{"1": {"fulltext": "", "height": "3636", "width": "2282", "jp2-path": "compendiumofast00olm_0001.jp2"}, "2": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0002.jp2"}, "3": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0003.jp2"}, "4": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0004.jp2"}, "5": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0005.jp2"}, "6": {"fulltext": "Telescopic wonders of the Starry Heavens.\\n1. Great Cluster of Stars in Hercules.\\n2. Whirlpool Nebula of Lord Ross.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0006.jp2"}, "7": {"fulltext": "A\\nCOMPENDIUM OF ASTRONOMY;\\nCONTAINING- THE\\nELEMENTS OF THE SCIENCE,\\nFAMILIARLY EXPLAINED AND ILLUSTRATED,\\nADAPTED TO THE USE OF\\nHIGH SCHOOLS AND ACADEMIES,\\nAND OF THE\\nGENERAL READER.\\nA NEW AND GREATLY IMPROVED EDITION,\\nCONTAINING THE\\nLATEST DISCOVERIES.\\nBY DEOTSOK OLMSTED, LL.D.,\\nPROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE.\\nfr/**l\\nNEW YORK:\\nROBERT B. COLLINS, 254 PEARL-STREET.\\n1855.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0009.jp2"}, "8": {"fulltext": "Entered according to Act of Congress, in the year 1855,\\nBy DENIS ON OLMSTED,\\nIn the Clerk s Office of the District Court of Connecticut.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0010.jp2"}, "9": {"fulltext": "N\\nPREFACE\\nThe extensive patronage which this work has enjoyed, both\\nas a private manual, and as a text-book in the schools, lays the\\nauthor under peculiar obligation to render it deserving of public\\nfavor. He has therefore, with much care and pains, prepared\\nthis revised edition, using his best endeavors to present to the\\nlearner, in a short compass, a clear, faithful, and comprehensive\\noutline of the noble science of Astronomy. The earlier portions\\nof the work, treating as they do of subjects which are in their\\nnature of a fixed character, such as definitions and the doctrine\\nof the sphere, have appeared to him susceptible of little improve-\\nment, and accordingly have been suffered to remain unchanged\\nbut the latter portions, relating to the Planets, Comets, Fixed\\nStars, and Nebulae, have required to be entirely rewritten, in\\norder to embrace those numerous and grand discoveries with\\nwhich astronomy has been enriched within a few years past.\\nTo render difficult subjects plain and intelligible to the young,\\nhas constituted with him the leading object of a life sedulously\\ndevoted to the instruction of youth, through the several grada-\\ntions of the common-school, the academy, and the university.\\nHe would not, however, encourage any one to suppose, that he\\ncan make any valuable attainments in this profound science,\\nwithout diligent study and close reflection. If any book on\\nastronomy is very easy, it is because it is very superficial, and\\ncontains little worth knowing. The riches of this mine lie deep", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0011.jp2"}, "10": {"fulltext": "IV PREFACE.\\nand no one can acquire them who is either incompetent or un-\\nwilling to dive beneath the surface.\\nThe author would beg leave to direct the attention of teachers\\nto the improvements introduced into the present edition for\\nlearning the Constellations. Although the diagrams here given\\nwill not supersede the necessity of resorting to the Celestial\\nglobe, or to maps of the stars, yet as a starting-point they will\\nbe found greatly to facilitate the study of the nocturnal heavens,\\nand to afford to the young learner such plain and conspicuous\\nlandmarks that he will be able afterwards, with little assistance,\\nto travel successively from constellation to constellation, until\\nhe becomes entirely familiar with every portion of the starry\\nfirmament.\\nYale College, April, 1855.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0012.jp2"}, "11": {"fulltext": "ANALYSIS.\\nThese Outlines the author has found very valuable as a basis for pub-\\nlic examinations. Instead of being interrogated in the usual way by indi-\\nvidual questions, the student is assigned at random (or by lot) some portion\\nof the Analysis, which, after a little time for collecting his thoughts, he is\\ncalled upon to expand; and the fulness and accuracy with which he per-\\nforms this process, determine the mark accorded to him on the scale of\\nmerit.\\nPreliminary Observations.\\nPAGE\\nAstronomy\u00e2\u0080\u0094 defined 1\\nDescriptive, Physical, and Practical. 1\\nHistory. Astronomy of the An-\\ncients 1\\nAstronomy of the Greeks 2\\nPythagoras, Ilipparchus, Ptolemy. 2\\nAstronomy of the Middle Ages 3\\nCopernicus, Tycho Brahe, Kepler,\\nGalileo 3\\nAstronomy of the Moderns 3\\nSir Isaac Newton, La Place 3\\nAstrology defined 3\\nNatural Astrology, Judicial Astrology 3\\nCopernican System briefly stated 4\\nFigure and Dimensions of the\\nEarth, and Doctrine of the\\nSphere.\\nFigure of the Earth 5\\nProofs of its being globular 5\\nIllustrations by Figs. 1 and 2 6\\nExact figure of the earth 6\\nDiameter, Circumference 7\\nDoctrine of the Sphere\u00e2\u0080\u0094 defined 8\\nGreat and small circles 9\\nAxis of a circle, pole, secondary 9\\nHorizon sensible and rational 11\\nZenith and Nadir 11\\nVertical Circles, Meridian 12\\nPrime Vertical, Altitude, Azimuth,\\nAmplitude 12\\nAxis of the earth, Poles of the earth\\nand heavens 12\\nEquator, Hour Circles, Latitude, Lon-\\ngitude 13\\nEcliptic, Equinoxes, Solstices, Signs\\nof the Zodiac 14\\nColures equinoctial and solstitial 15\\nEight Ascension, Declination 16\\nCelestial Latitude and Longitude 16\\nPAGE\\nParallels of Latitude, Tropics, Polar\\nCircles 16\\nElevation of the Pole in degrees 17\\nElevation of the Equator 17\\nZones Torrid,Temperate, and Frigid 17\\nZodiac 17\\nHuw to represent the Circles of the\\nSphere by an apple 17\\nProjection of the Sphere\u00e2\u0080\u0094 Fig. 5 19\\nDiurnal Revolution.\\nCircles of diurnal revolution 21\\nSidereal Day, Eight Sphere, Parallel\\nSphere 22\\nOblique Sphere\u00e2\u0080\u0094 Fig. 6 24\\nCircle of Perpetual Apparition 25\\nCircle of Perpetual Occultation 26\\nArtificial Globes\u00e2\u0080\u0094 described 2S\\nHour Circles, Hour Index, Quadrant\\nof Altitude 30\\nTo rectify the globe for any place 31\\nProblems on the Terrestrial Globe 31\\nTo find the Latitude and Longitude\\nof a place 31\\nTo find a place, the Latitude and Lon-\\ngitude being given 31\\nTo find the bearing and distance of\\ntwo places 32\\nTo determine the difference of time\\nin different places 32\\nThe hour being given at any place, to\\ntell what hour it is in any other\\npart df the Avorld 32\\nTo find what people live directly un-\\nder us 32\\nTo find what people of the southern\\nhemisphere live directly opposite\\nto us 32\\nTo find the Antipodes 33\\nTo rectify the globe for the Sun s\\nplace 33", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0013.jp2"}, "12": {"fulltext": "ANALYSIS.\\nPAGE\\nThe latitude of a place being given,\\nto find the time of the Sun s rising\\nand setting 34\\nFroblems on the Celestial Globe 84\\nTo find the right ascension and decli-\\nnation 34\\nTo represent the appearance of the\\nstars at any time 84\\nTo find the altitude and azimuth of a\\nstar 35\\nTo find the angular distance of two\\nstars 35\\nTo find the sun s meridian altitude. 35\\nParallax, Refraction, and Twi-\\nlight.\\nParallax\u00e2\u0080\u0094 defined, Fig. 7 86\\nHorizontal Parallax\u00e2\u0080\u0094 its importance. 37\\nRefraction\u00e2\u0080\u0094 defined, Fig. 8 33\\nIts amount at different altitudes 40\\nEffects of refraction upon the sun and\\nmoon when near the horizon 41\\nTwilight\u00e2\u0080\u0094 defined, Fig. 9 42\\nIts appearance in different latitudes 43\\nIts uses 44\\nTime.\\nTime defined 44\\nSidereal day, Solar day 45\\nApparent time, Mean time 46\\nAstronomical day, Equation of Time 46\\nClocks, how regulated 46\\nThe Calendar 47\\nAstronomical year, Civil year 47\\nBissextile or Leap-year 48\\nRule for Leap-year 49\\nHow the common year begins and\\nends 50\\nAstronomical Instruments.\\nWhen first used 51\\nAngular measurement illustrated 52\\nTelescope, principle, Fig. 11 53\\nEefractors and Eeflectors 55\\nTransit Instrument, Fig. 12 56\\nIts use, Noon mark 57\\nAstronomical Clock 59\\nTo what kind of time adapted 59\\nAltitude and Azimuth Instrument, 60\\nSextant, Fig. 14 63\\nFigure and Density of the Earth.\\nSpheroidal figure, Fig. 15 63\\nHow measured by arcs of the merid-\\nian 66\\nBy the Pendulum 67\\nDifference in the polar and equatorial\\ndiameters 67\\nEarth s ellipticity 67\\nDensity of the earth 68\\nHow estimated, Fig. 16 68\\nPAGE\\nSun Solar Spots Zodiacal\\nLight.\\nSun figure, distance, diameter, size,\\ndensity 70\\nSolar Spots\u00e2\u0080\u0094 described, Fig. 17 72\\nPart of the sun s disk occupied by\\nthem 72\\nPeriod of their revolution\u00e2\u0080\u0094 Extent. 74\\nZodiacal Light\u00e2\u0080\u0094 described, Fig. 20 76\\nEarth s Annual Motion Seasons\\nFigure of the Earth s Orbit.\\nAnnual motion illustrated, Fig. 21. 79\\nObliquity of the Ecliptic SI\\nApparent motion of the Sun 82\\nDimensions of the Earth s orbit 83\\nSeasons cause of the change of sea-\\nsons 84\\nIllustration by Fig. 22 85\\nConsequences had the ecliptic been\\nperpendicular to the equator 86\\nFigure of the Earth s Orbit, Fig. 23 8S\\nHow the variations of the distances\\nfrom the sun are found 89\\nUniversal Gravitation.\\nTendency of all matter to all other\\nmatter 91\\nIllustration by Fig. 24 92\\nLaw of gravity in thr ee parts 93\\nLaw of falling bodies 94\\nFirst law of motion 94\\nUniversal Gravitation defined 96\\nIllustrated by Fig. 25 97\\nKepler s Laws 98\\nFirst law, figure of the planetary or-\\nbits 99\\nSecond law, spaces described by the\\nradius vector 101\\nThird law, relations between times\\nand distances 101\\nMotion in an elliptical orbit 102\\nIllustrated by Figs. 28, 29, 30 104\\nPrecession of the Equinoxes 107\\nIts annual amount 107\\nTropical year 109\\nThe Moon.\\nDistances, diameter, terminator 110\\nProofs of mountains and valleys 111\\nNames of the lunar spots 112\\nHeights of lunar mountains 113\\nForms of lunar mountains and val-\\nleys 114\\nLunar atmosphere 117\\nWhether there is water in the moon. 117\\nWhether inhabitants US\\nPhases of the moon 120\\nSyzygies, quadratures, octants 121\\nPhases illustrated by Fig. 81 121\\nRevolutions of the moon 122", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0014.jp2"}, "13": {"fulltext": "ANALYSIS.\\nVll\\nP-AGE\\nInclination of the orbit 123\\nWhy the moon runs high and low 124\\nMoon s revolution on her axis 125\\nMoon s three librations 126\\nWhether the earth carries the moon\\nround the sun 128\\nCauses of both motions explained. 129\\nCauses of the lunar irregularities 130\\nFigure of the moons orbit 132\\nBackward motion of the nodes s 133\\nSynodical revolution of the node 133\\nThe Saros explained 134\\nMetonic Cycle 134\\nRevolution of the apsides 135\\nPeriodical and secular irregularities 135\\nEclipses.\\nWhen an eclipse of the moon happens 137\\nWhen an eclipse of the sun happens. 137\\nIllustration by Fig. 32 13S\\nRepresentation, Figs. 33. 34 139\\nWhy the moon s surface is visible. 142\\nHow eclipses are foretold 143\\nNature of eclipses explained 144\\nAnnular eclipses 146\\nLongitude and Tides.\\nHow difference of longitude is found 150\\nMode by chronometers 151\\nBy eclipses 152\\nBy the lunar method 153\\nTides defined 155\\nHigh, low, spring, neap tides 155\\nCause of tides explained 156\\nInfluence of the declination of the sun\\nand moon 160\\nTides of rivers, bays, and lakes 162\\nAtmospheric tide 166\\nPlanets.\\nOrigin of the name 167\\nPlanets long known 167\\nPlanets recently discovered 167\\nNumber of Planets and Asteroids 168\\nDistances Dimensions of the system 169\\nMean distances, how determined by\\nKepler s law 170\\nMagnitudes diameters in miles 170\\nPeriodic times 171\\nInferior Planets, Mercury and Ye-\\nnus 172\\nMotions illustrated by Fig. 40 173\\nInferior and superior conjunction 173\\nSynodical revolution 173\\nDirect and retrograde motions 174\\nWhen the inferior planets are station-\\nary 175\\nPhases of Mercury- and Yenus 176\\nEccentricity and inclination of their\\norbits 177\\nWhen brightest 177\\nRevolutions on their axes 178\\nPAGE\\nYenus as the evening and morning\\nI star 178\\nPosition every eight years 178\\nTransits of the inferior planets 179\\nTransits of Mercury ISO\\nTransits of Yenus 181\\nSun s Hor. Parallax by Transits of\\nYenus 1S2\\nSuperior Planets 183\\nMars distance, color 1S3\\nChanges in apparent size 184\\nPhases, revolution on his axis 185\\nI Jupiter size, telescopic appearance.. 186\\nBelts, satellites 1S7\\nEclipses of the satellites. Fig. 44 139\\nj Longitude by these eclipses 191\\nDiscovery of the progressive motion\\nof light 193\\nSaturn, telescopic appearance 194\\nDimensions of his system 194\\nSaturn s Rings. Fig. 46 196\\nSaturn s Satellites, number and ap-\\npearances 200\\nUranus size, distance, discovery 201\\nSatellites, number and motions 202\\nUniformity of direction in the plane-\\ntary motions 202\\nNeptune size, distance, periodic time 203\\nHistory of its discovery 203\\nAsteroids, history of their discovery 204\\nNumber and names 206\\nDistances, periodic times, size 206\\nMotions of the Planetary System.\\nTwo methods of considering them 208\\nConception of absolute space 20S\\nMotions of the planets as seen from\\nthe sun 209\\nIllustrated by the motions of Mercury 210\\nInadequate representations by dia-\\ngrams and orreries 211\\nApparent motions of the planets 212\\nOf the Inferior planets by Fig. 40. 213\\nOf Superior planets by Fig. 47 213\\nMasses of the Planets 216\\nComparative density 216\\nStability of the Solar System 217\\nCauses of disturbance 217\\nHow the perturbations were discov-\\nered 218\\nExtreme minuteness of some of them 219\\nProvisions for the stability of the sys-\\ntem 220\\nNumerical arrangement of the planets 221\\nComets and Meteoric Showers,\\nComet described, Fig. 43 221\\nNumber Six most remarkable 223\\nMagnitude and brightness 224\\nPeriods, distances, light 225\\nMass, proofs of its smallness 227\\nOrbits and Motions 229\\nElements 230", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0015.jp2"}, "14": {"fulltext": "Vlll\\nANALYSIS.\\nPARK\\nHow the return is predicted 23.2\\nHalley s Comet 232\\nEncke s Comet 233\\nProofs of a resisting medium 234\\nComet of 1843 235\\nPhysical nature of comets 236\\nDangers from them 237\\nMeteoric Showers 238\\nMeteoric shower of Nov. 18, 1833. 238\\nConclusions respecting them 240\\nThe Constellations.\\nFixed Stars\u00e2\u0080\u0094 Classes 242\\nConstellations 244\\nCatalogues of the Stars 244\\nAries, Taurus 246\\nGemini 247\\nCancer, Leo 24S\\nVirgo, Libra, Scorpio 249\\nSagittarius, Capricornus, Aquarius 250\\nPisces, Little Bear 251\\nGreat Bear 252\\nDraco 253\\nCepheus, Cassiopeia 254\\nCamelopard, Andromeda, Perseus,\\nAuriga 255\\nLeo Minor, Grey Hounds, Berenice 255\\nBootes, Crown, Hercules 256\\nLyre, Swan 257\\nLittle Fox, Eagle, Antinous 258\\nDolphin, Pegasus, Ophiuchus 258\\nPAGE\\nWhale, Orion, Hare, Canis Major and\\nMinor 260\\nMonoceros, Hydra 261\\nLesson for September 261\\nLesson for December 2G2\\nLesson for March 263\\nLesson for June 264\\nDouble, Temporary, and Variable\\nStars, and Nebulae.\\nGreat Telescopes 265\\nDouble Stars, Number 267\\nMultiple Stars 268\\nTemporary Stars, Variable Stars 269\\nClusters 270\\nNebulas, 271\\nNebula of Hercules 272\\nNebulous Stars 274\\nPlanetary Nebulae 275\\nGalaxy 275\\nMotions of the Stars 276\\nBinary Stars 277\\nProper motions of the stars 278\\nMotion of the Solar System 278\\nDistances of the Stars 281\\nDistance of 61 Cygni 2S2\\nAmount of its parallax 282\\nNature of the Stars 284-\\nSystem of the World 285\\nCopernican System 286", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0016.jp2"}, "15": {"fulltext": "COMPENDIUM OF ASTRONOMY.\\nPRELIMINARY OBSERVATIONS.\\n1. Astronomy is that science which treats of the heav-\\nenly bodies.\\nMore particularly, its object is to teach what is known\\nrespecting the Sun, Moon, Planets, Comets, and Fixed\\nStars and also to explain the methods by which this\\nknowledge is acquired.\\nAstronomy is sometimes divided into Descriptive,\\nPhysical, and Practical. Descriptive Astronomy re-\\nspects facts Physical Astronomy, causes; Practical As-\\ntronomy, the means of investigating the facts, whether\\nby instruments, or by calculation. It is the province of\\nDescriptive Astronomy to observe, classify, and record,\\nall the phenomena of the heavenly bodies, whether per-\\ntaining to those bodies individually, or resulting from\\ntheir motions and mutual relations. It is the part of\\nPhysical Astronomy to explain the causes of these phe-\\nnomena by investigating and applying the general laws\\non which they depend especially by tracing out all the\\nconsequences of the law of universal gravitation. Prac-\\ntical Astronomy lends its aid to both the other depart-\\nments.