west of opposition. A satellite will then come\\nbetween C and the planet, sooner than between S and the\\nplanet. We do not usually see the satellite itself projected on", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0225.jp2"}, "226": {"fulltext": "202 THE PLANETS.\\nthe disk of the primary, for, being illuminated like the prima-\\nry, it is not readily distinguishable from it but sometimes,\\nwhen it happens to be projected on one of the belts, it is seen\\nas a brig/it spot, making its transit across the disk. Occasion-\\nally, also, it is seen as a dark spot of smaller dimensions than\\nthe shadow. This curious fact has led to the conclusion that\\ncertain of the satellites have sometimes on their own bodies, or\\nin their atmospheres, obscure spots of great extent.*\\n337. A very singular relation subsists between the mean\\nmotions of the three first satellites of Jupiter. The mean longi-\\ntude of the first, plus twice that of the third, minus three times\\nthat of the second, always equals 180 degrees. A curious\\nconsequence of this relation is, that the three satellites can\\nnever be all eclipsed at the same time; for then, having sev-\\nerally the same longitude as the primary, their longitudes\\nwould be equal, and that of the first, plus twice that of the\\nthird, minus three times that of the second, would be nothing,\\nand of course could not be 180 degrees. f The longitudes here\\nmentioned are such as would be observed by a spectator on\\nJupiter, and not a spectator on the earth.\\n338. The discovery of the system of Jupiter and his satel-\\nlites, soon after the invention of the telescope, lent a powerful\\nsupport to the Copernican system of astronomy, then just be-\\nginning to be received by astronomers, since it presented to\\nthe eye an exact miniature of the solar system, and exhibited\\nan actual model of that arrangement of the sun and planets\\nwhich had before only been contemplated by the eye of the\\nmind and the laws of the planetary system, discovered by\\nKepler, were here actually seen to be verified, in the motions\\nof this miniature system. Moreover, the eclipses of Jupiter s\\nsatellites, furnished one of those instantaneous events, occur-\\nring at the same moment of absolute time wherever seen,\\nwhich are available for finding the longitudes of different\\nplaces; and at that period it was deemed a more eligible\\nmethod of determining this great practical problem of astrono-\\nmy than any method then in use.\\nSir J. Herschel. t Biot.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0226.jp2"}, "227": {"fulltext": "JUPITER. 203\\n339. The eclipses of these satellites seem to have various\\nrequisites for determining longitudes, being, as already re-\\nmarked, seen at the same moment at all places where the\\nplanet is visible, being wholly independent of parallax, and\\nbeing predicted beforehand with great accuracy the instant\\nthey occur at Greenwich, and given in the Nautical Almanac\\nbut several circumstances conspire to render this method of\\nfinding the longitude less eligible than several other methods\\nat present in use. The extinction of light in the satellite at its\\nimmersion, and the recovery of its light at its emersion, are\\nnot instantaneous, but gradual for the satellite, like the moon,\\noccupies some time in entering into the shadow or in emerging\\nfrom it, which occasions a progressive diminution or increase\\nof light. The better the light afforded by the telescope with\\nwhich the observation is made, the later the satellite will be\\nseen at its immersion, and the sooner at its emersion.* In\\nnoting the eclipses even of the first satellite, the time must be\\nconsidered as uncertain to the amount of 20 or 30 seconds;\\nand those of the other satellites involve still greater uncer-\\ntainty. Two observers, in the same room, observing with\\ndifferent telescopes the same eclipse, will frequently disagree\\nin noting its time to the amount of 15 or 20 seconds, and the\\ndifference will always be the same way.f 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 eli-\\ngible in many cases where extreme accuracy is not required.\\nAs a telescope is essential for observing an eclipse of one of\\nthese satellites, this method can not be practiced at sea.\\n340. The grand discovery of the progressive motion of light\\nwas first made by observations on the eclipses of Jupiter s sat-\\nellites. Tn 1675, Roemer, a Danish astronomer, noticed that\\non comparing the average intervals and the true intervals be-\\ntween the eclipses of a certain satellite, the true intervals are\\nalways shorter when the earth is approaching the planet, so\\nthat at the nearest point, the eclipse occurs 16m. 2 6 s 6 too\\nThis is the reason why observers are directed, in the Nautical Almanac, to\\nuse telescopes of a certain power j Woodhouse, p. 840.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0227.jp2"}, "228": {"fulltext": "204 THE PLANETS.\\nsoon. And, as the earth departs from Jupiter, Roemer per-\\nceived that the eclipses occur later than they should do accord-\\ning to the average interval, and that they are 16m. 26\\\\6 too\\nlate, when at the greatest distance. He attributed this effect\\nto the progressive motion of light. Dividing 190,000,000\\nmiles, the diameter of the earth s orbit, by 16m. 26 s .6, the\\ntime of crossing, he found 192,600 miles per second to be the\\nvelocity of light. This seemed, at first, quite incredible, and\\nwas received with distrust. But its correctness was soon es-\\ntablished, by the discovery of the aberration of the stars,\\nwhich gives the same result.\\n341. Saturn comes next in the series as we recede from\\nthe sun, and has, like Jupiter, a system within itself, on a\\nscale of great magnificence. In size it is, next to Jupiter, the\\nlargest of the planets, being 79,000 miles in diameter, or nearly\\n10 times as large as the earth in diameter, and about 1000\\ntimes as large in volume. It has likewise belts on its surface,\\nand is attended by eight satellites. But a still more wonderful\\nappendage is its Ring, a broad wheel encompassing the planet\\nat a great distance from it. We have already intimated that\\nSaturn s system is on a grand scale. As, however, Saturn is\\ndistant from us nearly 900,000,000 miles, we are unable to ob-\\ntain the same clear and striking views of his phenomena that\\nwe do of the phenomena of Jupiter, although they really pre-\\nsent a more wonderful mechanism. The disk of Saturn was\\ndescribed by Sir William Ilerschel as having the form of a\\nrectangle with rounded corners but refined measurements,\\nmore recently made, show that it is an ellipse, and the planet,\\ntherefore, an ellipsoid. Its equatorial exceeds its polar diam-\\neter by about one-tenth.*\\nThe belts of Saturn, although clearly discerned by a good\\ntelescope, are far more indistinct than those of Jupiter. Spots,\\nwhich occasionally appear on the belts, have enabled astrono-\\nmers to determine the time of the diurnal rotation of Saturn,\\nwhich is found to be about ten hours and a half (lOh. 29m.).\\n342. When viewed with a good telescope, the body of the\\nHind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0228.jp2"}, "229": {"fulltext": "SATURN. 205\\nplanet is seen to be surrounded by a broad thin ring, placed\\nobliquely to our line of vision, so that it appears elliptical,\\nshowing one part in front of the planet and having a part hid\\nbehind it. At the ends of the ellipse, and sometimes entirely\\naround it, is seen a division of the ring into two parts, of which\\nthe inner is the broadest. Though this division, on account of\\nits immense distance, appears as a delicate line, yet it is, in\\nreality, an interval of 1800 miles. The dimensions of the\\nwhole system, in round numbers, are as follows\\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 (Frontispiece) represents Saturn, as it appears to\\na powerful telescope, surrounded by its rings, and having its\\nbody striped with dark belts, somewhat similar, but broader\\nand less strongly marked than those of Jupiter, and owing,\\ndoubtless, to a similar cause, f The ring is opaque, since it\\ncasts a deep shadow on the planet. The earth is generally so\\nsituated that we can see some part, both of the shadow cast by\\nthe ring on the planet, and by the planet on the ring.\\nThe rings of Saturn have been long and carefully observed\\nby Prof. G*. P. Bond, with the celebrated Cambridge refractor.\\nHe finds that there is a third ring within the others, which re-\\nflects a dim light, and is about half as wide as the inner bright\\nring, but not separated from it by a noticeable interval. He\\nalso finds the two bright rings to be divided at times into sev-\\neral rings, with very narrow intervals. In one instance the\\nouter ring was divided into two, in another, into four parts\\nand the inner one, in some cases, into six or eight delicate\\nrings. The dark separating lines are usually traceable only at\\nthe ends of the ellipse. The investigations of Professor Peirce,\\naided by Bond s observations, have nearly, if not fully, estab-\\nlished the fact of the fluidity of the rings, or at least, of the\\nProfessor Struve, Mem. Art. Soc, iii., p. 301. f Sir J. Herscbel.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0229.jp2"}, "230": {"fulltext": "206 THE PLANETS.\\nincohereftcy of their parts, if they consist of solid matter. A\\nchangeableness of form and condition is indicated, also, when\\nthe ring presents to us its edge view. It sometimes appears\\nas a delicate, uniform line at others, as a line of unequal\\nthickness, whose thinner parts occasionally become entirely\\ninvisible and the inequalities change their aspects, from time\\nto time, in a manner not to be accounted for by the revolution\\nwhich the system is known to have.\\nA most remarkable fact relating to the rings, is their exceed-\\ning thinness. They have generally been regarded as about 100\\nmiles thick. But Bond s observations lead to the conclusion\\nthat their thickness is less than 40 miles. If a model of the\\nrings, one foot in diameter, were cut out of common writing-\\npaper, the thickness would be too great to represent them\\nproperly.\\n343. 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\\na piece of coin, it will appear as a complete circle when it is\\nat right angles to the axis of vision but when oblique to that\\naxis, it will be projected into an ellipse more and more narrow,\\nas its obliquity is increased, until, when its plane coincides\\nwith the axis of vision, it is projected into a straight line. Let\\nus place on the table a lamp or a ball, to represent the sun,\\nand, holding the ring at a certain distance, inclined a little\\ntoward the central body, let us carry it round, always keeping\\nit parallel to itself. During its revolution it will twice present\\nits edge to the lamp or ball at opposite points, and twice, at\\n90\u00c2\u00b0 distance from those points, it will present its broadest face\\ntoward the central body. At intermediate points it will ex-\\nhibit an ellipse more or less open, according as it is nearer one\\nor the other of the preceding positions. It will be seen, also,\\nthat in one-half of the revolution the lamp shines on one side\\nof the ring, and in the other half of the revolution on the other\\nside. Such would be the successive appearances of Saturn s\\nring to a spectator on the sun and since the earth is, in re-\\nspect to so distant a body as Saturn, very near the sun, those\\nappearances are presented to us nearly in the same manner as\\nthough we viewed them from the sun. Accordingly, we some-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0230.jp2"}, "231": {"fulltext": "SATURN.\\n207\\ntimes see Saturn s ring under the form of a broad ellipse,\\nwhich grows continually more and more narrow until it passes\\ninto a line, and we either lose sight of it altogether, or, with\\nthe aid of the most powerful telescopes, we see it as a fine line\\ndrawn across the disk, and projecting out from it on each side.\\nAs the whole revolution occupies nearly 30 years, and the plane\\nof the ring passes across the earth s orbit twice in the revolu-\\ntion, the phenomena attending the edge view occur every 15\\nyears, when the ring may within a single year disappear re-\\npeatedly, and for different reasons, as described in Art. 346.\\n344. The learner may perhaps gain a clearer idea of the\\nforegoing appearances from the following diagram.\\nLet A, B, C, c, Fig. 66, represent successive positions of\\nSaturn and his ring in different parts of his orbit, while db\\nFig. 66.\\nrepresents the orbit of the earth.* Were the ring when at C\\nand G perpendicular to the line joining CG, it would be seen\\nby a spectator situated at a or h as a perfect circle, but being\\ninclined to the line of vision 28\u00c2\u00b0 ll 7 it is projected into an\\nellipse. This ellipse gradually contracts to a straight line, as\\nthe ring passes to A and E, where its nodes are in the direc-\\ntion of the earth s orbit. From E to G the ellipse widens\\nagain, till at G the breadth is nearly half as great as its length.\\nThrough the quadrant from G to A it contracts, and from A\\nto C it expands, occupying about 7\u00c2\u00a3 years in going from the\\nIt may be remarked by tbe learner, that these orbits are made so elliptical,\\nnot to represent the eccentricity of either the earth s or Saturn s orbit, but merely\\nas the projection of circles seen very obliquely.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0231.jp2"}, "232": {"fulltext": "208\\nTHE PLANETS.\\nmaximum breadth to the minimum, and the reverse. These\\nchanges are visible in a telescope of moderate powers, except\\nthat the ring is too thin to be seen at A and E.\\n345. There are three ways in which the ring may fail to be\\nvisible during the period when the line of its nodes is crossing\\nthe earth s orbit. 1st. It may present its edge exactly to the\\nearth, when in common telescopes, it subtends too small an\\nangle to be seen. 2d. It may present its edge exactly to the\\nsun, so that neither side of the ring is enlightened. 3d. Its\\nplane may be directed between the earth and sun, when the\\ndark side is toward us. The two first causes may be consid-\\nered as only momentary for the plane of the ring passes the\\nbreadth of the sun in less than two days, and of the earth in\\nabout 20 minutes. But the third cause may continue to ren-\\nder the ring invisible for several months.\\nIn Fig. 67 let S be the sun, C the place of Saturn, when the\\nFig. 67.\\nnodes of its ring are in the line CS, passing through the sun.\\nLet EFGH be the earth s orbit; then EB, GD, parallel to SO,\\nwill include BD, the arc of Saturn s orbit in which the ring\\nwill present its edge to the earth s orbit. If the orbits are\\nsupposed to be in the plane of the paper, we must conceive the\\nsmall ellipses at B, C, D, representing the ring, to be inclined\\nabout 28\u00c2\u00b0, having their section with the orbit, in BE, CS, and\\nDG, respectively. While Saturn passes over the arc BD, the\\nplane of its ring will pass once through the sun, and may re-\\npeatedly pass through the earth, on account of the revolution\\nof the latter. The time of describing BD differs only about\\nsix days from a year for, since Saturn is 9.54 times as far", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0232.jp2"}, "233": {"fulltext": "SATURN. 209\\nfrom the sun as the earth is, therefore, 9.54 1 SB SE\\nrad sin SBE which is thus found to be 6\u00c2\u00b0 1 Hence, BSO\\n6\u00c2\u00b0 1 and BSD=12\u00c2\u00b0 2 But Saturn describes 12\u00c2\u00b0 2 in 359\u00c2\u00a3\\ndays, near six days less than a year. The earth therefore very\\nnearly describes the orbit EFGH, while Saturn describes the\\narc BCD.\\n346. The disappearances of the ring may be variously\\nmodified during the year of passing the node, according to the\\nplace of the earth when the nodal line first reaches its orbit.\\nA few cases are here described. If the earth is at G, when the\\nplane of the ring passes E, then, while the nodal line moves\\nfrom BE to CS, the earth will go from G through H to E, and\\nmust cross that line below H. The ring will begin its disap-\\npearance at that moment but the disappearance will continue,\\nas the earth proceeds to E, because the dark side is toward it.\\nThis disappearance will last about two months, and close when\\nthe plane of the ring at C passes the sun for after that, the\\nilluminated side will be toward the earth. While the earth\\nproceeds from E through F to G, the plane of the ring will\\nmove from CS to DG, before the earth can overtake it.\\nAgain, if the earth had advanced some distance on the\\nquadrant GH, when the ring s line of nodes was at E, then\\nthey will meet further from H than before, say at M after\\nwhich the dark side will be toward the earth. The plane of\\nthe ring will pass the sun, when the earth is on the quadrant\\nEF, after which the bright side is presented to the earth. But\\nthe earth will overtake the nodal line before reaching G, and\\ntherefore look again upon the dark side, until it recrosses the\\nline on the quadrant GH. Thus there are two periods of dis-\\nappearance. These two may possibly unite in one, of 8\\nmonths continuance this will happen when the earth and\\nnode-line pass F at the same time for then the plane of the\\nring is between the earth and sun both before and after pass-\\ning through the sun.\\nIt is a possible thing, that no disappearance at all should\\nhappen during the nodal year. Suppose the earth at F, when\\nthe line of nodes arrives at E. Then, while the line moves\\nfrom BE to CS, the earth will describe FGH, all the time on\\nthe luminous side of the ring the earth and sun will both bn\\n14", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0233.jp2"}, "234": {"fulltext": "210 THE PLANETS.\\nin the line CS at once, the planet being in conjunction with\\nthe snn; and, after the earth has passed H toward F, the\\nbright side of the ring is again in view. Thus, there is only a\\nmomentary disappearance, and that when the planet itself is\\nlost in the blaze of the sun s light.\\nBut in general there are two periods of disappearance within\\nthe nodal year, arising from the third cause (Art. 345), each\\nbeginning and ending with a disappearance from the first or\\nsecond cause.\\n347. The rings of Saturn must present a magnificent spec-\\ntacle to that hemisphere of the planet to which their illuminated\\nside is turned, appearing as bright arches several degrees in\\nwidth, and spanning the sky from one side of the horizon to\\nthe other. They revolve diurnally in the same plane as the\\nplanet itself, and in about the same time, 10^ hours.\\n348. Saturn is attended by eight satellites. Their sizes\\nvary from 500 to 2,850 miles but, on account of their great\\ndistance, they are seen only with the best instruments. They\\nare all external to the rings, and the eighth at the distance of\\n2,500,000 miles from the planet.f The seventh was discovered\\nin Cambridge, Mass., by Professor Bond. Their orbits are\\nnearly in the plane of the ring, and make an angle of about\\n28\u00c2\u00b0 with the orbit of the planet. Only the two interior ones\\nare eclipsed, except when the ring is seen edgewise.;):\\n349. Uranus, the next planet in the series, was discovered\\nby Sir William Herschel, in 1781. Previous to this time,\\nSaturn had, from a high antiquity, been considered li the\\noutermost boundary of the solar system but this discovery\\ndoubled the dimensions of the system, bringing to light a large\\nplanet at about twice the distance of Saturn from the sun, and\\nabout 19 times the distance of the earth, or 1800 millions of\\nmiles. It was named by the discoverer the Georgian^ in honor\\nof his patron, George III. but this name being unacceptable\\nHind.\\nf They have received the names, Mimas, Enceladus, Tethys, Dione, Rhea,\\nTitan, Hyperion, and Japetus.\\nX Sir J, HerscheL", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0234.jp2"}, "235": {"fulltext": "URANUS NEPTUNE. 211\\nto astronomers of other countries, the planet was called Herschel\\nin America, after the name of the discoverer, and Uranus* on\\nthe continent of Europe, which last appellation is now uni-\\nversally adopted. The diameter of Uranus is about 35,000\\nmiles, and consequently its volume more than 80 times that of\\nthe earth. Its revolution around the sun occupies nearly 84\\nyears, so that its position among the stars varies but little for\\nseveral years in succession, since it shifts its place only a little\\nmore than four degrees in a year, and of course would remain\\nin the same sign of the Zodiac seven years. Its path lies very\\nnear the ecliptic, being inclined to it less than 0\u00c2\u00b0 47 The sun\\nhimself, when seen from Uranus, dwindles almost to a star,\\nsubtending, as it does, an angle of only V 40 so that the\\nsurface of the sun would appear there nearly 400 times less\\nthan it does to us.\\n350. The satellites of Uranus are exceedingly minute ob-\\njects, and visible only to the most powerful telescopes. Al-\\nthough Sir William Herschel assigned six satellites to this\\nplanet, yet only two of the number (the second and fourth in\\nthe order of distances) have, until quite recently, been seen by\\nother astronomers. Two others have of late been added, and\\nan increasing confidence is beginning to be felt that the entire\\nnumber announced by Herschel will be identified. The orbits\\nof these satellites, says Sir John Herschel, offer remarkable,\\nand indeed quite unexpected and unexampled peculiarities.\\nContrary to the unbroken analogy of the whole planetary\\nsystem, whether of primaries or secondaries, the planes of their\\norbits are nearly perpendicular to the ecliptic, being inclined\\nno less than 78\u00c2\u00b0 58 to that plane, and in these orbits their\\nmotions are retrograde. Instead of advancing from west to\\neast, as is the case with every other planet and satellite, they\\nmove in the opposite direction, or from east to west. With\\nthis exception, all the motions of the planets, whether around\\ntheir own axes or around the sun, and that of the sun himself\\non his axis, are from west to east.\\n351. Neptune is (so far as is known) the last planet of the\\nFrom ovpavot, the father of Saturn.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0235.jp2"}, "236": {"fulltext": "212 THE PLAKETS.\\nseries, being removed from the sun to the immense distance of\\nnearly 3000 millions of miles (2,862,457,000). Its diameter is a\\nlittle less than that of Uranus, being 31,000 miles,* Its volume\\nis nearly sixty times that of the earth. Its periodic time is\\n164-! years, which is about twice that of Uranus. Its orbit is\\nnearly circular, 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\\nas the most extraordinary discovery ever made in physical\\nscience. The leading steps of the process were as follows.\\nThe planet Uranus had long been known to be subject to cer-\\ntain irregularities in its revolution around the sun, not accounted\\nfor by all the known causes of perturbation. In some cases\\nthe deviation from the true place, as given by the tables, dif-\\nfers from actual observation two minutes of a degree a quan-\\ntity indeed which seems small, but which is still far greater\\nthan occurs in the case of the other planets, and far too great\\nto satisfy the extreme accuracy required by modern astronomy.\\nThis fact long since suggested to astronomers the possibility of\\none or more additional planets, hitherto undiscovered, which,\\nby their attractions, exert on Uranus a great disturbing influ-\\nence. Le Yerrier, a distinguished French astronomer, assum-\\ning the existence of such a planet, applied himself, by the aid\\nof the calculus, guided by the law of universal gravitation, to\\nthe inquiry where the hidden planet was situated at what\\ndistance from the sun and at what point of the starry heav-\\nens From Bode s law of the planetary distances (Art. 299),\\naccording to which Saturn is nearly twice as far from the sun\\nas Jupiter, and Uranus twice as far as Saturn, he inferred that,\\nif a planet exists beyond Uranus, its distance is probably about\\ntwice that of Uranus, or about 3,600 millions of miles from the-\\nsun, which is nearly thirty-eight times that of the earth. He\\nassumed it, however, to be thirty-six times the earth s mean\\ndistance. The corresponding periodic time would be 216 years.\\nAfter reasoning from analogy, and the doctrine of universal\\ngravitation, respecting the position and mass which a body\\nmust have in order to account for the perturbations of Uranus,\\nequations were formed between these perturbations and the\\nHind.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0236.jp2"}, "237": {"fulltext": "NEPTUNE. 213\\nassumed and unassumed elements of trie body in question.\\nThese equations were exceedingly complex and difficult of re-\\nduction but, by the most ingenious artifices, the several un-\\nknown quantities were successively eliminated, either directly\\nor by repeated approximations, until the great geometer ar-\\nrived at expressions for the elements of the unknown planet,\\nwhich indicated its place among the stars, its quantity of mat-\\nter, the shape of its orbit, and the period of its revolution.\\nHaving placed the body in various positions in the orbit thus\\ndetermined, he found that when situated at a point in the con-\\nstellation Oapricornus, its effect upon Uranus would be such\\nas corresponded to the irregularities to be accounted for that\\non the 1st of January, 1847, the hidden planet would have a\\nlongitude of 326\u00c2\u00b0 32 and would lie about five degrees east-\\nward of the well-known star Delta Capricomi. He further\\nasserted that it would have an apparent diameter of about 3\\nand therefore be visible to large telescopes.\\n352. Having communicated these results to tbe French\\nAcademy, at their sitting on the 31st of August, 1846, Le\\nYerrier soon afterward made them known to Dr. Galle, one of\\nthe astronomers of the Hoyal Observatory of Berlin, with the\\nrequest that he would search for the stranger with the power-\\nful telescope at his command. On the same evening that Dr.\\nGalle received the communication, namely, on the 23d of Sep-\\ntember, he directed his telescope toward the spot assigned for\\nthe planef, and there it was, within less than a degree of the\\nplace indicated by Le Terrier, and having an apparent mag-\\nnitude within half a second of that assigned. To show the\\nnear correspondence between theory and observation, we may\\nremark that the predicted longitude, for the 23d of September,\\nat midnight, was 324\u00c2\u00b0 58 and the observed longitude was\\n325\u00c2\u00b0 5_2 .8 the predicted diurnal motion in longitude was 69\\nand the observed 74 These results struck the scientific world\\nwith astonishment, and their confirmation w r as one of the\\ngreatest achievements of the human mind.\\n353. It has often happened, in the history of great discov-\\neries, that the same hidden truth is revealed simultaneously to\\ndifferent inquirers, and accordingly, by a singular coincidence.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0237.jp2"}, "238": {"fulltext": "214 THE PLANETS.\\na young mathematician of the University of Cambridge (Eng.),\\nMr. Adams, had, without the least knowledge of what JVL Le\\nYerrier was doing, arrived at the same great result. But\\nhaving failed to publish his paper until the world was made\\nacquainted with the facts through the other medium, he has\\nlost much of the honor which the priority of discovery would\\nhave gained for him. Thus two distinguished mathematicians,\\nunknown to each other, and by entirely independent processes,\\nhad arrived at the same results, as regarded both the existence\\nof the supposed planet, and the region of the starry heavens\\nwhere at that moment it lay concealed; and, to crown all,\\nastronomers, in obedience to the direction of one of them, had\\npointed their telescopes to the spot and found it there. The\\nconviction on the mind of every one was, that nothing but\\nabsolute truth could abide a test so unequivocal. It still\\nremained, however, to determine by observation whether the\\nbody actually conformed, in all respects, to the results of\\ntheory. To settle this point completely, that is, to determine\\nwith precision the elements of the orbit from observation,\\nwould require a long time in a planetary body whose motion\\nwas 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\\na fixed star, then, by comparing that place with its present\\nposition, and noting the interval of time between the two\\nobservations, we might thus learn the rate of its motion, and\\nits periodic time, and might thence deduce various other par-\\nticulars dependent on these elements. Our distinguished coun-\\ntryman, Mr. Sears C. Walker, then connected with the observ-\\natory at Washington, undertook this investigation. First,\\nfrom the observations already accumulated, he calculated the\\npath which the planet must have pursued for the last fifty or\\nsixty years, and by tracing this path among the stars of La-\\nlande s catalogue, he found that it passed within two minutes\\nof a star of the seventh magnitude, which was recorded as\\nbeing seen in May, 1795. Professor Hubbard, of the same\\nobservatory, on reconnoitering for this star, found that it was\\nmissing. Little doubt remained that the star seen by Lalande\\nwas the planet of Le Yerrier; and this conclusion was con", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0238.jp2"}, "239": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 215\\nfirmed by calculating its orbit on this supposition, and com-\\nparing the results with the places it has actually occupied since\\nit fell within the sphere of observation. The results thus\\nobtained, however, were materially different from those of Le\\nTerrier and Adams. Instead of a period of 216 years, they\\ngive only a period of 164^ years and instead of a distance of\\n3,600 millions of miles, the new period would require a distance\\nof only 2,862 millions. The eccentricity of the orbit, moreover,\\naccording to Walker, is much less than had been assigned to\\nit, the orbit being in fact very nearly circular, while, by Le\\nTerrier s estimate, it was considerably elliptical. The longi-\\ntude, in fact, proved to be nearly the same as that assigned to\\nit. But this close agreement is to be considered accidental\\nfor Le Terrier himself fixed on the precise place which he\\nnamed, as only the most probable. On account of uncertainty\\nin the data, he stated that there might be a variation of 9\u00c2\u00b0\\neither way.