\\n2. Astronomy is the most ancient of all the sciences.\\nAt a period of very high antiquity, it was cultivated in\\nEgypt, in Chaldea, and in India. Such knowledge of\\nthe heavenly bodies as could be acquired by close and\\nlong continued observation, without the aid of instru-\\n1 Define Astronomy. What does it teach 1 Name the three\\nparts into which it is divided. What does Descriptive Astron-\\nomy respect What does Physical Astronomy What does\\nPractical Astronomy What is the peculiar province of each\\n1", "height": "3576", "width": "2132", "jp2-path": "compendiumofast00olm_0017.jp2"}, "16": {"fulltext": "2 PRELIMINARY OBSERVATIONS.\\nmerits, was diligently amassed and tables of the celes-\\ntial motions were constructed, which could be used in\\npredicting eclipses, and other astronomical phenomena.\\nAbout 500 years before the Christain era, Pythago-\\nras, of Greece, taught astronomy at the celebrated school\\nat Crotona, (a Greek town on the southeastern coast of\\nItaly.) and exhibited more correct views of the nature\\nof the celestial motions, than were entertained by any\\nother astronomer of the ancient world. His views, how-\\never, were not generally adopted, but lay neglected for\\nnearly 2000 years, when they were revived and estab-\\nlished by Copernicus and Galileo. The most celebrated\\nastronomical school of antiquity, was at Alexandria in\\nEgypt, which was established and sustained by the Ptol-\\nemies, (Egyptian princes,) 300 years before the Chris-\\ntian era. The employment of instruments for measur-\\ning angles, and bringing in trigonometrical calculations\\nto aid the naked powers of observation, gave to the Alex-\\nandrian astronomers great advantages over all their pre-\\ndecessors.\\nThe most able astronomer of the Alexandrian school\\nwas Hipparchus, who was distinguished above all the\\nancients for the accuracy of his astronomical measure-\\nments and determinations. The knowledge of astron-\\nomy possessed by the Alexandrian school, and recorded\\nin the Almagest, or great work of Ptolemy, constituted\\nthe chief of what was known of our science during the\\nmiddle ages, until the fifteenth and sixteenth centuries,\\nwhen the labors of Copernicus of Prussia, Tycho Brake\\n2. Trace the history of Astronomy. Among what ancient\\nnations was it cultivated What kind of knowledge of the\\nheavenly bodies was amassed Who was Pythagoras? When\\nand where did he live Where was his school How correct\\nwere his views 1 Were they generally adopted Give an ac-\\ncount of the Alexandrian school. When was it established and\\nby whom What gave it great advantages over all its prede-\\ncessors Give some account of Hipparchus of Ptolemy of\\nCopernicus of Tycho Brahe of Kepler of Galileo o!\\nNewton of La Place. Specify the respective labors of each.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0018.jp2"}, "17": {"fulltext": "PRELIMINARY OBSERVATIONS 3\\nof Denmark, Kepler of Germany, and Galileo of Italy,\\nlaid the solid foundations of modern astronomy. Coper-\\nnicus expounded the true system of the world, or the\\narrangement and motions of the heavenly bodies Ty-\\ncho Brahe carried the use of instruments, and the art of\\nastronomical observation, to a far higher degree of accu-\\nracy than had ever been done before Kepler discovered\\nthe v great laws which regulate the movements of the\\nplanets and Galileo, having first enjoyed the aid of the\\ntelescope, made innumerable discoveries in the solar\\nsystem. Near the beginning of the eighteenth century,\\nSir Isaac Newton discovered, in the law of universal\\ngravitation, tbo great principle mat explains the causes\\nof all celestial phenomena and recently, La Place has\\nmore fully completed what Newton begun, having fol-\\nlowed out all the consequences of the law of universal\\ngravitation, in his great work, the Mecanique Celeste.\\n3. Among the ancients, astronomy was studied chiefly\\nas subsidiary to astrology. Astrology was the art of dv\\nvining future events by the stars. It was of two kinds,\\nnatural and judicial. Natural Astrology, aimed at pre-\\ndicting remarkable occurrences in the natural world, as\\neathquakes, volcanoes, tempests, and pestilential dis-\\neases. Judicial Astrology, aimed at foretelling the fates\\nof individuals, or of empires.\\n4. Astronomers of every age, have been distinguished\\nfor their persevering industry, and their great love of ac-\\ncuracy. They have uniformly aspired to an exactness\\nin their inquiries, far beyond what is aimed at in most\\ngeographical investigations, satisfied with nothing short\\nof numerical accuracy wherever this is attainable and\\nyears of toilsome observation, or laborious calculation,\\nhave been spent with the hope of attaining a few se-\\n3. Define Astrology. What was Natural and what Judicial\\nAstrology\\n4. What is said of the industry and accuracy of astrono-\\nmers 1 Can this science be taught by artificial aids alone", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0019.jp2"}, "18": {"fulltext": "PRELIMINARY OBSERVATIONS.\\nconds nearer to the truth. Moreover, a severe but de-\\nlightful labor is imposed on all, who would arrive at a\\nclear and satisfactory knowledge of the subject of astron-\\nomy. Diagrams, artificial globes, orreries, and familiar\\ncomparisons and illustrations, proposed by the author or\\nthe instructor, may afford essential aid to the learner,\\nbut nothing can convey to him a perfect comprehension\\nof the celestial motions, without much diligent study\\nand reflection.\\n5. In this treatise, we shall for the present assume the\\nCopernican system as the true system of the world,\\npostponing the discussion of the evidence on which it\\nrests to a late period, when the learner has been made ex-\\ntensively acquainted with astronomical facts. This sys-\\ntem maintains (1,) That the apparent diurnal revolution\\nof the heavenly bodies, from east to west, is owing to\\nthe real revolution of the earth on its own axis from\\nwest to east, in the same time and (2,) That the sun\\nis the center around which the earth and planets all re-\\nvolve from west to east, contrary to the opinion that the\\nearth is the center of motion of the sun and planets.\\n5. What system is assumed as the true system of the world\\nSpecify the two leading points in the Copernican system.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0020.jp2"}, "19": {"fulltext": "PART I. OF THE EARTH,\\nCHAPTER I.\\nOF THE FIGURE AND DIMENSIONS OF THE EARTH, AND THE\\nDOCTRINE OF THE SPHERE.\\n6. The figure of the earth is nearly globular. This\\nfact is known, lirst, by the circular form of its shadow\\ncast upon the moon in a lunar eclipse secondly, from\\nanalogy, each of the other planets being seen to be\\nspherical thirdly, by our seeing the tops of distant ob-\\njects while the other parts are invisible, as the topmast\\nof a ship, while either leaving or approaching the shore,\\nor the lantern of a light-house, which when first descried\\nat a distance at sea, appears to glimmer upon the very\\nsurface of the water fourthly, by the testimony of nav-\\nigators who have sailed around it and, finally, by ac-\\ntual observations and measurements, made for the ex-\\npress purpose of ascertaining the figure of the earth, b\\\\\\nmeans of which astronomers are enabled to compute the\\ndistances from the center of the earth of various places\\non its surface, which distances are found to be nearly\\nequal.\\nThe effect of the rotundity of the earth upon the ap-\\npearance of a ship, when either leaving or approaching\\nthe spectator, is illustrated by Fig. 1.\\nAs light proceeds in straight lines, it is evident that,\\nif the earth is round, the top of the ship ought to come\\ninto view before the lower parts, when the ship is ap-\\nproaching the spectator at A, and to remain longest in\\nview when the ship is leaving him. But, were the earth\\n6. What is the figure of the earth 1 Enumerate the various\\nproofs of its rotundity.\\n1*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0021.jp2"}, "20": {"fulltext": "a continued plane, then the spectator would see all parts\\nof the ship at the same time, as is represented in the an-\\nnexed figure.\\nFig. 2.\\n7. The foregoing considerations show that the form\\nof the earth is spherical but more exact determinations\\nprove, that the earth, though nearly globular, is not ex-\\nactly so its diameter from the north to the south pole\\nis about 26 miles less than through the equator, giving\\nto the earth the form of an oblate spheroid, or a flattened\\nsphere resembling an orange. We shall reserve the ex-", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0022.jp2"}, "21": {"fulltext": "FIGURE AND DIMENSIONS. 7\\nplanations of the methods by which this fact is estab-\\nlished, until the learner is better prepared than at present\\nto understand them.\\nThe mean or average diameter of the earth, is 7912.4\\nmiles, a measure which the learner should fix in his\\nmemory as a standard of comparison in astronomy, and\\nof which he should endeavor to form the most adequate\\nconception in his power. The circumference of the\\nearth is about 25,000 miles. Although the surface of\\nthe earth is uneven, sometimes rising in high mountains,\\nand sometimes descending in deep valleys, yet these ele-\\nvations and depressions are so small in comparison with\\nthe immense volume of the globe, as hardly to occasion\\nany sensible deviation from a surface uniformly curvi-\\nlinear. The irregularities of the earth s surface, in this\\nview, are no greater than the rough points on the rind\\nof an orange, which do not perceptibly interrupt its con\\ntinuity for the highest mountain on the globe is only\\nabout five miles above the general level and the deep-\\nest mine hitherto opened is only about half a mile.*\\n5 i\\nNow or about one sixteen hundredth part\\n7912 1582 F\\nof the whole diameter, an inequality which, in an arti-\\nficial globe of eighteen inches diameter, amounts to only\\nthe eighty eighth part of an inch.\\n8. The greatest difficulty in the way of acquiring\\ncorrect views in astronomy, arises from the erroneous\\nnotions trial pre-occupy the mind. To divest himself\\n7. What is the exact figure of the earth 1 Flow much greater\\nis its diameter through the equator than through the poles\\nWhat is the mean average diameter of the earth What is its\\ncircumference Do the inequalities on the earth s surface af-\\nfect its rotundity To what may these be compared How-\\nhigh is the highest mountain above the general level 1 How\\ndeep is the deepest mine To how much would this amount\\non an artificial globe eighteen inches in diameter\\nSir John Herschel.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0023.jp2"}, "22": {"fulltext": "8\\nTHE EARTH.\\nof these, the learner should conceive of the earth as a\\nhuge globe occupying a small portion of space, and en-\\ncircled on all sides with the starry sphere. He should\\nfree his mind from its habitual proneness to consider one\\npart of space as naturally up and another down, and\\nview himself as subject to a force which binds him to\\nthe earth as truly as though he were fastened to it by\\nsome invisible cords or wires, as the needle attaches it-\\nself to all sides of a spherical loadstone. He should\\nFig. 3.\\ndwell on this point until it appears to him as truly up in\\nthe direction of BB, CC, DD, (Fig. 3,) when he is at\\nB, C, and D, respectively, as in the direction AA, when\\nhe is at A.\\nDOCTRINE OF THE SPHERE.\\n9. The definitions of the different lines, points, and\\ncircles, which are used in astronomy, and the proposi-\\ntions founded upon them, compose the Doctrine of the\\nSphere.\\n8. Whence arises the greatest difficulty in acquiring correct\\nviews in astronomy How should the learner conceive of\\nthe earth? Illustrate by figure 3.\\n9. Doctrine of the sphere define it.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0024.jp2"}, "23": {"fulltext": "DOCTRINE OF THE SPHERE.\\n10. A section of a sphere by a plane cutting it in any\\nmanner, is a circle. Great circles are those which pass\\nthrough the center of the sphere, and divide it into two\\nequal hemispheres Small circles, are such as do not\\npass through the center, but divide the sphere into two\\nunequal parts. Every circle, whether great or small, is\\ndivided into 360 equal parts called degrees. A degree,\\ntherefore, is not any fixed or definite quantity, but only\\na certain aliquot part of any circle.*\\nThe axis of a circle, is a straight line passing through\\nits center at right angles to its plane.\\nAs this work may be read by some who are unacquainted with\\neven the rudiments of geometry, we annex a few particulars respecting\\nangular measurements.\\nA line drawn from the center to the circumference of a circle is\\ncalled a radius, as CD, fig. 4.\\nAny part of the circumference of a circle is called an arc, as AB,\\norBD.\\nFig. 4.\\nAn angle is measured by the\\narc included between two radii.\\nThus, in the annexed figure, the\\nangle contained between the two\\nradii CA and CB, that is, the an-\\ngle ACB, is measured by the arc\\nAB. But this arc is the same part\\nof the smaller circle that EF is of\\nthe greater. The arc AB there-\\nfore contains the same number of\\ndegrees as the arc EF, and either\\nmay be taken for the measure of\\nthe angle ACB. As the whole\\ncircle contains 360\u00c2\u00b0, it is evident\\nthat the quarter of a circle, or quad-\\nrant ABD, contains 90\u00c2\u00b0, and the\\nsemicircle ABDG contains 180\u00c2\u00b0.\\nThe complement of an arc or an-\\ngle, is what it wants of 90\u00c2\u00b0. Thus BD is the complement of AB, and\\nAB is the complement of BD. If AB denotes a certain number of de-\\ngrees of latitude, BD will be the complement of the latitude or the co-\\nlatitude, as it is commonly written.\\nThe supplement of an arc or angle, is what it wants of IHtP.\\nThus BA is the supplement of GDB, and GDB, is the supplement\\nof BA. If BA were 20\u00c2\u00b0 of longitude, GDB its supplement would\\nbe 160\u00c2\u00b0.\\nAn angle is said to be subtended by the side which is opposite to it.\\nThus in the triangle ACK, the angle at C is subtended by the side AK,\\nthe angle at A by CK, and the angle at K by CA. In like manner a\\nside is said to be subtended by an angle, as AK by the angle at C.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0025.jp2"}, "24": {"fulltext": "10 the Earth.\\nThe pole of a great circle, is the point on the sphere\\nwhere its axis cuts through the sphere. Every great\\ncircle has two poles, each of which is every where 90\u00c2\u00b0\\nfrom the great circle.\\nAll great circles of the sphere cut each other in two\\npoints diametrically opposite, and consequently, their\\npoints of section are 180\u00c2\u00b0 apart.\\nA great circle which passes through the pole of an-\\nother great circle, cuts the latter at right angles.\\nThe great circle which passes through the pole of an-\\nother great circle and is at right angles to it, is called a\\nsecondary to that circle.\\nThe angle made by two great circles on the surface\\nof the sphere, is measured by the arc of another great\\ncircle, of which the angular point is the pole, being the\\narc of that great circle intercepted between those two\\ncircles.\\n11. In order to fix the position of any plane, either on\\nthe surface of the earth or in the heavens, both the earth\\nand the heavens are conceived to be divided into sepa-\\nrate portions by circles, which are imagined to cut\\nthrough them in various ways. The earth thus inter-\\nsected is called the terrestrial, and the heavens the ce-\\nlestial sphere. The learner will remark, that these cir-\\ncles have no existence in nature, but are mere land-\\nmarks, artificially contrived for convenience of refer-\\n10. What figure is produced by the section of a sphere?\\nDefine great circles. Define small circles. Into how many\\ndegrees is every circle divided Is a degree any fixed or defi-\\nnite quantity What is the axis of a circle What is the pole\\nof a circle How do all great circles cut each other? How\\nis a great circle cut by another great circle passing through its\\npole What is the secondary of a circle How is the angle\\nmadeby two great circles on the surface of the sphere measured?\\n11. How are the earth and the heavens conceived to be di-\\nvided What constitutes the terrestrial sphere What the\\ncelestial Have these circles any existence in nature In\\nwhat do the heavenly bodies appear to be fixed", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0026.jp2"}, "25": {"fulltext": "OiiCTRlNh OF THE SPHERE. 11\\nence. On account of the immense distance of the heav-\\nenly bodies, they appear to us, wherever we are placed.\\nto be fixed in the same concave surface, or celestial\\nvault. The great circles of- the globe, extended every\\nway to meet the concave surface of the heavens, become\\ncircles of the celestial sphere.\\n12. The Horizon is the great circle which divides\\nthe earth into upper and lower hemispheres, and sepa-\\nrates the visible heavens from the invisible. This is\\nthe rational horizon. The sensible horizon, is a circle\\ntouching the earth at the place of the spectator, and is\\nbounded by the line in which the earth and skies seem\\nto meet. The sensible horizon is parallel to the ra-\\ntional, but is distant from it by the semi-diameter of the\\nearth, or nearly 4,000 miles. Still, so vast is the dis-\\ntance of the starry sphere, that both these planes appear\\nto cut that sphere in the same line so that we see the\\nsame hemisphere of stars that we should see if the up-\\nper half of the earth were removed, and we stood on the\\nrational horizon.\\n13. The poles of the horizon are the zenith and na-\\ndir. The Zenith is the point directly over our head,\\nand the Nadir that directly under our feet. The plumb\\nline is in the axis of the horizon, and consequently di-\\nrected towards its poles.\\nEvery place on the surface of the earth has its own\\nhorizon; and the traveller has a new horizon at every\\nstep, always extending 00 degrees from him in all di-\\nrections.\\n12. Define the horizon. Distinguish between the rational\\nand the sensible horizon. What is the distance between the\\nsensible and rational horizons How do both appear to cut\\nthe starry heavens\\n13. What are the poles of the horizon Define the zenith.\\nDefine the nadir. How is the plumb line situated with respect\\nto the horizon? How manv horizons are there on the earth", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0027.jp2"}, "26": {"fulltext": "12 THE EARTH.\\n14. Vertical circles are those which pass through the\\npoles of the horizon, perpendicular to it.\\nThe Meridian is that vertical circle which passes\\nthrough the north and south points.\\nThe Prime Vertical, is that vertica. circle which\\npasses through the east and west points.\\nThe Altitude of a body, is its elevation above the ho-\\nrizon, measured on a vertical circle.\\nThe Azimuth of a body, is its distance measured on\\nthe horizon from the meridian to a vertical circle passing\\nthrough the body.\\nThe Amplitude of a body, is its distance on the hori-\\nzon, from the prime vertical, to a vertical circle passing\\nthrough the body.\\nAzimuth is reckoned 90\u00c2\u00b0 from either the north or\\nsouth point and amplitude 90\u00c2\u00b0 from either the east or\\nwest point. Azimuth and amplitude are mutually com-\\nplements of each other. When a point is on the hori-\\nzon, it is only necessary to count the number of degrees\\nof the horizon between that point and the meridian, in\\norder to find its azimuth but if the point is above the\\nhorizon, then its azimuth is estimated by passing a ver-\\ntical circle through it, and reckoning the azimuth from\\nthe point where this circle cuts the horizon.\\nThe Zenith Distance of a body is measured on a ver-\\ntical circle, passing through that body. It is the com-\\nplement of the altitude.\\n15. The Axis of the Earth is the diameter, on which\\nthe earth is conceived to turn in its diurnal revolution.\\nThe same line continued until it meets the starry con-\\ncave, constitutes the axis of the celestial sphere.\\n14. Define vertical circles the meridian the prime verti-\\ncal altitude azimuth amplitude. How many degrees of\\nazimuth are reckoned from what points How are azimuth\\nand amplitude related to each other Define zenith distance\\nHow is it related to the altitude 1\\n15. Define the axis of the earth the axis of the celestial\\nsphere the poles of the earth the poles of the heavens.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0028.jp2"}, "27": {"fulltext": "DOCTRINE OF THE SPHERE. 13\\nThe Poles of the Earth are the extremities of the\\nearth s axis the Poles of the Heavens, the extremities\\nof the celestial axis.\\n16. The Equator is a great circle cutting the axis of\\nthe earth at right angles. Hence the axis of the earth\\nis the axis of the equator, and its poles are the poles of\\nthe equator. The intersection of the plane of the equa-\\ntor with the surface of the earth, constitutes the terres-\\ntrial, and with the concave sphere of the heavens, the\\ncelestial equator. The latter, by way of distinction, is\\nsometimes denominated the equinoctial.\\n17. The secondaries to the equator, that is, the great\\ncircles passing through the poles of the equator, are\\ncalled Meridians, because that secondary which passes\\nthrough the zenith of any place is the meridian of that\\nplace, and is at right angles both to the equator and the\\nhorizon, passing as it does through the poles of both.\\nThese secondaries are also called Hour Circles, because\\nthe arcs of the equator intercepted between them are\\nused as measures of time.\\n18. The Latitude of a place on the earth, is its dis-\\ntance from the equator north or south. The Polar Dis-\\ntance, or angular distance from the nearest pole, is the\\ncomplement of the latitude.\\n19. The Longitude of a place is its distance from\\nsome standard meridian, either east or west, measured\\non the equator. The meridian usually taken as the\\nstandard, is that of the Observatory of Greenwich, in\\nLondon. If a place is directly on the equator, we have\\nonly to inquire how many degrees of the equator there\\n16. Define the equator. What constitutes the terrestrial\\nequator? what, the celestial equator What is this also called?\\n17. What are the secondaries of the equator called 7\\n18. Define the Latitude of a place- the polar distance.\\n2", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0029.jp2"}, "28": {"fulltext": "14 THE EARTH.\\nare between that place and the point where the meridian\\nof Greenwich cuts the equator. If the place is north or\\nsouth of the equator, then its longitude is the arc of the\\nequator intercepted between the meridian which passes\\nthrough the place, and the meridian of Greenwich.\\n20. The Ecliptic is a great circle in which the earth\\nperforms its annual revolution around the sun. It passes\\nthrough the center of the earth and the center of the\\nsun. It is found by observation that the earth does not\\nlie with its axis at right angles to the plane of the eclip-\\ntic, but that it is turned about 23^ degrees out of a per-\\npendicular direction, making an angle with the plane\\nitself of 66^\u00c2\u00b0. The equator, therefore, must be turned\\nthe same distance out of a coincidence with the ecliptic,\\nthe two circles making an angle with each other of 23 J\u00c2\u00b0.\\nIt is particularly important for the learner to form cor-\\nrect ideas of the ecliptic, and of its relations to the equa-\\ntor, since to these two circles a great number of astro-\\nnomical measurements and phenomena are referred.\\n21. The Equinoctial Points, or Equinoxes* are the\\nintersections of the ecliptic and equator. The time\\nwhen the sun crosses the equator in going northward\\nis called the vernal, and in returning southward, the au-\\ntumnal equinox. The vernal equinox occurs about\\nthe 21st of March, and the autumnal the 22d of Sep-\\ntember.\\n19. Define the Longitude of a place. What is the standard\\nmeridian When a place is on the equator, how is its longi-\\ntude measured 1 how when it is north or south of the equator\\n20. Define the ecliptic. How does it pass with respect to\\nthe earth and the sun How is it situated with respect to the\\nequator\\n21. Define the equinoctial points. When is the vernal equi-\\nnox, and when the autumnal\\nThe term Equinoxes strictly denotes the times when the sun ar-\\nrives at the equinoctial points, but it is frequently used to denote those\\npoints themselves.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0030.jp2"}, "29": {"fulltext": "DOCTRINE OF THE SPHERE. 15\\n22.. The Solstitial Points are the two points of the\\necliptic most distant from the equator. The times when\\nthe sun comes to them are called solstices. The sum-\\nmer solstice occurs about the 22d of June, and the win-\\nter solstice about the 22d of December.\\nThe ecliptic is divided into twelve equal parts of 30\u00c2\u00b0\\neach, called signs, which, beginning at the vernal equi-\\nnox, succeed each other in the following order\\nNorther 7i.\\nSouthern.\\n1.\\nAries\\ncyo\\n7. Libra\\n2.\\nTaurus\\n8\\n8. Scorpio\\nm\\n3.\\nGemini\\nH\\n9. Sagittarius\\nt\\n4.\\nCancer\\no\\n10. Capricornus\\nvs\\n5.\\nLeo\\na\\n11. Aquarius\\nAAA/\\nAW\\n6.\\nVirgo\\nm\\n12. Pisces\\nX\\nThe mode of reckoning on the ecliptic, is by signs, de-\\ngrees, minutes, and seconds. The sign is denoted either\\nby its name or its number. Thus 100\u00c2\u00b0 maybe express-\\ned either as the 10th degree of Cancer, or as 3 s 10\u00c2\u00b0.\\n23. Of the various meridians, two are distinguished\\nby the name of Colures. The Equinoctial Colure, is\\nthe meridian which passes through the equinoctial\\npoints. From this meridian, right ascension and celes-\\ntial longitude are reckoned, as longitude on the earth is\\nreckoned from the meridian of Greenwich. The Sol-\\nstitial Colure, is the meridian which passes through the\\nsolstitial points.\\n24. The position of a celestial body is referred to the\\nequator by its right ascension and declination. Bight\\n22. Define the solstitial points, and solstices. When does\\nthe summer solstice occur when does the winter solstice oc-\\ncur Into how many signs is the ecliptic divided How\\nmany degrees are there in each Name the signs. What is\\nthe mode of reckoning on the ecliptic 1 In what two ways\\nmay 100\u00c2\u00b0 be expressed?\\n23. What is the equinoctial colure the solstitial colure 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0031.jp2"}, "30": {"fulltext": "16 THE EARTH.\\nAscension, is the angular distance from the vernal equi-\\nnox measured on the equator. If a star is situated on\\nthe equator, then its right ascension is the number of\\ndegrees of the equator between the star and the vernal\\nequinox. But if the star is north or south of the equa-\\ntor, then its right ascension is the arc of the equator, in-\\ntercepted between the vernal equinox and that secon-\\ndary to the equator which passes through the star. De-\\nclination is the distance of a body from the equator,\\nmeasured on a secondary to the latter. Therefore, right\\nascension and declination correspond to terrestrial longi-\\ntude and latitude, right ascension being reckoned from\\nthe equinoctial colure, in the same manner as longitude\\nis reckoned from the meridian of Greenwich. On the\\nother hand, celestial longitude and latitude are referred,\\nnot to the equator, but to the ecliptic. Celestial Longi-\\ntude, is the distance of a body from the vernal equinox\\nreckoned on the ecliptic. Celestial Latitude, is distance\\nfrom the ecliptic measured on a secondary to the latter.\\nOr, more briefly, Longitude is distance on the eclip-\\ntic Latitude, distance from the ecliptic. The North\\nPolar Distance of a star, is the complement of its de-\\nclination.\\n25. Parallels of Latitude are small circles parallel to\\nthe equator. They constantly diminish in size as we go\\nfrom the equator to the pole.\\nThe Tropics are the parallels of latitude that pass\\nthrough the solstices. The northern tropic is called the\\ntropic of Cancer the southern, the tropic of Capricorn.\\nThe Polar Circles are the parallels of latitude that\\npass through the poles of the ecliptic, at the distance of\\n23^ degrees from the pole of the earth.\\n24. Define right ascension and declination. To what do\\nthey correspond on the terrestrial sphere Define celestial\\nlongitude and latitude.\\n25. What are parallels of latitude tropics polar circles 1\\nTo what is the elevation of the pole always equal also that\\nof the equator", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0032.jp2"}, "31": {"fulltext": "DOCTRINE OF THE SPHERE. 17\\nThe elevation of the pole of the heavens above the\\nhorizon of any place, is always equal to the latitude of\\nthe place. Thus, in 40\u00c2\u00b0 of north latitude we see the\\nnorth star 40\u00c2\u00b0 above the northern horizon, whereas, if\\nwe should travel southward its elevation would grow\\nless and less, until we reached the equator, where it\\nwould appear in the horizon or, if we should travel\\nnorthward, the north star would rise constantly higher\\nand higher, until, if we could reach the pole of the earth,\\nthat star would appear directly over head. The eleva-\\ntion of the equator above the horizon of any place, is\\nequal to the complement of the latitude. Thus, at the\\nlatitude of 40\u00c2\u00b0 N. the equator is elevated 50\u00c2\u00b0 above the\\nsouthern horizon.\\n26. The earth is divided into five zones. That por-\\ntion of the earth which lies between the tropics, is called\\nthe Torrid Zone that between the tropics and polar\\ncircles, the Temperate Zones; and that between the\\npolar circles and the poles, the Frigid Zones.\\n27. The Zodiac is the part of the celestial sphere,\\nwhich lies about 8 degrees on each side of the ecliptic.\\nThis portion of the heavens is thus marked off by itself,\\nbecause all the planets move within it.\\n28. After endeavoring to form, from the definitions,\\nas clear an idea as he can of the various circles of the\\nsphere, the learner may next resort to an artificial globe,\\nand see how they are severally represented there. Or if\\nhe has not access to a globe, he may aid his conceptions\\nby the following easy device. To represent the earth,\\nselect a large apple, (a melon when in season will be\\nfound still better.) The shape of the apple, flattened as\\n26. Define each of the zones.\\n27. Define the zodiac.\\n28. Show how to represent the artificial sphere by any round\\nbody as an apple, and point out the various circles on it.\\n2*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0033.jp2"}, "32": {"fulltext": "18 THE EARTH.\\nit usually is at the two ends, will not inaptly exhibit\\nthe spheroidal figure of the earth, while the larger diam-\\neter through the middle will indicate the excess of mat-\\nter about the equator although we should remark, thai\\nthe disproportion between the polar and equatorial diam\\neters of the earth is in fact so slight, that it would be\\nscarcely perceptible in a model. The eye and the stem\\nof the apple will indicate the position of the two poles\\nof the earth. Applying the thumb and finger of the\\nleft hand to the poles, and holding the apple so that the\\npoles may be in a north and south line, turn the globe\\nfrom west to east, and its motion will correspond to the\\ndiurnal movement of the globe. Pass a wire, as a knit-\\nting needle, through the poles, and it will represent the\\naxis of the sphere. A circle cut around the apple half\\nway between the poles, will be the equator; and several\\nother circles cut between the equator and the poles, par-\\nallel to the equator, will represent parallels of latitude,\\nof which, two drawn 23 J degrees from the equator, will\\nbe the tropics, and two others at the same distance from\\nthe poles, will be the polar circles. A great circle cut\\nthrough the poles in a north and south direction, will\\nform the meridian, and several other great circles drawn\\nthrough the poles, and of course perpendicularly to the\\nequator, will be secondaries to the equator, constituting\\nmeridians or hour circles. A great circle cut through the\\ncenter of the earth from one tropic to the other, will rep-\\nresent the plane of the ecliptic, and consequently, a line\\ncut around the apple where such a section meets the sur-\\nface, is the terrestrial ecliptic. The points where this\\ncircle meets the tropics, are the solstices, and its intersec-\\ntions with the equator are the equinoctial points.