* The elements thus corrected account fully and\\ncompletely for the irregularities of Uranus sought to be ex-\\nplained, within a single second, as determined by Professor\\nPeirce.f\\nMOTIONS OF THE PLANETARY SYSTEM.\\n354. We have waited until the learner maybe supposed\\nto be familiar with the heavenly bodies individually, before\\ninviting his attention to a systematic view of the planets in\\ntheir revolutions around the sun, and their grand laws.\\nThere are two methods of arriving at a knowledge of the\\nmotions of the. heavenly bodies. One is, to begin with the\\napparent, and from these to deduce the real motions; the\\nother is to begin with considering things as they really are in\\nnature, and then to inquire why they appear as they do. The\\nlatter of these methods is by far the more eligible. It is much\\neasier than the other and proceeding from the less difficult to\\nthat which is more so from motions which are very simple to\\nsuch as are complicated, it finally puts the learner in possession\\nof the whole machinery of the heavens. We shall in the first\\nplace, therefore, endeavor to introduce the student to an ac-\\nLoomis s Recent Prog, of Astron., pp. 50-52.\\nf Amer. Journal of Science, New Series, vol. v., p. 436.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0239.jp2"}, "240": {"fulltext": "216 THE PLANETS.\\nquaintance with the simplest motions of the planetary system,\\nand afterward to conduct him gradually through such as are\\nmore complicated and difficult.\\n355. When viewed from the center of their motions, the\\nrevolutions of the planets would appear simple and harmonious,\\nall coursing round the spectator from west to east in regular\\norder, in nearly the same great highway, though with very\\ndifferent degrees of velocity. Let us, then, suppose ourselves\\nstanding on the sun, and contemplate the revolutions of the\\nplanets, first, severally, and then as forming one grand whole,\\nconsisting of numerous parts, but bound together under the\\nsame laws in one vast empire. We should see Mercury making\\nvery perceptible progress around the heavens, like the moon in\\nits motions about the earth, his rate of motion eastward being\\nabout one-third as rapid as that of the moon, since he com-\\npletes his entire revolution in about three months. It will, at\\nfirst, aid our conceptions of the respective positions of the\\nplanetary orbits, to imagine the ecliptic to be marked out on\\nthe face of the visible heavens in a palpable line distinctly vis-\\nible to the eye. If we, stationed at the sun, watch the motions\\nof Mercury, we shall see it cross the ecliptic in two opposite\\npoints of the heavens, constituting its nodes; and we shall see\\nit, when half way between the nodes, at an angular distance\\nfrom the ecliptic of about 7\u00c2\u00b0, this being the inclination of its\\norbit. Knowing the position of the orbit of Mercury with\\nrespect to the ecliptic, we may now, in imagination, represent\\nthat orbit in a great circle passing through the center of the\\nplanet and the center of the sun, and cutting the plane of\\nthe ecliptic in two opposite points in an angle of 7 de-\\ngrees. The paths of both planets appear as circles among\\nthe stars; and if we suppose them to be visibly traced on\\ntheir respective planes, the observer, while at the sun, can\\nnot distinguish them from circles, of which he is the cen-\\nter. But, if we imagine him transported to a great distance\\nfrom the sun, in a line at right angles to the ecliptic, he will\\ndiscern the true forms of the orbits. The earth s orbit can not\\neven now be distinguished from a circle, but the sun is plainly\\na little out of its center. The orbit of Mercury, however, is\\ndistinctly elliptical, with the sun in one of its foci. On his", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0240.jp2"}, "241": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 217\\nreturn to liis station at the sun, he loses all perception of this\\nelliptical form, and of his eccentric position. But he perceives\\nthe consequences of these facts, an alternate increase and de-\\ncrease of size and of velocity in the planets. The earth slowly\\nbecomes larger, and moves more swiftly, till it reaches a cer-\\ntain position, and then diminishes both in size and velocity,\\nand attains a minimum at a point 180\u00c2\u00b0 from the maximum.\\nMercury passes through still greater changes of the same kind.\\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\\nto which they recede from the ecliptic, or their inclinations.\\nWe have supposed the observer to select the plane of the earth s\\norbit as his standard of reference, and to see how each of the\\nother orbits is related to it but such a selection of the ecliptic\\nis entirely arbitrary the spectator on the sun, who views the\\nmotions of the planets as they actually exist in nature, would\\nmake no distinction between the different orbits, but merely\\ninquire how they are mutually related to each other. Taking,\\nhowever, the ecliptic as the plane to which all the others are\\nreferred, we do not, as in the case of the other planets, inquire\\nhow its plane is inclined, nor what are its nodes, since it has\\nneither inclination nor node.\\n357. Such, in general, are the real motions of the planets,\\nand such the appearances which the planetary system would\\nexhibit to a spectator at the center of motion. But, in order\\nto represent correctly the positions of the planetary orbits, at\\nany given time, three things must be regarded the Inclination\\nof the orbit to the ecliptic the position of the line of the\\nNodes, and the position of the line of the Apsides. In our\\ncommon diagrams, the orbits are incorrectly represented, be-\\ning all in the same plane, as in the following diagram, where\\nAEB (Fig. 68) represents the orbit of Mercury as lying in the\\nsame plane with the ecliptic. To exhibit its position justly,", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0241.jp2"}, "242": {"fulltext": "218\\nTHE PLANETS.\\nAB being taken as the line of the nodes, the plane should be\\nelevated on one side about 7\u00c2\u00b0, and depressed the same number\\nof degrees on the other side, turning on the line AB as on a\\nhinge. But even then the representation may be incorrect in\\nother respects, for we have taken it for granted that the line\\nof the nodes coincides with the line of the apsides, or that the\\norbit of Mercury cuts the ecliptic in the line AB, the major\\naxis of the orbit, whereas it may lie in any given position with\\nrespect to the line of apsides, according to the longitude of the\\nnodes. If, for example, the line of nodes had chanced to pass\\nFig. 68.\\nthrough Taurus and Scorpio instead of Cancer and Capricorn,\\nthen it would have been represented by the line b fll instead of\\nthe line passing through S and the plane, when elevated or\\ndepressed with respect to the plane of the ecliptic, would be\\nturned on this line in our figure. Moreover, our diagram rep-\\nresents the line of apsides as passing through Cancer and Cap-\\nricorn, 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\\nthe planetary system, as seen from the sun, and of the posi-\\ntions of the orbits with respect to the ecliptic, let us next in-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0242.jp2"}, "243": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 219\\nquire into the nature and causes of the apparent motions. The\\napparent motions of the planets are exceedingly unlike the real\\nmotions, a fact which is owing to two causes first, we view\\nthem out of the center of their orbits secondly, we are our-\\nselves in motion. From the first cause, the apparent places of\\nthe planets are greatly changed by perspective and, from the\\nsecond cause, we attribute to the planets changes of place\\nwhich arise from our own motions, of which we are uncon-\\nscious.\\n359. The situation of a heavenly body, as seen from the\\ncenter of the sun, is called its heliocentric place as seen from\\nthe center of the earth, its geocentric place. The geocentric\\nmotions of the planets must, according to what has just been\\nsaid, be far more irregular and complicated than the heliocen-\\ntric, as will be evident from the following diagram, which\\nrepresents the geocentric motions of Mercury for two entire\\nrevolutions, embracing a period of nearly six months. Let S\\n(Fig. 69) represent the sun, 1, 2, 3, c, the orbit of Mercury,\\na, b, c, c, that of the earth, and GT the concave sphere of the\\nheavens. The orbit of Mercury is divided into 12 equal parts,\\neach of which he describes in 7J days and a portion of the\\nearth s orbit described by that body in the time that Mercury\\ndescribes the two complete revolutions, is divided into 21\\nequal parts. Let us now suppose that Mercury is at the point\\n1 in his orbit, when the earth is at the point a Mercury will\\nthen appear* in the heavens at A. In 7 J days Mercury will\\nhave reached 2, while the earth has reached h, when Mercury\\nwill appear at B. By laying a ruler on the point c and 3, d\\nand 4, and so on, in the order of the alphabet, the successive\\napparent places of Mercury in the heavens will be obtained.\\nFrom A to C, the apparent motion is direct, or in the order of\\nthe signs from C to G it is retrograde at G it is stationary a\\nwhile, and then direct through the whole arc GT. At T the\\nplanet is again stationary, and afterward retrograde along the\\narc 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\\na nearly uniform rate, and in the same unvarying direction\\naround the sun. It moves forward when near the superior", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0243.jp2"}, "244": {"fulltext": "220\\nTHE PLANETS.\\nconjunction, backward when near the inferior, and is station-\\nary near the points of greatest elongation. The planet moves\\nsometimes very slowly, and then rapidly at one time back-\\nward over a small space, and then forward for a great distance.\\nYet all these apparent irregularities are owing to the two\\ncauses already adverted to, viz., the effects produced by per-\\nspective, and by the motions of the spectator himself. Yenus\\nexhibits a variety of motions similar to those of Mercury, ex-\\ncept that the changes do not succeed each other so rapidly,\\nsince her period of revolution approaches more nearly to that\\nof the earth.\\n360. The apparent motions of the superior planets are, like", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0244.jp2"}, "245": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM.\\n221\\nthose of Mercury and Yenns, alternately direct and retrograde,\\nand between the two the planets are stationary. In this case,\\nhowever, the earth moves faster than the planet, and the\\nplanet has its opposition, but no inferior conjunction whereas\\nan inferior planet has its inferior conjunction, but no opposi-\\ntion. These differences render the apparent motions of the\\nsuperior planets in some respects unlike those of Mercury and\\nYenus. On the side of the sun most remote from the earth,\\nthe motion of a superior planet is direct, because, as is the case,\\nwith Yenus in her superior conjunction (see figure 61), the\\nonly effect of the earth s motion is to accelerate it but when\\nthe planet is in opposition, the earth is moving past it with\\ngreater velocity, and makes the planet seem to move back-\\nward, like the apparent backward motion of a vessel when we\\novertake it and pass rapidly by it in a steamboat.\\n361. Let ABCD (Fig. 70) represent the earth in different\\npositions in its orbit, M a superior planet as Mars, and NR an\\narc of the concave sphere of the heavens. First, suppose the\\nplanet to remain at rest in M, and let us see what apparent\\nmotions it would receive from the real motions of the earth.\\nWhen the earth is at B, it will see the planet in the heavens", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0245.jp2"}, "246": {"fulltext": "222 THE PLANETS.\\nat N and as the earth moves successively through CDEF, the\\nplanet will appear to move through OPQK B and F are the\\ntwo points of greatest elongation of the earth from the sun, as\\nseen from the planet between these two points, while passing\\nthrough the part of its orbit most remote from the planet (at\\nwhich time the planet is seen in superior conjunction), the\\nearth, by its own motion, gives an apparent motion to the\\nplanet in the order of the signs that is, the apparent motion\\ngiven by the earth s motion, when the planet is seen toward\\nits superior conjunction, is direct. But in passing from F to B\\nthrough A, when the planet is seen toward its opposition, the\\napparent motion given to the planet by the earth s motion is\\nretrograde. But the superior planets are not in fact at rest, as\\nwe have supposed, but are all the while moving eastward,\\nthough with a slower motion than the earth. Indeed, with\\nrespect to the remotest planets, as Saturn and Uranus, the for-\\nward motion is so exceedingly slow, that each remains for a\\nlong time in the same sign of the zodiac. Still, the effect of\\nthe 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.\\ntlHAPTEK XI.\\nDETERMINATION OF THE PLANETARY ORBITS\\nERIES ELEMENTS OF THE ORBIT OF A PLANET QUANTITY OF\\nMATTER IN THE SUN AND PLANETS.\\n362. In Chapter IT. we have shown that the figure of the\\nearth? s orbit is an ellipse, having the sun in one of the foci,\\nand that the earth s radius describes equal spaces in equal\\ntimes and in Chapter III. we have remarked that these are\\nonly particular examples under the law of Universal Gravita-\\ntion, as is also the additional fact, that the squares of the\\nperiodic times of the planets are as the cubes of the major", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0246.jp2"}, "247": {"fulltext": "DETERMINATION OF THE PLANETARY ORBITS. 223\\naxes of their orbits. We may now learn more particularly\\nthe process by which the illustrious Kepler was conducted to\\nthe discovery of these grand laws of the planetary system.\\nFrom the apparent motions of the heavenly bodies, as seen\\nprojected on the face of the sky, the ancient astronomers in-\\nferred that their orbits were necessarily circular, and the mo-\\ntions actually uniform. Still, Hipparchus and Ptolemy were\\nnot ignorant of the fact that the sun moves faster through the\\nwinter 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\\nnot in the center of the circle, but nearer to one side of the\\ncircle than to the other, by which means the sun would appear\\nto move more rapidly in that part of its orbit than in the op-\\nposite part, just as a steamboat appears, to a spectator on the\\nshore, to move faster when nearer than when more remote\\nfrom the shore, although her actual speed is the same in both\\ncases. On a similar supposition Tycho Brahe made a great\\nnumber of very accurate observations on the planetary motions,\\nwhich served Kepler as standards of comparison for results,\\nwhich he deduced from calculations, founded on the applica-\\ntion of geometrical reasoning to various hypotheses which he\\nsuccessively assumed as to the figure of the planetary orbits;\\nfirst supposing the orbit to be of a certain figure, then determ-\\nining from the geometrical properties of the curve what mo-\\ntions the body would appear to us to have when moving in\\nsuch a path, and finally testing his conclusions by comparing\\nthem with the facts, as determined by Tycho, from observa-\\ntion.\\n363. Kepler first applied himself to investigate the figure\\nof the orbit of Mars, the motions of which planet appeared\\nmore irregular than those of any other planet except Mercury,\\nwhich, being seldom seen, had been very little studied. Like\\nPtolemy and Tycho, he first supposed the orbit to be circular,\\nand the planet to move uniformly about a point at a certain\\ndistance from the sun. He made seventy suppositions before\\nhe obtained one that agreed with observation, the calculation\\nof which was extremely long and tedious, occupying him more", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0247.jp2"}, "248": {"fulltext": "224: THE PLANETS.\\nthan five years.* The supposition of an equable motion in a\\ncircle, however varied, could not be made to conform to the\\nobservations of Tycho, whereas the supposition that the orbit\\nwas an oval figure, depressed at the sides, but coinciding with\\na circle at the perihelion, agreed so nearly with observation as\\nto leave no doubt that the orbit of Mars is an ellipse, having\\nthe sun in one of its foci. He immediately inferred that the\\nsame is true of the orbits of all the other planets and a simi-\\nlar comparison of this hypothesis with observation, confirmed\\nits truth. Thus he established the first great law, viz., The\\nplanets revolve about the sun in ellipses, having the sun in one\\nof the foci.\\n364. Kepler also discovered, from observation, that the\\nvelocities of a planet, when in the apsides of its orbit, are in-\\nversely as the distances, and therefore the product of the ve-\\nlocity into the distance would, in those two points, make the\\nsame quantity. But the velocity is the length of arc described\\nin a unit of time and the length of an arc multiplied by its\\nradius, is double the sector upon that arc. Therefore the area\\ndescribed by the radius vector at one apsis equals that de-\\nscribed at the other apsis in the same time. (Fig. 32, p. 86.)\\nAlthough he could not prove, from observation, that the same\\nwas true in every point of the orbit, yet analogy suggested\\nthat such was probably the fact. Therefore, assuming this\\nprinciple as true, and hence deducing the equation of the\\ncenter (Art. 200), he found the result to agree with observa-\\ntion, and thus arrived at the conclusion (which has since been\\nproved true (Art. 181) from the principles of common mechan-\\nics), that the radius vectors of the planetary orbits describe about\\nthe sun equal 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\\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 hvjus laboriosce methodi perteesum fueril, jure\\nmei te misereat, qui earn ad minimum septuagies ivi cum plurima temporis jactura et mirari\\ndesines hunt quintum jam annum abire, ex quo Martem aggressus sum.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0248.jp2"}, "249": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 225\\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 analo-\\ngies in nature. He saw at once that the more distant a planet\\nis from the sun, the slower it moves so that the periodic times\\nof the remoter planets are increased on two accounts first,\\nbecause they have a longer path to traverse and secondly,\\nbecause they actually move more slowly in their orbits than\\nthe planets nearer the sun. Saturn, for example, is 9-J times\\nfurther from the sun than the earth is and since the circum-\\nferences of circles are as their radii, the orbit of Saturn must\\nbe larger than the earth s in the same ratio so that if the\\nperiodic time of Saturn were longer than the earth s, merely\\nbecause its orbit is larger, that period would be 9 J years,\\nwhereas it is 30 years. Hence it is evident that the periodic\\ntimes of the planets increase in a greater ratio than their dis-\\ntances from the sun, but in a less ratio than the squares of the\\ndistances, for then the time of Saturn would be about 90 years.\\nKepler then compared the squares of the times with the cubes\\nof the distances, and found an exact agreement between them.\\nThus he discovered the famous law, the squares of the periodic\\ntimes of all the planets are as the cubes of their mean distances\\nfrom the sun.*\\n366. This law is strictly true only in relation to planets\\nwhose quantity of matter in comparison with that of the cen-\\ntral body is inappreciable. When this is not the case, the\\nperiodic time is. shortened in the ratio of the square root of the\\nsun s mass divided by the sun s plus the planet s mass, as ex-\\npressed by the formula (tjtt ^he mass of the planets\\nis, however, so small compared to the sun s, that this modifica-\\ntion of the law is unnecessary except where extreme accuracy\\nis required.\\nELEMENTS OF THE PLANETARY ORBITS.\\n367. The particulars necessary to be known in order to\\ndetermine the precise situation of a planet at any instant, are\\nVince s Complete System, i., p. 98.\\n15", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0249.jp2"}, "250": {"fulltext": "226 THE PLANETS.\\ncalled the Elements of its Orbit. They are seven in number:\\nof which the first two determine the position of the plane of\\nthe orbit, and the other five relate to the orbit and the planet\\nin that plane. These elements are\\n1. The position of the line of the nodes.\\n2. The inclination to the ecliptic.\\n3. The periodic time.\\n4. The m,ean distance from the sun, or semi-axis major.\\n5. The eccentricity.\\n6. The place of the perihelion.\\n7. The place of the planet in its orbit at a particular epoch.\\n368. It may at first view be supposed that we can proceed\\nto find the elements of the orbit of a planet in the same man-\\nner as we did those of the solar or lunar orbit, namely, by ob-\\nservations on the right ascension and declination of the body,\\nconverted into latitudes and longitudes by means of spherical\\ntrigonometry (see Art. 132). But in the case of the moon,\\nwe are situated in the center of her motions, and the apparent\\ncoincide with the real motions and in respect to the sun, our\\nobservations on his apparent motions give us the earth s real\\nmotions, allowing 180\u00c2\u00b0 difference in longitude. But as we\\nhave already seen, the motions of the planets appear exceed-\\ningly different to us, from what they would if seen from the\\ncenter of their motions. It is necessary, therefore, to deduce\\nfrom observations made on the earth the corresponding results\\nas they would be if viewed from the center of the sun; that is,\\nin the language of astronomers, having the geocentric place of\\na planet, it is required to find its heliocentric place.\\n369. The first steps in this process are the same as in the\\ncase of the sun and moon. That is, for the purpose of finding\\nthe right ascension and declination, the planet is observed on\\nthe meridian with the Transit Instrument and Mural Circle\\n(see Arts. 155 and 230), and from these observations, the\\nplanet s geocentric longitude and latitude are computed by\\nspherical trigonometry. The distance of the planet from the\\nsun is known nearly by Kepler s law. From these data it is\\nrequired to find the heliocentric longitude and latitude.\\nLet S and E (Fig. 71) be the sun and earth, ASOEH the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0250.jp2"}, "251": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 227\\nplane of the ecliptic, SA and EH parallels in that plane, point-\\ning to the vernal equinox (which is considered infinitely dis-\\ntant), P the planet, PO the perpendicular from it to the plane\\nof the ecliptic. Let HEO, the angular distance in the plane\\nFig. 71.\\nof the ecliptic (from H to O on the right side of the lines), be\\nthe geocentric longitude of the planet then ASO will be its\\nheliocentric longitude. Also PEO, the angular distance of the\\nplanet from the ecliptic in a plane perpendicular to it, is the\\ngeocentric latitude, and PSO is the heliocentric latitude. The\\nplanet s angular distance from the sun, PES, is also known\\nfrom observation. Hence, in the triangle SEP, we know SP\\nand SE and the angle SEP, from which we can find PE and\\nknowing PE and the angle PEO, in the right-angled triangle,\\nwe calculate EO. Next, in the triangle OES, EO and ES are\\nknown also OES, found by subtracting the planet s longitude\\nfrom the sun s, i. e., HEO from HES (reckoned to the right\\nfrom H) hence OSE and OS are calculated. If OSE be added\\nto ASE, the supplement of HES, we have ASO, the heliocen-\\ntric longitude of the planet. The line OS just found, is called\\nthe curtate distance of the planet from the sun and this, with\\nthe actual distance SP, gives us, in the right-angled triangle\\nSPO, the heliocentric latitude PSO. Thus, by a few processes\\nin plane trigonometry, we can do what is equivalent to making\\na transfer of our position from the earth to the sun.\\n370. Having now learned how observations made at the\\nearth may be converted into corresponding observations made", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0251.jp2"}, "252": {"fulltext": "228 THE PLANETS.\\nat the sun, we may proceed to explain the mode of finding the\\nseveral elements before enumerated although our limits will\\nnot permit us to enter further into detail on this subject, than\\nto explain the leading principles on which each of these ele-\\nments is determined.*\\n37 1. First, to determine the position of the Nodes, and the\\nInclination of the Orbit.\\nThese two elements, which deter- Fi s- 72\\nmine the situation of the orbit (Art. J?.\\n867), may be derived from two helio-\\ncentric longitudes and latitudes. Let a. jf\\nANRS be an arc of the ecliptic, A\\nthe vernal equinox, NQ an arc of a planet s orbit, and IT its\\nnode. Let AR, AS, be the two heliocentric longitudes PR,\\nQS, the corresponding heliocentric latitudes, which have been\\ndetermined as by Art. 369.\\nBy Napier s rule,\\nsin NS tan QS x cot PNR,\\nand sin NR tan PR x cot PNR.\\nEliminating cot PNR, we have\\nsmNS_sin_NR\\ntan QS~tanPR\\nsubstituting AS AN for NS, and AR AN for NR, then\\nsin AS x cos AN cos AS x sin AN _\\ntan QS _\\nsin AR x cos AN cos AR x sin AN\\ntan PR\\n(cos AR x tan QS cos AS x tan PR) sin AN\\n(sin AR x tan QS sin AS x tan PR) cos AN.\\nm sin AN a AT\\\\ sm x tan Q^ s n x tan\\ncos AN cos AR x tan QS cos AS x tan PR\\nThus AN, the longitude of the node is found for all the\\nquantities on the second member of the equation are known.\\nAgain, since AN is found, we may deduce from the first\\nMost of these elements admit of being determined in several different ways,\\nan explanation of which may be found in the larger works on Astronomy.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0252.jp2"}, "253": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 229\\nequation above, the value of PNR, which is the inclination of\\nthe orbit.\\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 re-\\nturns to the same node. We may know when a planet is at\\nthe node, because then its latitude is nothing. If, from a series\\nof observations on the right ascension and declination of a\\nplanet, we deduce the latitudes, and find that one of the obser-\\nvations gives the latitude 0, Ave infer that the planet was at\\nthat moment at the node. But if, as commonly happens, no\\nobservation gives exactly 0, then we take two latitudes that\\nare nearest to 0, but on opposite sides of the ecliptic, one south\\nand the other north, and as the sum of the arcs of latitude is\\nto the whole interval, so is one of the arcs to the corresponding\\ntime in which it was described, which time being added to the\\nfirst observation, or subtracted from the second, will give the\\nprecise moment when the planet was at the node.\\nBy repeated observations it is found, that the nodes of the\\nplanets have a very slow retrograde motion.\\n373. If the orbit of a planet cut the ecliptic at right angles,\\nthen small changes of place would be attended by appreciable\\ndifferences of latitude but in fact the planetary orbits are in\\ngeneral but little inclined to the ecliptic, and some of them lie\\nalmost in*the same plane with ft. Hence arises a difficulty in\\nascertaining the exact time when a planet reaches its node.\\nAmong the most valuable observations for determining the\\nelements of a planet s orbit, are those made when a superior\\nplanet is in or near its opposition to the sun, for then the helio-\\ncentric and geocentric longitudes are the same. When a num-\\nber of oppositions are observed, the planet s motion in longi-\\ntude, as would be observed from the sun, will be known. The\\ninferior planets also, when in superior conjunction, have their\\ngeocentric and heliocentric longitudes the same. When in in-\\nferior conjunction, these longitudes differ 180\u00c2\u00b0; but the inferior\\nplanets can seldom be observed in superior conjunction, on\\naccount of their proximity to the sun, nor in inferior conjunc-\\ntion except in their transits, which occur too rarely to admit of", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0253.jp2"}, "254": {"fulltext": "230 THE PLANETS.\\nobservations sufficiently numerous. Therefore, we can not so\\nreadily ascertain by simple observation, the motions of the\\ninferior planets seen from the sun, as we can those of the su-\\nperior.*\\n374. Hence, to obtain accurately the periodic time of a su-\\nperior planet, we find the interval elapsed between two opposi-\\ntions separated by a long interval, when the planet was nearly\\nin the same part of the zodiac. From the periodic time, as\\ndetermined approximately by other methods, it may be found\\nwhen the planet has the same heliocentric longitude as at the\\nfirst observation. Thus the time of a complete number of rev-\\nolutions will be known, and thence the time of one revolution.\\nThe greater the interval of time between the two oppositions,\\nthe more accurately the periodic time will be obtained, be-\\ncause the errors of observation will be divided between a great\\nnumber of periods therefore by using very accurate observa-\\ntions, much precision may be attained. For example, the\\nplanet Saturn was observed in the year 228 b. c, March 2\\n(according to our reckoning of time), to be near a certain star\\ncalled y Yirginis, and it was at the same time nearly in oppo-\\nsition to the sun. The same planet was again observed in op-\\nposition to the sun, and having nearly the same longitude, in\\nFeb., 1714. The exact difference between these dates was\\n1943y. 118d. 21h. 15m. It is known from other sources, that\\nthe time of a revolution is 29J years nearly, and hence it was\\nfound that in the above period there were 66 revolutions of\\nSaturn and dividing the interval by this number, we obtain\\n29.444 years, which is nearly the periodic time of Saturn ac-\\ncording to the most accurate determination.\\n375. Thirdly, to determine the distance from the sun, and\\nmajor axes of the planetary orbits.\\nThe distance of the earth from the sun being known, the\\nmean distance of any planet (its periodic time being known)\\nmay be found by Kepler s law, that the squares of the periodic\\ntimes are as the cubes of the distances. The method of find-\\ning the distance of an inferior planet from the sun by observa-\\nBrinkley, p. 167.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0254.jp2"}, "255": {"fulltext": "ELEMENTS OF THE PLANETARY OEBITS. 