\\n29. The horizon is best represented by a circular\\npiece of pasteboard, cut so as to fit closely to the apple,\\nbeing movable upon it. When this horizon is slipped\\n29. How is the horizon represented in our model? How is\\nit placed to represent the horizon of the equator 1 How for the\\nhorizon of the poles How for our own horizon 1 How shall\\nwe represent the prime vertical", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0034.jp2"}, "33": {"fulltext": "DOCTRINE OF THE SPHERE. ]p,\\nup to the poles, it becomes the horizon of the equator\\nwhen it is so placed as to coincide with the earth s\\nequator, it becomes the horizon of the poles and in\\nevery other situation it represents the horizon of a place\\non the globe 90\u00c2\u00b0 every way from it. Suppose we are\\nin latitude 40\u00c2\u00b0, then let us place our movable paper par-\\nallel to our own horizon, and elevate the pole 40\u00c2\u00b0 above\\nit, as near as we can judge by the eye. If we cut a cir-\\ncle around the apple, passing through its highest parts\\nand through the east and west points, it will represent\\nthe prime vertical.\\n30. We cannot too strongly recommend to the young\\nlearner to form for himself such a sphere as is here de-\\nscribed, and to point out on it the various arcs of azimuth\\nand altitude, right ascension and declination, terrestrial\\nand celestial latitude and longitude, these last being re-\\nferred to the equator on the earth, and to the ecliptic in\\nthe heavens.\\n31. When the circles of the sphere are well learned,\\nwe may advantageously employ projections of them in\\nvarious illustrations. By the projection of the sphere is\\nmeant a representation of all its parts on a plane. The\\nplane itself is called the plane of projection. Let us take\\nany circular ring, as a wire bent into a circle, and hold\\nit in different positions before the eye. If we hold it\\nparallel to the face, or directly opposite to the eye, we\\nsee it as an entire circle. If we turn it a little sideways,\\nit appears oval, or as an ellipse and as we continue to\\nturn it more and more round, the ellipse grows narrower\\nand narrower, until, when the edge is presented to the\\neye, we see nothing but a line. Now imagine the ring\\nto be near a perpendicular wall, and the eye to be re-\\n30. What is particularly recommended to the young learner?\\n31 What is meant by the projection of the sphere What\\nis the projection of a circle when seen directlybefore the face\\nwhat when seen obliquely 1 what when seen edgewise", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0035.jp2"}, "34": {"fulltext": "20\\nTHE EARTH.\\nmoved at such a distance from it, as not to distinguish\\nany interval between the ring and the wall then the\\nseveral figures under which the ring is seen, will appear\\nto be inscribed on the wall, and we shall see the ring as\\na circle when perpendicular to a straight line joining\\nthe center of the ring and the eye, as an ellipse when\\noblique to this line, or as a straight line when its edge is\\ntowards us.\\n32. It is in this manner that the circles of the sphere\\nare projected, as represented in the following diagram\\nHere various circles are represented as projected on the\\nmeridian, which is supposed to be situated directly be-\\nfore the eye, at some distance from it. The horizon HO\\nbeing perpendicular to the meridian is seen edgewise, and\\nconsequently is projected into a straight line. The same\\nis the case with the prime vertical ZN, with the equator\\nEQ, and the several small circles parallel to the equator,\\nwhich represent the two tropics and the two polar cir-\\n32. In figure 5, what represents the plane of projection\\nWhy are certain circles represented by straight lines 1 why are\\nothers represented by ellipses How is the eye supposed to\\nbe situated", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0036.jp2"}, "35": {"fulltext": "DIURNAL REVOLUTION 21\\ncles. In fact, all circles whatsoever, which are perpen-\\ndicular to the plane of projection, will be represented\\nby straight lines. But every circle which is perpendic-\\nular to the horizon, except the prime vertical, being seen\\nobliquely as ZMN, will be projected into an ellipse.\\nIn the same manner, PRP, an hour circle, being oblique\\nto the eye, is represented by an ellipse on the plane of\\nprojection.\\nCHAPTER II.\\nDIURNAL REVOLUTION ARTIFICIAL GLOBES.\\n33. The apparent diurnal revolution of the heavenly\\nbodies from east to west, is owing to the actual revolu-\\ntion of the earth on its own axis from west to east. If\\nwe conceive of a radius of the earth s equator extended\\nuntil it meets the concave sphere of the heavens, then\\nas the earth revolves, the extremity of this line would\\ntrace out a curve on the face of the sky, namely, the ce-\\nlestial equator. In curves parallel to this, called the cir-\\ncles of diurnal revolution, the heavenly bodies actually\\nappear to move, every star having its own peculiar cir-\\ncle. After the learner has first rendered familiar the\\nreal motions of the earth from west to east, he may\\nthen, without danger of misconception, adopt the com-\\nmon language, that all the heavenly bodies revolve\\naround the earth once a day from east to west, in circles\\nparallel to the equator and to each other.\\n34. The time occupied by a star in passing from any\\npoint in the meridian until it comes round to the same\\n33. To what is the apparent diurnal revolution of the heav-\\nenly bodies from east to west owing If a radius of the earth s\\nequator were extended to meet the concave sphere of the heav-\\nens, what would it trace out as the earth revolves What\\nare circles of diurnal revolution 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0037.jp2"}, "36": {"fulltext": "22 THE EARTH.\\npoint again, is called a sidereal day, and measures the\\nperiod of the earth s revolution on its axis. If we watch\\nthe returns of the same star from day to day, we shall\\nfind the intervals exactly equal to one another that is\\nthe sidereal days are all equal. Whatever star we se-\\nlect for the observation, the same result will be obtained.\\nThe stars, therefore, always keep the same relative posi-\\ntion, and have a common movement round the earth\\na consequence that naturally flows from the hypothesis,\\nthat their apparent motion is all produced by a single\\nreal motion, namely, that of the earth. The sun, moon,\\nand planets, as well the fixed stars, revolve in like man-\\nner, but their returns to the meridian are not, like those\\nof the fixed stars, at exactly equal intervals.\\n35. The appearances of the diurnal motions of the\\nheavenly bodies are different in different parts of the\\nearth, since every place has its own horizon, (Art. 8,)\\nand different horizons are variously inclined to each\\nother. Let us suppose the spectator viewing the diurnal\\nrevolutions from several different positions on the earth.\\nOn the equator, his horizon would pass through both\\npoles for the horizon cuts the celestial vault at 90 de-\\ngrees in every direction from the zenith of the spectator\\nbut the pole is likewise 90 degrees from his zenith, and\\nconsequently, the pole must be in the horizon. The ce-\\nlestial equator would coincide with the Prime Vertical\\n34. Define a sidereal day. Are the sidereal days equal oi\\nunequal Are the returns of the sun, moon, and planets to\\nthe meridian, likewise at equal intervals\\n35. How are the appearances of the diurnal motions in dif-\\nferent parts of the earth When the spectator is on the equa-\\ntor, where would his horizon pass with respect to the poles of\\nthe earth? With what great circle would the celestial equator\\ncoincide How would all the circles of diurnal revolution be\\nsituated with respect to the horizon Define a right sphere.\\nIn a right sphere, how would a star situated in *he celestial\\nequator perform its circuit? how would stars nearer the poles\\nappear to move 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0038.jp2"}, "37": {"fulltext": "DIURNAL REVOLUTION. 23\\nbeing a great circle passing through the east and west\\npoints. Since all the diurnal circles are parallel to the\\nequator, consequently, they would all, like the equator,\\nbe perpendicular to the horizon. Such a view of the\\nheavenly bodies, is called a right sphere or,\\nA Right Sphere is one in which all the daily revolu-\\ntions of the stars, are in circles perpendicular to the horizon.\\nA right sphere is seen only at the equator. Any star\\nsituated in the celestial equator, would appear to rise di-\\nrectly in the east, when on the meridian to be in the\\nzenith of the spectator, and to set directly in the west\\nin proportion as stars are at a greater distance from the\\nequator towards the pole, s they describe smaller and\\nsmaller circles, until, near the pole, their motion is hardly\\nperceptible.\\n36. If the spectator advances one degree towards the\\nnorth pole, his horizon reaches one degree beyond the\\npole of the earth, and cuts the starry sphere one degree\\nbelow the pole of the heavens, or below the north star,\\nif that be taken as the place of the pole. As he moves\\nonward towards the pole, his horizon continually reaches\\nfarther and farther beyond it, until when he comes to\\nthe pole of the earth, and under the pole of the heavens,\\nhis horizon reaches on all sides to the equator and coin-\\ncides with it. Moreover, since all the circles of daily\\nmotion are parallel to the equator, they become, to the\\nspectator at the pole, parallel to the horizon. This is\\nwhat constitutes a parallel sphere. Or,\\nA Parallel Sphere is that in which all the circles of\\ndaily motion arc parallel to the horizon.\\nTo render this view of the heavens familiar, the\\nlearner should follow round in his mind a number of\\n36. What changes take place in one s horizon as he moves\\nfrom the equator towards the pole How would it be situated\\nwhen he reached the pole 1 Define a parallel sphere. Explain\\nthe appearances of the stars and of the sun in a parallel sphere.\\nWhere only can such a sphere be seen Has the pole of the\\nearth ever been reached by man 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0039.jp2"}, "38": {"fulltext": "24 THE EARTH.\\nseparate stars, one near the horizon, one a few degrees\\nabove it, and a third near the zenith. To one who\\nstood upon the north pole, the stars of the northern hemi-\\nsphere would all be perpetually in view when not ob-\\nscured by clouds or lost in the sun s light, and none of\\nthose of the southern hemisphere would ever be seen.\\nThe sun would be constantly above the horizon for six\\nmonths in the year, and the remaining six constantly\\nout of sight. That is, at the pole the days and nights\\nare each six months long. The phenomena at the south\\npole are similar to those at the north.\\nA 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 discovery ships pene-\\ntrated within a few degrees of the north pole, and of\\ncourse enjoyed the view of a sphere nearly parallel.\\n37. As the circles of daily motion are parallel to the\\nhorizon of the pole, and perpendicular to that of the\\nequator, so at all places between the two, the diurnal\\nmotions are oblique to the horizon. This aspect of the\\nheavens constitutes an oblique sphere, which is thus de-\\nfined:\\nAn Oblique Sphere is that in which the circles of\\ndaily motion are oblique to the horizon.\\nSuppose, for example, the spectator is at the latitude of\\nfifty degrees. His horizon reaches 50\u00c2\u00b0 beyond the pole\\nof the earth, and gives the same apparent elevation to\\nthe pole of the heavens. It cuts the equator, and all\\nthe circles of daily motion, at an angle of 40\u00c2\u00b0, being al-\\nways equal to the co-altitude of the pole. Thus, let HO\\n(Fig. 6,) represent the horizon, EQ, the equator, and\\nPP the axis of the earth. Also, 11, mm, c, parallels\\nof latitude. Then the horizon of a spectator at Z, in\\nlatitude 50\u00c2\u00b0 reaches to 50\u00c2\u00b0 beyond the pole and the\\nangle ECH, is 40\u00c2\u00b0. As we advance still farther north\\n37. Define an oblique sphere. Where is it seen At the\\nlatitude of 50\u00c2\u00b0 how is the horizon situated Illustrate by fig. 6.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0040.jp2"}, "39": {"fulltext": "25\\n77^^?\\n*x\\ne/\\n7\\\\\\nID\\n7^0\\nl^\\n7i\\nW s\\nthe elevation of the diurnal circles grows less and less,\\nand consequently the motions of the heavenly bodies\\nmore and more oblique, until finally, at the pole, where\\nthe latitude is 90\u00c2\u00b0, the angle of elevation of the equator\\nvanishes, and the horizon and equator coincide with\\neach other, as before stated.\\n38. The circle of perpetual apparition, is the\\nboundary of that space around the elevated pole, where\\nthe stars never set. Its distance from the pole is equal\\nto the latitude of the place. For, since the altitude of\\nthe pole is equal to the latitude, a star whose polar dis-\\ntance is just equal to the latitude, will when at its low-\\nest point only just reach the horizon and all the stars\\nnearer the pole than this will evidently not descend so\\nfar as the horizon.\\nThus, mm (Fig. 6,) is the circle of perpetual appari-\\ntion, between which and the north pole, the stars never\\nset, and its distance from the pole OP is evidently equal\\nto the ehvation of the pole, and of course to the lati-\\ntude.\\n38. What is the circle of perpetual apparition?\\nby fig. 6.\\n3\\nIllustrate", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0041.jp2"}, "40": {"fulltext": "26 THE EARTH\\n39. In the opposite hemisphere, a similar part of the\\nsphere adjacent to the depressed pole never rises. Hence\\nThe circle of perpetual occultation, is the boun-\\ndary of that space around the depressed pole, within\\nwhich the stars never rise. Thus, m m (Fig. 6,) is the\\ncircle of perpetual occultation, between which and tho\\nsouth pole, the stars never rise.\\n40. In an oblique sphere, the horizon cuts the circles\\nof daily motion unequally. Towards the elevated pole,\\nmore than half the circle is above the horizon, and a\\ngreater and greater portion as the distance from the\\nequator is increased, until finally, within the circle of\\nperpetual apparition, the whole circle is above the hori-\\nzon. Just the opposite takes place in the hemisphere\\nnext the depressed pole. Accordingly, when the sun is\\nin the equator, as the equator and horizon, like all other\\ngrsat circles of the sphere, bisect each other, the days\\nand nights are equal all over the globe. But when the\\nsun is north of the equator, the days become longer than\\nthe nights, but shorter when the sun is south of the\\nequator. Moreover, the higher the latitude, the greater\\nis the inequality in the lengths of the days and nights.\\nAll these ooints will be readily understood by inspecting\\nfigure\\n41. Most of the appearances of the diurnal t evolution\\ncan be explained, either on the supposition that the ce-\\nlestial sphere actually all turns around the earth once in\\n24 hours, or that this motion of the heavens is merely\\napparent, arising from the revolution of the earth on its\\n39. What is the circle of perpetual occultation Illustrate\\nby fig. 6.\\n40. How does the horizon of an oblique sphere cut the cir-\\ncles of daily motion Towards the elevated pole what portion\\nof the circles is above the horizon? Towards the depressed\\npole, how is the fact? When are the days and nights equal\\nall over the world When are the days longer, and whsii\\nshorter than the nights", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0042.jp2"}, "41": {"fulltext": "DIURNAL REVOLUTION. 27\\naxis in the opposite direction a motion of which we\\nare insensible, as we sometimes lose the consciousness\\nof our own motion in a ship or a steamboat, and observe\\nall external objects to be receding from us with a com-\\nmon motion. Proofs entirely conclusive and satisfac-\\ntory, establish the fact, that it is the earth and not the\\ncelestial sphere that turns but these proofs are drawn\\nfrom various sources, and the student is not prepared to\\nappreciate their value, or even to understand some of\\nthem, until he has made considerable proficiency in the\\nstudy of astronomy, and become familiar with a great\\nvariety of astronomical phenomena. To such a period\\nof our course of instruction, we therefore postpone the\\ndiscussion of the hypothesis of the earth s rotation on\\nits axis.\\n42. While we retain the same place on the earth, the\\ndiurnal revolution occasions no change in our horizon,\\nbut our horizon goes round as well as ourselves. Let\\nus first take our station on the equator at sunrise our\\nhorizon now passes through both the poles, and through\\nthe sun, which we are to conceive of as at a great dis-\\ntance from the earth, and therefore as cut, not by the\\nterrestrial but by the celestial horizon. As the earth\\nturns, the horizon dips more and more below the sun, at\\nthe rate of 15 degrees for every hour, and, as in the case\\nof the polar star, the sun appears to rise at the same rate.\\nIn six hours, therefore, it is depressed 90 degrees below\\nthe sun, which brings us directly under the sun, which,\\nfor our present purpose, we may consider as having all\\nthe while maintained the same fixed position in space.\\n4 1 On what suppositions can the appearances of the diurnal\\nrevolution be explained Is it the earth or the heavens that\\nreally move I Why is the discussion of this subject postponed\\n42. Explain the true cause of the sun s appearing to rise and\\nset, as observed at the equator. What is the position of the ho-\\nrizon at sunrise What at. six hours afterwards 1 What at\\nthe end of twelve hours 1 What at the end of eighteen hours", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0043.jp2"}, "42": {"fulltext": "28 THE EARTH.\\nThe earth continues to turn, and in six hours more, it\\ncompletely reverses the position of our horizon, so that\\nthe western part of the horizon which at sunrise was\\ndiametrically opposite to the sun now cuts the sun, and\\nsoon afterwards it rises above the level of the sun, and\\nthe sun sets. During the next twelve hours, the sun\\ncontinues on the invisible side of the sphere, until the\\nhorizon returns to the position from which it started, and\\na new day begins.\\n43. Let us next contemplate the similar phenomena\\nat the poles. Here the horizon, coinciding as it does\\nwith the equator, would cut the sun through its center,\\nand the sun would appear to revolve along the surface\\nof the sea, one-half above and the other half below the\\nhorizon. This supposes the sun in its annual revolution\\nto be at one of the equinoxes. When the sun is north\\nof the equator, it revolves continually round in a circle,\\nwhich, during a single revolution, appears parallel to the\\nequator, and it is constantly day and when the sun\\nis south of the equator, it is, for the same reason, contin-\\nual night.\\nWe have endeavored to conceive of the manner in\\nwhich the apparent diurnal movements of the sun are\\nreally produced at two stations, namely, in the right\\nsphere, and in the parallel sphere. These two cases\\nbeing clearly understood, there will be little difficulty in\\napplying a similar explanation to an oblique sphere.\\nARTIFICIAL GLOBES.\\n44. Artificial globes are of two kinds, terrestrial and\\ncelestial. The first exhibits a miniature representation\\nof the earth the second, of the visible heavens and\\nboth show the various circles by which the two spheres\\n43. Explain the similar phenomena at the poles, first, when\\nthe sun is at the equinoxes, and secondly, when it is north and\\nwhen it is south of the equator.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0044.jp2"}, "43": {"fulltext": "ARTIFICIAL GLOBES. 29\\nare respectively traversed Since all globes are similar\\nsolid figures, a small globe, imagined to be situated at\\nthe center of the earth or of the celestial vault, may rep-\\nresent all the visible objects and artificial divisions of\\neither sphere, and with great accuracy and just propor-\\ntions, though on a scale greatly reduced. The study of\\nartificial globes, therefore, cannot be too strongly recom-\\nmended to the student of astronomy.*\\n45. An artificial globe is encompassed from north to\\nsouth by a strong brass ring to represent the meridian of\\nthe place. This ring is made fast to the two poles and\\nthus supports the globe, while it is itself supported in a\\nvertical position by means of a frame, the ring being\\nusually let into a socket in which it may be easily slid,\\nso as to give any required elevation to the pole. The\\nbrass meridian is graduated each way from the equator\\nto the pole 90\u00c2\u00b0, to measure degrees of latitude or decli-\\nnation, according as the distance from the equator refers\\nto a point on the earth or in the heavens. The horizon\\nis represented by a broad zone, made broad for the con-\\nvenience of carrying on it a circle of azimuth, another of\\namplitude, and a wide space on w T hich are delineated\\nthe signs of the ecliptic, and the sun s place for every\\nday in the year not because these points have any spe-\\ncial connexion with the horizon, but because this broad\\nsurface furnishes a convenient place for recording them.\\n44. What does the terrestrial globe exhibit What does\\nthe celestial globe What do both show\\n45. How is the meridian of the place represented To what\\npoints is the brass meridian fastened What supports the ring\\nHow is it graduated How is the horizon represented Why\\nis it made broad What circles are inscribed on it 1\\nIt were .esirable, indeed, that every student of the science should\\nhave a celestial globe, at least, constantly before him. One of a\\nsmall size, as eight or nine inches, will answer the purpose, although\\nglobes of these dimensions cannot usually be relied on for nice meas-\\nurements\\n3*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0045.jp2"}, "44": {"fulltext": "30 THE EARTH.\\n46. Hour Circles are represented on the terrestrial\\nglobe by great circles drawn through the pole of the\\nequator but, on the celestial globe, corresponding cir-\\ncles pass through the poles of the ecliptic, constituting\\ncircles of latitude, while the brass meridian, being a se-\\ncondary to the equinoctial, becomes an hour circle of\\nany star which, by turning the globe, is brought under it.\\n47. The Hour Index is a small circle described around\\nthe pole of the equator, on which are marked the hours\\nof the day. As this circle turns along with the globe, it\\nmakes a complete revolution in the same time with the\\nequator or, for any less period, the same number of de-\\ngrees of this circle and of the equator pass under the\\nmeridian. Hence the hour index measures arcs of right\\nascension, 15\u00c2\u00b0 passing under the meridian every hour.\\n48. The Quadrant of Altitude is a flexible strip of\\nbrass, graduated into ninety equal parts, corresponding\\nin length to degrees on the globe, so that when applied to\\nthe globe and bent so as closely to fit its surface, it meas-\\nures the angular distance between any two points.\\nWhen the zero, or the point where the graduation be-\\ngins, is laid on the pole of any great circle, the 90th de-\\ngree will reach to the circumference of that circle, and\\nbeing therefore a great circle passing through the pole\\nof another great circle, it becomes a secondary to the\\nlatter. Thus the quadrant of altitude may be used as a\\nsecondary to any great circle on the sphere but it is\\nused chiefly as a secondary to the horizon, the point\\n46. How are hour circles represented on the terrestrial\\nglobe How are circles of latitude represented on the celes-\\ntial globe\\n47. Describe the hour index. What does it measure\\n48. What is the quadrant of altitude? How is it gradua-\\nted When the zero point is laid on the pole of any great cir-\\ncle, to what will the 90th degree reach How may it be used\\nas a secondary to any great circle When screwed on the\\nzenith what does it become What arcs does it then measure", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0046.jp2"}, "45": {"fulltext": "TERRESTRIAL GLOBE. 31\\nmarked 90\u00c2\u00b0 being screwed fast to the pole of the hori-\\nzon, that is, the zenith, and the other end, marked 0.\\nbeing slid along between the surface of the sphere and\\nthe wooden horizon. It thus becomes a vertical circle,\\non which to measure the altitude of any star through\\nwhich it passes, or from which to measure the azimuth\\nof the star, which is the arc of the horizon intercepted\\nbetween the meridian and the quadrant of altitude pass-\\ning through the star.\\n49. To rectify the. globe for any place, the north pole\\nmust be elevated to the latitude of the place then the\\nequator and all the diurnal circles will have their due in-\\nclination in respect to the horizon and, on turning the\\nglobe, every point on either globe will revolve as the\\nsame point does in nature and the relative situations of\\nall places will be the same as on the native spheres.\\nPROBLEMS ON THE TERRESTRIAL GLOBE.\\n50. To find the Latitude and Longitude of a place\\nTurn the globe so as to bring the place to the brass me-\\nridian then the degree and minute on the meridian di-\\nrectly over the place will indicate its latitude, and the\\npoint of the equator under the meridian, will show its\\nlongitude.\\nEx. What is the Latitude and Longitude of the city\\nof New York?\\n51. To find a place having its Latitude and Longitude\\ngiven Bring to the brass meridian the point of the equa-\\ntor corresponding to the longitude, and then at the de-\\ngree of the meridian denoting the latitude, the place will\\nbe found.\\nEx. What place on the globe is in Latitude 39\u00c2\u00b0 N. and\\nLongitude 77\u00c2\u00b0 W. 1\\n49. How do .ve rectify the globe for any place\\n50. Find the latitude and longitude of Washington City.\\n51. What place lies in latitude 39\u00c2\u00b0 N.and longitude 77\u00c2\u00b0 W.?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0047.jp2"}, "46": {"fulltext": "32 THE EARTH\\n52. To find the bearing and distance of two places\\nRectify the globe for one of the places screw the quad-\\nrant of altitude to the zenith,* and let it pass through\\nthe other place. Then the azimuth will give the bear-\\ning of the second place from the first, and the number\\nof degrees on the quadrant of altitude, multiplied by G9,\\n(the number of miles in a degree,) will give the distance\\nbetween the two places.\\nEx. What is the bearing of New Orleans from New\\nYork, and what is the distance between these places 1\\n53. To determine the difference of time in different\\nplaces Bring the place that lies eastward of the other\\nto the meridian, and set the hour index at XII. Turn\\nthe globe eastward until the other place comes to the\\nmeridian, then the index will point to the hour required.\\nEx. When it is noon at New York, what time is it at\\nLondon\\n54. The hour being given at any place, to tell what\\nhour it is in any other part of the world: Bring the\\ngiven place to the meridian, and set the hour index to\\nthe given time then turn the globe, until the other\\nplace comes under the meridian, and the index will\\npoint to the required hour.\\nEx. What time is it at Canton, in China, when it is\\n9 o clock A. M. at New York\\n55. To find what people on the earth live under us,\\nhaving their noon at the time of our midnight Bring\\nthe place where we dwell to the meridian, and set the\\n52. What is the bearing and distance of New Orleans from\\nNew York\\n53. When it is noon at New York, what time is it at Pekin\\n54. What time is it at London when it is noon at Boston 1\\nThe zenith will of course be the point of the meridian over the\\nplace.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0048.jp2"}, "47": {"fulltext": "TERRESTRIAL GLOBE. 33\\nhour index to XII then turn the globe until the other\\nXII comes under the meridian; the point under the\\nsame part of the meridian where we were before, will\\nbe the place sought.\\nEx. Find what place is directly under New York.\\n56. To find what people of the southern hemisphere\\nare directly opposite to us Bring our place to the me-\\nridian the place in the same latitude south, then un-\\nder the meridian, will be the place in question.\\nEx. What place in the southern hemisphere corres-\\nponds to New Haven\\n57. To find the antipodes of a place, or the people\\nwhose feet are exactly opposite to ours Bring our place\\nto the meridian set the hour index to XII, and turn the\\nglobe until the other XII comes under the meridian\\nthen the point of the southern hemisphere under the me-\\nridian and having the same latitude with ours, will be\\nthe place of our antipodes.\\nEx. Who are antipodes to the people of Philadelphia\\n58. To rectify the globe for the sun s place: On the\\nwooden horizon, find the day of the month, and against\\nit is given the sun s place in the ecliptic, expressed by\\nsigns and degrees.* Look for the same sign and degree\\non the ecliptic, bring that point to the meridian and set\\nthe hour index to XII. To all places under the merid-\\nian it will then be noon.\\nEx. Rectify the globe for the sun s place on the 1st\\nof September.\\n55. Find what place is directly under Philadelphia.\\n56. What place in south latitude corresponds to Boston 7\\n51. Who are the antipodes of the people of London\\n58. Rectify the globe for the sun s place for the first of June.\\nThe larger globes have the day of the month marked against *he\\ncorresponding sign on the ecliptic itself.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0049.jp2"}, "48": {"fulltext": "34 THE EARTH.\\n59. Trie latitude of the place being given, to find the\\ntime of the sun s rising and setting on any given day\\nat that place: Having rectified the globe for the lati-\\ntude, bring the sun s place in the ecliptic to the gradua-\\nted edge of the meridian, and set the hoar index to XII\\nthen turn the globe so as to bring the sun to the eastern\\nand then to the western horizon, and the hour index\\nwill show the times of rising and setting respectively.\\nEx. At what time will the sun rise and set at New\\nHaven, Lat. 41\u00c2\u00b0 18 on the 10th of July\\nPROBLEMS ON THE CELESTIAL GLOBE.\\n60. To find the Declination and Right Ascension of\\na heavenly body Bring the place of the body (whether\\nsun or star) to the meridian. Then the degree and\\nminute standing over it will show its declination, and\\nthe point of the equinoctial under the meridian will give\\nits right ascension. It will be remarked, that the decli-\\nnation and right ascension are found in the same man-\\nner as latitude and longitude on the terrestrial globe.\\nRight ascension is expressed either in degrees or in\\nhours both being reckoned from the vernal equinox.\\nEx. What is the declination and right ascension of the\\nbright star Lyra? also of the sun on the 5th of June?\\n61. To represent the appearance of the heavens at any\\ntime Rectify the globe for the latitude, bring the sun s\\nplace in the ecliptic to the meridian, and set the hour\\nindex to XII then turn the globe westward until the\\nindex points to the given hour, and the constellations\\nwould then have the same appearance to an eye situated\\n59. Find the time of the sun s rising and setting at Boston\\n(Lat. 42\u00c2\u00b0, Lon. 71\u00c2\u00b0) on the first day of December.\\n60. On the celestial globe, What is the right ascension and\\ndeclination of any star taken at pleasure\\n61. Represent the appearance of the heavens at Tuscaloosa\\n(Lat. 33\u00c2\u00b0, Lon. 87\u00c2\u00b0) at 8 o clock in the evening of Nov. 13th.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0050.jp2"}, "49": {"fulltext": "CELESTIAL GLOBE. 35\\nat the center of the globe, as they have at that moment\\nin the sky.\\nEx. Required the aspect of the stars at New Haven,\\nLat. 41\u00c2\u00b0 18 at 10 o clock, on the evening of Decem-\\nber 5th.\\n62. To find the altitude and azimuth of any star\\nRectify the globe for the latitude, and let the quadrant\\nof altitude be screwed to the zenith, and be made to pass\\nthrough the star. The arc on the quadrant, from the\\nhorizon to the star, will denote its altitude, and the arc\\nof the horizon from the meridian to the quadrant, will be\\nits azimuth.\\nEx. What is the altitude and azimuth of Sirius (the\\nbrightest of the fixed stars) on the 25th of December at\\n10 o clock in the evening, in Lat. 41\u00c2\u00b0 1\\n63. To find the angular distance of two stars from\\neach other Apply the zero mark of the quadrant of alti-\\ntude to one of the stars, and the point of the quadrant\\nwhich falls on the other star, will show the angular dis-\\ntance between the two.\\nEx. What is the distance between the two largest\\nstars of the Great Bear.*\\n64. To find the sun s meridian altitude, the latitude\\nind day of the month being given Having rectified\\nthe globe for the latitude, bring the sun s place in the\\necliptic to the meridian, and count the number of de-\\n62. Find the altitude and azimuth of Lyra at 10 o clock in\\nthe evening of June 18th, in Lat. 42\u00c2\u00b0.\\n63. Find the angular distance between any two stars taken\\nat pleasure.\\nThese two stars are sometimes called the Pointers, from the line\\nwhich passes through them being always nearly in the direction of the\\nnorth star. The angular distance between them is about 5\u00c2\u00b0, and may\\nbe learned as a standard of reference in estimating by the eye, the dis-\\ntance between any two points on the celestial vault.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0051.jp2"}, "50": {"fulltext": "36\\nTHE EARTH,\\ngrees and minutes between that point of the meridian\\nand the zenith. The complement of this arc will be\\nthe sun s meridian altitude.