231\\ntions at the greatest elongation, has been already explained\\n(see Art. 308). The distance of a superior planet may be\\nfound from observations on its retrograde motion at the time\\nof opposition. The periodic times of two planets being\\nknown, we of course know their mean angular velocities,\\nwhich are inversely as the times. Therefore, let Ee (Fig. 73)\\nbe a very small portion of the earth s orbit, and Mm a corre-\\nsponding portion of that of a superior planet, described on the\\nFisr. To\\nday of opposition, about the sun S, on which day the three\\nbodies lie in one straight line SEMX. Then the angles ES\\nand MSm, representing the respective angular velocities of the\\ntwo bodies, are known. Now if em be joined, and prolonged\\nto meet SM continued in X, the angle EXe, which is equal to\\nthe alternate angle ~K.ey, being equal to the retrogradation of\\nthe planet in the same time (being known from observation),\\nis also given. E#, therefore, and the angle EX^ being given\\nin the right-angled triangle EXe, the side EX is easily calcu-\\nlated, and thus SX becomes known. Consequently, in the\\ntriangle SmX, we have given the side SX, and the two angles\\nmSX and wsXS, whence the other sides Sm and mX are easily\\ndetermined. Now Sm is the radius vector of the orbit of the\\nsuperior planet at the point through which it was passing at\\nthe time of the observation- Of course, one such observation\\ncould not be relied on as giving the mean distance; but it\\nwould be a satisfactory approximation in the case of any plan-\\netary orbit, since these orbits are all very nearly circular.\\nAnd by repeating the process every year, as the earth passes\\nbetween the sun and planet, the average of all will ultimately\\nexpress the mean distance, or semi-major axis of the orbit in\\nquestion.*\\n376. Fourthly, to determine the place of the perihelion,\\nthe time of passing it, and the eccentricity.\\nA method applicable to the inferior planets, is to make a\\nSir J. Herschel.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0255.jp2"}, "256": {"fulltext": "232\\nTHE PLANETS.\\nseries of observations upon them at the times of their greatest\\nelongations, as described in Art. 308. If the length of the\\nradius vector be thus obtained at each return to the point of\\ngreatest elongation, there will be found among them all, one\\nthat is a maximum, and another that is a minimum. The\\nlatter point is approximately the place of the perihelion. Thus\\n(Fig. 60), if in a long series of observations on the greatest\\nelongations of Mercury, the value of SB were, at a certain\\ntime, to be the least of all, we should know that that point is\\nthe place of perihelion, and, of course, that the point diametri-\\ncally opposite is the place of the aphelion. Moreover, by cal-\\nculating the distances of the planet from the sun at these two\\npoints, as described in Art. 308, we ascertain the length of the\\nleast and greatest radius vector; and half the difference of\\nthese two lines constitutes the eccentricity.\\nFor the superior planets, we might suppose the method de-\\nscribed in Art. 375, to be pursued every year at the time of\\nopposition, till a radius vector is found, which is less than any\\nother; that is approximately the place of perihelion. For\\nthe most distant planets, however, the angle of retrogradation\\nX^y, or ?XS, is so minute, that the calculated value of Sm is\\nvery uncertain. Moreover, the distant planets pass their\\naphelion and perihelion at long intervals. So that, in a given\\ncase, it may be necessary to wait 40 years for Uranus, or 80\\nfor J^eptune, to pass either of the apsides.\\nBut trigonometry, building on a\\nfew instrumental observations, af-\\nfords other modes of arriving at these\\nelements of a planetary orbit, one\\nof which is derived from the greatest\\nequation of the center (Art. 200). For\\nsince the two points in the orbit\\nwhere this becomes greatest are\\nequally 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\\nat S. In an ellipse, the square root of the product of the semi-\\nFisr. 74.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0256.jp2"}, "257": {"fulltext": "ELEMENTS OF THE PLANETARY ORBITS. 233\\naxes gives the radius of a circle of the same area as the\\nellipse. Therefore, with the center S, at the distance SE=\\nVAKxOK, describe the circle CEGF, then will the area of\\nthis circle be equal to that of the ellipse. At the same time\\nthat a body departs from A the aphelion, let a body begin to\\nmove with a uniform motion from C through the periphery\\nCEGF, and perform a whole revolution in the same period\\nthat the planet describes the ellipse the motion of this body\\nwill represent the equable or mean motion of the planet, and\\nit will describe around S areas or sectors of circles which are\\nproportional to the times, and equal to the elliptic areas de-\\nscribed in the same time by the planet. Suppose the body\\ndescribing the circle to be at M then taking the sector ASP\\nCSM, P is the true place of the planet. The angle CSM is\\nis the mean anomaly,* CSD the true, and DSM the equation\\nof the center. But in a circle, sectors vary as their arcs\\ntherefore, the sector DSM may be used for the equation but\\ntaking CSD from the equals CSM and ASP, DSM=ACDP,\\nwhich therefore measures the equation of the center. Now\\nACDP obviously increases till it becomes ACE, that is, when\\nthe planet has reached the point where the two orbits intersect.\\nIt may be shown, that after passing E, the equation dimin-\\nishes. The half orbits AEB, CEG, are described in the same\\ntime; and the mean place, therefore, remains in advance of\\nthe true, till they reach G and B together. Let Y be the\\nmean place, and R the true place, at a certain moment then\\nthe angle CSY is the mean anomaly, and CSm the true, and\\nYSm the equation. The sectors ASR, CSY, are equal, being\\ndescribed in the same time. Taking CERS from each, ACE\\nEraK+YSra; YSra=ACE-EmR; that is, the equation\\nYSm has diminished by EmR since the planet was at E.\\nTherefore E is the place of greatest equation of the center.\\nBut E is also the place where the mean and true angular\\nmotions are equal, because the equal sectors of the two orbits\\ndescribed in each instant, have the same length at that point,\\nand therefore the same angle. Hence, the greatest equation\\noccurs where the mean angular motion is equal to the true.\\nAnomaly is now reckoned from perihelion (Art. 200) but that change does\\nnot affect the correctness of this reasoning.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0257.jp2"}, "258": {"fulltext": "234: THE PLANETS.\\nThe mean angular motion being known from the periodic time\\nof the planet, it is then ascertained by observation when the\\ntrue motion equals it, and thus the time of the greatest equa-\\ntion of the center is obtained. Now, this occurs twice in the\\nrevolution, at E and F and half way between these points lie\\nthe apsides A and B. Therefore, observing the times of the\\ngreatest equation of the center, E and F, and bisecting the in\\nterval, we have the time of the planet s passing the perihelion\\nB. But the same observations also determine the heliocentric\\nplaces of E and F, and the middle of the arc EBF is the place\\nof the perihelion.\\n37 7. The amount of the greatest equation evidently de-\\npends on the eccentricity of the orbit, since it arises wholly\\nfrom the departure of the ellipse from the figure of a perfect\\ncircle hence, the greatest equation affords the means of deter-\\nmining the eccentricity itself. In orbits of small eccentricity,\\nas is the case with most of the planetary orbits, it is found that\\nthe arc which measures the greatest equation is very nearly\\nequal to the distance between the foci, which always equals\\ntwice the eccentricity, the measure of the eccentricity being\\nthe distance from the focus to the center of the ellipse. The\\nangular value of radius is 57\u00c2\u00b0 17 44 8 for,\\n3.14159 1 180\u00c2\u00b0 57\u00c2\u00b0 17 44 .8.\\nTherefore, 57\u00c2\u00b0 11 44 8 radius half the greatest equation\\nof the center the eccentricity*\\nThe foregoing explanations of the methods of finding the\\nelements of the orbits, will serve in general to show the learner\\nhow these particulars are or may be ascertained: yet the\\nmethods actually employed are usually more refined and intri-\\ncate than these. In astronomy, scarcely an element is presented\\nsimple and unmixed with others. Its value, when first disen-\\ngaged, must partake of the uncertainty to which the other ele-\\nments are subject, and can be supposed to be settled to a\\ntolerable degree of correctness, only after multiplied observa-\\ntions and many revisions. f Indeed, a large part of the most\\narduous labors of astronomers have been employed in finding\\nVince s Complete System, i., p. 113. f Woodhouse, p. 579.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0258.jp2"}, "259": {"fulltext": "QUANTITY OF MATTER IN THE SUN AND PLANETS. 235\\nthe elements of the planetary orbits, with the wonderful degree\\nof precision which has finally been attained.\\nQUANTITY OF MATTER IN THE SUN AND PLANETS.\\n378. It would seem at first view very improbable, that an\\ninhabitant of this earth would be able to weigh the sun and\\nplanets, and estimate the exact quantity of matter which they\\nseverally contain. But the principles of Universal Gravitation\\nconduct us to this result, by a process remarkable for its sim-\\nplicity. By comparing the relations of a few elements that are\\nknown to us, we ascend to the knowledge of such as appeared\\nbeyond the pale of human investigation. We learn the quantity\\nof matter in a body by the force of gravity it exerts. Let us see\\nhow this force is ascertained.\\n379. The quantities of matter in two bodies may be found\\nin terms of the distances and periodic times of two bodies re-\\nvolving around them respectively, being as the cubes of the dis-\\ntances divided by the squares of the periodic times.\\nThe force of gravity G in a body whose quantity of matter\\nis M and distance D, varies directly as the quantity of matter,\\nM\\nand inversely as the square of the distance that is, G x 2\\nBut it is shown of circular orbits (Art. 177), that the force of\\ngravity also varies as the distance divided by the square of the\\nperiodic time, or G oo Therefore, p~2 an( p2-\\nThus we may find the respective quantities of matter in the\\nearth and the sun by comparing the distance and periodic time\\nof the moon revolving around the earth, with the distance and\\nperiodic time of the earth revolving around the sun. For the\\ncube of the moon s distance from the earth divided by the\\nsquare of her periodic time, is to the cube of the earth s dis-\\ntance from the sun divided by the square of her periodic time,\\nas the quantity of matter in the earth is to that in the sun.\\n238,54:5 s 95,000,000 s QKO QQ _\\nThat 1S vfW nkaw ::1: 3o3 8bo The raost exact\\ndetermination of this ratio gives for the mass of the sun", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0259.jp2"}, "260": {"fulltext": "9,2*\\nTHE PLANETS.\\n354,936 times that of the earth. Hence it appears that the sun\\ncontains more than three hundred and fifty-four thousand times\\nas much matter as the earth. Indeed, the sun contains eight\\nhundred 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\\nfind the space which the moon descends toward the earth, and\\nthe earth toward the sun, in any given time, as an hour,\\nThus (Fig. 75), if we know the radius AE of the orbit, we can\\ndetermine the length of the arc A5, described in an hour, and\\nalso the length of the hypotenuse BE. But BE\u00e2\u0080\u0094 AE=B\\nthe space through which the central attracts the revolving body\\nin the given time. It was shown (Art. 182) that the earth\\ndraws the moon from a tangent, .0536 of an inch in a second\\nif a calculation of the same kind be made in relation to the\\norbit of the earth, it will be found that the sun draws the earth\\nnearly .12 of an inch per second from a tangent that is, the\\nsun exerts a force 2J greater on the earth than the earth does\\non the moon. But were the sun at the same distance as the\\nmoon, his force of attraction would be the square of 400, or\\n160,000 times as great as it is now; that is, it would be\\n2Jx 160,000 times as great as the earth s attraction, and, con-\\nsequently, must have 2^x160,000 352,000 times as much\\nmatter a result agreeing nearly with the former. The agree-\\nment would be exact if more precise numbers were employed,\\nbut our object is here merely to illustrate the method.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0260.jp2"}, "261": {"fulltext": "QUANTITY OF MATTER IN THE SUN AND PLANETS. 237\\n380. The mass of each of the other planets that have satel-\\nlites may be found by comparing the periodic time of one of\\nits satellites with its own periodic time around the sun. By\\nthis means we learn the ratio of its quantity of matter to that\\nof the sun. The masses of those planets which have no satel-\\nlites, as Yenus or Mars, have been determined by estimating\\nthe force of attraction which they exert in disturbing the mo-\\ntions of other bodies. Thus, the effect of the moon in raising\\nthe tides, leads to a knowledge of the quantity of matter in\\nthe moon and the effect of Yenus in disturbing the motions\\nof the earth, indicates her quantity of matter.*\\n381. The quantity of matter in bodies varies as their mag-\\nnitudes and densities conjointly. Hence, their densities vary\\nas their masses divided by their magnitudes and since we\\nknow the magnitudes of the planets, and can compute as above\\ntheir masses, we can thus learn their densities, which, when\\nreduced to a common standard, give us their specific gravities,\\nor show us how much heavier they are than water. Worlds,\\ntherefore, are weighed with the same certainty as a pebble, or\\nan article of merchandise.\\nThe densities and specific gravities of the sun, moon, and\\nplanets, are estimated as follows :f\\nDensity. Specific Gravity.\\nSun, 0.25 1.37J\\nMoon, 0.56 3.07\\nMercury, 1.12 6.13\\nYenus, 0.92 5.04\\nEarth, 1.00 5.48\\nMars, 0.95 5.20\\nJupiter, 0.24 1.31\\nSaturn, 0.14 0.76\\nUranus, 0.24 1.31\\nNeptune, 0.14 0.76\\nThese estimates are made by the most profound investigations in Laplace s\\nMecanique Ce leste, vol. iii.\\nf Herschel.\\nThe earth being taken, according to Baily, at 5.48, the specific gravities of\\nthe other bodies (which are found by multiplying the density of each by the\\nspecific gravity of the earth) are here stated somewhat higher than they are\\ngiven in most works.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0261.jp2"}, "262": {"fulltext": "238 THE PLANETS.\\nFrom tins table it appears that the sun consists of matter\\nbut little heavier than water but that the moon is more than\\nthree times as heavy as water, though less dense than the\\nearth, which is five and a half times heavier than water. It\\nalso appears that the nearer planets are more dense than the\\nmore remote. Mercury is heavier than most metallic ores,\\nwhile Saturn and Neptune are one-fourth lighter than water.\\nThe density, however, does not, in all cases, diminish outward\\nfor Yenus is less dense than the earth, and Saturn than\\nUranus.\\nCHAPTEE XII.\\nPERTURBATIONS OF THE PLANETS STABILITY OF THE SYSTEM\\nNUMERICAL RELATIONS OF THE PLANETS PROBLEMS.\\n382. The perturbations occasioned in the motions of the\\nplanets by their action on each other are very numerous, since\\nevery body in the system exerts an attraction on every other,\\nin conformity with the law of universal gravitation. Yenus\\nand Mars, approaching as they do at times comparatively near\\nto the earth, sensibly disturb its motions; and Jupiter and\\nSaturn, although very far asunder, still, in consequence of\\ntheir great masses, exert on each other, when on the same side\\nof the heavens especially, a decided influence. Moreover, the\\nsun, by his unequal action on the several planets, in conse-\\nquence of the peculiar figure of each, produces various irregu-\\nlarities in their motions. As in the case of the earth and\\nmoon (Art. 243), these perturbations are divided into periodi-\\ncal and secular periodical, when completed in comparatively\\nshort periods, as those, for example, which undergo all their\\nchanges during one revolution of the planet and secular,\\nwhen completed only in very long periods, as those which\\naffect the form and inclination of the orbits.\\n383. If the only bodies in the system were a central body\\nlike the sun, and a revolving body like Yenus, then, when the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0262.jp2"}, "263": {"fulltext": "PERTURBATIONS OF THE PLANETS. 239\\nplanet was once put in motion with such a projectile force as\\nto make it describe an ellipse, it would forever continue to\\ndescribe the same figure without the least variation, the radius\\nvector always passing over equal spaces in equal times but\\nnow introduce a third body so near as to exert on it a decided\\nattraction, and its motions no longer retain their simplicity,\\nbut become complicated by the conflicting influences of the\\ntwo attracting bodies. The sun, however, in consequence of\\nits mass, which is eight hundred times as great as that of all\\nthe planets, and, of course, vastly greater than that of any one\\nof them, exerts a force so much superior to that of any or all\\nthe other disturbing bodies, that the elliptical figure of the\\norbits is nearly maintained, and a near approximation to the\\nplace of a planet is obtained by neglecting all those minor\\nforces, and simply contemplating it as revolving in an ellipti-\\ncal orbit. Still it is essential, in order to find the exact place\\nof a planet at any given time, that all these irregularities,\\nminute as they may be, be carefully summed up, and their\\nresultant applied to the elliptical motions. To investigate\\nthese perturbations, to estimate their precise amount, and to\\nregister them in tables, for the use of the practical astronomer,\\nhave constituted a large part of the labors of modern astrono-\\nmy. The knowledge gained by astronomers of the planetary\\nmotions, considering the very numerous irregularities, both\\nperiodical and secular, to which they are subject, is truly won-\\nderful. The motion of Jupiter, for instance, is so perfectly\\ncalculated, that astronomers have computed ten years before-\\nhand the time at which it will pass the meridian of different\\nplaces, and we find the prediction correct within half a second\\nof tiine.* The more obvious irregularities have been detected\\nby observation the more minute, by following out the conse-\\nquences of universal gravitation. Even those at first revealed\\nto the instruments of the astronomer have been confirmed and\\nestimated with greater accuracy by the same far-reaching\\nprinciple and many of the irregularities have been first\\nDrought to light by this theory, which had before eluded ob-\\nservation although, when once pointed out as a result of the\\nprinciple of gravitation, careful instrumental measurements\\nAiry.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0263.jp2"}, "264": {"fulltext": "240 THE PLANETS.\\nhave confirmed them, except in cases where the force was too\\nminute to be reached by the most refined observation. Peri-\\nodical perturbations among the bodies of the solar system\\nmay be compared to the regular flux and reflux of the tides,\\nby which the ocean daily oscillates about its mean level,\\nwithout any permanent change of level while secular pertur-\\nbations would resemble any slow changes of level, which, ac-\\ncumulating from time to time, might finally become obvious\\nto measures of the depths of the ocean, as recorded from age\\nto age. As an example of the extreme minuteness of some of\\nthese secular perturbations, we may instance the changes in\\nthe eccentricity of the earth s orbit. The entire eccentricity is\\nso small that the figure, when drawn on paper in just propor-\\ntions, can scarcely be distinguished from a circle, the focus of\\nthe ellipse being distant from the center only about part of\\nthe semi-major axis. But the change of eccentricity in a\\ncentury is only the twenty- five thousandth part of the whole,\\nor the fifteen hundred thousandth part of the semi-major axis.\\n384. But although the secular inequalities of the planetary\\nmotions are exceedingly slow, yet may they not, in time, accu-\\nmulate so as to derange the whole system and do they not,\\nat least, indicate that the system carries within it the seeds of\\nits own dissolution So far is this from being the case, that\\nthe stability of the solar system is a fact established on the\\nmost satisfactory evidence, and its demonstration is among the\\nfinest triumphs of physical astronomy. Even a superficial\\nview of the system will convince us that care has been be-\\nstowed on this point by several obvious arrangements. One\\nis, that the planets have, severally, so small masses, compared\\nwith the sun, as to interfere but little, at most, with the\\nsupremacy of his control over the planetary motions. An-\\nother is, that the planets are placed at such great distances\\nfrom each other a distance which is greater among the\\nlargest bodies, as Jupiter and Saturn, than among the smaller,\\nas the Earth and Yenus and another still, that the orbits are\\nless eccentric when the masses of the bodies are greater, by\\nwhich provision they are always maintained at a remote dis-\\ntance from the sun. Were the orbit of Jupiter as eccentric as\\nthat of Mars, he would approach so near the earth at his peri-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0264.jp2"}, "265": {"fulltext": "STABILITY OF THE SYSTEM. 24:1\\nhelion, as greatly to endanger its stability. But if even these\\ngeneral considerations might convince us that the stability of\\nthe solar system is provided for, a more profound investiga-\\ntion will reveal this truth in a far more admirable light. This\\nobject is especially secured by the following remarkable pro-\\nvisions.\\nFirst, by the invariability of the major axes, and of the\\nperiodic times secondly, by the fact, that whatever irregu-\\nlarities a planet undergoes on one side of its orbit (so far as\\nrespects the periodical perturbations), they are compensated\\non the other side so that, when it returns to a given point,\\nas the node or the perihelion, any irregularities it may have\\nfelt in different parts of its orbit neutralize one another, and\\ntherefore do not constitute an accumulating mass of errors\\nand, thirdly, by this, that all the secular perturbations are\\nrestricted within narrow limits, oscillating to and fro but,\\nbefore they can proceed so far on one side as to endanger the\\nstability of the system, they turn about and proceed, for a\\nsimilar period, in the opposite direction.\\n385. These truths have been established by the most rigor-\\nous mathematical demonstrations, by the successive labors of\\nthree very celebrated mathematicians Euler, Lagrange, and\\nLaplace. It was demonstrated that the major axes of the\\nplanetary orbits, and the times of their revolutions around the\\nsun, are subject to no secular perturbations, nor to any varia-\\ntion whatever, but such as, in the course of a single revolution,\\nexactly compensate and neutralize each other. This is a most\\nimportant point in relation to the stability of the system for\\nif the lengths of the major axes varied, then, of course, the\\ntimes of revolution would vary (since, by Kepler s third law,\\nthe squares of the periodic times are in a constant ratio to the\\ncubes of the major axes), and we should have years of unequal\\nlength, and the earth, by approaching at one time nearer to\\nthe sun, and at another receding further from it, would render\\nthe changes of temperature too great for the existence of ani-\\nmal or vegetable life and similar evils, it is probable, would\\nresult to the economy of the other planets. It was next estab-\\nlished, that the eccentricities of the planetary orbits, although\\nthey have been undergoing constant changes in all time past,", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0265.jp2"}, "266": {"fulltext": "242 THE PLANETS.\\nand will continue to undergo them in all future ages, can never\\nvary beyond a certain moderate limit, entirely within the\\nbounds of safety to the stability of the system. The eccentri-\\ncity of the earth s orbit, for example, has been diminishing ever\\nsince the creation of man and although, as we have seen, the\\nrate of diminution is exceedingly slow, yet, in the progress of\\ncenturies, it would totally change the character of the earth s\\norbit first reducing it to the circular form, and finally carry-\\ning its eccentricity to a fatal extreme. In like manner, the\\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\\nthis variation exceed three degrees. It is worthy of remark,\\nthat those perturbations, such as changes in the place of the\\nperihelion, affecting a change of direction in space of the major\\naxis of the orbit, or in the place of the nodes, which, by accu-\\nmulating, do not endanger the stability of the system, proceed\\nonward through the entire circuit of the heavens while per-\\nturbations which, by indefinite accumulation, would bring ruin\\nto the system, such as variations of eccentricity and of inclina-\\ntion, are not progressive, but oscillatory, waving to and fro\\nwithin the limits of entire safety.\\n386. These great ends would not have been secured, had\\nthe system been constructed differently from what it is. Nu-\\nmerous conditions must concur in order to produce these re-\\nsults the mass of the sun must have greatly exceeded that of\\nany or all the planets the eccentricities of the orbits must have\\nbeen small and the planets must all have revolved around the\\nsun in the same direction, and in planes but little inclined to each\\nother.* It was also necessary that the periodic times of the\\nplanets should, in general, be incommensurable for were\\ntheir periods such that one planet would revolve a certain\\nLaplace, Sys. du Monde. Herschel s outlines. Grant s History of Physical\\nAstronomy. Pontecoulant s Trait. Elemen. de Phys. C61este.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0266.jp2"}, "267": {"fulltext": "RELATIONS BETWEEN BODIES OF THE SOLAR SYSTEM. 243\\nnumber of times exactly, while another planet, next to it, re-\\nvolved a certain other even number of times, then, when they\\nonce came into the sphere of each other s influence, they might\\nremain under it so long, and return to their relative position\\nso often, as seriously to derange their orbits. An instance of\\nthis, in fact, occurs in the case of Jupiter and Saturn, five rev-\\nolutions of Jupiter being nearly equal to two of Saturn, a re-\\nlation which gives rise to what is called the long inequality of\\nSaturn and Jupiter. Similar effects result from a near com-\\nmensurability of the mean motions of any other two planets.\\nOne exists between the Earth and Yenus, 13 times the period\\nof Yenus being very nearly equal to 8 times that of the Earth\\nstill, the influence of this disturbing cause is so nicely compen-\\nsated, and its effects so distributed, that, according to Mr. Airy\\n(who was the first to detect it), it amounts, at its maximum, to\\nno more than a few seconds for a period of 240 years. The\\nlaws which regulate the eccentricities and inclinations of the\\nplanetary orbits (says an able writer on Physical Astronomy),\\ncombined with the invariability of the mean distances, secure\\nthe permanence of the solar system throughout an indefinite\\nlapse of ages, and offer to us an impressive indication of the\\nSupreme Intelligence which presides over nature, and perpet-\\nuates her beneficent arrangements. When contemplated\\nmerely as speculative truths, they are unquestionably the most\\nimportant which the transcendental analysis has disclosed to\\nthe researches of the geometer and their complete establish-\\nment would suffice to immortalize the names of Lagrange and\\nLaplace, even although these great geniuses possessed no other\\nclaim to the recollection of posterity.*\\nNUMERICAL RELATIONS BETWEEN THE BODIES OF THE\\nSOLAR SYSTKM.f\\n387. If we contemplate the relations subsisting between a\\ncentral body, as the sun, and a revolving body, as one of the\\nGrant s Hist. Phys. Ast., p. 56.\\nf In the preparation of this article, the author has derived much assistance\\nfrom a small work, now nearly out of print, containing the suhstance of three\\nlectures delivered to the students of Yale College in 1781, by Rev. Nehemiah\\nStrong, at that time Professor of Mathematics and Natural Philosophy.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0267.jp2"}, "268": {"fulltext": "244 THE PLANETS.\\nplanets, it will be readily understood, that if the quantity of\\nmatter in the central body is increased, while the distance of\\nthe revolving body remains the same, the velocity of the re-\\nvolving body must be increased also, in order to generate a\\nsufficient centrifugal force to counterbalance the increased\\nforce of attraction in the central body, arising from the increase\\nof its mass and that, were the force of attraction diminished,\\nby removing the body to a greater distance from the center,\\nthen the rate of its motion would also have to be diminished\\notherwise the centrifugal force would overpower the force of\\nattraction. It is a remarkable fact, that the members of the\\nsolar system are so adjusted to each other, in respect to their\\nvelocities, distances from the sun, periodic times, and gravita-\\ntion toward the central body, that if any one of these particu-\\nlars is known, all the rest become known also. Thus, if it\\nwere found that a new-discovered planet moved with one-sixth\\nthe velocity of the earth, we should know at once that its dis-\\ntance from the sun was thirty-six times as great as the earth s\\ndistance, that its time of revolution was two hundred and six-\\nteen years, and that its gravitation toward the sun was twelve\\nhundred and ninety-six times less than that of the earth for\\nthe distance is as the square of the number expressing the recipro-\\ncal of its velocity, compared with that of the earth its periodic\\ntime as the cube and the reciprocal of gravity as the fourth\\npower of the same number. All this follows from Kepler s\\nthird law that the squares of the periodic times are as the\\ncubes of the distances and from the law of universal gravita-\\ntion that the force of attraction is inversely as the square of\\nthe distance. The four particulars named, therefore, constitute\\na series of numbers in geometrical progression, of which the\\nfirst term is equal to the ratio. The truth of this proposition\\nmay be demonstrated as follows\\nLet D be the mean distance of a planet from the sun, 7r 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\\nexpression lor the velocity is V =-w- p- And V 2 oo\\nBut, by Kepler s law, P 2 oo D 3 V 2 oo or Y 2 oo A Since", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0268.jp2"}, "269": {"fulltext": "NUMERICAL RELATIONS. 245\\na body moves with less velocity, when the distance from the\\nsun is greater, it will be convenient, in order to avoid fraction-\\nal forms, to use the reciprocal of Y, instead of Y itself. Let\\nR (retardation) be equal to then Y= and Y 2 hence\\ngc H 2 co D (IV If, therefore, R indicates how much\\nIv L)\\nslower a planet moves than another, as the earth, taken as a\\nstandard, the square of R will show how much further from\\nthe sun the planet is than the earth.\\nB D 3\\nAgain, since Yco p, Y 3 go But, by Kepler s law, D 3 co P 2\\nv 3 p r v 3 p R 3 (2).\\nConsequently, if R expresses how many times slower than\\nthe earth a given planet moves, the cube of R will express the\\nrelative periodic time.\\nFftially, by the law of gravitation, the force of gravitation\\ntoward the central body varies as the square of the distance\\ninversely, or G- co But if the reciprocal of gravity be call-\\ned Levity, and expressed by L, then L co B 2 but R 2 co D,\\nin R 4 co D 2 and R 4 co L (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\\nsame body gravitates toward the central body. Collecting\\nthese several results, it appears that the reciprocal of velocity\\nR, the distance D, the periodic time P, and the reciprocal of\\ngravity L, are respectively denoted by the geometrical series^\\nR, R 2 R 3 R 4 in which the first term and the ratio are equal.\\n388. A number of very useful and convenient rules, may\\nbe derived from this numerical relation between the members\\nof the solar system since, when any one of the four things\\nnamed is given, all the rest may be found from it; and each\\nof the four may be found in four different ways when the other\\nmembers of the series are given. This will be obvious from a\\nfew examples.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0269.jp2"}, "270": {"fulltext": "246 THE PLANETS.\\nI. Given the 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 recipro-\\ncal of gravity.\\nII. Given the distance (D).\\n1. Take its square root for reciprocal of velocity.\\n2. Take the cube of the square root of the distance for the\\nperiodic time.\\n3. Take its square for the reciprocal of gravity.\\nIII. Given the periodic time (P).\\n1. Take the cube root of the periodic time for the reciprocal\\nof velocity.\\n2. Take the square of the cube root of the periodic time for\\nthe distance.\\n3. Take the fourth power of its cube root for the reciprocal\\nof gravity.\\nIV. Given the reciprocal of gravity (L).\\n1. Take the fourth root for the reciprocal of velocity.\\n2. Take the square root for the distance.\\n3. Take the cube of the fourth root for the periodic time.\\nV. Required the reciprocal of velocity.\\nThis may be obtained by taking the square root of the dis-\\ntance, or the cube root of the periodic time, or the fourth root\\nof the reciprocal of gravity, or by dividing the reciprocal of\\ngravity by the periodic time.\\nYI. Required the distance.\\nTake the square of the reciprocal of velocity, or the square\\nof the cube root of the time, or the square root of the reciprocal\\nof gravity, or divide the time by the reciprocal of velocity.\\nVII. Required the periodic time.\\nTake the cube of the reciprocal of velocity, or the cube of\\nthe square root of the distance, or the f power of the reciprocal\\nof gravity, or divide the reciprocal of gravity by that of ve-\\nlocity.\\nVIII. Required the diminished gravitation.\\nTake the fourth power of the reciprocal of velocity, or the\\nsquare of the distance, or the J power of the time, or multiply\\nthe time by the reciprocal of velocity.\\nAccording to the foregoing rules, tables may be formed, ex-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0270.jp2"}, "271": {"fulltext": "PROBLEMS.\\n247\\nhibiting, in a striking light, the numerical relations of the\\nmembers of the solar system. In the following table the dis-\\ntances are taken from Herschel s Astronomy, and from these\\nthe other particulars are determined by the preceding rules.\\nIf Mercury were taken as the standard of comparison, then the\\nretardations of all the other planets would be greater than\\nunity but, as it is convenient to take the earth as the stand-\\nard, the retardations of Mercury and Yenus will be less than\\nunity showing that the velocity (which is expressed by the\\nfraction inverted) is greater than that of the earth. In like\\nmanner, the force of gravitation of an inferior planet, being\\ngreater than that of the earth, is the reciprocal of the tabular\\nnumber.\\nTable showing the Numerical Relations of the Primary\\nPlanets.\\nPlanets-\\nRetardations.\\nDistances.\\nPer. Times.\\nRecip. of Gravity.\\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 4f years. How much slower does it move in its orbit\\nthan the earth how much further is it from the sun and\\nhow much less does it gravitate toward the sun? Ans. R\\n1.67, D 2.79, L 7.80.\\nBy applying the proportional numbers determined by this\\nproblem respectively to the earth s motion per second, to its\\ndistance from the sun in miles, and to the space through which\\nthe earth departs in a second from a tangent to her orbit, we\\nmay obtain the numerical value of each of these elements.\\nProb. 2. What would be the periodical time of a meteor or\\nplanet revolving close to the earth.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0271.jp2"}, "272": {"fulltext": "248 THE PLANETS.\\nAs the moon is a body revolving around the earth at a known\\ndistance, and with a known periodic time, it will evidently\\nfurnish the necessary standard of comparison. The distance of\\nthe moon from the center of the earth being 60 times the\\nearth s radius, and, of course, 60 times that of the meteor, its\\nrate of motion is \\\\/60 times less. The retardation being n/60,\\n.3\\nthe periodic time will be 60 2 Now, what part of the moon s\\nperiod is 60 2 Divide the moon s period (27.32 days) by 60 2\\nand we have for the answer, 1 hour, 24 minutes, 38.88 seconds.\\nProb. 3. What would be the periodic time of a body re-\\nvolving about the earth at the distance of 5000 miles from the\\ncenter? Am. lh. 59m. 23.28s.\\nProb. 4. 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\\nthe surface of the earth, is 1.4108 hours and since, in a cir-\\ncular orbit, the force of gravity and the centrifugal force are\\nequal, therefore a body like that contemplated in problem 2,\\nis in equilibrium between these two forces consequently, such\\na body may be considered as having lost all its gravity, and\\nbeing, by the supposition, close to the earth, we have only to in-\\nquire how much its velocity exceeds that of the earth. Now, 24\\ndivided by 1.4108 gives 17.01 which shows that were the\\nearth to revolve on its axis about 17 times faster than it does\\nat present, the bodies on the surface would lose all their weight\\nand were the velocity greater than this, the centrifugal force\\nwould prevail over the centripetal, and the same would fly off\\nfrom the earth in tangents.\\nProb. 5. Were the moon to be removed so far from the\\nearth as to revolve about it but once a year, how much greater\\nwould be its distance than at present, how much less its veloci-\\nty, and its gravitation toward the earth\\nIts period being increased 13.37 times, its retardation is\\n13.37* 2.373 its distance 2.373 2 5.631 and its diminished\\ngravity 5.631 2 31.71. Or R 2.373, D 5.631, and L\\n31.71.\\nMultiplying the present distance of the moon, 238,545 miles,\\nby 5.631, we obtain about 1,343,000 miles for the distance at", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0272.jp2"}, "273": {"fulltext": "PROBLEMS. 249\\nwhich the moon must have been placed in order to complete\\nits revolution in one year.\\nPeob. 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 by\\nthe squares of the periodic times, letting the required time\\nbe denoted by x, 1 (the earth s mass) 354.000 (the sun s mass)\\nP 3 D s 1 1 1_ 354,000 27.32\\n2T.32 2 W 2T.32 2 a? 2 ~x~ l 2T.32 2 X v/354,000\\nlh. 6m. 7s.\\nComets, in passing their perihelion, especially when that\\nhappens to be very near the sun, as in the great comet of 1843,\\nmove with an astonishing rapidity requiring a velocity not\\nmerely sufficient to generate the centrifugal force necessary to\\nbalance the powerful force of attraction exerted by the sun v\\nbut greatly to exceed that force, since they are carried far\\nwithout a circular orbit into an elliptical or even a hyperbolic\\norbit.\\nPeob. 7. The perihelion distance of the great comet of 1843\\nbeing 502,000 miles from the center of the sun, what must\\nhave been its velocity per hour, if in a circular orbit\\nPeob. 8. How much must the mass of the earth be in-\\ncreased in order that the moon may revolve about it in the\\nsame time as at present, when removed to three times her\\npresent distance\\nPeob. 9. How much must the mass of the earth be in-\\ncreased to make the moon, at her present distance, revolve in\\n24 hours\\nPeob. 10. The semi-diameter of Jupiter being 11 times\\nthat of the earth, and the distance of its fourth satellite from\\nthe center of the planet being 27 times the radius of the\\nplanet; also the sidereal revolution of the satellite being 16.69\\ndays, while that of the moon is 27.3217 days, and her distance\\n60 times the radius of the earth How much does the quantity\\nof matter in Jupiter exceed that of the earth Ans. 324.49\\ntimes.\\nPeob. 11. Suppose volcanic matter to be thrown from the\\nmoon toward the earth, required the point where it would be\\nin equilibrium between the two, the mass of the moon being", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0273.jp2"}, "274": {"fulltext": "250 THE PLANETS.\\none-eightieth that of the earth Ans. 24,000 miles from the\\ncenter of 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 satel-\\nlite. What would be the periodic time of the satellite, at the\\ndistance of one foot, in a circular orbit Ans. 2 days, 10\\nhours, 13 minutes.*\\n6 The elements used in the solution of this problem are, for the diameter of\\nthe earth, 7912.4 for the distance of the moon 238,545 miles and for its peri-\\nodic time, 27.32 days. The solution, conducted in the ordinary mode, will be\\nfound susceptible of great abridgment. But the following ingenious method is\\nstill shorter. It was suggested to the author by one of his pupils, Mr. Samuel\\nEmerson, of the class of 1848.\\nLemma. The periodic times of two satellites revolving about primaries of equal densities,\\nat 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, d the distances of their satellites.\\nD 3 ds\\nThen, M m\\nBut since D and d are equimultiples of R, r, by some number n, therefore\\nD 3 =R 3 ?i 3 and d* r 3 n s\\nR 3 /t 3 r 3 n 3 R 3 r 3\\nHence, M m \u00e2\u0080\u0094z. But, R 3 and r 3 oo M and m.\\npa p pa p i\\nM wi MXm MXm\\nTherefore, M. m P=z\\nP 2 p* p i P 2 r\\nThe moon being distant 60.296 radii of the earth (as would result from the\\nabove elements), at the distance of 60.296 inches that of the small satellite from\\nits primary would be the same multiple of its radius, and consequently, its peri-\\nodic time the same. What then is its period at 12 inches\\n27. 32 2 :p* 60.296 3 12 s jt 2d. 10b. 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 for\\nthe case becomes this when n=l. 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 of\\ntheir respective primaries.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0274.jp2"}, "275": {"fulltext": "CHAPTEE XIII.\\nCOMETS METEORIC SHOWERS.\\n390. A Comet,* when perfectly formed, consists of three\\nparts the Nucleus, the Envelope, and the Tail. The Nucleus,\\nor body of the comet, is generally distinguished by its forming\\na bright point in the center of the head, conveying the idea of\\na solid, or at least of a very dense portion of matter. Though\\nit is usually exceedingly small when compared with the other\\nparts of the comet, yet it sometimes subtends an angle capable\\nof being measured by the telescope. The Envelope (sometimes\\ncalled the coma) is a dense nebulous covering, which fre-\\nquently renders the edge of the nucleus so indistinct, that it is\\nextremely difficult to ascertain its diameter with any degree of\\nprecision. Many comets have no nucleus, but present only a\\nnebulous mass extremely attenuated on the confines, but grad-\\nually increasing in density toward the center. Indeed, there\\nis a regular gradation of comets, from such as are composed\\nmerely of a gaseous or vapory medium, to those which have a\\nwell-defined nucleus. In some instances on record, astrono-\\nmers have detected with their telescopes small stars through\\nthe densest part of a comet. The Tail is regarded as an ex-\\npansion or prolongation of the coma and presenting, as it\\nsometimes does, a train of appalling magnitude, and of a pale,\\nportentous light, it confers on this class of bodies their pecu-\\nliar celebrity.\\n391. The number of comets belonging to the solar system,\\nis probably very great. Many, no doubt, escape observation\\nby being above the horizon in the daytime. Seneca mentions,\\nthat during a total eclipse of the sun, which happened 60 years\\nbefore the Christian era, a large and splendid comet suddenly\\nmade its appearance, being very near the sun. The elements\\nof at least 180 comets have been computed, and arranged in a\\nK6[irj, coma, from the bearded appearance of comets.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0275.jp2"}, "276": {"fulltext": "252\\nCOMETS.\\ncatalogue for future comparison.* Of these, six are particu-\\nlarly remarkable, viz., the comets of 1680, 1770, and 1843;\\nand those which bear the names of Halley, Encke, and Biela.\\nThe comet of 1680 was distinguished not only for its astonish-\\ning size and splendor, but is remarkable for having been the\\nfirst comet whose elements were determined on the sure basis\\nof mathematics, as was done by Sir Isaac Newton, it having\\nappeared in his time. The comet of 1770 is memorable for\\nFig. 76.\\nFig. 77.\\nCOMET OF 1811,\\nCOMET OF 1680.\\nthe changes its orbit has undergone by the action of Jupiter,\\nand for having approached very near to the earth. The comet\\nof 1843 was the most remarkable in its appearance of all that\\nhave been seen in modern times, having been visible at noon-\\nday. Halley s comet (the same which reappeared in 1835) is\\ndistinguished as that whose return was first successfully pre-\\ndicted, and whose orbit was first accurately determined and\\nBiela s and Encke s comets are well known for their short\\ne See a complete catalogue of cornets, whose elements have been determined,\\nin the American Almanac for 1847.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0276.jp2"}, "277": {"fulltext": "COMETS. 253\\nperiods of revolution, which subject them frequently to the\\nview of astronomers. Biela s comet, at its return in 1846, dis-\\nplayed another remarkable feature a separation into two dis-\\ntinct parts. This strange peculiarity was first seen from the\\nObservatory of Tale College, by Messrs. Herrick and Bradley,\\nbut was first publicly announced from the Observatory at\\nWashington. At one time, the distance of one nucleus from\\nthe other, was estimated at 157,000 miles.\\n392. In magnitude and brightness, comets exhibit a great\\ndiversity. They are sometimes so bright as to be distinctly\\nvisible in the daytime, even at noon and in the brightest sun-\\nshine, as was the case with that of 1813 and such was the\\ncomet seen at Rome a little before the assassination of Julius\\nCaesar. The comet of 1680 covered an arc of the heavens of\\n97\u00c2\u00b0, and its length was estimated at 123,000,000 miles.* That\\nof 1811 had a nucleus of only 428 miles in diameter, but a tail\\n132,000,000 miles long.f Had it been coiled round the earth\\nlike a serpent, it would have reached round more than 5000\\ntimes. Other comets are of exceedingly small dimensions, the\\nnucleus being estimated at only 25 miles; and some which are\\ndestitute of any perceptible nucleus, appear to the largest\\ntelescopes, even when nearest to us, only as a small speck of\\nfog, or as a tuft of down. The majority of these bodies can be\\nseen only by the aid of the telescope.\\nThe same comet, indeed, has often very different aspects, at\\nits different returns. Halley s comet in 1305 was described by\\nthe historians of that age, as cometa horre?idw magnitudinis\\nin 1156 its tail reached from the horizon to the zenith, and\\ninspired such terror, that, by a decree of the Pope of Rome,\\npublic prayers were offered up at noonday in all the Catholic\\nchurches to deprecate the wrath of heaven, while in 16S2, its\\ntail was only 30\u00c2\u00b0 in length, and in 1759 it was visible only to\\nthe telescope, until after it had passed its perihelion. At its\\nrecent return in 1835, the greatest length of the tail was about\\n12\u00c2\u00b04 These changes in the appearances of the same comet\\nare partly owing to the different positions of the earth with\\nArago. f Milne s Prize Essay on Comets.\\nJ But might be seen much longer by indirect vision. (Prof. Joslin, Am. Journ.\\nScience, xxxi., p. 328.)", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0277.jp2"}, "278": {"fulltext": "254\\nCOMETS.\\nrespect to them, being sometimes much nearer to them when\\nthey cross its track than at others also one spectator so situ-\\nated as to see the comet at a higher angle of elevation or in a\\npurer sky than another, will see the train longer than it appears\\nto one less favorably situated but the extent of the changes\\nare such as indicate also a real change in their magnitude and\\nbrightness.\\n393. The periods of comets in their revolutions around the\\nsun, are equally various. Encke s comet, which has the short-\\nest known period, completes its revolution in 3J years, or more\\naccurately, in 1205.23 days; while that of 1811 is estimated to\\nhave a period of 3,383 years. The distances to which different\\ncomets recede from the sun, are also very various. While\\nEncke s comet performs its entire revolution within the orbit\\nof Jupiter, Halley s comet recedes from the sun to twice the\\nFig. 78.\\njtr\\ndistance of Uranus, or nearly 3,600,000,000 miles. Figure 78\\nis a representation, in due proportions, of the orbit of this\\ncomet. Its vast dimensions will be truly conceived of by\\nreflecting that the radius of the small circle E of the earth s\\norbit implies a space of nearly 100,000,000 miles that, as the\\ncomet recedes from the sun, it soon reaches the orbit of Jupiter,\\nand successively traverses the orbits of Saturn, Uranus, and\\nNeptune, reaching its aphelion 600,000,000 miles beyond the\\npresent boundaries of the planetary system. Some comets,\\nindeed, are thought to go to a much greater distance from the\\nMilne.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0278.jp2"}, "279": {"fulltext": "COMETS. 255\\nsun than this, as that of 1811 must have receded from it more\\nthan 45,000,000,000 miles, while some even are supposed to\\npass into parabolic or hyperbolic orbits, and never to return.\\n394. Comets shine by reflecting the light of the sun. In one\\nor two instances they have exhibited distinct phases,* although\\nthe nebulous matter with which the nucleus is surrounded,\\nwould commonly prevent such phases from being distinctly\\nvisible, even when they would otherwise be apparent. More-\\nover, certain qualities of polarized light enable the optician to\\ndecide whether the light of a given body is direct or reflected\\nand M. Arago, of Paris, by experiments of this kind on the\\nlight of the comet of 1819, ascertained it to be reflected light, f\\nThe tail of a comet usually increases very much as it ap-\\nproaches the sun and frequently does not reach its maximum\\nuntil after the perihelion passage. In receding from the sun\\nthe tail again contracts, and nearly or quite disappears before\\nthe body of the comet is entirely out of sight. The tail is fre-\\nquently divided into two portions, the central parts, in the\\ndirection of the axis, being less bright than the marginal parts.\\nIn 1741, a comet appeared which had six tails, spread out like\\na 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\\nor feather, being convex on the side next to the direction in\\nwhich they are moving (Fig. 77) a figure which may result\\nfrom the less velocity of the portions most remote from the\\nsun. Expansions of the envelope have also been at times\\nobserved on the side next the sun,:f but these seldom attain\\nany considerable length.\\n395. The quantity of matter in comets is exceedingly small.\\nTheir tails consist of matter of such tenuity that the smallest\\nstars are visible through them. They can only be regarded\\nas great masses of thin vapor, susceptible of being penetrated\\nthrough their whole substance by the sunbeams, and reflecting\\nthem alike from their interior parts and from their surfaces.\\nDelambre, t. iii p. 400. f Franoceur, p. 181.\\nJ See Dr. Joslin s remarks on Halley s comet, Amer. Journ. Science, xxxi.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0279.jp2"}, "280": {"fulltext": "256 COMETS.\\nIt appears, perhaps, incredible that so thin a substance should\\nbe visible by reflected light, and some astronomers have held\\nthat the matter of comets is self-luminous but it requires but\\nYevj little light to render an object visible in the night, and a\\nlight vapor may be visible when illuminated throughout an\\nimmense stratum, which could not be seen if spread over the\\nface of the sky like a thin cloud. The highest clouds that\\nfloat in our atmosphere, must be looked upon as dense and\\nmassive bodies, compared with the filmy and all but spiritual\\ntexture of a comet.* The small quantity of matter in comets\\nis further proved by the fact that they have sometimes passed\\nvery near to some of the planets without disturbing their mo-\\ntions in any appreciable degree. Thus the comet of 1770, in\\nits way to the sun, got entangled among the satellites of Jupi-\\nter, and remained near them four months, yet it did not per-\\nceptibly change their motions. The same comet also came\\nvery near the earth so near, that, had its mass been equal to\\nthat of the earth, it would have caused the earth to revolve in\\nan orbit so much larger than at present, as to have increased\\nthe length of the year 2h. 47m. Yet it produced no sensible\\neffect on the length of the year, and therefore its mass, as is\\nshown by Laplace, could not have exceeded 5^0 of that of the\\nearth, and might have been less than this to any extent. It\\nmay indeed be asked, what proof we have that comets have\\nany matter. The answer is, first, they reflect light second,\\nthough not sufficient to disturb so heavy bodies as planets or\\nsatellites, 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\\nagitated by the vicinity of a mass of iron, while the iron is\\nnot sensibly affected by the attraction of the needle.\\n396. By approaching very near to a large planet, a comet\\nmay have its orbit entirely changed. This fact is strikingly\\nexemplified in the history of the comet of 1770. At its appear-\\nance in 1770, its orbit was found to be an ellipse, requiring for\\na complete revolution only 5\u00c2\u00a3 years; and the wonder was,\\nthat it had not been seen before, since it was a very large and\\nSir J. Herschel. -j- Laplace.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0280.jp2"}, "281": {"fulltext": "COMETS. 257\\nbright comet. Astronomers suspected that its path had been\\nchanged, and that it had been recently compelled to move in\\nthis short ellipse, by the disturbing force of Jupiter and his\\nsatellites. The French Institute, therefore, offered a high\\nprize for the most complete investigation of the elements of\\nthis comet, taking into account any circumstances which could\\npossibly have produced an alteration in its course. By tracing\\nback its movements for some years previous to 1770, it was\\nfound that, at the beginning of 1767, it had entered considera-\\nbly within the sphere of Jupiter s attraction. Calculating the\\namount of this attraction from the known proximity of the two\\nbodies, it was found what must have been its orbit previous to\\nthe time when it became subject to the disturbing action of\\nJupiter. The result showed that it then moved in an ellipse\\nof greater extent, having a period of 50 years, and having its\\nperihelion instead of its aphelion near Jupiter. It was there-\\nfore evident why, as long as it continued to circulate in an\\norbit so far from the center of the system, it was never visible\\nfrom the earth. In January, 1767, Jupiter and the comet\\nhappened to be very near each other, and as both were moving\\nin 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 5-|- years.\\nBut as it was approaching the sun in 1779, it happened again\\nto fall in with Jupiter. It was in the month of June that the\\nattraction of the planet began to have a sensible effect and it\\nwas not until the month of October following that they were\\nfinally separated.\\nAt the time of their nearest approach, in August, Jupiter\\nwas distant from the comet only T J T of its distance from the\\nsun, and exerted an attraction upon it 225 times greater than\\nthat of the sun. By reason of this powerful attraction, Jupiter\\nbeing further from the sun than the comet, the latter was\\ndrawn out into a new orbit, which, even at its perihelion, came\\nno nearer to the sun than the planet Ceres. In this third or-\\nbit, the comet requires about 20 years to accomplish its revo-\\nlution and being at so great a distance from the earth, it is\\ninvisiblej and will forever remain so, unless, in the course of\\n17", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0281.jp2"}, "282": {"fulltext": "258 COMETS.\\nages, it shall undergo new perturbations and move again in\\nsome smaller orbit as before.*\\nORBITS AND MOTIONS OF COMETS.\\n397. The planets, as we have seen (with the exception of\\nthe asteroids, which seem to be an intermediate class of bodies\\nbetween 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\\nof comets are far more eccentric than those of the planets\\nthey are inclined to the ecliptic at various angles, being some-\\ntimes even nearly perpendicular to it; and the motions of\\ncomets are sometimes retrograde.\\n398. The elements of a comet s orbit as usually obtained,\\nare five (1), longitude of the node (2), inclination to the\\necliptic (3), perihelion distance (4), longitude of perihelion\\n(5), time of perihelion passage.\\nIn comparing these with the elements of a planetary orbit\\n(Art. 367), we perceive two to be omitted the periodic time,\\nand the eccentricity j while perihelion distance is substituted\\nfor mean distance. The reason for this is, that in these orbits,\\nno reliance can be placed on the determination of the size and\\nform of orbit, or the time of describing it, from observations\\nwhich are limited to a short arc near the perihelion. The\\ncomplete problem is not only extremely difficult, as Newton\\npronounced it, but rather wholly impracticable. It is during\\nonly a very small portion of their course that they are visible\\nfrom the earth, and the observations made in that short period\\ncan not afterward be verified on more convenient occasions\\nwhereas in the case of the planets, whose orbits are nearly cir-\\ncular, and whose movements may be followed uninterruptedly\\nthroughout a complete revolution, no such impediments to the\\ndetermination of their orbits occur. There is also some una-\\nvoidable uncertainty in observations made upon bodies whose\\noutlines are so ill-defined. It is not unfrequently the case ioo,\\nthat comets move in a direction opposite to the order of the\\nMilne.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0282.jp2"}, "283": {"fulltext": "CEBITS AND MOTIONS OF COMETS. 259\\nsigns in the zodiac, and sometimes nearly perpendicular to the\\nplane of the ecliptic so that their apparent course through\\nthe heavens is rendered extremely complicated, on account of\\nthe contrary motion of the earth. Since it is possible there\\nshould be any number of elliptic orbits, whose perihelion dis-\\ntances are equal, it is obvious that, in the case of very eccentric\\norbits, the slightest change in the position of the curve near the\\nvertex, where alone the comet can be observed, must occasion\\na very sensible difference in the length of the orbit (as will be\\nobvious from Fig, 79) and therefore, though a small error\\nproduces no perceptible discrepancy between the observed and\\nthe calculated course, while the comet remains visible from the\\nearth, its effect, when diffused over the whole extent of the\\norbit, may acquire a most material or even a fatal importance.\\nOn account of these circumstances, it is found exceedingly\\ndifficult to lay down, even in the rudest manner, the path\\nwhich a comet actually pursues, when gone for years beyond\\nthe limit of our vision and least of all to determine with ac-\\ncuracy the length of the major axis of the ellipse, so as to de-\\nrive from it, by Kepler s third law, the time of its revolution,\\nand thus to be able to predict its next perihelion passage. An\\nerror of only a few seconds may cause a difference of many\\nhundred years. In this manner, though Bessel determined the\\nrevolution of the comet of 1769 to be 2,089 years, it was found", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0283.jp2"}, "284": {"fulltext": "260 COMETS.\\nthat an error of no more than 5 in observation, would alter\\nthe period either to 2,678 years, or to 1,692 years. Some as-\\ntronomers, in calculating the orbit of the great comet of 1680,\\nhave found the length of its greater axis 426 times the earth s\\ndistance from the sun, and consequently its period 8,792 years;\\nwhile others estimate the greater axis 430 times the earth s dis-\\ntance, which alters the period to 8,916 years. Newton and\\nHalley, however, judged that this comet accomplished its rev-\\nolution in only 570 years.