\\nEx. What is the sun s meridian altitude at noon on\\nthe 1st of August, in Lat. 41\u00c2\u00b0 18\\nCHAPTER III.\\nOF PARALLAX, REFRACTION, AND TWILIGHT.\\n65. Parallax is the apparent change of place which\\nbodies undergo by being viewed from different points.\\nFig- 7\\nThus in figure 7, let A represent the earth, CH the ho-\\nrizon. HZ a quadrant of a great circle of the heavens,\\n64. What is the sun s meridian altitude at noon on the 18th\\nof June, in latitude 35\u00c2\u00b0\\n65. Define parallax. Illustrate by the figure. What angle\\nmeasures the parallax? Why do astronomers consider the\\nheavenly bodies as viewed from the center of the earth", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0052.jp2"}, "51": {"fulltext": "PARALLAX. 3?\\nextending from the horizon to the zenith and let E, F,\\nG, O, be successive positions of the moon at different\\nelevations, from the horizon to the meridian. Now a\\nspectator on the surface of the earth at A, would refer\\nthe place of E to h, whereas, if seen from the center of\\nthe earth, it w T ould appear at H. The arc Hh is called\\nthe parallactic arc, and the angle HEA, or its equal AEC,\\nis the angle of parallax. The same is true of the angles\\nat F, G, and O, respectively.\\nSince then a heavenly body is liable to be referred to\\ndifferent points on the celestial vault, when seen from\\ndifferent parts of the earth, and thus some confusion\\noccasioned in the determination of points on the celes-\\ntial sphere, astronomers have agreed to consider the true\\nplace of a celestial object to be that, where it would\\nappear if seen from the center of the earth. The doc-\\ntrine of parallax teaches how to reduce observations\\nmade at any place on the surface of the earth, to such as\\nhey would be if made from the center.\\n66. The angle AEC is called the horizonta parallax,\\nwhich may be thus defined. Horizontal Parallax, is\\nthe change of position which a celestial body, appearing\\nin the horizon as seen from the surface of the earth,\\nwould assume if viewed from the earth s center. It is\\nthe angle subtended by the semi-diameter of the earth,\\nas viewed from the body itself.\\nIt is evident from the figure, that the effect of parallax\\nupon the place of a celestial body is to depress it. Thus,\\nin consequence of parallax, E is depressed by the arc\\nHh F by the arc Vp G by the arc Rr while O sus-\\ntains no change. Hence, in all observations on the al-\\ntitude of the sun, moon, or planets, the amount of par-\\nallax is to be added the stars, as we shall see here-\\nafter, have no sensible parallax.\\n66. Define horizontal parallax By what is it subtended?\\n(See Art. 10. Note.) What is the effect of parallax upon the\\nplace of a heavenly body?\\n4", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0053.jp2"}, "52": {"fulltext": "38\\nTHE EARTH.\\n67. The determination of the horizontal parallax of a\\ncelestial body is an element of great importance, since it\\nfurnishes the means of estimating the distance of the\\nbody from the center of the earth. Thus, if the angle\\nAEC (Fig 7,) be found, the radius of the earth AC be-\\ning known, we have in the right angled triangle AEC,\\nthe side AC and all the angles, to find the side CE,\\nwhich is the distance of the moon from the center of\\nthe earth.*\\nREFRACTION.\\n68. While parallax depresses the celestial bodies sub-\\nject to it, refraction elevates them and it affects alike\\n(he most distant as well as nearer bodies, being occa-\\nsioned by the change of direction which light undergoes\\nFig. 8.\\n67. Why is the determination of the parallax of a heavenly\\nbody an element of great importance Illustrate by figure 7.\\nShould the reader be unacquainted with the principles of trigonom-\\netry, yet he ought to know the fact that these principles enable us,\\nwhen we have ascertained certain parts in a triangle, to find the un-\\nknown parts. Thus, in the above case, when w T e have found the an-\\ngle of parallax, AEB, (which is determined by certain astronomical ob-\\nservations,) knowing also the semi-diameter of the earth AC, we can\\nfind by trigonometry, the length of the side CE, which is the distance\\nof the body from the center of the earth.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0054.jp2"}, "53": {"fulltext": "REFRACTION. 39\\nm passing through the atmosphere. Let us conceive of\\nthe atmosphere as made up of a great number of concen-\\ntric strata, as AA, BB, CC, and DD, (Fig. 8,) increasing\\nrapidly in density (as is known to be the fact) in ap-\\nproaching near to the surface of the earth. Let S be a\\nstar, from which a ray of light S\u00c2\u00ab enters the atmosphere\\nat where, being much turned towards the radius of\\nthe convex surface,* it would change its direction into\\nthe line ab, and again into be, and cO, reaching the\\neye at O. Now, since an object always appears in the\\ndirection in which the light finally strikes the eye, the\\nstar would be seen in the direction of the ray Oc, and\\ntherefore, the star would apparently change its place,\\nin consequence of refraction, from S to S being ele-\\nvated out of its true position. Moreover, since on ac-\\ncount of the continual increase of density in descending\\nthrough the atmosphere, the light would be continually\\nturned out of its course more and more, it would there-\\nfore move, not in the polygon represented in the figure,\\nbut in a corresponding curve, whose curvature is rapidly\\nincreased near the surface of the earth.\\n68. What effect has refraction upon the place of a heavenly\\nbody? By whatis it occasioned Illustrate by figure 8. How-\\nis a ray of light affected by passing out of a rarer into a denser\\nmedium? Why is an oar bent in the water In what line\\ndoes the light move as it goes through the atmosphere\\nThe operation of this principle is seen when an oar, or any stick,\\nis thrust into water. As the rays of light by which the oar is seen, have\\ntheir direction changed as they pass out of water into air, the apparent\\ndirection in which the body is seen is changed in the same degree,\\ngiving it a bent appearance. Thus, in the figure, if Sax represents- the\\noar, Sab will be the bent appearance as affected by refraction. The\\ntransparent substance through which any ray of light passes, is called\\na medium. It is a general fact in optics, that when light passes out of\\na rarer into a denser medium, as out of air into water, or out of space\\ninto air, it is turned towards a perpendicular to the surface of the me-\\ndium, and when it passes out of a denser into a rarer medium, as out\\nof water into air, it is turned from the perpendicular. In the above\\ncase the light, passing out of space into air, is turned towards the ra-\\ndius of the earth, this being perpendicular to the surface of the atmos-\\nphere; and it is turned more and more towards that radius the nearer\\nit approaches to the earth, because the density of the air rapidly in-\\ncreases.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0055.jp2"}, "54": {"fulltext": "40\\nTHE EARTH.\\n69. When a body is in the zenith, since a ray of light\\nfrom it enters the atmosphere at right angles to the re-\\nfracting medium, it suffers no refraction. Consequently,\\nthe position of the heavenly bodies, when in the zenith,\\nis not changed by refraction, while, near the horizon,\\nwhere a ray of light strikes the medium very obliquely,\\nand traverses the atmosphere through its densest part,\\nthe refraction is greatest. The following numbers, ta-\\nken at different altitudes, will show how rapidly refrac-\\ntion diminishes from the horizon upwards. The amount\\nof refraction at the horizon is 34 00 At different ele-\\nvations it is as follows\\nI Elevation.\\nRefraction.\\nElevation.\\nRefraction.\\n0\u00c2\u00b0 10\\n32 00\\n30\u00c2\u00b0\\nr 40\\n0\u00c2\u00b0 20\\n30 00\\n40\u00c2\u00b0\\n1 09\\n1\u00c2\u00b0 00\\n24 25\\n45\u00c2\u00b0\\n0 58\\n5\u00c2\u00b0 00\\n10 00\\n60\u00c2\u00b0\\n0 33\\n10\u00c2\u00b0 00\\n5 20\\n80\u00c2\u00b0\\n0 10\\n20\u00c2\u00b0 00\\n2 39\\n90\u00c2\u00b0\\n0 00\\nFrom this table it appears, that while refraction at the\\nhorizon is 34 minutes, at so small an elevation as only\\n10 above the horizon it loses 2 minutes, more than the\\nentire change from the elevation of 30\u00c2\u00b0 to the zenith.\\nFrom the horizon to 1\u00c2\u00b0 above, the refraction is dimin-\\nished nearly 10 minutes. The amount at the horizon,\\nat 45\u00c2\u00b0, and at 90\u00c2\u00b0, respectively, is 34 58 and 0. In\\nfinding the altitude of a heavenly body, the effect of pa-\\nrallax must be added, but that of refraction subtracted.\\n70. Since the whole amount of refraction near the\\nhorizon exceeds 33 and the diameters of the sun and\\nmoon are severally less than this, these luminaries are in\\n69. Has refraction any effect on a body in the zenith 1 Why\\nnot When is the refraction greatest What is the amount\\nof refraction at the horizon How much does it lose within\\n10 of the horizon What is the amount of refraction at an\\nelevation of 45\u00c2\u00b0", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0056.jp2"}, "55": {"fulltext": "REFRACTION. 41\\nview both before they have actually risen and after they\\nhave set.\\nThe rapid increase of refraction near the horizon, is\\nstrikingly evinced by the oval figure which the sun as-\\nsumes when near the horizon, and which is seen to the\\ngreatest advantage when light clouds enable us to view\\nthe solar disk. Were all parts of the sun equally raised\\nby refraction, there would be no change of figure but\\nsince the lower side is more refracted than the upper,\\nthe effect is to shorten the vertical diameter and thus to\\ngive the disk an oval form. This effect is particularly\\nremarkable when the sun, at his rising or setting, is ob-\\nserved from the top of a mountain, or at an elevation\\nnear the sea shore for in such situations the rays of\\nlight make a greater angle than ordinary, with a perpen-\\ndicular to the refracting medium, and the amount of re-\\nfraction is proportionally greater. In some cases of this\\nkind, the shortening of the vertical diameter of the sun\\nhas been observed to amount to 6 7 or about one fifth of\\nthe whole.\\n71. The apparent enlargement of the sun and moon\\nin the horizon, arises from an optical illusion. These\\nbodies in fact are not seen under so great an angle when\\nin the horizon, as when on the meridian, for they are\\nnearer to us in the latter case than in the former. The\\ndistance of the sun is indeed so great that it makes very\\nlittle difference in his apparent diameter, whether he is\\nviewed in the horizon or on the meridian but with the\\nmoon the case is otherwise its angular diameter, when\\nmeasured with instruments, is perceptibly larger at the\\ntime of its culmination. Why then do the sun and\\nmoon appear so much larger when near the horizon? It\\n70. What effect has refraction upon the appearances of the\\nsun and moon when near rising or setting Explain the oval\\nfigure of the sun when near the horizon. In what position of\\nthe spectator does this phenomenon appear most conspicuous?\\nHow much has the vertical diameter of the sun ever appeared\\nto re shortened I\\n4*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0057.jp2"}, "56": {"fulltext": "42 THE EARTH.\\nis owing to that general law, explained in optics, by\\nwhich we judge of the magnitudes of distant objects,\\nnot merely by the angle they subtend at the eye, but\\nalso by our impressions respecting their distance, allow-\\ning, under a given angle, a greater magnitude as we im-\\nagine the distance of a body to be greater. Now, on ac-\\ncount of the numerous objects usually in sight between\\nus and the sun, when on the horizon, he appears much\\nfarther removed from us than when on the meridian, and\\nwe assign to him a proportionally greater magnitude. If\\nwe view the sun, in the two positions, through smoked\\nglass, no such difference of size is observed, for here no\\nobjects are seen but the sun himself.\\nThe extraordinary enlargement of the sun or moon,\\nparticularly the latter, when seen at its rising through a\\ngrove of trees, depends on a different principle. Through\\nthe various openings between the trees, we see differ-\\nent images of the sun or moon, a great number of which\\noverlapping each other, swell the dimensions of the\\nbody under the most favourable circumstances, to a very\\nunusual size.\\nTWILIGHT.\\n72. Twilight also is another phenomenon depending\\nupon the agency of the earth s atmosphere. It is that\\nillumination of the sky which takes place just before\\nsunrise, and which continues after sunset. It is due\\npartly to refraction and partly to reflexion, but mostly to\\nthe latter. While the sun is within 18\u00c2\u00b0 of the horizon,\\nbefore it rises or after it sets, some portion of its light is\\nconveyed to us by means of numerous reflections from\\n71. To what is the apparent enlargement, of the sun and\\nmoon when near the horizon owing Are these bodies seen\\nunder a greater angle when in the horizon than in the zenith 1\\nTo what general law of optics is the enlargement to be ascri-\\nbed 1 How is it when we view the sua through smoked glass\\nTo what is the extraordinary enlargement of these luminaries\\nowing, when seen through a grove of trees 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0058.jp2"}, "57": {"fulltext": "the atmosphere. Let AB (Fig. 9,) be the horizon of\\nthe spectator at A, and let SS be a ray of light from the\\nsun when it is two or three degrees below the horizon.\\nThen to the observer at A, the segment of the atmos-\\nphere ABS would be illuminated. To a spectator at C,\\nwhose horizon was CD, the small segment SDa; would\\nbe the twilight while, at E, the twilight would disap-\\npear altogether.\\n73. At the equator, where the circles of daily motion\\naie perpendicular to the horizon, the sun descends\\nthrough 18\u00c2\u00b0 in an hour and twelve minutes (-ff=lih-)\\nand the light of day therefore declines rapidly, and as\\nrapidly advances after day break in the morning. At the\\npole, a constant twilight is enjoyed while the sun is\\nwithin 18\u00c2\u00b0 of the horizon, occupying nearly two-thirds\\nof the half year when the direct light of the sun is with-\\ndrawn, so that the progress from continual day to con-\\n72. Define twilight How many degrees below the horizon\\nis the sun when it begins and ends How is the light of the\\nsun conveyed to us Explain by the figure.\\n73. What is the length of twilight at the equator How\\nlong does it last at the poles How is the progress from con-\\ntinual day to constant night? To the inhabitants of an oblique\\nsphere, in what latitudes is twilight longest", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0059.jp2"}, "58": {"fulltext": "44 THE EARTH.\\nstant night is exceedingly gradual. To the inhabitants\\nof an oblique sphere, the twilight is longer in proportion\\nas the place is nearer the elevated pole.\\n74. Were it not for the power the atmosphere has of\\ndispersing the solar light, and scattering it in various di-\\nrections, no objects would be visible to us out of direct\\nsunshine every shadow of a passing cloud would be\\npitchy darkness the stars would be visible all day, and\\nevery apartment into which the sun had not direct ad-\\nmission, would be involved in the obscurity of night.\\nThis scattering action of the atmosphere on the solar\\nlight, is greatly increased by the irregularity of tempera-\\nture caused by the sun, which throws the atmosphere\\ninto a constant state of undulation, and by thus bringing\\ntogether masses of air of different temperatures, produces\\npartial reflections and refractions at their common boun-\\ndaries, by which means much light is turned aside from\\nthe direct course, and diverted to the purposes of general\\nillumination. In the upper regions of the atmosphere,\\nas on the tops of very high mountains, where the air is\\ntoo much rarefied to reflect much light, the sky assumes\\na black appearance, and stars become visible in the day\\ntime.\\nCHAPTER IV\\nOF TIME.