\\n399. Disheartened by the difficulty of attaining to any pre-\\ncision in the circumstances by which an elliptic orbit is char-\\nacterized, and, moreover, taking into account the laborious cal-\\nculations necessary for its investigation, astronomers usually\\nsatisfy themselves with ascertaining the elements of a comet\\non the supposition of its describing a parabola and, as this is\\na curve whose axis is infinite, the procedure is greatly simpli-\\nfied by leaving entirely out of consideration the periodic revo-\\nlution. It is true that a parabola may not represent, with\\nmathematical strictness, the course which a comet actually fol-\\nlows but as a parabola is the intermediate curve between the\\nhyperbola and ellipse, it is found that this method, which is so\\nmuch more convenient for computation, also accords sufficient-\\nly with observations, except in cases when the ellipse is a com-\\nparatively short one, as that of Encke s comet, for example,\\nWhen the elements of a comet are determined, Kepler s law of\\nareas enables astronomers to find, by computation, the exact\\nplace of the comet in its orbit at any given time, on the sup-\\nposition that its path is a parabola and comparing this place\\nwith that determined by observation for the same instant, it is\\nseen whether the orbit is truly parabolic, or whether its devia-\\ntion from that path is such as to indicate that its real path is an\\nellipse and the amount of such deviation will give some idea\\nof the degree of eccentricity of the ellipse.\\n400. The elements of a comet, with the exception of its pe-\\nriodic 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 ascer-\\ntaining its position with respect to certain stars, whose right", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0284.jp2"}, "285": {"fulltext": "ORBITS AND MOTIONS OF COMETS.\\n261\\nascensions and declinations are accurately known) afford the\\nmeans of calculating these elements.\\nThe appearances of the same comet at different periods of its\\nreturn are so various (Art. 392), that we can never pronounce\\na given comet to be the same with one that has appeared before,\\nfrom any peculiarities in its physical aspect. The identity of\\na comet with one already on record, is determined by the\\nidentity of the elements. When a new comet appears, we first\\ndetermine its elements, and then turning to a catalogue of\\ncomets whose elements have previously been found and placed\\non record, we see whether these new elements agree with any\\nset of those in the catalogue. If they do, we infer that the\\npresent comet is identical with that on record and the interval\\nbetween the two appearances of the body will indicate its pe-\\nriodic time. If, for example, we find respecting a comet now\\nvisible in the sky, that its path makes the same angle with the\\necliptic as that of a certain comet in our catalogue, that it\\ncrosses the ecliptic in the same degree of longitude, that it\\ncomes to its perihelion in the same place, that its perihelion\\ndistance is the same, and its course the same in regard to the\\norder of the signs, then we infer that the two bodies are one\\nand the same; and the number of years that have elapsed\\nsince its former appearance indicates the period of its revolu-\\ntion around the sun. But if these particulars differ wholly\\nfrom any set of recorded elements, we infer that the present is\\na comet which has never visited our sphere before, or at least\\none 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 par-\\nticulars were left on record, as to enable him to calculate the\\nelements at each period. These were as in the following table.\\nTime of ap-\\npearance.\\nInclination of\\nthe Orbit\\nLongitude of\\nthe Node.\\nLongitude of\\nPerihelion.\\nPerihelion\\nDistance.\\nCourse.\\n1456\\n1531\\n1607\\n1682\\n17\u00c2\u00b0 56\\n17 56\\n17 02\\n17 42\\n48\u00c2\u00b0 30\\n49 25\\n50 21\\n50 48\\n301\u00c2\u00b0 00\\n301 39\\n302 16\\n301 36\\n0.58\\n0.57\\n0.58\\n0.58\\nRetrograde.\\nRetrograde.\\nRetrograde.\\nRetrograde.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0285.jp2"}, "286": {"fulltext": "262 COMETS.\\nOn comparing these elements, no doubt could be entertained\\nthat they belonged to one and the same body and since the\\ninterval 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 was found,\\nhowever, that on its way toward the sun it would pass very\\nnear to Jupiter and Saturn, and by their action on it, would\\nbe retarded for a long time. Clair aut, a distinguished French\\nmathematician, undertook the laborious task of estimating the\\nexact amount of this retardation, and found it to be no less\\nthan 618 days, namely, 100 days by the action of Jupiter, and\\n518 days by that of Saturn. This would delay its appearance\\nuntil early in the year 1759, and Clairaut fixed its arrival at\\nthe perihelion within a month of April 13th. It came to the\\nperihelion on the 12th of March.\\n401. The return of Halley s comet in 1835 was looked for\\nwith no less interest than in 1759. Several of the most accu-\\nrate mathematicians of the age had calculated its elements\\nwith inconceivable labor. Their zeal was rewarded by the\\nappearance of the expected visitant at the time and place\\nassigned it traversed the northern sky, presenting the very\\nappearances, in most respects, that had been anticipated and\\ncame to its perihelion on the 16th of November, within one\\nday of the time predicted by Pontecoulant, a French mathe-\\nmatician, who had, it appeared, made the most successful cal-\\nculation.* On its previous return, it was deemed an extraor-\\ndinary achievement to have brought the prediction within a\\nmonth of the actual time.\\nMany circumstances 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\\nof astronomy and it inspired new confidence in the power of\\nSee Professor Loomis s Observations on Halley s Comet, Amer. Journ. Science,\\nxxx., 209. Pontecoulant s Phys. Celeste Precis, p. 586.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0286.jp2"}, "287": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 263\\nthat instrument (the Calculus) by means of which its elements\\nhad been investigated.\\n402. Encke s comet, by its frequent returns, affords pecu-\\nliar facilities for ascertaining the laws of its revolution and it\\nhas kept the appointments made for it with great exactness.\\nOn its return in 1839, it exhibited to the telescope a globular\\nmass of nebulous matter resembling fog, and moved toward its\\nperihelion with 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\\nthe earth and planets revolve in a perfect void, or whether a\\nfluid of extreme rarity may not be diffused through space. A\\nperfect vacuum was deemed most probable, because no such\\neffects on the motions of the planets could be detected as indi-\\ncated that they encountered a resisting medium. But a feather\\nor a lock of cotton, propelled with great velocity, might render\\nobvious the resistance of a medium which would not be per-\\nceptible in the motions of a cannon-ball. Accordingly, Encke s\\ncomet is thought to have plainly suffered a retardation from\\nencountering a resisting medium in the planetary regions.\\nThe effect of this resistance, from the first discovery of the\\ncomet to the present time, has been to diminish the time of its\\nrevolution about two days. Such a resistance, by destroying\\npart of tha projectile force, would cause the comet to approach\\nnearer to the sun, and thus to have its periodic time shortened.\\nThe ultimate effect of this cause will be to bring the comet\\nnearer to the sun at every revolution, until it finally falls into\\nthat luminary, although many thousand years will be required\\nto produce this catastrophe.* It is conceivable, indeed, that\\nthe effects of such a resistance may be counteracted by the at-\\ntraction of one or more of the planets near which it may pass\\nin its successive returns to the sun. It is peculiarly interesting\\nto see a portion of matter of a tenuity exceeding the thinnest\\nfog, pursuing its path in space, in obedience to the same laws\\nas those which regulate such large and heavy bodies as Jupiter\\nHalley s comet, at its return in 1835, did not appear to be affected by the\\nsupposed resisting medium, and its existence is considered as still doubtful.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0287.jp2"}, "288": {"fulltext": "264 COMETS.\\nor Saturn. In a perfect void, a speck of fog, if propelled by a\\nsuitable projectile force, would revolve around the sun, and\\nhold on its way through the widest orbit, with as sure and\\nsteady a pace as the heaviest and largest body in the system.\\n403. The most remarkable comet of the present century\\nhitherto observed, was the great comet of 1843. (See Plate I.\\nat the end of the volume.) On the 28th of February of that\\nyear, the attention of numerous observers in various parts of\\nthe world was arrested by a comet seen in the broad light of\\nday, a little eastward of the sun. In Mexico it was observed,\\nand its altitude repeatedly measured with a sextant, from nine\\nin the morning until sunset. In New England, it was seen at\\nseveral places from half-past seven in the morning until after\\nthree in the afternoon, when the sky became obscured by hazi-\\nness and clouds. Accurate measures were taken by Capt.\\nClark, at Portland, Maine, of the distance of the nucleus from\\nthe sun s limb. At 3h. 2m. 15s. mean time, the distance of the\\nsun s furthest limb from the nearest limb of the nucleus was\\n4\u00c2\u00b0 6 15 The comet resembled a white cloud of great density,\\nbeing nearly equally shining throughout, with a nucleus as\\nbright as the full moon at midnight in a clear sky. During\\nthe first week in March, the appearance of this body was\\nsplendid and magnificent, enhanced in both respects by the\\ntransparency of a tropical sky, and the higher angle of eleva-\\ntion above that at which it was seen by northern observers.\\nAt ISTew Haven, it was first seen after sunset, on the 5th. of\\nMarch. It then lay far in the southwest. On account of the\\npresence of the moon, it was not seen most favorably until the\\nevening 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 ap-\\npearance on the 20th of March. All the astronomers of the\\nage have agreed in the opinion that this is one of the most re-\\nmarkable exhibitions of a comet ever witnessed, although they", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0288.jp2"}, "289": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 265\\nare not fully agreed respecting the elements of its orbit, or its\\nperiodic time. Its elements resemble those of the comet of\\n1688, which would give a period of 175 years and to this pe-\\nriodic time, authority at present inclines but Prof. Hubbard,\\nof the Washington Observatory, after an elaborate discussion\\nof all the observations, thinks the most probable period 170\\nyears.\\nOf all the comets on record, the great comet of 1843 ap-\\nproached nearest to the sun. It came within about 60,000\\nmiles of his luminous surface, or only about one-fourth of the\\ndistance of the moon from the earth. It will be recollected\\nthat to a spectator on the earth the sun s angular diameter but\\na little exceeds half a degree but were we to approach as near\\nto the sun as this body did in its perihelion, that diameter\\nwould appear no less than 121\u00c2\u00b0 32 and the light and heat\\n(which increase as the square of the distance is diminished)\\nwould be 47,000 times as great as at present, the heat exceed-\\ning nearly twenty-five times that produced by Parker s great\\nburning lens, although this instrument is capable of producing\\neffects beyond those of the most powerful blast-furnace. The\\nvelocity of the comet was still more astonishing, being at the\\nrate of more than one and a quarter million of miles per hour,\\na velocity sufficient to carry it through 180\u00c2\u00b0, or half round the\\nsun, in two hours. f\\nAn interesting comet appeared in 1858, called the comet of\\nDonati, who first saw it at Florence, June 2d. It continued in\\nsight till Oct. 15th. Its tail, when at perihelion, Oct. 10th,\\nwas 60\u00c2\u00b0 long. Its nucleus was uncommonly bright, and be-\\nyond it, in the axis of the envelope and tail was a dark, straight\\nline, like a shadow. The long period of its visibility gave un-\\nusual opportunity for careful observations. Its periodic time is\\nvariously estimated, from 1,620 to 2,495 years.J\\n404. Of the physical nature of comets, little is understood.\\nIt is usual to account for the variations which their tails un-\\nSee American Almanac for 1844, p. 94. Amer. Journal of Science, xlv.,\\np. 188. Astronomical Journal, vol. ii., p. 156.\\nHerschel s Outlines, p. 318.\\nSee Bond s Account of Donati s Comet, with fine illustrations, in Math.\\nMonthly, Dec, 1853.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0289.jp2"}, "290": {"fulltext": "266 COMETS.\\ndergo by referring them to the agencies of heat and cold. The\\nintense heat to which they are subject in approaching so near\\nthe sun as some of them do, is alleged as a sufficient reason for\\nthe great expansion of the thin nebulous atmospheres forming\\ntheir tails and the inconceivable cold to which they are sub-\\nject in receding to such a distance from the sun, is supposed to\\naccount for the condensation of the same matter until it returns\\nto its original dimensions. The temperature experienced by\\nthe comets of 1680 and 1813 at their perihelion, would be suf-\\nficient to volatilize the most obdurate substances, and to ex-\\npand the vapor to vast dimensions and the opposite effects\\nof the extreme cold to which it would be subject in the re-\\ngions remote from the sun, would be adequate to condense it\\ninto 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\\nto the sun. Some writers, therefore, as Delambre,* suppose\\nthat the nebulous matter of the comet, after being expanded\\nto such a volume that the particles are no longer attracted to\\nthe nucleus unless by the slightest conceivable force, is carried\\noff in a direction from the sun by the impulse of the solar rays\\nthemselves. Others conceive of a force of repulsion, independ-\\nent of any mechanical impulse emanating from the sun. But\\nto assign such a power of communicating motion to the sun s\\nrays while they have never been proved to have any momen-\\ntum, or to a repulsive force which has no independent. proof\\nof its existence, is unphilosophical and we are compelled to\\nplace the phenomena of comets tails among the points of as-\\ntronomy yet to be explained.-)*\\n405. Since those comets which have their perihelion very\\nnear the sun, like the comet of 1680, cross the orbits of all the\\nplanets, the possibility that one of them may strike the earth,\\nhas frequently been suggested. Still, it may quiet our apprehen-\\nsions on this subject, to reflect on the vast extent of the planet-\\nary spaces, in which these bodies are not crowded together as\\n5 5 Delambre s Astronomy, t. iii., p. 401.\\nf Prof. Norton on the Formation of Comets Tails, (Amer. Journal,\\nxlvii., p. 104).", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0290.jp2"}, "291": {"fulltext": "METEORIC SHOWERS. 267\\nwe see tliein* erroneously represented in orreries and diagrams,\\nbut are sparsely scattered at immense distances from each\\nother. They are like insects flying in the expanse of heaven.\\nIf a comet s tail lay with its axis in the plane of the eclip-\\ntic when it was near the sun, we can imagine that the tail\\nmight sweep over the earth but the tail may be situated at\\nany angle with the ecliptic as well as in the same plane with\\nit, and the chances that it will not be in the same plane are\\nalmost infinite. It is also extremely improbable that a comet\\nwill cross the plane of the ecliptic precisely at the earth s path\\nin that plane, since it may as probably cross it at any other\\npoint nearer or more remote from the sun. Still, some comets\\nhave occasionally approached near to the earth. Thus Biela s\\ncomet, in returning to the sun in 1832, crossed the ecliptic very\\nnear to the earth s track, and had the earth been then at that\\npoint of its orbit, it might have, passed through a portion of\\nthe nebulous atmosphere of the comet. The earth was within\\na month of reaching that point. This might at first view seem\\nto involve some hazard yet we must consider that a month\\nshort implied a distance of nearly 50,000,000 miles. Laplace\\nhas assigned the consequences that would ensue in case of a di-\\nrect collision between the earth and a comet but terrible as\\nhe has represented them on the supposition that the nucleus of\\nthe comet is a solid body, yet considering a comet (as most of\\nthem doubtless are) as a mass of exceedingly light nebulous\\nmatter, it is not probable, even were the earth to make its way\\ndirectly through a comet, that a particle of the comet would\\nreach the earth. The portions encountered by the earth, would\\nbe arrested by the atmosphere, and probably inflamed and\\nthey would perhaps exhibit, on a more magnificent scale than\\nwas ever before observed, the phenomena of shooting stars or\\nmeteoric showers.\\nMETEORIC SHOWERS.\\n406. The remarkable exhibitions of shooting stars which\\nhave occurred within a few years past, have excited great in-\\nterest among astronomers, and led to some new views respect-\\ning the construction of the solar system. Their attention was\\n8 Syst. du Monde, 1. iv. T c. 4.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0291.jp2"}, "292": {"fulltext": "268 METEORIC SHOWERS.\\nfirst turned toward this subject by the great meteoric shower\\nof November 13, 1833, On that morning, from two o clock\\nuntil broad daylight, the sky being perfectly serene and cloud-\\nless, the whole heavens were lighted with a magnificent dis-\\nplay of celestial fireworks. Numerous bright bodies, which\\nmight be compared with stars of the largest magnitudes, and\\nwith planets, were darting toward the earth on all sides, describ-\\ning arcs of great circles, of all lengths from 70\u00c2\u00b0 to less than a\\nsingle degree. In many cases, they left long trains of light in\\ntheir paths, which lasted a few seconds and occasionally, when\\na meteor of unusual brightness descended, the train of light con-\\ntinued for minutes. The light which some of them shed was\\nequal to that of the moon at the quarter. The whole number\\nseen at any one place of observation could not have been less\\nthan 200,000.\\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\\nrepetition of the meteoric shower of November, the radiant\\npoint has occupied nearly the same situation.\\nThis shower pervaded nearly the whole of North America,\\nhaving appeared in almost equal splendor from the British\\npossessions on the north, to the West India Islands and Mexico\\non the south, and from sixty-one degrees of longitude east of\\nthe American coast, quite to the Pacific ocean on the west.\\nThroughout this immense region the duration was nearly the\\nsame. The meteors began to attract attention by their un-\\nusual frequency and brilliancy, from nine to twelve o clock in\\nthe evening were most striking in their appearance from two\\nto four y arrived at their maximum, in many places, about\\nfour o clock and continued until rendered invisible by the\\nlight of day. The meteors moved in right lines, or in such\\napparent curves, as, upon optical principles, can be resolved\\ninto right lines. Their general tendency was toward the north-\\nwest, although by the effect of perspective they appeared to\\nmove in all directions.\\n407. Soon after this occurrence, it was ascertained that a\\nsimilar meteoric shower had appeared in 1799, and what was", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0292.jp2"}, "293": {"fulltext": "METEORIC SHOWERS. 269\\nremarkable, almost exactly at the same time of the year, name-\\nly, on the morning of the 12th of November; and it soon ap-\\npeared, by accounts received from different parts of the world,\\nthat this phenomenon had occurred on the same 13th of No-\\nvember, in 1830, 1831, and 1832. Hence, this was evidently\\nan event independent of the casual changes of the atmosphere\\nfor, having a periodical return, it was undoubtedly to be re-\\nferred to astronomical causes, and its recurrence, at a certain\\ndefinite period of the year, plainly indicated some relation to\\nthe revolution of the earth around the sun.\\nIt remained, however, to develop the nature of this relation,\\nby investigating, if possible, the origin of the meteors. The\\nviews to which the author of this work was led, suggested the\\nprobability that the same phenomenon would recur at the\\ncorresponding seasons of the year for at least several years\\nafterward and such proved to be the fact, although the\\nappearances, at every succeeding return, were less and less\\nstriking, until 1839, when, so far as is known, they ceased\\naltogether.\\nMeanwhile, three other distinct periods of meteoric showers\\nhave also been determined one on the 9th of August, and\\n(more rare) on the 21st of April and 7th of December respect-\\nively.\\n408. The following conclusions respecting the meteoric\\nshower of November, are believed to be well established, and\\nmost of them are now generally admitted by astronomers,\\nthough we can not here exhibit the evidence on which they\\nwere founded.*\\nIt is considered, then, as established, that the periodical\\nmeteors of November (and most of the conclusions apply\\nequally to those of August) have their origin beyond the\\natmosphere, descending to us from some body (which, from\\nthe known constitution of the meteors, may be called a nebu-\\nlous body) with which the earth falls in, and near or through\\nthe borders of which it passes that this body has an inde-\\npendent existence as a member of the solar system, its periodic\\nWe beg leave to refer the reader to various publications on the subject, by\\nthe author and others, in the American Journal of Science, commencing with the\\n25th volume and also to Letters on Astronomy, by the author of this work.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0293.jp2"}, "294": {"fulltext": "270 METEORIC SHOWERS.\\ntime being nearly commensurable with the earth s, either a\\nyear or half a year, so that for a number of years in succession\\nthe two bodies meet near the same part of the earth s orbit.\\nTt is further established, that the meteors consist of light com-\\nbustible matter; that they move with great velocities, amount-\\ning, in some instances, to not less than that of the earth in\\nits orbit, or 19 miles per second that some of them are bodies\\nof large size, sometimes several thousand feet in diameter\\nthat when they enter the atmosphere, they rapidly and power-\\nfully condense the air before them, and thus elicit the heat\\nthat sets them on fire, as a spark is elicited in the air-match,\\nby being suddenly condensed by means of a piston and cylin-\\nder and that they are burned up at a considerable height\\nabove the earth, sometimes not less than 30 miles.\\n409. Calling the body from which the meteors descended\\nthe meteoric body, it is inferred that it is a body of great\\nextent, since, without apparent exhaustion, it has been able to\\nafford such copious showers of meteors at so many different\\ntimes and hence we regard the part that has descended to the\\nearth only as the extreme portions of a body or collection of\\nmeteors, of unknown extent, existing in the planetary spaces.\\nSince the earth fell in with the meteoric body, in the same\\npart of its orbit for several years in succession, the body must\\neither have remained there while the earth was performing its\\nwhole revolution around the sun, or it must itself have had a\\nrevolution, as well as the earth. No body can remain station-\\nary within the planetary spaces for, unless attracted to some\\nnearer body, it would be drawn directly toward the sun, and\\ncould not have been encountered by the earth again in the\\nsame part of her orbit. E or can any mode be conceived in\\nwhich this event could have happened so many times in regu-\\nlar succession, unless the body had a revolution of its own\\naround the sun. Finally, to have come into contact with the\\nearth at the same part of her orbit, in two or more successive\\nyears, the body must have a period which is either nearly the\\nsame with the earth s period, or some aliquot part of it. ~No\\nperiod will fulfil these conditions, but either a year or half a\\nyear. Which of these is the true period of the meteoric body,\\nis not fully determined.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0294.jp2"}, "295": {"fulltext": "PART III. -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,\\nit has 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\\nvery definite scale, but are merely ranked according to their\\nrelative degrees of brightness, and this is left in a great meas-\\nure to the decision of the eye alone, although it would appear\\neasy to measure the comparative degree of light in a star by a\\nphotometer, and upon such measurement to ground a more\\nscientific classification of the stars. The brightest stars to the\\nnumber of 15 or 20 are considered as stars of the first magni-\\ntude the 50 or 60 next brightest, of the second magnitude\\nthe next 200 of the third magnitude and thus the number of\\neach class increases rapidly as we descend the scale, so that no\\nless than fifteen or twenty thousand are included within the\\nfirst seven magnitudes.\\n411. The stars have been grouped in Constellations from\\nthe most remote antiquity a few, as Orion, Bootes, and Ursa\\nMajor, are mentioned in the most ancient writings under the\\nsame names as they bear at present. The names of the con-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0295.jp2"}, "296": {"fulltext": "272 FIXED STARS.\\nstellations are sometimes founded on a supposed resemblance\\nto the objects to which the names belong; as the Swan and\\nthe Scorpion were evidently so denominated from their like-\\nness to those animals but in most cases it is impossible for us\\nto find any reason for designating a constellation by the figure\\nof the animal or the hero which is employed to represent it.\\nThese representations were probably once blended with the\\nfables of pagan mythology. The same figures, absurd as they\\nappear, are still retained for the convenience of reference\\nsince it is easy to find any particular star, by specifying the\\npart of the figure to which it belongs, as when we say a star is\\nin the neck of Taurus, in the knee of Hercules, or in the tail of\\nthe Great Bear. This method furnishes a general clue to its\\nposition but the stars belonging to any constellation are dis-\\ntinguished according to their apparent magnitudes, as follows\\nfirst, by the Greek letters, Alpha, Beta, Gamma, e. Thus a\\nOnonis, denotes the largest star in Orion, (3 Andromeda?, the\\nsecond star in Andromeda, and y Zeonis, the third brightest\\nstar in the Lion. Where the number of the Greek letters is\\ninsufficient to include all the stars in a constellation, recourse\\nis had to the letters of the Roman alphabet, a, b, c, c. and\\nin cases where these are exhausted, the final resort is to num-\\nbers. This is evidently necessary, since the largest constella-\\ntions contain many hundreds or even thousands of stars. Cat-\\nalogues of particular stars have also been published by different\\nastronomers, each author numbering the individual stars em-\\nbraced in his list, according to the places they respectively\\noccujyy in the catalogue. These references to particular cata-\\nlogues are sometimes entered on large celestial globes. Thus\\nwe meet with a star marked 84 H., meaning that this is its\\nnumber in Herschel s catalogue, or 140 M., denoting the place\\nthe star occupies in the catalogue of Mayer.\\n412. The earliest catalogue of the stars was made by Hip-\\nparchus, 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\\nthat posterity might be able to judge of the permanency of the\\nconstellations. His catalogue contains all that were conspicu-\\nous to the naked eve in the latitude of Alexandria, being 1,022.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0296.jp2"}, "297": {"fulltext": "CONSTELLATIONS. 273\\nMost persons unacquainted with the actual number of the stars\\nwhich compose the visible firmament, would suppose it to be\\nmuch greater than this but it is found that the catalogue of\\nHipparchus embraces nearly all that are easily seen in the same\\nlatitude, and that on the equator, where the spectator has the\\nnorthern and southern hemispheres both in view, the number\\nof stars that can be counted does not exceed 3000. A hasty\\nglance over the sky gives us the impression of a countless mul-\\ntitude of stars but the greater part vanish as soon as we try\\nto number them. This is owing to the indirect vision of\\nthousands of faint stars, which are unseen as soon as we turn\\nthe axes of the eyes directly upon them.\\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\\nof the most remarkable individual stars. The task of learning\\nthem is comparatively easy, when they are taken up at suitable\\nintervals throughout the year, the moon being absent and the\\nsky clear. After becoming familiar with such constellations\\nas are visible on any given evening (suppose the first of Jan-\\nuary), these may be carefully reviewed after an interval of a\\nmonth, and the several new ones added which have in the\\nmean time risen above the eastern horizon. By repeating this\\nprocess near the beginning of every month of the year, the\\nlearner will acquire a competent knowledge of the whole that\\nare visible in his latitude, and with a small expenditure of time.\\nIt may at first be advisable to obtain, for an evening or two.\\nthe assistance of some one who is acquainted with the constel-\\nlations, to point out such as are then visible in the evening sky.\\nThen, by the aid of a celestial map, or, what is better, a celes-\\ntial globe, the learner will pursue the study without difficulty.\\nWe begin by rectifying the globe for the time, according to the\\ndirections given in Article 76.\\nIn the following sketch of the leading constellations, we will\\nis", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0297.jp2"}, "298": {"fulltext": "274 FIXED STARS.\\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 Oi\\nglobe, one of which, indeed, is presumed to be before him.*\\nLet us begin with the constellations of the Zodiac, which,\\nsucceeding each other as they do in a known order, are most\\neasily found.f\\nAries (the Ram), the first constellation of the Zodiac, is\\nknown by two bright stars, Alpha (a) on the northeast, and\\nBeta (|3) on the southwest, 4\u00c2\u00b0^: apart, forming the head. South\\nof Beta, at the distance of 2\u00c2\u00b0, is a smaller star, Gamma (y).\\nThe next brightest star of the Ram, Delta ((5), is in the tail,\\n15\u00c2\u00b0 southeast of Alpha. The feet of the figure rest on the\\nhead of the Whale. It has been already intimated (Art. .193),\\nthat the vernal equinox was near the head of Aries, when the\\nsigns of the Zodiac received their present names, but that the\\nequinox is now found 30\u00c2\u00b0 westward of a Arietis, in consequence\\nof the precession of the equinoxes.\\nTaurus (the Bull) will be readily found by the seven 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 red-\\ndish color, and resembles the planet Mars. The other eye of\\nA celestial globe, sufficient for studying the constellations, may be purchased\\nfor a small sum, and is, in other respects, a valuable possession to the astronom-\\nical student but even cheap maps of the stars, like those of Burritt or Kendal,\\nwill answer for beginners and the Celestial Atlas, published by the Society for\\nthe Diffusion of Useful Knowledge, which is suitable for the more advanced\\nstudent, may 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 equi-\\nnoxes and at the solstices, according to the directions given in the closing article\\nof this chapter.\\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 es-\\ntimate with the eye of distances in degrees on the celestial sphere and he may,\\nat the outset, fix on the distance between Alpha and Beta Arietis as a standard\\nmeasure (4\u00c2\u00b0) by which to estimate other angular distances among the stars.\\nThus, half this length applied from Beta to Gamma, indicates that the two latter\\nstars are 2\u00c2\u00b0 apart and two and a half times the same measure (10\u00c2\u00b0) will reach\\nfrom the Pleiades to Aldebaran. Or the Pointers in the Great Bear will furnish\\na measure of 5\u00c2\u00b0.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0298.jp2"}, "299": {"fulltext": "CONSTELLATIONS. 275\\nthe figure is EpsRon (e), 3\u00c2\u00b0 northwest of Aldebaran. Five small\\nstars, situated a little west of Aldebaran, in the face of the\\nBull, constitute the Hyade-s. Although the Pleiades are usually\\ndenominated the seven stars, jet it has been remarked, from a\\nhigh antiquity, that only six are present.\\nQuse 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\\nWith a moderate telescope, not less than 50 or 60 stars, of con-\\nsiderable brightness, may be counted in this group, and a much\\nlarger number of very small stars are revealed to the more\\npowerful telescopes. The beautiful allusion, in the book of\\nJob, to the sweet influences of the Pleiades, and the special\\nmention made of this group by Homer and Hesiod, show how\\nearly it had attracted the attention of mankind. The horns of\\nthe Bull are two stars, Beta and Zeta, situated 25\u00c2\u00b0 east of the\\nPleiades, being 8\u00c2\u00b0 apart. The northern horn, Beta, also forms\\none of the feet of Auriga, the Charioteer.\\nGemini (the Twins) is represented by two well-known stars,\\nCastor and Pollux, in the head of the figure, 5\u00c2\u00b0 asunder.\\nCastor, the northern, is of the first, and Pollux of the second\\nmagnitude. Four conspicuous stars, extending in a line from\\nsouth to north, 25\u00c2\u00b0 S. W. of Castor, form the feet, and two\\nothers, parallel to these at the distance of six or seven degrees\\nnortheastward, are in 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\\nthe Zodiac. The two most conspicuous stars, Alpha and Beta,\\nare in the southern claws of the figure, and in its body are the\\nnorthern and southern Asellus, which may be readily found\\non a celestial globe. But the most remarkable object in this\\nconstellation is a misty group of very small stars, so close to-\\ngether, when seen by the naked eye, as to resemble a comet,\\nTheir names were Electra, Maia, Taygeta, Alcyone, Celreno. Asterope, and\\nMerope, the last being the Lost Pleiad of the poets. Alcyone, according to\\na recent celebrated hypothesis, is distinguished as the center around which the\\nstarry host revolve.\\nf Smyth s Cycle, ii., p. 86.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0299.jp2"}, "300": {"fulltext": "276 FIXED STARS.\\nbut easily separated by the telescope into a beautiful collection\\nof brilliant points. 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\\nwest to east along the Zodiac, over more than 40\u00c2\u00b0 of longi-\\ntude, all parts of the figure excepting the feet lying north of\\nthe ecliptic.\\nYirgo (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,\\nis a star of the first magnitude, and lies a little east of the ver-\\nnal equinox. Vindemiatrix, in the arm of Yirgo, 18\u00c2\u00b0 east of\\nDenebola, and 23\u00c2\u00b0 north of Spica, is easily found, and directly\\nsouth of Denebola 13\u00c2\u00b0, is (3 Virginis while four other conspic-\\nuous stars, in the form of a trapezium, between this and Yin-\\ndemiatrix, lie in the wing and shoulders of the figure. The\\nfeet are near the Balance.\\nLibra (the Balance) is composed of a few scattered mem-\\nbers situated between the feet of Yirgo and the head of Scor-\\npio, but has no very distinctive marks. Two stars of the\\nsecond magnitude, Alpha on the south, and Beta 8\u00c2\u00b0 northeast\\nof Alpha, together with a few smaller stars, form the scales.\\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 com-\\nposed of five stars, arranged in a line slightly curved, which is\\ncrossed in the center by the ecliptic, nearly at right angles, a\\ndegree south of the brightest of the group (3 Scorpionis. Nine\\ndegrees southeast of this is a remarkable star of the first mag-\\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\\nstars composing this figure, beginning with Reguius, are a, n, y, n, e.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0300.jp2"}, "301": {"fulltext": "CONSTELLATIONS. 277\\nnitude, called Antares, and sometimes the Heart of the Scor-\\npion (Cor Scovpioms). It is of a red color, resembling the\\nplanet Mars. South and east of this, a succession of not less\\nthan nine bright stars sweep round in a semicircle, terminating\\nin several small stars forming the sting of the Scorpion. The\\ntail of the figure extends into the Milky Way.\\nSagittarius (the Aechee). Ten degrees eastward of the\\nScorpion s tail, on the eastern margin of the Milky Way, we\\ncome to the bow of Sagittarius, consisting of three stars about\\n6\u00c2\u00b0 apart, the middle one being the brightest, and situated in\\nthe bend of the bow, while a fourth star, 4\u00c2\u00b0 westward of it,\\nconstitutes the arrow. The archer is represented by the figure\\nof a Centaur (half horse and half man), and proceeding about\\nten degrees east from the bow, we come to a collection of seven\\nor eight stars of the second and third magnitudes, which lie in\\nthe human or upper part of the figure.\\nCapeicoenus (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 con-\\nstellation. Two stars of the second magnitude, a on the north,\\nand /3 on the south, 3\u00c2\u00b0 apart, constitute the head of Caprieor-\\nnus, while a collection of stars of the third magnitude, lying\\n20\u00c2\u00b0 southeast of these form the tail.\\nAquaeics (the Watee Beasee) is closely in contact with\\nthe tail of Capricornus, immediately north of which, at the\\ndistance of 10\u00c2\u00b0, is the western shoulder (/I), and 10\u00c2\u00b0 further\\neast is the eastern shoulder (a) of Aquarius. About 3\u00c2\u00b0 south-\\neast of a is y Aquarii, which, together with the other two,\\nmakes an acute triangle, of which fi forms the vertex. In the\\neastern arm of Aquarius are found four stars, which together\\nmake the figure Y, the open part being westward, or toward\\nthe shoulders of the constellation. Aquarius ranges nearly\\n30\u00c2\u00b0 from north to south, being 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, com-\\npose this constellation. The Southern Fish, Piseis Austral is,\\notherwise called Fomalhaut, lies directly below the feet of\\nAquarius, and being the only conspicuous star in that part of\\nthe heavens, is much used in astronomical measurements. It\\nis 30\u00c2\u00b0 south of the equator.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0301.jp2"}, "302": {"fulltext": "278 FIXED STAES.\\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,\\nwhich is one of the northern members of the constellation\\nPisces and far to the northeast of this figure, north of the\\nhead of Aries, lies the third member, the three being repre-\\nsented as connected together by a -ribbon, or wavy band, com-\\nposed of minute stars.\\n414. The Constellations of the Zodiac being first well\\nlearned, so as to be readily recognized, will facilitate the learn-\\ning of others that lie north and south of them. Let us there-\\nfore next review the principal Northern Constellations, begin-\\nning at the North Pole.\\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\\nhalf of the North Pole of the heavens, it serves at present to\\nindicate the position of the pole. It will be recollected, how-\\never, that on account of the precession of the equinoxes, the\\npole of the heavens is constantly shifting its place from east to\\nwest, revolving about the pole of the ecliptic, and will in time\\nrecede so far from the pole-star, that this will no longer retain\\nits present distinction (Art. 190). Three stars in a straight\\nline, 4\u00c2\u00b0 or 5\u00c2\u00b0 apart, commencing with Polaris, lead to a trape-\\nzium of four stars, the whole seven together forming the figure\\nof a dipper, the trapezium being the body, and the three first-\\nmentioned stars being the handle.\\nUrsa Major (the Great Bear) is one of. the largest and\\nmost celebrated of the constellations. It is usually recognized\\nby the figure of a larger and more perfect dipper than the one\\nin the Little Bear three stars, as before, constituting the han-\\ndle, and four others, in the form of a trapezium, the body of\\nthe figure. The two western stars of the trapezium, ranging\\nnearly with the North Star, are called the Pointers and be-\\nginning with the northern of these two, and following round\\nfrom left to right through the whole seven, they correspond in\\nrank to the succession of the first seven letters of the Greek\\nalphabet, Alpha. Beta, Gamma, Delta, Epsilon, Zeta, Eta.\\nSeveral of them also are known by their Arabic names. Thus,\\nthe first in the tail, corresponding to Epsilon, is Alioth, the", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0302.jp2"}, "303": {"fulltext": "CONSTELLATIONS. 279\\nnext (Zeta) Mizar, and the last (Eta) Benetnasch. These are\\nall bright and beautiful stars, Alpha being of the first magni-\\ntude; Beta, Gamma, Delta, of the second; and the three form-\\ning the tail, of the third. But it must be remarked that this\\nvery remarkable figure of a dipper or ladle composes but a\\nsmall part of the entire constellation, being merely the hinder\\nhalf of the body and the tail of the Bear. The head and breast\\nof the figure, lying about ten or twelve degrees west of the\\nPointers, contain a great number of minute stars in a triangu-\\nlar 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\\npaws consisting each of two stars very similar in appearance,\\nand only a degree and a half apart. The two paws are distant\\nfrom each other about 18\u00c2\u00b0 and following westward about the\\nsame number of degrees, we come to another very similar pair\\nof stars, which constitute one of the fore paws, the other foot\\nbeing without any corresponding pair.\\nIn a clear winter s night, when the whole constellation is\\nabove the pole, these various parts may be easily recognized,\\nand the entire figure will be seen to resemble a large animal,\\nreadily accounting for the name given to this constellation\\nfrom the earliest ages.\\nDeaco {the Deagon) is also a very large constellation, ex-\\ntending for a great length from east to west. Beginning at\\nthe tail which lies half way between the Pointers and the Pole-\\nstar, and winding round between the Great and the Little\\nBear, by a continued succession of bright stars from 5\u00c2\u00b0 to 10\u00c2\u00b0\\nasunder, it coils around under the feet of the Little Bear,\\nsweeps round the pole of the ecliptic, and terminates in a\\ntrapezium formed by four conspicuous stars, from thirty to\\nthirty-five degrees from the North Pole. A few of the mem-\\nbers of this constellation are of the second, but the greater part\\nof the third magnitude, and below it.\\n415. With the constellations already described as general\\nlandmarks, we may now proceed with each of the principal\\nremaining ones, by stating its boundaries, as we do those of\\ncountries in geography their relative situations being thus\\nfirst learned from a ma}), or (what is better) from a celestial", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0303.jp2"}, "304": {"fulltext": "280 FIXED STARS.\\nglobe, and then being severally traced out on the sky itself.\\nWe will begin with those which 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\\nhead lies in the Milky Way, and the feet extend toward the\\npole. It 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 constella-\\ntions of the Milky Way. It is readily distinguished by the\\nfigure of a chair inverted, of which two stars constitute the\\nback, and four, in the form of a square, the body of the chair.\\nIt is on the opposite side of the pole from the Great Bear, and\\nnearly at the same distance from it.\\nCamelopardalus (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 oc-\\ncupies a large space, yet it has no conspicuous stars.\\nAndkomeda is bounded N. by Cassiopeia, E. by Perseus, S.\\nby Pegasus, and W. by the Lizard. The direction of the figure\\nis from S. W. to N. E., the head coming down within 30\u00c2\u00b0 of\\nthe equator, and being recognized by a star of the second mag-\\nnitude, which forms the northeastern corner of the great square\\nin Pegasus, to be described hereafter. At the distance of six\\nor seven degrees from the head, are three conspicuous stars in\\na row, ranging from north to south, which lie in the breast of\\nthe figure and about the same distance from these, and par-\\nallel to them, three more, which constitute the girdle of An-\\ndromeda. Near the northernmost of the three, is a faint,\\nmisty object, often mistaken for a comet, but is a nebula, and\\none of the most remarkable in the heavens.\\nPekseus is bounded 1ST. by Cassiopeia, E. by Auriga, S. by\\nTaurus, and W. by Andromeda. The figure extends from\\nnorth to south, and is represented by a giant holding aloft a\\nsword in his right hand, while his left grasps the head of Me-\\ndusa, a group of stars on the western side of the figure, em-\\nbracing the celebrated star Algol. A series of bright stars de-\\nscend along the shoulders and the waist, and there divide into\\nthe two legs. The western foot is 8\u00c2\u00b0 degrees north of the\\nPleiades. The eastern leg is bent at the knee, which is distin-\\nguished by a group of small stars. Near the sword handle,", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0304.jp2"}, "305": {"fulltext": "CONSTELLATIONS. 281\\nunder Cassiopeia s chair, is a fine cluster of stars, so close to-\\ngether as scarce to be separable by the eye.\\nAuriga (the Wagoner) is bounded 1ST. 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 Cajpella,\\na white and beautiful star of the first magnitude, (a Aurigse),\\nwhile Beta forms the right shoulder, S\u00c2\u00b0 east of Capella. These\\ntwo bright stars form, with the northern horn of the Bull, at\\nthe distance of 18\u00c2\u00b0, an isosceles triangle.\\nLeo Minor (the Lesser Lton) is bounded !N by Ursa Ma-\\njor, E. by Coma Berenices, S. by Leo, and W. by the Lynx.\\nIt lies directly under the hind feet of the Great Bear, and over\\nthe sickle in Leo, and is easily distinguished. Four stars in\\nthe central part of the figure, from 4\u00c2\u00b0 to 5\u00c2\u00b0 apart, form a pretty\\nregular parallelogram.\\nCanes Yenatici (the Greyhounds). This constellation lies\\nbetween the hind legs of the Great Bear on the west, and\\nBootes on the east Cor Caroli, a solitary star of the third\\nmagnitude, 18\u00c2\u00b0 south of Alioth, in the tail of the Great Bear,\\nwill serve to mark this constellation.\\nComa Berenices (Berenice s Hair) is a cluster of small\\nstars, composing a rich group, 15\u00c2\u00b0 N. E. of Denebola, in the\\nLion s tail, in a line between this star and Cor Caroli, and half\\nway between 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\\nand the Hounds. It reaches for a great distance from north to\\nsouth, the head being within 20\u00c2\u00b0 of the Dragon, and the feet\\nreaching to the Zodiac. In the knee of Bootes is Arcturus, a\\nstar of the first magnitude. The next brightest star, Beta, is\\nin the head of Bootes, 23\u00c2\u00b0 north of Arcturus, and 15\u00c2\u00b0 east of\\nthe last star in the tail of the Great Bear.\\nCorona Borealis (the Northern Crown) is bounded N.\\nand E. by Hercules, S. by the head of Serpentarius, and W. by\\nBootes. It is formed of a semicircle of bright stars, six in\\nnumber, of which Gemma, near the center of the curve, is of\\nthe second magnitude.\\nHercules is bounded N by Draco, E. by Lyra, S. by Ophi-\\nuchus, and W. by Corona Borealis. It is a very large constel-\\nlation, and contains some brilliant objects for the telescope, al-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0305.jp2"}, "306": {"fulltext": "282 FIXED STARS.\\nthough its components are generally very small. The figure\\nlies north and south, with the head near the head of Ophiu-\\nchus, and the feet under the head of Draco. Being between\\nthe Crown and the Lyre, its locality is easily determined. The\\neastern foot of Hercules forms an isosceles triangle with the two\\nsouthern stars of the trapezium in the head of Draco while\\nthe head of Hercules is far in the south, within 15\u00c2\u00b0 of the\\nequator, being 6\u00c2\u00b0 west of a similar star which constitutes the\\nhead of Ophiuchus.\\nLyra (the Lyre) is bounded U. by the head of Draco, E. by\\nthe Swan, S. and W. by Hercules. Alpha Lyrse, or Yega y is\\nof the first magnitude. It is accompanied by a small acute\\ntriangle of stars. Its color is a shining white, resembling Ca-\\npella and the Eagle.\\nCyg-nus (the Swan) extends along the Milky Way, below\\nCepheus, and immediately eastward of the Lyre, and has the\\nfigure of a large bird flying along the Milky Way from north\\nto south, with outstretched wings and long neck. Commen-\\ncing with the tail 25\u00c2\u00b0 east of Lyra, and following down the\\nMilky Way, we pass along a line of conspicuous stars which\\nform the body and neck of the figure and- then returning to\\nthe second of the series, we see two bright stars at eight or\\nnine degrees on the right and left (the three together ranging\\nacross the Milky Way) which form the wings of the Swan.\\nThis constellation is among the few which exhibit some resem-\\nblance to the animals whose names they bear.\\nVulpecula (the Little Fox) is a small constellation, in\\nwhich a fox is represented as holding a goose in his mouth. It\\nlies in the Milky Way, between the Swan on the north and\\nthe Dolphin and the Arrow on the south.\\nAquila (the Eagle) stretches across the Milky Way, and is\\nbounded 1ST. by Sagitta, a small constellation which separates\\nit from 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.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0306.jp2"}, "307": {"fulltext": "CONSTELLATIONS. 283\\nDelpbtnus (the Dolphin) is situated east and north of Al-\\ntair, and is composed of five stars of the third magnitude, of\\nwhich four in the form of a rhombus, compose the head, and\\nthe fifth forms the tail.\\nPegasus (the Flying Horse) is a very large constellation,\\nand is bounded !N~. by the Lizard and Andromeda, E. and S.\\nby Pisces, W. by the Dolphin. The head is near the Dolphin,\\nwhile the back rests on Pisces, and the feet extend toward\\nAndromeda.\\nA large square, composed of four conspicuous members, one\\n(3farJcab) 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\\nbeing near the head of Hercules, and the feet reaching to Scor-\\npio, the western foot being almost in contact with Antares.\\nThe figure is that of a giant holding* a serpent in his hands.\\nThe head of the serpent is a little south of the Crown, and the\\ntail reaches far eastward toward the Eagle.\\n416. Of the Constellations which lie south of the Zodiac,\\nwe shall notice only Cetus, Orion, Lepus, Monoceros, Canis\\nMajor, Canis Minor, Hydra, Crater, and Corvus.\\nCetus (the Whale) is distinguished rather for its extent than\\nits brilliancy t occupying a large tract of the sky south of the\\nconstellations Pisces and Aries. The head is directly below\\nthe head of Aries, and the tail reaches westward 45\u00c2\u00b0, being\\nabout 10\u00c2\u00b0 south of the vernal equinox. Menkar Ceti), the\\nlargest of its components, is situated in the mouth, 25\u00c2\u00b0 south-\\neast of a Arietis; and Mira (o Ceti) in the neck, 14\u00c2\u00b0 west of\\nMenkar, is celebrated as a variable star, which exhibits differ-\\nent magnitudes at different times.\\nOrion is one of the most magnificent of the constellations,\\nand one of those that have longest attracted the admiration of\\nmankind, being alluded to in the book of Job, and mentioned\\nby Homer. The head of Orion lies southeast of Taurus, 15\u00c2\u00b0\\nfrom Aldebaran, and is composed of a cluster of small stars.\\nTwo very bright stars, Betalgeuse of the first, and BeUatrix of\\nthe second magnitude, form the shoulders three more, re-", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0307.jp2"}, "308": {"fulltext": "284: FIXED STARS.\\nsembling the three stars of the eagle, compose the girdle and\\nthree smaller stars, in a line inclined to the girdle, form the\\nsword. Rigel) of the first magnitude, makes the west foot, bnt\\nthe corresponding star, 9\u00c2\u00b0 southeast of this, which is sometimes\\ntaken for the other foot, is above the knee, this foot being con-\\ncealed behind the Hare. Orion s club is marked by three stars\\nof the fifth magnitude, close together, in the Milky Way, just\\nbelow the southern horn of the Bull. Orion is a favorite con-\\nstellation with the practical astronomer, abounding, as it does,\\nin addition to the splendor of its components, with fine nebulae,\\ndouble stars, and other objects of peculiar interest when viewed\\nwith the telescope. It embraces 70 stars, plainly visible to the\\nnaked eve, including two of the first, four of the second, and\\nthree of the third magnitude.\\nLi-pus (the Hake). Below Pigel, 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 mag-\\nnitudes, south and east of these, make up the remaining parts\\nof the figure.\\nCanis Major (the Greater Dog) lies directly east of the\\nHare, and is highly distinguished by containing Sirius, the\\nmost splendid of all the fixed stars, which lies in the mouth of\\nthe figure. In the fore paw, 6\u00c2\u00b0 west of Sirins, is a star of the\\nsecond magnitude (/3 Can is Majoris), and from 10\u00c2\u00b0 to 15\u00c2\u00b0 south\\nof Sinus, is a collection of stars of the second and third magni-\\ntudes, which make up the hinder portions of the figure. The\\nEgyptians, who anticipated the rising of the Nile by the ap-\\npearance of Sirius in the morning sky, represented the constella-\\ntion by the figure of a dog, the symbol of a faithful watchman.\\nCanis Minor (the Lesser Dog). About 25\u00c2\u00b0 north of Sirius,\\nis the bright star Procyon, also of the first magnitude, which\\nmarks the side of the Lesser Dog. A star of the third magni-\\ntude (3), 4\u00c2\u00b0 northwest of this, in the head of the figure, forms\\nwith Procyon the lower side of an elongated parallelogram, of\\nwhich Castor 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", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0308.jp2"}, "309": {"fulltext": "CONSTELLATIONS. 285\\nof four stars of the fourth magnitude, of nearly uniform appear-\\nance and about 15\u00c2\u00b0 S. E. of these is the Heart {Cor Hydrce),\\n23\u00c2\u00b0 south of Regulus. Resting on Hydra, and south of the\\nhind feet of Leo, is Crater (the Cup), consisting of six stars of\\nthe fourth magnitude, arranged in the form of a semicircle;\\nand a little further east, also perched on the back of Hydra, is\\nCorvus (the Croio), the two brightest components of which are\\nsituated in one of the wings of the figure, in a line between\\nCrater and Spica Yirginis.\\n417. According to an intimation given in a note on p. 274,\\nthe constellations may be advantageously studied at four dif-\\nferent periods of the year, as near the equinoxes and the sol-\\nstices, according to the following directions. The latitude sup-\\nposed is 41\u00c2\u00b0.\\nLksson 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 mar-\\ngin of the Milky Way, the arrow being directed to a point a\\nlittle below Antares. At 9 o clock, the horns of the Goat come\\nupon the meridian and at 10 o clock, the western shoulder of\\nAquarius. The other shoulder, and the figure Y in the arm,\\nmay also be easily found from the descriptionsgiven on p. 277\\nalso, the Pentagon, in Pisces, and Fomalhaut (the Southern\\nPish), a solitary bright star far in the south, only 16\u00c2\u00b0 above\\nthe horizon. The head of Aries appears in the east, and the\\nPleiades are but little above the horizon, while Aldebaran is\\njust rising. Returning now to the west (at 10 o clock), the\\nCrown is seen a little north of west, about 20\u00c2\u00b0 high Lyra is\\n30\u00c2\u00b0 west of the zenith the Swan is nearly overhead and fol-\\nlowing down the Milky Way, the Eagle is seen on its eastern\\nmargin over against Lyra on the western and the Dolphin, a\\nlittle eastward of the Eagle, and as far above the horns of Cap-\\nricornus, as the latter are above the southern horizon. Follow-\\ning on east of the meridian, the great square in Pegasus may\\nnext be identified and since the northeastern corner of the\\nsquare is in the head of Andromeda, this constellation may\\nnext be learned and then Perseus and Auriga, which appear\\nstill further east. Directly north of Perseus, is Cassiopeia s", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0309.jp2"}, "310": {"fulltext": "286 FIXED STARS.\\nchair; and next to that we may take the Pole-star, the Little\\nBear, and the Great Bear, the Dipper only being traced for\\nthe present. Commencing now at the tail of the Dragon, we\\nmay trace round this figure between the two Bears to the head,\\nwhich brings us back to Lyra and the head of Hercules. The\\nboundaries of this constellation, and of Ophiuchus, which lies\\nsouth of it, will end the first lesson.\\nLesson II. For the middle of December, from 7 to 10 o clock.\\nOf the constellations of the Zodiac, Taurus and Gemini are\\nnow favorably situated for observation in the east. At 7 o clock,\\nthe tail of Cetus just reaches the meridian, its head being seen\\nbelow the feet of Aries. Orion is just risen in the S. E. At\\n9 o clock, just above the western horizon, are seen in succession\\nfrom south to north, Aquarius, the Dolphin, the Eagle, the\\nLyre, and the Dragon s head. Between the Eagle and the\\nLyre, at a little higher altitude, we perceive the Swan, flying\\ndirectly downward. Between the tail of the Swan and the\\nPole-star, is Cepheus and from the pole, along the meridian,\\nwe trace Cassiopeia, the feet of Andromeda, the head of Aries,\\nand the neck of the Whale. At 10 o clock, Perseus has reached\\nthe meridian, the star Algol, in the head of Medusa, being di-\\nrectly overhead. The Pleiades are but little eastward of the\\nzenith and following along south from the pole, at the inter-\\nval of from one to two hours east of the meridian, we may\\ntrace in succession, Camelopard, Auriga, Taurus, Orion, and\\nthe Hare. Turning along the eastern horizon, we find Canis\\nMajor, Monoceros, Canis Minor, the head of Hydra (just rising),\\nCancer, Leo, the sickle just appearing about 3\u00c2\u00b0 north of the\\neast point. Leo Minor and Ursa Major complete the survey;\\nand we may now advantageously trace out the various parts\\nof the Great Bear, as described on p. 278 the two stars com-\\nposing 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, toward 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", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0310.jp2"}, "311": {"fulltext": "DOUBLE STARS. 287\\nhead of Orion, we see Auriga and Camelopard. In the S. W.,\\nHydra is now fully displayed and following on north, we ob-\\ntain fine views of the Greater and the Lesser Lion, and the Great\\nBear. At 9 o clock, Crater and Corvus appear in the S. E., on\\nthe back of Hydra Virgo extends from Leo down to the hori-\\nzon, Spica Virginia being about 5\u00c2\u00b0 high and north of Virgo,\\nwe trace in succession Coma Berenices, Cor Caroli, Bootes, with\\nArct urus, and 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\\nSerpent, and Scorpio, lie along on either side of the meridian.\\nCastor and Pollux are just setting, and Leo is about an hour\\nhigh. East of Leo, Virgo is seen extending along toward the\\nmeridian, Spica being about 30\u00c2\u00b0 above the southern horizon.\\nNorth of Leo and Virgo we recognize Leo Minor, Coma Bere-\\nnices, Cor Caroli, and Ursa Major. At 10 o clock, we trace\\nalong the eastern side of the meridian, Draco, Hercules, and\\nOphiuchus and east of these, the Lyre, the Eagle, Antinous,\\nSagittarius, and Capricornus. North of the Eagle, and round\\nto the east, we find Cepheus and Cassiopeia, Andromeda rising\\nin the northeast, Pegasus in the east, and Aquarius in the\\nsoutheast. Thus we may advantageously complete a review\\nof the constellations.\\nCHAPTEE II\\nDOUBLE STARS TEMPORARY STARS VARIABLE STARS CLUSTERS\\nAND NEBULAE.\\n418. The view hitherto taken of the starry heavens presents\\nlittle that is new, since most of the Constellations, visible in\\nour latitude, and the most conspicuous of the individual stars,\\nhave been known from antiquity. But the objects to be de-\\nscribed in the present chapter, are chiefly such as have been\\ndiscovered by modern astronomy, aided by the powerful tele-\\nscopes which, since the time of Sir William Herschel, have been\\ndirected to the heavens. Different orders and systems of stars", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0311.jp2"}, "312": {"fulltext": "288 FIXED STARS.\\nhave been brought to light, and a new and still more wonder-\\nful class of bodies, called Nebulae, have been reached in the\\ndepths of the stellar universe.