\\n75. Time is a measured portion of indefinite duration*\\nThe great standard of time is the period of the revo-\\nlution of the earth on its axis, which, by the most exact\\n74. What would happen were it not for the power the at-\\nmosphere has of dispersing the solar light What would every\\nshadow of a cloud produce How is the scattering action of\\nthe atmosphere increased What is the aspect of the sky in\\nthe upper regions of the atmosphere\\nFrom old Eternity s mysterious orb,\\nWas Time eiu off and cast beneath the skies. Young", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0060.jp2"}, "59": {"fulltext": "TIME. 45\\nobservations, is found to be always the same. The time\\nof the earth s revolution on its axis is called a sidereal\\nday, and is determined by the revolution of a star from\\nthe instant it crosses the meridian, until it comes round\\nto the meridian again. This interval being called a si-\\ndereal day, it is divided into 24 sidereal hours. Obser-\\nvations taken upon numerous stars, in different ages of\\nthe world, show that they all perform their diurnal rev-\\nolutions in the same time, and that their motion during\\nany part of the revolution is perfectly uniform.\\n76. Solar time is reckoned by the apparent revolution\\nof the sun, from the meridian round to the same meridian\\nagain. Were the sun stationary in the heavens, like a\\nfixed star, the time of its apparent revolution would be\\nequal to the revolution of the earth on its axis, and the\\nsolar and the sidereal days would be equal. But since\\nthe sun passes from west to east, through 360\u00c2\u00b0 in 365A\\ndays, it moves eastward nearly 1\u00c2\u00b0 a day, (59 8 .S).\\nWhile, therefore, the earth is turning round on its axis,\\nthe sun is moving in the same direction, so that when\\nwe have come round under the same celestial meridian\\nfrom which we started, we do not find the sun there,\\nbut he has moved eastward nearly a degree, and the\\nearth must perform so much more than one complete\\nrevolution, in order to come under the sun again. Now\\nsince a place on the earth gains 359\u00c2\u00b0 in 24 hours, how\\nlong will it take to gain 1\u00c2\u00b0 1\\n24\\n359 24 1 g7g=4m nearly.\\n75. Deline time What is the standard of time What is\\na sidereal day Do the stars all perform their revolutions in\\nthe same time Is their motion uniform\\n76. How is the solar time reckoned? How far does the sun\\nmove eastward in a day How much longer is the solar than the\\nsidereal day If we reckoned the sidereal day 24 hours, how\\nshould we reckon the solar? Reckoning the solar day at 24\\nhours, how long is the sidereal", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0061.jp2"}, "60": {"fulltext": "46 THE EARTH.\\nHence the solar day is about 4 minutes longer than\\nthe sidereal and if we were to reckon the sidereal day\\n24 hours, we should reckon the solar day 24h. 4m. To\\nsuit the purposes of society at large, however, it is found\\nmost convenient to reckon the solar day 24 hours, and to\\nthrow the fraction into the sidereal day. Then,\\n24h 4m. 24 24 23h. 56m. nearly (23h. 56 in 4*.09)\\nrrthe length of a sidereal day.\\n77. The solar days, however, do not always differ from\\nthe sidereal by precisely the same fraction, since the in-\\ncrements of right ascension, which measure the differ-\\nence between a sidereal and a solar day, are not equal to\\neach other. Apparent time, is time reckoned by the\\nrevolutions of the sun from the meridian to the meridian\\nagain. These intervals being unequal, of course the\\napparent solar days are unequal to each other.\\n78. Mean time, is time reckoned by the average\\nlength of all the solar days throughout the year. This\\nis the period which constitutes the civil day of 24 hours,\\nbeginning when the sun is on the lower meridian, name-\\nly, at 12 o clock at night, and counted by 12 hours from\\nthe lower to the upper culmination, and from the upper\\nto the lower. The astronomical day is the apparent so-\\nlar day counted through the whole 24 hours, instead of\\nby periods of 12 hours each, and begins at noon. Thus\\n10 days and 14 hours of astronomical time, would be\\n1 1 days and 2 hours of apparent time for when the 10th\\nastronomical day begins, it is 10 days and 12 hours of\\ncivil time.\\n79. Clocks are usually regulated so as to indicate mean\\nsolar time yet as this is an artificial period, not marked\\n77. Do the solar days always differ from the sidereal by the\\nsame quantity 1 Define apparent time.\\n78. Define mean time. What constitutes the civil day 1\\nWhat makes an astronomical day 1 When does the civil day\\nbegin When does the astronomical day begin 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0062.jp2"}, "61": {"fulltext": "THE CALENDAR. 47\\noff, like the sidereal day, by any natural event, it is ne-\\ncessary to know how much is to be added to or sub-\\ntracted from the apparent solar time, in order to give the\\ncorresponding mean time. The interval by which ap-\\nparent time differs from mean time, is called the equation\\nof time. If a clock were constructed (as it may be) so\\nas to keep exactly with the sun, going faster or slower\\naccording as the increments of right ascension were\\ngreater or smaller, and another clock were regulated to\\nmean time, then the difference of the two clocks, at any\\nperiod, would be the equation of time for that moment.\\nIf the apparent clock were faster than the mean, then\\nthe equation of time must be subtracted but if the ap-\\nparent clock were slower than the mean, then the equa-\\ntion of time must be added, to give the mean time.\\nThe two clocks would differ most about the 3d of No-\\nvember, when the apparent time is 16 T m greater than the\\nmean (16 m 16 s .7). But, since apparent time is some-\\ntimes greater and sometimes less than mean time, the\\ntwo must obviously be sometimes equal t$ each other.\\nThis is in fact the case four times a year, namely, April\\n15th, June 15th, September 1st, and December 24th.\\nTHE CALENDAR.\\n80. The astronomical year is the time in which the\\nsun makes one revolution in the ecliptic, and consists of\\n365d. 5h. 48m. 51 s 60. The civil year consists of 365\\ndays. The difference is nearly 6 hours, making one day\\nin four years.\\nThe most ancient nations determined the number of\\ndays in the year by means of the stylus, a perpendicular\\n79 What time do clocks commonly keep Define the equa-\\ntion of time. How might two clocks be regulated so that their\\ndifference would indicate the equation of time How must\\nthe equation of time be applied when the apparent clock is\\nfaster than the mean How when it is slower When would\\nthe two clocks differ most 1 How much would they then differ 7\\nWhen would they come together 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0063.jp2"}, "62": {"fulltext": "48 THE EARTH\\nrod which casts its shadow on a smooth plane, bearing a\\nmeridian line. The time when the shadow was shortest,\\nwould indicate the day of the summer solstice and the\\nnumber of days which elapsed until the shadow returned\\nto the same length again, would show the number of\\ndays in the year. This was found to be 365 wn\u00c2\u00bb: ie\\ndays, and accordingly this period was adopted for tne\\ncivil year. Such a difference, however, between the\\ncivil and astronomical years, at length threw all dates\\ninto confusion. For, if at first the summer solstice hap-\\npened on the 21st of June, at the end of four years, the\\nsun would not have reached the solstice until the 22d of\\nJune, that is, it would have been behind its time. At\\nthe end of the next four years the solstice would fall on\\nthe 23d and in process of time it would fall succes-\\nsively on every day of the year. The same would be\\ntrue of any other fixed date. Julius Caesar made the\\nfirst correction of the calendar, by introducing an inter-\\ncalary day every fourth year, making February to con-\\nsist of 29 instead of 28 days, and of course the whole\\nyear to consist of 366 days. This fourth year was de-\\nnominated Bissextile. It is also called Leap Year.\\n81. But the true correction was not 6 hours, but 5h.\\n49m. hence the intercalation was too great by 11 min-\\nutes. This small fraction would amount in 100 years\\nto f of a day, and in 1000 years to more than 7 days.\\nFrom the year 325 to 1582, it had in fact amounted to\\nabout 10 days for it was known that in 325, the vernal\\nequinox fell on the 21st of March, whereas, in 1582 it\\nfell on the 11th. In order to restore the equinox to the\\nsame date, Pope Gregory XIII, decreed, that the year\\n80. Define the astronomical year What is its exact period?\\nOf how many days does the civil year consist? How much\\nshorter is the civil than the astronomical year How did the most\\nancient nations determine the number of days in the year\\nWhen would the stylus mark the shortest day and when the\\nlongest Explain the confusion which arose by reckoning the\\nyearonly 365 days. How did Julius Caesarreform the calendar", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0064.jp2"}, "63": {"fulltext": "THE CALENDAR 49\\nsnould be brought forward 10 days, by reckoning the\\n5th of October the 15th. In order to prevent the cal-\\nendar from falling into confusion afterwards, the follow-\\ning rule was adopted\\nEvery year whose number is not divisible by 4 with-\\nout a remainder consists of 365 days every year which\\nis so divisible, but is not divisible by 100, of 366; every\\nyear divisible by 100 but not by 400, again of 365; and\\nevery year divisible by 400, of 366.\\nThus the year 1838, not being divisible by 4, contains\\n365 days, while 1836 and 1840 are leap years. Yet to\\nmake every fourth year consist of 366 days would in-\\ncrease it too much by about f of a day in 100 years\\ntherefore every hundredth year has only 365 days.\\nThus 1800, although divisible by 4 was not a leap year,\\nbut a common year. But we have allowed a whale day\\nin a hundred years, whereas w r e ought to have allowed\\nonly three fourths of a day. Hence, in 400 years we\\nshould allow a day too much, and therefore we let the\\n400th year remain a leap year. This rule involves an\\nerror of less than a day in 4237 years. If the rule were\\nextended by making every year divisible by 4000 (which\\nwould now consist of 366 days) to consist of 365 days,\\nthe error would not be more than one day in 100,000\\nyears.\\n82. This reformation of the calendar was not adopted\\nin England until 1752, by which time the error in the\\nJulian calendar amounted to about 1 1 days. The year\\nwas brought forward, by reckoning the 3d of September\\nthe 14th. Previous to that time the year began the 25th\\n81. By how many minutes was the allowance made by the\\nJulian calendar too great To how much would the error\\namount m one hundred years To how much in a thousand\\nyears To how much had it amounted from the year 325 to\\n1582 What changes did Pope Gregory make in the year?\\nState the rule for the calendar. Of the three years 1836,\\n1838, and 1840, which are leap years Was 1800 a leap year?\\nHow is every 400th year\\n5", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0065.jp2"}, "64": {"fulltext": "50 THE EARTH.\\nof March but it was now made to begin on the 1st oi\\nJanuary, thus shortening the preceding year, 1751, one\\nquarter.*\\nAs in the year 1582, the error in the Julian calendar\\namounted to 10 days, and increased by f of a day in a\\ncentury, at present the correction is 12 days and the\\nnumber of the year wiM differ by one with respect to\\ndates between the 1st of January and the 25th of March.\\nExamples. General Washington was born Feb. 11\\n1781, old style to what date does this correspond in\\nnew style\\nAs the date is the earlier part of the 18th century, the\\ncorrection is 1 1 days, which makes the birth day fall on\\nthe 22d of February; and since the year 1731 closed\\nthe 25th of March, while according to new style 1732\\nwould have commenced on the preceding 1st of Janu-\\nary therefore, the time required is Feb. 22, 1732. It\\nis usual, in such cases, to write both years, thus Feb.\\n11, 1731-2, O. S.\\n2. A great eclipse of the sun happened May 15th,\\n1 836 to what date would this time correspond in old\\nstyle 1 Ans. May 3d.\\n83. The common year begins and ends on the same\\nday of the week but leap year ends one day later in the\\nweek than it began.\\nFor 52x7 384 days; if therefore the year begins\\non Tuesday, for example, 364 days would complete 52\\nweeks, and one day would be left to begin another week,\\n82. When was this reformation first adopted in England\\nHow was the year brought forward 1 When did the year be-\\ngin before that time 1 To how many days did the error amount\\nin 1752 How many days are allowed at present between\\nold and new style\\nRussia, and the Greek Church generally, adhere to the old style.\\nfn order to make the Russian dates correspond to ours, we must add to\\nthem 12 days. France and other Catholic countries, adopted the Gre-\\ngorian calendar soon after it was promulgated", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0066.jp2"}, "65": {"fulltext": "ASTRONOMICAL INSTRUMENTS 51\\nand the following year would begin on Wednesday.\\nHence, any day of the month is one day later in the\\nweek than the corresponding day of the preceding year.\\nThus, if the 16th of November, 1838, falls on Friday,\\nthe 10th of November, 1837, fell on Thursday, and in\\n1839 will fall on Saturday. But if leap year begins on\\nSunday, it ends on Monday, and the following year be-\\ngins on Tuesday while any given day of the month is\\ntwo days latei in the week than the corresponding date\\nof the preceding year.\\nCHAPTER V.\\nOF ASTRONOMICAL INSTRUMENTS FIGURE AND DENSITY OF\\nTHE EARTH.\\n84. The most ancient astronomers employed no in-\\nstruments of observation, but acquired their knowledge\\nof the heavenly bodies by long continued and most at-\\ntentive inspection with the naked eye. Instruments for\\nmeasuring angles were first used in the Alexandrian\\nschool, about 300 years before the Christian era.\\n85. Wherever we are situated on the earth we appear\\nto be in the center of a vast sphere, on the concave sur-\\nface of which all celestial objects are inscribed. If we\\ntake any two points on the surface of the sphere, as two\\nstars for example, and imagine straight lines to be drawn\\nto them from the eye, the angle included between these\\n83. If the common year begins on a certain day of the week,\\nhow will it end How is it with leap year How does any\\nday of the month compare in the preceding and following yeai\\nwith respect to the day of the week 1 How is this in leap\\nyear\\n84. How did the most ancient nations acquire their knowl-\\nedge of the heavenly bodies When were astronomical in-\\nstruments first introduced 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0067.jp2"}, "66": {"fulltext": "52 THE EARTH.\\nlines will be measured by the arc of the sky contained\\nbetween the two points. Thus if HBD, (Fig. 10,) rep-\\nFig. 10.\\nresents the concave surface of the sphere, A, B, two\\npoints on it, as two stars, and CA, CB, straight lines\\ndrawn from the spectator to those points, then the angu-\\nlar distance between them is measured by the arc AB,\\nor the angle ACB. But this angle may be measured on\\na much smaller circle, having the same center, as EFG,\\nsince the arc EF will have the same number of degrees\\nas the arc AB. The simplest mode of taking an angle\\nbetween two stars, is by means of an arm opening at a\\njoint like the blade of a penknife, the end of the arm\\nmoving like CE upon the graduated circle KEG.\\nThe common surveyor s compass affords a simple ex-\\nample of angular measurement. Here the needle lies in\\na north and south line, while the circular rim of the\\ncompass, when the instrument is level, corresponds to\\nthe horizon. Hence the compass shows how many de-\\ngrees any object to which we direct the eye, lies east or\\nwest of the meridian.\\n85. How is the angular distance between two points on the\\ncelestial sphere measured Explain figure 10, Show how the\\ncircles of the sphere may be truly represented by the smaller\\ncircles of the instrument, as the horizon by the surveyor s com-\\npass. Explain the simplest mode of taking angles by figure 10", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0068.jp2"}, "67": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 53\\n86. It is obvious that the larger the graduated circle\\nis, the more minutely its limb may be divided. If the\\ncircle is one foot in diameter, each degree will occupy\\n\u00c2\u00a3o of an inch. If the circle is 20 feet in diameter, a\\ndegree will occupy the space of two inches and could\\nbe easily divided to minutes, since each minute would\\ncover a space of of an inch. Refined astronomical\\ncircles are now divided with very great skill and accu-\\nracy, the spaces between the divisions being, when read\\noff, magnified by a microscope but in former times,\\nastronomers had no mode of measuring small angles\\nbut by employing very large circles. But the telescope\\nand microscope enable us at present to measure celestial\\narcs much more accurately than was done by the older\\nastronomers.