\\n419. The introduction into practical astronomy of Her-\\nscheTs great Forty-feet Reflector, in 1789, was a great event\\nin the study of the stars. This instrument in its previous\\nhumble forms had been very little employed upon the stars,\\nthey being supposed to be too remote for its powers, which\\nseemed only suited to nearer worlds, as the sun and planets.\\nIt was not, however, an increase of magnifying power that\\nwas wanted for researches on these distant objects, but\\nan increase of light, by which a few scattered rays sent to\\nus from bodies hidden in the depths of space, might be col-\\nlected in such numbers, and directed into the eye, as would\\nrender visible objects otherwise invisible, not because they do\\nnot transmit us any light, but because not enough of what they\\ntransmit enters the small pupil of the eye for the purposes of\\ndistinct vision. Telescopes of great aperture, therefore, by col-\\nlecting a large beam of light and conveying it to the eye,\\ngreatly enlarge the powers of this organ, and enable it to pen-\\netrate porportionally further into the most distant regions of\\nthe universe. Sir W Herschel himself made wonderful prog-\\nress in the knowledge of the starry heavens, and by his own\\nresearches discovered a large portion of those bodies which we\\nare now to describe and his son, Sir John Herschel, has cul-\\ntivated, with great success, the same field, and especially by a\\nresidence of five years at the Cape of Good Hope, devoted as-\\nsiduously to observations with large instruments, has greatly\\naugmented our knowledge of the stellar systems of the south-\\nern hemisphere. Moreover, telescopes of still greater power\\nthan that of the elder Herschel, and especially instruments ca-\\npable of nicer angular measurements, have recently enriched\\nthe department of practical astronomy. The most remarkable\\nof these are the grand Reflector constructed by Lord Rosse, an\\nIrish nobleman, and the great Refractors belonging respect-\\nively to the Pulkova and Cambridge Observatories. Lord\\nRosse s telescope considerably exceeds in dimensions and in\\npower the forty-feet reflector of Sir W. Herschel, being 50 feet\\nin focal length, and having a diameter of 6 feet, whereas that", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0312.jp2"}, "313": {"fulltext": "DOUBLE STABS. 289\\nof the Herschelian telescope was only 4 feet. This unexampled\\nmagnitude makes this instrument superior to all others in light,\\nand fits it pre-eminently for observations on the most remote\\nand obscure celestial objects, such as the faintest nebulae. But\\nits unwieldy size, and its liability to loss of power, by the tar-\\nnishing or temporary blurring of the great speculum, will\\nrender it far less available for actual research than the great\\nrefractors which come into competition with it. Until recently,\\nit was thought impossible to form perfect achromatic object-\\nglasses 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. Petersburg) has a clear aperture of\\nabout 15 inches, and a focal length of 22 feet. The telescope\\nrecently acquired by Harvard University, is perhaps the finest\\nrefractor hitherto constructed. It was made by the same\\nartists, and upon the same scale with that, but its performances\\nare thought even to exceed those of the Pulkova instrument.\\nWe now proceed to review some of the discoveries among the\\nstars, which the researches made with such instruments as the\\nforegoing have brought to light.\\nDOUBLE STABS.\\n420. Double Stabs are those which appear single to the\\nnaked eye, but are resolved into two by the telescope or if\\nnot visible to the naked eye, are seen in the telescope very close\\ntogether. Sometimes three or more stars are found in this\\nnear connection, constituting triple or multiple stars.* Castor,\\nfor example, when seen by the naked eye, appears as a single\\nstar but in a telescope, even of moderate powers, it is resolved\\ninto two stars, between the third and fourth magnitudes, with-\\nin 5 of each other. These two stars are of nearly equal size,\\nbut frequently one is exceedingly small in comparison with the\\nother, resembling a satellite near its primary, although in dis-\\ntance, in light, and in other characteristics, each has all the at-\\ntributes of a star, and the combination, therefore, cannot be\\nthat of a planet with a satellite. The distance between these\\nSee several figures of double and multiple stars, in Plate III. at the end of\\nthe volume,\\n19", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0313.jp2"}, "314": {"fulltext": "290 FIXED STAKS.\\nobjects varies from a fraction of a second to thirty-two seconds.\\nIn some cases, the extreme closeness, and the exceeding\\nminuteness of double stars, require, for their separation, the\\nbest telescope, united with the most acute powers of observa-\\ntion. Indeed, certain of these objects are regarded as the\\nseverest tests both of the excellence of the instrument, and of\\nthe skill of the observer.\\n421. When Sir William Herschel began his observations\\non double stars, about the year 1780, he was acquainted with\\nonly 4. By his own researches he extended the number to\\n2,400. Sir John Herschel, Sir James South, and M. Struve,\\nthe great Russian astronomer, prosecuted the same line of re-\\nsearch and when Sir John Herschel left England for the\\nCape of Good Hope, in 1833, the whole number of double stars\\nenrolled was 3,346 and this number was increased, by that\\neminent astronomer, by adding those of the southern hemi-\\nsphere, to 5,542. It appears, therefore, that the number of\\ndouble stars considerably exceeds all the stars visible to the\\nnaked eye. In some instances, this proximity arises undoubt-\\nedly from the two members lying nearly in the same line of\\nvision, and therefore being projected very near to each other on\\nthe face of the sky but in most cases the double stars are\\nproved to have a physical relation to each other, and are there-\\nfore said to be physically double, while the former are said to\\nbe optically double. There is no longer any doubt that among\\nthe stars are separate systems, in which two, three, and even\\nin one instance at least, six stars are bound together in rela-\\ntions of mutual dependence, suns with suns, as the members\\nof the solar system compose an individual province in the\\ngreat empire of nature. A star in Orion s sword (Theta\\nOrionis) has been for some time known as a quadruple star,\\nthe members of which form a small trapezium and recent ob-\\nservations have detected in two of these, severally, companions\\nof extreme minuteness, the whole composing a figure like the\\nfollowing", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0314.jp2"}, "315": {"fulltext": "TEMPORARY AND VARIABLE STARS. 291\\nMany of the double stars are distinguished by the compo-\\nnents exhibiting different colors, often finely contrasted with\\neach other as orange with blue or green, yellow with blue,\\nand white with purple. Gamma Andromedse is a close double\\nstar, the components of which are both green. Insulated stars\\nof a red color, almost as deep as that of blood, occur in many\\nparts of the heavens, but no green or blue star of any decided\\nhue has ever been noticed unassociated with a companion\\nbrighter than itself.*\\n422. TEMPORARY STARS.\\nTemporary Stars are new stars which have suddenly made\\ntheir appearance, and after a certain interval, as suddenly dis-\\nappeared, and returned no more. It was the appearance of a\\nnew star of this kind, 125 years before the Christian era, that\\nprompted Hipparchus to form a catalogue of the stars, the first\\non record. Such also was the star which suddenly shone out,\\na. d. 389, in the Eagle, as bright as Venus, and after remain-\\ning three weeks, disappeared entirely. At other periods, at\\ndistant intervals, similar phenomena have presented them-\\nselves. Thus the appearance of a new star in 1572 was so sud-\\nden, that Tycho Brahe, returning home one evening, was sur-\\nprised to find a collection of country people gazing at a star\\nwhich he was sure did not exist half an hour before. It was\\nthen as bright as Sirius, and continued to increase until it sur-\\npassed Jupiter when brightest, and was visible at mid-day. In\\na month it began to diminish, and in three months afterward\\nit had entirely disappeared. Some stars are now missing which\\nwere registered in the older catalogues. In one instance, at\\nleast (that of Neptune), the supposed star has proved to have\\nbeen 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,\\nbeing then, on some occasions, equal to a star of the second\\nHerschel.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0315.jp2"}, "316": {"fulltext": "292 FIXED STARS.\\nmagnitude. It then decreases about three months, until it be-\\ncomes completely invisible, and remains so about five months,\\nwhen it again becomes visible, and continues increasing during\\nthe remaining three months of its period.\\nAnother very remarkable variable star is Algol (fl Persei).\\nIt is suddenly visible as a star of the second magnitude, and\\ncontinues such for 2d. lih., when it begins rapidly to diminish\\nin splendor, and in about BJ hours is reduced to the fourth\\nmagnitude. It then begins again to increase, and in 3\u00c2\u00a3 hours\\nmore, is restored to its usual brightness, going through all its\\nchanges in less than three days. This remarkable law of vari-\\nation appears strongly to suggest the revolution round it of\\nsome opaque body, which, when interposed between us and\\nAlgol, cuts off a large portion of its light. It is (says Sir\\nJ. Herschel) an indication of a high degree of activity in regions\\nwhere, but for such evidence, we might conclude all to be life-\\nless. Our sun requires almost nine times this period to perform\\na revolution on its axis. On the other hand, the periodic time\\nof an opaque revolving body, sufficiently large, which would\\nproduce a similar temporary obscuration of the sun, seen from\\na fixed star, would be less than fourteen hours.\\nThe duration of these periods is extremely various. While\\nthat of j3 Persei, above mentioned, is less than three days,\\nothers are more than a year, and others many years.\\n424. CLUSTERS AND NEBULAE.\\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\\nof small stars. Such are the Pleiades, Coma Berenices, and\\nPrsesepe, or the Beehive in Cancer. The Pleiades, or /Seven\\nStars, as they are called, in the neck of Taurus, is the most\\nconspicuous cluster. When we look directly at this group, we\\ncan not distinguish more than six stars, but by turning the eyes\\na little to one side,* we discover that there are many more.\\nIndirect vision is far more delicate than direct. Thus we can see the Zodiacal\\nLight or a Cornet s tail much more distinctly and of greater length, if, instead\\nof looking directly at it, we turn the eyes to various points near it, the attention all\\nthe while being given to the object itself.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0316.jp2"}, "317": {"fulltext": "CLUSTERS AND NEBULA. 293\\nThe telescope only can, however, display the real magnificence\\nof the Pleiades. (See Plate III., Fig. 1.) Coma Berenices has\\nfewer stars, but they are of a larger class than those which com-\\npose the Pleiades. The Beehive, or Nebula of Cancer, is one\\nof the finest objects of this kind for a small telescope, being, by\\nits aid, converted into a rich congeries of shining points. A\\ncluster in the sword-handle of Perseus, below Cassiopeia s chair,\\nthough but a dim speck to the naked eje, is a very elegant\\nobject to a large telescope, being separated into bright and\\nbeautiful stars, embracing several distinct subordinate clusters\\nof exceedingly minute stellar points. The head of Orion af-\\nfords an example of another cluster, though less remarkable\\nthan the others.\\n425. Nebula are faint misty objects seen in various parts\\nof the firmament, always maintaining a fixed position, which\\nresemble comets, or patches of fog. The Galaxy, or Milky\\nWay, presents a constant succession of large nebulae. Of the\\nindividual nebulae, seen by the naked eye, the most conspicu-\\nous is that near the girdle of Andromeda. It is the oldest\\nknown nebula, having attracted the attention of star-gazers\\nas early as the beginning of the tenth century,* although it is\\ncommonly said to have been discovered by Simon Marius, in\\n1612. No powers of the telescope have been able to resolve\\nthis into separate stars, although the great Cambridge tele-\\nscope reveals a vast number of stars, more than 1,500, of various\\ndegrees of brightness, scattered over its surface; but these ap-\\npear not to belong to the nebula itself, which has hitherto af-\\nforded no evidence of resolution, f Its dimensions are aston-\\nishingly great, since it covers a space of a quarter of a degree\\nin diameter and we must bear in mind that, at such a dis-\\ntance as the fixed stars, a space of 15 implies an immense ex-\\ntent. Its figure is oval, and elliptical nebulae constitute a com-\\nmon variety among the figures which these bodies exhibit.\\n(See Plate III., Fig. 2, for a representation of the great nebula\\nof Andromeda.) Another very common figure are the globular-\\nnebulae. A grand specimen of this variety may be easily\\nSmyth s Cycle, ii., p. 15.\\nf Memoirs of the Amer. Acad., vol. iii.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0317.jp2"}, "318": {"fulltext": "294 FIXED STARS.\\nfound in the constellation Hercules, between Zeta and Eta.\\n\u00c2\u00a9raw a line from Lyra to Gemma of the Crown, and 3\u00c2\u00b0 above\\nthe center of that line will be the place of this nebula. When\\nviewed with a small telescope, it exhibits only a circular cloud\\n(Plate III., Fig. 3, a), but to a more powerful instrument it re-\\nveals its real glories in a form truly exciting to the beholder\\n(Fig. 3, b). About 4000 nebulae have been detected and de-\\nscribed, of which about 1,700 have recently been added by\\nSir John Herschel, from his Results of Observations at the\\nCape of Good Hope Among the latter are two remarkable\\nspots, well known to navigators, situated near the south pole,\\ncalled Magellanic clouds by sailors, but by astronomers, the\\nNubecula Major and the Nubecula Minor. They are found\\nto consist of a wonderful collection of nebulae, the greater em-\\nbracing 278 nebulae, and the lesser 37. Both together com-\\npose 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 Re-\\nflector of Lord Rosse, and more recently the great Refractor\\nof the Cambridge Observatory, have succeeded in a partial\\nresolution, at least, of this grand object, and have authorized\\nthe anticipation that, with a small increase of telescopic power,\\nthe whole will be shown to consist of an immense collection of\\nexceedingly minute stars.\\nThese great telescopes, by the superior light they afford, dis-\\nplay their peculiar powers in this department of astronomy,\\nand those astronomers who, for the first time, have gazed at\\nthese sidereal pictures as seen in the Leviathan of Lord\\nRosse, have expressed, in glowing terms, their mingled delight\\nand astonishment. The perfect forms, and strange but sym-\\nmetrical configurations, exhibited by these instruments, of\\nnebulae that were before seen of irregular or fantastic shapes,\\nafford grounds for believing that such irregularities are often\\nif not always owing to the objects being but partly developed.\\nThus the Crab Nebula of Lord Rosse (Plate III., Fig. 4) had\\nbeen long known as a faint, ill-defined nebula of an elliptical\\nshape but the higher powers of that instrument exhibit the\\nbefore-concealed appendages which are essential to the com-\\npleteness of the figure. The Whirlpool Nebula of Rosse\\n(Plate III., Fig. 5), when seen in separate parts, exhibited no", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0318.jp2"}, "319": {"fulltext": "CLUSTERS AND NEBULA. 295\\nsigns of order or symmetry but when viewed with the great\\nReflector, it develops the wonderful structure of a perfect\\nspiral.\\n426. Nebulae were formerly divided into two classes, re-\\nsolvable and irresolvable, the former term implying that the\\nbody was shown by the telescope to consist of stars, and the\\nlatter implying that the body is not composed of stars, but of a\\nshining, cloudy kind of matter diffused throughout the mass.\\nAstronomers, at present, include all resolvable nebulae under\\nthe head of clusters, appropriating the term nebulae exclusively\\nto such of these bodies as have never been resolved. The\\nquestion whether this distinction is not merely relative to the\\npowers of the telescope, and whether, on the increase of these\\npowers, this class of bodies would not all be resolved into stars,\\nis not easily determined, since the same increase of telescopic\\npower which converts existing nebulae into clusters, brings to\\nlight a greater number of those which are irresolvable.\\nThese remote objects of the universe occasionally exhibit\\ntraces of that regard to beauty which everywhere, in these\\nnether worlds, characterizes the works of the Creator. In the\\nCross, a brilliant constellation of the southern hemisphere, for\\nexample, is a cluster surrounding the star Kappa Crucis, which\\nconsists of about 110 stars from the seventh magnitude down-\\nward, eight of the more conspicuous of which are colored with\\nvarious shades of red, green, and blue, so as to give to the\\nwhole the appearance of a rich piece of jewelry.\\n427. Nebulous stars are such as exhibit a sharp and bril-\\nliant star, surrounded by a disk or atmosphere of nebulous\\nmatter. These atmospheres in some cases, present a circular,\\nin others an oval figure and in certain instances, the nebula\\nconsists of a long, narrow, spindle-shaped ray, tapering away\\nat both ends to points. Annular Nebulae (Ring-shaped) are\\namong the rarest objects in the heavens. The most conspicu-\\nous of this class is in the constellation Lyra, between the stars\\nBeta and Gamma, about 6\u00c2\u00b0 S. E. of Alpha Lyrae. This re-\\nmarkable object is believed to be in fact a resolvable nebula\\nor cluster, and yet the greatest powers of the telescope hitherto\\napplied have only effected such changes as are regarded as", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0319.jp2"}, "320": {"fulltext": "296 FIXED STAKS.\\ngiving signs of resolvability, but its perfect resolution has not\\nbeen attained. Should it be achieved by an increased power\\nof the instrument, astronomers look for a splendid coronet of\\nstars, more glorious f perhaps, than any thing hitherto discovered\\nin the starry heavens.\\nPlanetary Wehulce constitute another variety, and are very\\nremarkable objects. They have, as their name imports, exactly\\nthe appearance of planets. Whatever may be their nature,\\nthey must be of enormous magnitude. One of them is to be\\nfound in the parallel of v Aquarii, and about 5m. preceding\\nthat star. Its apparent diameter is about 20 Another in\\nthe constellation Andromeda, presents a visible disk of 12\\nperfectly defined and round. Granting these objects to be\\nequally distant from us with the stars, their real dimensions\\nmust be such as, on the lowest computation, would fill the or-\\nbit of Uranus. It is no less evident that, if they be solid\\nbodies, of a solar nature, the intrinsic splendor of their surfaces\\nmust be almost infinitely inferior to that of the sun. A circular\\nportion of the sun s disk, subtending an angle of 20 would give\\na light equal to 100 full moons while the objects in question\\nare hardly, if at all, discernible with the naked eye.*\\n428. The Milky Way, or Galaxy, is a well-known lumi-\\nnous zone, encircling the sphere nearly in the direction of a\\ngreat circle. Near the Swan, in the northern sky, it is seen\\nto be divided into two bands, which remain asunder for 150\u00c2\u00b0,\\nand then reunite. The Galaxy owes its peculiar appearance\\nto the blended light of myriads of small stars too minute to be\\nindividually recognized by the naked eye, but which are seen\\nin their true character by a telescope of only moderate powers.\\nSir William Herschel estimated, that, on one occasion, in forty-\\none minutes, no less than 258,000 stars passed through the\\nsmall field of his telescope.f In approaching the border of\\nthe Milky Way, there is found a regular but rapid increase in\\nthe number of stars, even before entering the limits of the lu-\\nminous zone itself. Sir J. Herschel computes the whole num-\\nHerschel.\\nf Plate II., Fig. 1, exhibits a telescopic view of a part of the southern portion\\nof the Milky Way.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0320.jp2"}, "321": {"fulltext": "MOTIONS OF THE FIXED STARS. 297\\nber of stars in the Milky Way 2Xfive and a half million s, in-\\ncluding such only as are visible in his twenty-feet reflector.\\nThe Galaxy is supposed to be one of the numerous nebulse,\\nand the sun of our own solar system to be one of the stars\\nwhich compose it. It appears comparatively large to us, and\\nextends entirely round the heavens, only because we are in\\nthe midst of it, and see it projected in different directions\\nfrom us.\\nCHAPTER III.\\nMOTIONS OF THE FIXED STARS DISTANCES NATURE.\\n429. In 1803, Sir William Herschel first determined and\\nannounced to the world, that there exist among the stars sepa-\\nrate systems, composed of two stars, revolving about each\\nother in regular orbits. These he denominated Binary Stars,\\nto distinguish them from other double stars where no such\\nmotion is detected, and whose proximity to each other may\\npossibly arise from casual juxtaposition, or from one being in\\nthe range of the other. At present, more than a hundred of\\nthe binary stars are known, and as the number of such revo-\\nlutions known among the double stars is constantly increasing\\nas the times of comparison increase, it may be anticipated that,\\nin after ages, so large a proportion of all the double stars will\\nbe found to possess this character, as to authorize the belief\\nthat they universally consist of subordinate systems, of which\\nthe members have a revolution around a common center of\\ngravity. The periodic times of the binary stars are very\\nvarious. While some (as Herculis, and t\\\\ Coronas) 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\\nthe long period of 3000 years.* Their orbits are in general\\nmore eccentric than those of the planets. That of Gamma\\nVirginis, including the relative positions of the two components\\nSmyth s Cycle, i., p. 300.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0321.jp2"}, "322": {"fulltext": "298 FIXED STARS.\\nfrom 1837 to 1860, is figured on Plate IT. as drawn by Mr. E.\\nP. Mason, in 1810.*\\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\\nbounds of the solar system. Indeed, our belief of the fact\\nrested more upon our idea of unity of design in all the works\\nof the Creator, than upon any certain proof; but the revolu-\\ntion of one star around another, in obedience to forces which\\nmust be similar to those that govern the solar system, estab-\\nlishes the grand conclusion, that the law of gravitation is truly\\nthe law of the material universe.\\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\\nplanetary or cometary nature round a solar center that we are\\nnow concerned it is with that of sun around sun, each, per-\\nhaps, accompanied with its train of planets and their satellites,\\nclosely shrouded from our view by the splendor of their re-\\nspective suns, and crowded into a space, bearing hardly a\\ngreater proportion to the enormous interval which separates\\nthem, than the distances of the satellites of our planets from\\ntheir primaries, bear to their distances from the sun itself.\\n431. Some of the fixed stars appear to have a Proper Mo-\\ntion, or a real motion in space.\\ne 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\\ndate of 1838, combined with his own of 1840, found that this period was too\\ngreat, and assigned as the true period 171 years, which is now acknowledged by\\nthe highest authorities, and even by Herschel himself, to be nearly its real time\\nof revolution.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0322.jp2"}, "323": {"fulltext": "MOTIONS OF THE FIXED IYTARS. 299\\nThe apparent change of place in the stars arising from the\\nprecession of the equinoxes, the nutation of the earth s axis, the\\ndiminution of the obliquity of the ecliptic, and the aberration\\nof light, have been already mentioned but after all these cor-\\nrections are made, changes of place still occur, which cannot\\nresult from any changes in the earth, but must arise from\\nchanges in the stars themselves. Such motions are called the\\nproper motions of the stars. Nearly 2000 years ago, Hippar-\\nchus and Ptolemy made the most accurate determinations in\\ntheir power of the relative situations of the stars, and their ob-\\nservations have been transmitted to us in Ptolemy s Almagest\\nfrom which it appears that the stars retain at least very nearly\\nthe same places now as they did at that period. Still, the\\nmore accurate methods of modern astronomers, have brought\\nto light minute changes in the places of certain stars which\\nforce upon us the conclusion, either that our solar system causes\\nan apparent displacement of certain stars, by a motion of its\\nown in space, or that they have themselves a proper motion.\\nPossibly, 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\\nleaving, and the recession of those which lie in the part of the\\nheavens toward which he is traveling. Were two groves of\\ntrees situated on a plain at some distance apart, and we should\\ngo from 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\\nkind among two sets of stars in opposite points of the heavens,\\nand announced that the solar system was in motion toward a\\npoint in the constellation Hercules.* As, for many years after\\nthis announcement, other astronomers failed to find evidence\\nof such a motion of the solar system, the doctrine was generally\\ndiscredited, until, within a few years, new and very refined\\nresearches have been instituted by several of the most eminent\\nastronomers, which have fully confirmed the observations ol\\nPhil. Trans., 1783, 1805, and 1806.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0323.jp2"}, "324": {"fulltext": "300 FIXED STARS.\\nHerschel. The great Russian astronomer, Struve, by a com-\\nparison of the best observations, finds the exact point toward\\nwhich the solar system is moving is in a line which joins the\\ntwo stars and /x Herculis,* a point which can be easily found\\non the celestial globe, and thence transferred to the heavens.\\n(Right ascension 259\u00c2\u00b0, declination 34i\u00c2\u00b0.) The researches of\\nthe younger Struve have conducted him to the velocity with\\nwhich the solar system is moving in space. For having found\\nthat the arc traversed by the sun in a year is .3392, if viewed\\nat the mean distance of the stars of the first magnitude, and\\nhaving previously ascertained that the mean parallax of the\\nstars of this class amounts to 0 .2d9j he infers that the space\\nthrough which the sun moves annually is 154,000,000 miles.\\nGreat as this space is, yet it may be remarked that it is only\\nabout one-fourth that traversed by the earth in its revolution\\naround 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\\nleads to the belief that it is in fact a. motion of revolution, al-\\nthough on account of the immense size of the orbit, and, con-\\nsequently, its small curvature, many years will be requisite in\\norder to determine the deviation from the line of the tangent.f\\n433. When we reflect on the immense distance of the\\nstars, we may readily believe that they may be in fact in rapid\\nmotion, and yet appear quiescent as a distant ship, under full\\nsail, appears at rest, although actually moving at the rate of\\nten knots an hour. Thus we have seen above that a motion of\\nthe sun in space, as seen from the nearest fixed stars, would\\nmake it describe an arc of only about one-third of a second\\nannually, although traversing a space of 154 millions of miles.\\nBut a small change in the place of a star in a single year may,\\nin a long series of years, accumulate to a very sensible amount.\\nFor example, the latitudes of the three bright stars, Sirius,\\nArcturus, and Aldebaran, were determined by Hipparchus 130\\nyears before the Christian era, and their assigned places are\\ntransmitted to us in the Almagest of Ptolemy. About the\\nyear 1700, Dr. Halley found that these stars had, during the\\nEtudes d Astron. Stellaire, p. 108. f Grant s Hist. Phys. Ast., p. 557.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0324.jp2"}, "325": {"fulltext": "DISTANCES OF THE FIXED STARS. 301\\ninterval of nearly 2000 years, moved southerly through the\\nspaces respectively of 37 42 and 33 The immense pains\\nthat have of late years been bestowed upon catalogues of the\\nstars, and especially of particular portions of the heavens, with\\nthe view of furnishing to after ages the most accurate data for\\ncomparison, will enable future astronomers to study the proper\\nmotions of the stars with far greater advantages than the pres-\\nent generation enjoys. In most cases where a proper motion\\nin certain stars has been suspected, its annual amount has been\\nso 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 T 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\\nhave shifted their local situation in the heavens M 23 the\\nannual proper motion of each star being 5 .3, by which quan-\\ntity this system is every year carried along in some unknown\\npath, by a motion which for many centuries must be regarded\\nas uniform and rectilinear. A greater proportion of the double\\nstars than of any other indicate proper motions, especially the\\nbinary stars, or those which have a revolution around each\\nother. Among stars not double, and no way differing from\\nthe rest in any other obvious particular, Cassiopeiae has a\\nproper motion, amounting to nearly 4 annually and another\\nobscure star has been recently found to have a motion of\\nnearly S\\n434. DISTANCES OF THE FIXED STARS.\\nIt has long been considered one of the highest problems that\\ncan be proposed to the human mind, to measure the distance\\nto any of the fixed stars. Nothing more would be necessary\\nthan to measure the horizontal parallax, if it were possible\\nbut this is now known to be less than the 70,000th part of a\\nsecond for the nearest star, and therefore utterly inappreciable\\nby any method of measurement. For measuring the distances\\nHerschel s Outlines (Ed. 1851).", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0325.jp2"}, "326": {"fulltext": "302 FIXED STASS.\\nof the sun and planets, the diameter of the earth furnishes the\\nbase line (Art. 87). The length of this line being known, and\\nlikewise the horizontal parallax of the body whose distance is\\nsought, we readily obtain the distance by the solution of a\\nright-angled triangle (Art. 80, Fig. 6). But any star viewed\\nfrom the opposite sides of the earth would appear from both\\nstations to occupy precisely the same situation in the celestial\\nsphere, and of course it would exhibit no horizontal parallax.\\nBut astronomers have endeavored to find a parallax in some of\\nthe fixed stars, by taking the diameter of the earth s orbit as a\\nbase line. Yet even a change of position, amounting to 190\\nmillions of miles, has, until within a few years, proved insuffi-\\ncient to alter the apparent place of a single fixed star, from\\nwhich it was concluded that the fixed stars have not even any\\nannual parallax or that the angle subtended by the semi-di-\\nameter of the earth s orbit, at the nearest fixed star, is insensible.\\nThe errors to which instrumental measurements are subject,\\narising from defects of the instruments themselves, from errors\\nof refraction, of aberration, of precession, of nutation, and from\\nimperfections of observation, are such, that the angular deter-\\nminations of celestial arcs, it was supposed, could not be Fig 8 q\\nrelied on to less than and the change of place in any c\\nstar that had been examined for parallax being less than\\none second when viewed at opposite extremities of the\\nearth s orbit, the conclusion was, that the parallax of the\\nfixed stars, if any exist, is too minute ever to be measured\\nby instruments. According to this, the diameter of the\\nearth s orbit, when viewed from the nearest fixed star,\\nwould be insensible the spider-line of the telescope\\nwould more than cover it.\\nTaking, however, the annual parallax at I let ah\\n(Fig. 80) represent the radius of the earth s orbit, and c\\na fixed star, the angle at c being 1 and the angle at b\\na right angle then,\\nSin 1 Kad 1 200,000, nearly.\\nHence the hypotenuse of a triangle whose vertical ff\\nangle is 1 is about 200,000 times the base; consequently, the\\ndistance in question must exceed 95,000,000 x 200,000\\n190,000,000 x 100,000, or one hundred thousand times one\\nhundred and ninety millions of miles. Of a distance so vast", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0326.jp2"}, "327": {"fulltext": "DISTANCES OF THE FIXED STARS. 303\\nwe can form no adequate conceptions, and attempt to measure\\nit only by the time that light (which moves more than 192,000\\nmiles per second) would take to traverse it. Now,\\n192,000 Is. 19,000,000,000,000 3.1 years.\\n435. After many fruitless and delusory efforts to measure\\nthe immense interval that separates us from the fixed stars, the\\ngreat Prussian astronomer, Bessel, in the year 1838, determined\\nthis interesting and important element, by observations on a\\ndouble star in the Swan (61 Cygni). This star was selected\\nfor the following reasons first, it was known to have a great\\nproper motion (Art. 433), indicating a comparatively great\\nproximity 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 opportu-\\nnity of selecting favorable stationary points from which (inas-\\nmuch as these more remote objects might be considered as en-\\ntirely devoid of parallax) any changes of place in the nearer,\\nin consequence of an annual parallax, might be readily esti-\\nmated. By observations of the last degree of refinement, con-\\nducted for a period of several years, a parallax was decisively\\nindicated, amounting to about one-third of a second or, more\\nexactly, to 0 .3483, implying a distance of 592,200 times the\\nmean distance of the earth from the sun, or a space which it\\nwould take light, moving at the rate of twelve millions of miles\\nper minute, nine and a quarter years to traverse. Perhaps the\\nbest way to conceive of this distance, is to compare it with the\\ndimensions of the solar system, as represented by the diagram\\n(note, p. 178). The distance from the sun to Neptune being\\n30 feet, 61 Cygni should be placed 110 miles off. Thus isolated\\nare the systems of the universe from each other.\\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 the dis-\\ntance and proper motion of the star, we can now obtain its\\nvelocity, so far as it is perpendicular to our line of vision. This\\nis found to be about forty-four miles per second more than", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0327.jp2"}, "328": {"fulltext": "304 FIXED STARS.\\ndouble that of the earth in its orbit amounting to about one\\nthousand millions of miles per annum.\\nOn account of the smallness of the supposed parallax thus\\nfound, it would not be unreasonable still to entertain a linger-\\ning suspicion, that it is nothing more than the unavoidable im-\\nperfection of instrumental measurements, as proved to be the\\ncase in previous attempts to find the same element but the\\nmost satisfactory evidence which the world can have that such\\nis not the fact in the present instance, but that the parallax is\\ntruly found, is that the most celebrated astronomers of the age,\\nafter rigorous scrutiny, have acknowledged the reality and\\nsoundness of the determination. Our confidence that the par-\\nallax of 61 Cygni was truly determined by Bessel, is strength-\\nened by the fact that a separate determination recently made\\nby Peters at the Pulkova Observatory, gives almost precisely\\nthe same result, that of Bessel being 0 .348, and that of Peters\\n0 .349. In the case of several stars still more distant, the par-\\nallax has been found, with more or less probability, but with\\nsufficient to command the general confidence of astronomers.\\nThus, the parallax of Arcturus, Alpha Lyrse, and Polaris, were\\nalso found by Peters to be respectively 0 .127, /7 .123, 0 .067,\\nthat of the Pole-star being only one-fifth as great as that of 61\\nCygni and, consequently, if light would require 9^ years to\\ncome from that star, it would require more than 46 years to\\ncome to us from the Pole-star. A star in the southern hemi-\\nsphere (a Centauri) indicates a parallax of about 1 and hence\\nappears at present the nearest of the fixed stars.\\n436. NATURE OF THE STARS.\\nThe stars are bodies greater than our earth. If this were not\\nthe case they could not be visible at such an immense distance.\\nDr. Wollaston, a distinguished English philosopher, attempted\\nto estimate the magnitudes of certain of the fixed stars from\\nthe light which they afford. By means of an accurate photom-\\neter (an instrument for measuring the relative intensities of\\nlight) he compared the light of Sirius with that of the sun.\\nHe next inquired how far the sun must be removed from us\\nin order to appear no brighter than Sirius. He found the dis-\\ntance to be 141,400 times its present distance. But Sirius is", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0328.jp2"}, "329": {"fulltext": "NATURE OF THE STARS. 305\\nmore than 200,000 times as far off as the sun (Art. 434).\\nHence he inferred that, upon the lowest computation, Sirius\\nmust actually give out twice as much light as the sun or\\nthat, in point of splendor, Sirius must be at least equal to two\\nsuns. Indeed, he has rendered it probable that the light of\\nSirius is equal to fourteen suns.\\n437. The fixed stars are suns. We have already seen that\\nthey are large bodies that they are immensely further off\\nthan the furthest planet that they shine by their own light,\\nas is evident by the nature of the light as tested by polarization\\nin short, that their appearance is, in all respects, the same as the\\nsun would exhibit if removed to the region of the stars. Hence\\nwe infer that 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,\\nto which they severally dispense light and heat. Although\\nthe starry heavens present, in a clear night, a spectacle of in-\\neffable grandeur and beauty, yet it must be admitted that the\\nchief purpose of the stars could not have been to adorn the\\nnight, since by far the greater part of them are wholly invisi-\\nble to the naked eye nor as landmarks to the navigator, for\\nonly a very small proportion of them are adapted for this pur-\\npose; nor, finally, to influence the earth by their attractions,\\nsince their distance renders such an effect entirely insensible.\\nIf they are suns, and if they exert no important agencies upon\\nour world, but are bodies evidently adapted to the same pur-\\npose as our sun, then it is as rational to suppose that they were\\nmade to give light and heat, as that the eye was made for see-\\ning and the ear for hearing. It is obvious to inquire next, to\\nwhat they dispense these gifts, if not to planetary worlds and\\nwhy to planetary worlds, if not for the use of percipient\\nbeings We are thus led, almost inevitably, to the idea of a\\nPlurality of Worlds and the conclusion is forced upon us,\\nthat the spot which the Creator has assigned to us is but an\\nhumble province of his boundless empire.*\\nSee this argument, in its full extent, in Dick s Celestial Scenery.\\n20", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0329.jp2"}, "330": {"fulltext": "CHAPTEE IT.\\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,\\nindeed, in the System of the World, we figure to ourselves a\\nmachine, all the parts of which have a mutual dependence, and\\nconspire to one great end. The machines that are first in-\\nvented (says Adam Smith) to perform any particular move-\\nment, are always the most complex and succeeding artists\\ngenerally discover that with fewer wheels and with fewer prin-\\nciples of motion than had originally been employed, the same\\neffects may be more easily produced. The first systems, in the\\nsame manner, are always the most complex and a particular\\nconnecting chain or principle is generally thought necessary to\\nunite every two seemingly disjointed appearances but it often\\nhappens that one great connecting principle is afterward found\\nto be sufficient to bind together all the discordant phenomena\\nthat occur in a whole species of things. This remark is\\nstrikingly applicable to the origin and progress of systems of\\nastronomy.\\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\\ndid of the truths of astronomy. But Pythagoras, who lived\\n500 years before the Christian era, was acquainted with many\\nimportant facts in our science, and entertained many opinions\\nrespecting the System of the World which are now held to be\\ntrue. Among other things well known to Pythagoras were\\nthe following\\n1. The principal constellations. These had begun to be\\nformed in the earliest ages of the world. Several of them\\nbearing the same names as at present are mentioned in the\\nwritings of Hesiod and Homer; and the sweet influences of", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0330.jp2"}, "331": {"fulltext": "SYSTEM OF THE WORLD. 307\\nthe Pleiades and the bands of Orion, are beautifully alluded\\nto in the Book of Job.\\n2. Eclipses. Pythagoras knew both the causes of eclipses\\nand how to predict them not indeed in the accurate manner\\nnow employed, but by means of the Saros (Art. 233).\\n3. Pythagoras had divined the true system of the world,\\nholding that the sun, and not the earth (as was generally held\\nby the ancients, even for many years after Pythagoras), is the\\ncenter around which all the planets revolve, and that the stars\\nare so many suns, each the center of a system like our own.f\\nAmong lesser things, he knew that the earth is round that its\\nsurface is naturally divided into five zones; and that the eclip-\\ntic is inclined to the equator. He also held that the earth\\nrevolves daily on its axis, and yearly around the sun that the\\ngalaxy is an assemblage of small stars and that it is the same\\nluminary, namely, Yenus, that constitutes both the morning\\nand the evening star, whereas all the ancients before him had\\nsupposed that each was a separate planet, and accordingly the\\nmorning star was called Lucifer, and the evening star Hesper-\\nus.;): He held also that the planets were inhabited, and even\\nwent so far as to calculate the size of some of the animals in\\nthe moon.\u00c2\u00a7 Pythagoras was so great an enthusiast in music,\\nthat he not only assigned to it a conspicuous place in his system\\nof education, but even supposed* the heavenly bodies them-\\nselves to be arranged at distances corresponding to the diatonic\\nscale, and imagined them to pursue their sublime march to\\nnotes created by their own harmonious movements, called the\\nmusic of the spheres but he maintained that this celestial\\nconcert, though loud and grand, is not audible to the feeble\\norgans of man, but only to the gods.\\n441. With few exceptions, however, the opinions of Pythag-\\noras on the System of the World, were founded in truth. Yet\\nthey were rejected by Aristotle and by most succeeding astron-\\nomers down to the time of Copernicus, and in their place was\\nsubstituted the doctrine of Crystalline Spheres, first taught by\\nLong s Astronomy, ii., p. 671.\\nf Library of Useful Knowledge, History of Astronomy.\\nLong s Ast., ii., p. 673. Edin. Encyclopaedia", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0331.jp2"}, "332": {"fulltext": "308 SYSTEM OF THE WORLD.\\nEudoxus. According to this system, the heavenly bodies are\\nset like gems in hollow solid orbs, composed of crystal so pel-\\nlucid that no anterior orb obstructs in the least the view of any\\nof the orbs that lie behind it. The sun and the planets have\\neach its separate orb but the fixed stars are all set in the same\\ngrand orb and beyond this is another still, the Primwn Mo-\\nhile, which revolves daily from east to west, and carries along\\nwith it all the other orbs. Above the whole spreads the\\nGrand Einpyrean, or third heavens, the abode of perpetual\\nserenity.*\\nTo account for the planetary motions, it was supposed that\\neach of the planetary orbs, as well as that of the sun, has a\\nmotion of its own eastward, while it partakes of the common\\ndiurnal motion of the starry sphere. Aristotle taught that these\\nmotions are effected by a tutelary genius of each planet, resid-\\ning in it, and directing its motions, as the mind of man directs\\nhis motions.\\n442. On coming down to the time of Hipparchus, who\\nflourished about 150 years before the Christian era, we meet\\nwith astronomers who acquired far more accurate knowledge\\nof the celestial motions. Hipparchus was in possession of in-\\nstruments for measuring angles, and knew how to resolve\\nspherical triangles. He ascertained the length of the year\\nwithin 6m. of the truth. He discovered the eccentricity of the\\nsolar orbit (although he supposed the sun actually to move\\nuniformly in a circle, but the earth to be placed out of the\\ncenter), and the positions of the sun s apogee and perigee. He\\nformed very accurate estimates of the obliquity of the ecliptic\\nand of the precession of the equinoxes. He computed the exact\\nperiod of the synodic revolution of the moon, and the inclina-\\ntion of the lunar orbit discovered the motion of her node and\\nof her line of apsides and made the first attempts to ascertain\\nthe 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., p. 640 Robinson s Mech. Phil., ii., p. 83 Gregory s Ast.,\\np. 132; Playfair s Dissertations, p. 118.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0332.jp2"}, "333": {"fulltext": "THE PTOLEMAIC SYSTEM. 309\\n443. The systems of the world which have been most cele-\\nbrated are three the Ptolemaic, the Tychonic, and the Coper-\\nniean. We shall conclude this part of our work with a con-\\ncise statement and discussion of each of these systems of the\\nMechanism of the Heavens.\\nTHE PTOLEMAIC SYSTEM.\\n444. The doctrines of the Ptolemaic System were not origi-\\nnated by Ptolemy but being digested by him out of materials\\nfurnished by various hands, it has come down to us under the\\nsanction of his 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, Ptol-\\nemy had recourse to deferents and epicycles, an explanation\\ndevised by Apollonius, one of the greatest geometers of an-\\ntiquity.* He conceived that, in the circumference of a circle,\\nhaving the earth for its center, there moves the center of an-\\nother circle, in the circumference of which the planet actually\\nrevolves. The circle surrounding the earth was called the\\ndeferent, while the smaller circle, whose center was always in\\nthe periphery of the deferent, was called the epicycle. The mo-\\ntion in each was supposed to be uniform. Lastly, it was con-\\nceived that the motion of the center of the epicycle in the cir-\\ncumference of the deferent, and of the deferent itself, are in\\nopposite directions, the first being toward the east, and the\\nsecond toward the west.\\n445. But these views will be better understood from a dia-\\ngram. Therefore, let ABC (Fig. 81) represent the deferent, E\\nbeing the earth a little out of the center. Let abc represent\\nthe epicycle, having its center at v, on the periphery of the def-\\nerent. Conceive the circumference of the deferent to be carried\\nabout the earth every twenty-four hours in the order of the\\nletters and at the same time, let the center v of the epicycle\\nabed, have a slow motion in the opposite direction, and let a\\nbody revolve in this circle in the direction abed. Then it will\\nPlay fair, Dissertation Second, p. 119.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0333.jp2"}, "334": {"fulltext": "310\\nSYSTEM OF THE WORLD.\\nbe seen that the body would actually describe the looped\\ncurves klmnop that it would appear stationary at I and m,\\nand at n and o that its motion would be direct from k to I,\\nand then retrograde from I to m direct again from m to n y\\nFig. 81.\\nand retrograde from n to o. Thus, suppose Mercury to be sit-\\nuated at h in its epicycle. By the revolution of the deferent,\\nit would be carried along with the other heavenly bodies\\naround the earth from left to right, every twenty -four hours\\nbut, meanwhile, the center of the epicycle shifting its place\\nslowly from right to left, while Mercury was moving from h to\\nCj c itself would change its place to r, and therefore the path of\\nthe planet would be in the cycloid al arc hr. Again, while\\nMercury was passing through cda, the point c would be still\\nmoving eastward, which would have the effect apparently to\\ncompress the lower half of the epicycle into the looped curve\\nnor and as on this side the motion in the epicycle is in the\\nsame direction with that of the deferent, but at a slower rate,\\nthe apparent path is much shorter than where, as on the other\\nside, the two motions conspire", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0334.jp2"}, "335": {"fulltext": "THE TYCHONIC SYSTEM. 311\\n446. Sueli a deferent and epicycle may be devised for each\\nplanet as will fully explain all its ordinary motions but it is\\ninconsistent with the phases of Mercury and Yenus, which\\nbeing between us and the sun on both sides of the epicycle,\\nwould present their dark sides toward ns in both these posi-\\ntions, whereas at one of the conjunctions they are seen to shine\\nwith full face.* It is moreover absurd to speak of a geometri-\\ncal center, which has no bodily existence, moving around the\\nearth on the circumference of another circle and hence some\\nsuppose that the ancients merely assumed this hypothesis as\\naffording a convenient geometrical representation of the phe-\\nnomena a diagram simply, without conceiving the system to\\nhave any real existence in nature.\\n447. The objections to the Ptolemaic system, in general, are\\nthe following First, it is a mere hypothesis, having no evi-\\ndence in its favor, except that it explains the phenomena. This\\nevidence is insufficient of itself, since it frequently happens that\\neach of two hypotheses, directly opposite to each other, will\\nexplain all the known phenomena. But the Ptolemaic system\\ndoes not even do this, as it is inconsistent with the phases of\\nMercury and Yenus, as already observed. Secondly, now that\\nwe are acquainted with the distances of the remoter planets,\\nand especially of the fixed stars, the swiftness of motion implied\\nin a daily revolution of the starry firmament around the earth,\\nrenders such a motion wholly incredible. Thirdly, the centrif-\\nugal force that would be generated in these bodies, especially\\nin the sun, renders it impossible that they can continue to re-\\nvolve around the earth as 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\\ncenter of the universe, and accounted for the diurnal motions\\nin the same manner as Ptolemy had done, namely, by an actual\\nrevolution of the whole host of heaven around the earth every\\ntwenty-four hours. But he rejected the scheme of deferents\\nVince s Complete System, i. r p. 96.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0335.jp2"}, "336": {"fulltext": "312 SYSTEM OF THE WOULD.\\nand epicycles, and held that the moon revolves about the earth\\nas the center of her motions that the sun, and not the earth,\\nis the center of the planetary motions and that the sun, ac-\\ncompanied by the planets, moves around the earth once a year,\\nsomewhat in the manner that we now conceive of Jupiter and\\nhis satellites as revolving around the sun. The system of\\nTycho serves to explain all the common phenomena of the\\nplanetary motions, but it is encumbered with the same objec-\\ntions as those that have been mentioned as resting against the\\nPtolemaic system, namely, that it is a mere hypothesis that\\nit implies an incredible swiftness in the diurnal motions and\\nthat it is inconsistent with the known laws of universal gravi-\\ntation. But if the heavens do not revolve, the earth must, and\\nthis brings us to the system of Copernicus.\\nTHE COPEKNTCAN SYSTEM.\\n449. Copernicus was born at Thorn, in Prussia, in 1473.\\nThe system that bears his name was the fruit of forty years of\\nintense study and meditation upon the celestial motions. As\\nalready mentioned (Art. 6), it maintains (1), That the apparent\\ndiurnal motion of the heavenly bodies, from east to west, is\\nowing to the real revolution of the earth on its own axis from\\nwest to east and (2), That the sun is the center around which\\nthe earth and planets all revolve from west to easl It rests\\non the following arguments\\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 re-\\nvolve on 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\\na centrifugal force arising from such a revolution.\\n5. Bodies let fall from a high eminence, fall eastward of their\\noase, indicating that higher objects have greater velocity of\\nrotation than lower ones.\\n6. The precession of the equinoxes is explained by the earth s\\nrotation on its axis.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0336.jp2"}, "337": {"fulltext": "THE COPERNICAN SYSTEM. CI Z\\nSecondly, the planets, including the earth, revolve about the sun\\n1. The phases of Mercury and Yenus are precisely such as\\nwould result from their circulating around the sun in orbits\\nwithin that of the earth but they are never seen in opposition,\\nas they would 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\\nthat the sun, and not the earth, is the center of their motions,\\nis inferred from the greater symmetry of their motions as re-\\nferred to the sun than as referred to the earth, and especially\\nfrom the laws of gravitation, which forbid our supposing that\\nbodies so much larger than the earth, as some of these bodies\\nare, can circulate permanently around the earth, the latter re-\\nmaining all the while at rest.\\n3. The annual motion of the earth itself is indicated also by\\nthe most conclusive arguments. For, first, since all the planets\\nwith their satellites, and the comets, revolve about the sun,\\nanalogy leads us to infer the same respecting the earth and its\\nsatellite. Secondly, the motions of the satellites, as those of\\nJupiter and Saturn, indicate that it is a law of the solar system\\nthat the smaller bodies revolve about the larger. Thirdly, the\\ndirection of the periodical meteors of November, which, in a\\nmajority of cases, is from east to west, indicates the motion of\\nthe earth from west to east. Lastly, the aberration of light\\naffords a sensible proof of the motion of the earth, since that\\nphenomenon indicates both a progressive motion of light, and\\na motion of the earth from west to east. (Art. 195.)\\n45 O It only remains to inquire whether there subsist high-\\ner orders of relations between the stars themselves. The as-\\nsemblage of bodies in clusters, as in the Pleiades, and still\\nmore, as in the great nebula of Hercules (Art. 425), implies\\nmutual relations constituting for each a system within itself;\\nand the analogies of all that portion of the heavenly bodies,\\nwhose motions fall within our observation, and the known uni-\\nformity of the laws of nature, conspire to prove that those re-\\nlations are maintained by revolutions around a common center.\\nWhat theory would lead us to expect, we actually see exempli-\\nfied in the revolutions of the binary stars (Art. 430), and in", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0337.jp2"}, "338": {"fulltext": "314: SYSTEM OF THE WOULD.\\nthe motion of the sun himself with his attendant worlds (Art.\\n432). The Nebulm also compose peculiar systems, in which\\nthe members seem associated in mutual relations, and separated\\nfrom all the other heavenly bodies, each composing an island\\nuniverse. Thus we ascend from the lower to the higher com-\\nbinations, according to a uniform, plan, so characteristic of as-\\ncending orders in every department of nature. Beginning\\nwith the relation between the earth and its satellite, we see it\\nsustained by the prevalence of forces which subject it to Kepler s\\nlaws and the law of universal gravitation. We see the same\\nprinciples carried out on a larger scale, but exactly on the\\nsamej??\u00c2\u00ab\u00c2\u00ab, 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\\ntheir satellites, we ascend to the next higher order, consisting\\nof suns and planets, in which the same plan is exemplified on\\na still grander scale, but without any change in its peculiar\\nfeatures. We next ascend still higher to the third order, as in\\nthe binary stars, where sun revolves around sun, upon the same\\nunvarying plan as before seen in these nearer worlds. At\\npresent, observation leads us to no higher point of the scale in\\nthe structure of the universe but the mind of man, obtaining\\nfrom these lower systems a knowledge of the plan on which\\nthe universe is built, goes forward to complete the grand ma-\\nchine. A bold attempt has recently been made by Maedler,\\nan eminent European astronomer, to fix the center, around\\nwhich not only our sun, but all the stars of our firmament re-\\nvolve. It must evidently be such a point, that the known\\nproper motions detected among the fixed stars will conform to\\nit, like the motions of the planets around the sun. He places\\nthat center in the Pleiades, or, more exactly, in Alcyone, the\\ncentral star of the Pleiades, which body is therefore denomi-\\nnated the Central Sun.* The proofs of this remarkable hy-\\npothesis are deemed, too incomplete at present to command en-\\ntire assent but the method of investigation pursued by this\\ndistinguished astronomer, opens a new field of observation and\\nof speculation, and promises to lend a new interest to inquiries\\ninto the mechanism of the universe.\\nPlate III., 1.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0338.jp2"}, "339": {"fulltext": "STRUCTURE OF THE UNIVERSE. 315\\n451. This fact being now established, that the stars are\\nimmense bodies like the sun, and that they are subject to the\\nlaws of gravitation, we can not conceive how they can be pre-\\nserved from falling into final disorder and ruin, unless they\\nmove in harmonious concert like the members of the solar sys-\\ntem. Otherwise, those that are situated on the confines of\\ncreation, being retained by no forces from without, while they\\nare subject to the attraction of all the bodies within, must leave\\ntheir stations, and move inward with accelerated velocity, and\\nthus all the bodies in the universe would at length fall together\\nin the common center of gravity. The immense distances at\\nwhich the stars are placed from each other would indeed delay\\nsuch a catastrophe but such must be the ultimate tendency of\\nthe material world, unless sustained in one harmonious system\\nby nicely-adjusted motions.* To leave entirely out of view our\\nconfidence in the wisdom and preserving goodness of the\\nCreator, and reasoning merely from what we know of the sta-\\nbility of the solar system, we should be justified in inferring\\nthat other worlds are not subject to forces which operate only\\nto hasten their decay, and to involve them in final ruin.\\nWe conclude, therefore, that the material universe is one great\\nsystem that the combination of planets with their satellites\\nconstitutes the first or lowest order of worlds that next to\\nthese, planets are linked to suns that these are bound to other\\nsuns, composing a still higher order in the scale of being; and,\\nfinally, that all the different systems of worlds move around\\ntheir common center of gravity.\\nRobison s Physical Astronomy.", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0339.jp2"}, "340": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0340.jp2"}, "341": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0341.jp2"}, "342": {"fulltext": "", "height": "4120", "width": "2335", "jp2-path": "introductionto00olms_0342.jp2"}, "343": {"fulltext": "PLATE II.\\nNEBULA AND DOUBLE STARS.\\n1. Castor. 2. y Leonis. 3. 39 Drac. 4. X Opli. 5. 1 1 Monoo. \u00c2\u00a3Cancri.\\nRevolutions of y Virginia.\\n71", "height": "3943", "width": "2201", "jp2-path": "introductionto00olms_0343.jp2"}, "344": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0344.jp2"}, "345": {"fulltext": "PLATE IN.\\nCLUSTERS AND NEBUL", "height": "4322", "width": "2348", "jp2-path": "introductionto00olms_0345.jp2"}, "346": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0346.jp2"}, "347": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0347.jp2"}, "348": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0348.jp2"}, "349": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0349.jp2"}, "350": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0350.jp2"}, "351": {"fulltext": "", "height": "3825", "width": "2201", "jp2-path": "introductionto00olms_0351.jp2"}, "352": {"fulltext": "", "height": "4368", "width": "2504", "jp2-path": "introductionto00olms_0352.jp2"}}