\\nThe principal instruments employed in astronomy,\\nare the Telescope, the Transit Instrument, the Altitude\\nand Azimuth Instrument, and the Sextant.\\n87. The Telescope has greatly enlarged our knowl-\\nedge of astronomy, both by revealing to us many things\\ninvisible to the naked eye, and also by enabling us to\\nattain a much higher degree of accuracy than we could\\notherwise reach, in angular measurements. It was in-\\nvented by Galileo about the year 1600. The powers of\\nthe telescope were improved and enlarged by successive\\nefforts, and finally, about 50 years ago, telescopes were\\nconstructed in England by Dr. Herschel, of a size and\\npower that have not since been surpassed.\\nA complete knowledge of the telescope cannot be ac-\\nquired without an acquaintance with the science of op-\\ntics but we may perhaps convey to one unacquainted\\nwith that science, some idea of the leading principles of\\n86. What is the advantage of having large circles for angu-\\nlar measurements When the circle is one foot in diameter,\\nwhat space will 1\u00c2\u00b0 occupy on the limb 1 What space when\\nthe circle is twenty feet in diameter What are the princi-\\npal instruments used in astronomical observations 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0069.jp2"}, "68": {"fulltext": "54\\nTHE EARTH.\\nthis noble instrument. By means of the telescope, we\\nfirst form an image of a distant object as the moon for\\nexample, and then magnify that image by a microscope.\\nLet us first see how the image is formed. This may be\\ndone either by a convex lens, or by a concave mirror. A\\nconvex lens is a flat piece of glass, having its two faces\\nconvex, or spherical, as is seen in a common sun glass.\\nEvery one who has seen a sun glass, knows that when\\nheld towards the sun it collects the solar rays into a\\nsmall bright circle in the focus. This is in fact a small\\nimage of the sun. In the same manner the image of\\nany distant object, as a star, may be formed as is repre-\\nsented in the following diagram. Let ABCD represent\\nFig. 11.\\nthe tube of a telescope. At the front end, or at the end\\nwhich is directed towards the object, (which we will\\nsuppose to be the moon,) is inserted a convex lens,\\nL, which receives the rays of light from the moon, and\\ncollects them into the focus at a, forming an image of\\nthe moon. This image is viewed by a magnifier attach-\\ned to the end BC. The lens L is called the object-glass,\\nand the microscope in BC the eye-glass. We apply a\\nmagnifier to this image just as we would to any object\\n87. Who invented the telescope Who constructed tele-\\nscopes of great size and power Explain tne leading prin-\\nciple of the telescope. How is the image formed 1 What is\\na convex lens How does it affect parallel rays of light\\nHow do we view the image formed by the lens How is the\\nimage magnified 1 How is it rendered brighter", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0070.jp2"}, "69": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 5f\u00c2\u00bb\\nand by greatly enlarging its dimensions, we may render\\nits various parts far more distinct than they would other-\\nwise be, while at the same time the object lens collects\\nand conveys to the eye a much greater quantity of light\\nthan would proceed directly from the body under exam-\\nination. A very small beam of light only from a distant\\nobject, as a star, can enter the eye directly but a lens\\none foot in diameter will collect a beam of light of the\\nsame dimensions, and convey it to the eye. By these\\nmeans many obscure celestial objects become distinctly\\nvisible, which w r ould otherwise be either too minute, or\\nnot sufficiently luminous to be seen by us.\\n88. But the image may also be formed by means of a\\nconcave mirror, w T hich, as well as the convex lens, has\\nthe property of collecting the rays of light which pro-\\nceed from any luminous body, and of forming an image\\nof that body. The image formed by the concave mir-\\nror is magnified by a microscope in the same manner as\\nwhen formed by the convex lens. When the lens is\\nused to form an image, the instrument is called a Re-\\nfracting telescope when a concave mirror is used, it is\\ncalled a Reflecting telescope.\\nThe telescope in its simplest form is employed not so\\nmuch for angular measurements, as for aiding the pow-\\ners of vision in viewing the celestial bodies. When di-\\nrected to the sun, it reveals to us various irregularities on\\nhis disk not discernible by naked vision w T hen turned\\nupon the moon or the planets, it affords us new and in-\\nteresting views, and enables us to see in them the linea-\\nments of other worlds and w r hen brought to bear upon\\nthe fixed stars, it vastly increases their number and re-\\nveals to us many surprising facts respecting them.\\n88. How is an image formed by a concave mirror 1 How is\\nthis image magnified 1 When is the instrument called a re-\\nfracting and when a reflecting telescope I For what pur-\\nposes are telescopes chiefly employed", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0071.jp2"}, "70": {"fulltext": "56\\nTHE EARTH.\\n89. The Transit Instrument is a telescope, which is\\nfixed permanently in the meridian, and moves only in\\nthat plane. It rests on a horizontal axis, which consists\\nof two hollow cones applied base to base, a form uniting\\nlightness and strength. The two ends of the axis rest\\nFig. 12.\\nTV\\non two firm supports, as pillars of stone, for example, so\\nconnected with the building as to be as free as possible\\nfrom all agitation. In figure 12, AD represents the tele-\\n89. What is a Transit Instrument On what supports does\\nit rest as represented in figure 12. Why are they made so firm?\\nDescribe all parts of the instrument. What is its use 1 How\\nused to regulate clocks and watches What kind of time is\\nshown when the sun is on the meridian How is this con-\\nverted into mean t me Give an example.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0072.jp2"}, "71": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 57\\nscope, E, W, massive stone pillars supporting the hori-\\nzontal axis, beneath which is seen a spirit level, (which\\nis used to bring the axis to a horizontal position,) and n\\na vertical circle graduated into degrees and minutes.\\nThis circle serves the purpose of placing the instrument\\nat any required altitude, or distance from the zenith, and\\nof course for determining altitudes and zenith distances.\\nThe use of the transit instrument is to show the pre-\\ncise moment when a heavenly body is on the meridian.\\nOne of its uses is to enable us to obtain the true time,\\nand thus to regulate our clocks and watches. We find\\nwhen the sun s center is on the meridian, and this gives\\nus the time of noon or apparent time. (Art. 78.) But\\nwatches and clocks usually keep mean time, and there-\\nfore in order to set our time piece by the transit instru-\\nment, we must apply the equation of time.\\n90. A noon mark may easily be made by the aid of\\nthe Transit Instrument. A window sill is frequently\\nselected as a suitable place for the mark, advantage be-\\ning taken of the shadow projected upon it by the per-\\npendicular casing of the window. Let an assistant stand\\nwith a rule laid on the line of shadow and with a knife\\nready to make the mark, the instant when the observer\\nat the Transit Instrument announces that the center of\\nthe sun is on the meridian. By a concerted signal, as\\nthe stroke of a bell, the inhabitants of a town may all\\nfix a noon mark from the same observation. It must be\\nborne in mind, however, that the noon mark gives the\\napparent time, and that the equation of time must be\\nallowed for in setting the clock or watch. Suppose we\\nwish to set our clock right on the first of January. We\\nfind by a table of the equation of time, that mean time\\nthen precedes apparent time 3m. 43s. we must there-\\nfore set the clock at 3m. 43s. the instant the center of\\nthe sun is on the meridian. If the time had been the\\nfirst of May instead of the first of January, then we\\nfind by the table that 3m. is to be subtracted from the\\napparent time, and consequently, when the center of the\\n90 Describe the mode of making a noon mark.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0073.jp2"}, "72": {"fulltext": "58\\nTHE EARTH.\\nsun was on the meridian, we should set our clock at 1 lh.\\n57m. or 3m. before twelve.\\n91. The equation of time varies a little with different\\nyears, but the following table will always be found\\nwithin a few seconds of the truth. The equation for\\nthe current year is given exactly in the American Al-\\nmanac.\\nEquation of Time for Apparent Noon.\\nJan. 1 Feb.\\nMar. Apr.\\nMay\\nSub.\\nM. S.\\nJUN.\\nSub.\\nM. S\\nJul.\\nAdd.\\nAug\\nAdd.\\nSept.\\nAdd.\\nOct.\\nSub.\\nM. s.\\nNov.\\nSub.\\nSub.\\nM. S/.\\nAdd.\\nM. S.\\nAdd.\\nAdd.\\nAdd.\\nM. S.\\nM. S.\\nM. S.\\nM. S.\\nM. S.\\nM. S.\\nM. S.\\nl\\n3.4313.53\\n12.42\\n4. 7;\\n3. 2.38\\n3.19\\n6. 3\\nai). 1\\n10. 9\\n16.15\\n10.54\\n2\\n4.1l|l4. 1\\n12.30\\n3.48\\n3. 7 2.29\\n3.31\\n5.59\\n50.17\\n10.28\\n16.16\\n10.32\\n3\\n4.39;i4. 8\\n12.18\\n3.30\\n3.15\\n2.19\\n3.42\\n5 55\\n0.36\\n10.47\\n16.17\\n10. 8\\n4\\n5. 744.14\\n12. 5\\n3.12\\n3.21\\n2.10\\n3.53 5.50\\n0.56\\n11. 6\\n16.17\\n9.45\\n5\\n5.3414.19\\n11.51\\n2.54\\n2.37\\n3.27\\n3.32\\n2.\\n1.49\\n4. 4\\n5.45\\n1.15\\n11.24\\n16.16\\n9.20\\n6. 1)14.24\\n11.38\\n4.15\\n5.3 J\\n1.35\\n11.42\\n1614\\n8.55\\n7\\n6.27114.27\\n11.23\\n2.19\\n3.37\\n1.39\\n4.25\\n5.33\\n1.55\\n11.59\\n16.11\\n8.30\\nR\\n6.53|14.30\\n11. 8\\n2. 2\\n3.42\\n1.28\\n4.34\\n5.25\\n2.15\\n12.16\\n16. 7\\n8. 4\\n9\\n7.18.14.32\\n10.53\\n1.45\\n3.46\\n1.17\\n4.44\\n5.18\\n2.36\\n12.33 16. 3\\n7.37\\n10\\n11\\n743; 14.33\\n10.38\\n1.28\\n1.11\\n3.49\\n3.51\\n1. 5\\n0.53\\n4.53\\n5. 1\\n5. 9\\n5. 1\\n2.56\\n12.49 15.58\\n13. 515 51\\n7.10\\n8. 7 14.34\\n10.22\\n3.17\\n6.43\\n12\\n8.3114.33\\n10. 6\\n0.55\\n3.53\\n0.41\\n5. 9\\n4.51\\n3.38\\n13.20\\n15.44\\n6.15\\n13\\n8.5414.32\\n9.49\\n0.39\\n3.55\\n0.29\\n5.17\\n4.41\\n3.59\\n13.34\\n15.37\\n5.47\\nL4\\n9.1614.30\\n9.32\\n0.23\\n3.56\\n0.17\\n5.24\\n4.31\\n4.2013.49 15.28\\n5.18\\n15\\n9.37\\n14.28\\n9.15\\n0. 8\\n3.56\\n0. 4\\n5.30\\n4.20\\n4.41\\n14. 215.18\\n4.49\\nSub.\\nAdd.\\n16\\n9.5814.25\\n8.581\\n0. 7\\n3.56\\n0. 8\\n5.37\\n4. 8\\n5. 2\\n14.15\\n15. 8\\n4.20\\n17\\n10.19il4.20\\n8.41\\n0.22\\n3.55\\n0.21\\n5.42\\n3.56\\n5.23\\n14.28\\n14.56\\n3.50\\nIS\\n10.3814.16\\n8.23\\n0.36\\n3.54\\n0.34\\n5.48\\n3.44\\n5.44\\n14.39\\n14.44\\n3.21\\n19\\n10.5714.10\\n8. 5\\n0.50\\n3.52\\n0.47\\n5.52\\n3.31\\n6. 514.51\\n14.31\\n2.51\\n\u00e2\u0080\u00a220\\n21\\n11.1514. 4\\n7.47\\n1. 3\\n3.49\\n3.46\\n1.\\n1.13\\n5.57\\n6.\\n3.17\\n3. 3\\n6.26\\n6.47\\n15. 1|14.17\\n2.21\\n11.33113.58\\n7.29\\n1.16\\n15.11J14. 3\\n1.51\\n22\\n11.49113.50\\n7.11\\n1.29\\n3.42\\n1.26\\n6. 3 2.49\\n7. 8115.21:13.47\\n1.21\\n23\\n12. 513.42\\n6.52\\n1.41\\n3.38\\n1.39\\n6. 6\\n2.34\\n7.29 15.29J13.31\\n7.4915.37113.14\\n0.51\\n24\\n12.2013.34\\n6.34\\n1.52\\n3.33\\n1.52\\n6. 8\\n2.19\\n0.21\\n25\\n2G\\n12.3513.25\\n6.15\\n2. 4\\n3.28\\n3.22\\n2. 5\\n2.18\\n6. 9\\n6.10\\n2. 3\\n8.1015.4412.56\\n\u00c2\u00ab0. 9\\n12.4813.15\\n5.57 2,14\\n1.47\\n8.30115.51 12.38\\n8.5015.57il2.18\\n0.39\\n27\\n13. 1 13. 4\\n5.38\\n2.24\\n3.16\\n2.30\\n6.10\\n1.30\\n1. 9\\n28\\n13.13\\n12.54\\n5.20\\n2.34\\n3. 9\\n2.43\\n6.10\\n1.13\\n9.1116. 211.58\\n1.39\\n29\\n13.24\\n5. 1\\n2.43\\n3. 2\\n2.55\\n6. 9\\n6. 8\\n0.5G\\n9.3016. 6,11.38\\n2. 8\\n30\\n31\\n13.35\\n4.43\\n2.52\\n2 54\\n3. 8\\n0.38\\n9.50.16.1011.16\\n2.37\\n13.44\\n4.25\\n2.46\\n6. 5\\n0.20\\n116.13\\n3. 6\\n91. Is the equation of time the same or different in different\\nyears In what book mav it. be found exactly for the cur-\\nrent year", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0074.jp2"}, "73": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 59\\n92. The Astronomical Clock is the constant compan-\\nion of the Transit Instrument. This clock is so regu-\\nlated as to keep exact pace with the stars, and of course\\nwith the revolution of the earth on its axis that is, it\\nis regulated to sidereal time. It measures the progress\\nof a star, indicating an hour for every 15\u00c2\u00b0, and 24 hours\\nfor the whole period of the revolution of the star. Si-\\ndereal time, it will be recollected, commences when the\\nvernal equinox is on the meridian, just as solar time com-\\nmences when the sun is on the meridian. Hence, the\\nhour by the sidereal clock has no correspondence with\\nthe hour of the day, but simply indicates how long it is\\nsince the equinoctial point crossed the meridian. For\\nexample, the clock of an observatory points to 3h 20m.\\nthis may be in the morning, at noon, or any other time\\nof the day, since it merely shows that it is 3h. 20m.\\nsince the equinox was on the meridian. Hence, when\\na star is on the meridian, the clock itself shows its right\\nascension (Art. 24,) and the interval of time between\\nthe arrival of any two stars upon the meridian, is the\\nmeasure of their difference of right ascension.\\n93. Astronomical clocks are made of the best work-\\nmanship, with a compensation pendulum, and every\\nother advantage which can promote their regularity.\\nThe Transit Instrument itself, when once accurately\\nplaced in the meridian, affords the means of testing the\\ncorrectness of the clock, since one revolution of a star\\nfrom the meridian to the meridian again, ought to cor-\\nrespond to exactly 24 hours by the clock, and to con-\\n92. How is the astronomical clock regulated 1 What does\\nit measure How many degrees does a star pass over in an\\nhour When does sidereal time commence What is de-\\nnoted by the hour and minute of a sidereal clock 1 How do\\nwe determine the right ascension of a star\\n93. How is the workmanship of astronomical clocks How\\nis the correctness of a clock tested To what degree of\\nperfection are clocks brought? By what instrument are\\nclocks regulated?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0075.jp2"}, "74": {"fulltext": "60 THE EARTH.\\ntinue the same from day to day and the right ascen-\\nsion of various stars as they cross the meridian, ought\\nto be such by the clock as they are given in the tables,\\nwhere they are stated according to the accurate determi-\\nnations of astronomers. Or by taking the difference of\\nright ascension of any two stars on successive days, it\\nwill be seen whether the going of the clock is uniform\\nfor that part of the day and by taking the right ascen-\\nsion of different pairs of stars, we may learn the rate of\\nthe clock at various parts of the day. We thus learn,\\nnot only whether the clock accurately measures the\\nlength of the sidereal day, but also whether it goes uni-\\nformly from hour to hour.\\nAlthough astronomical clocks have been brought to a\\ngreat degree of perfection, so as to vary hardly a second\\nfor many months, yet none are absolutely perfect, and\\nmost are so far from it as to require to be corrected by\\nmeans of the Transit Instrument every few days. In-\\ndeed, for the nicest observations, it is usual not to at-\\ntempt to bring the clock to an absolute state of correct-\\nness, but after bringing it as near to such a state as can\\nconveniently be done, to ascertain how much it gains or\\nloses in a day that is, to ascertain its rate of going, and\\nto make allowance accordingly.\\n94. The Transit Instrument is adapted to taking obser-\\nvations on the meridian only but we sometimes require\\nto know the altitude of a celestial body when it is not\\non the meridian, and its azimuth, or distance from the\\nmeridian measured on the horizon. An instrument es-\\npecially designed to measure altitudes and azimuths, is\\ncalled an Altitude and Azimuth Instrument, whatever\\nmay be its particular form. When a point is on the hor-\\nizon its distance from the meridian, or its azimuth, may\\nbe taken by the common surveyor s compass, the direc-\\n94. To what kind of observations only is the transit instru-\\nment adapted What instrument is employed for finding alti-\\ntude and azimuth 1 Describe the Altitude and Azimuth In-\\nstalment; from fisrure 13.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0076.jp2"}, "75": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n61\\ntion of the meridian being determined by the needle\\nbut when the object, as a star, is not on the horizon, its\\nazimuth, it must be remembered, is the arc of the hori-\\nzon from the meridian to a vertical circle passing through\\nthe star at whatever different altitudes, therefore, two\\nstars may be, and however the plane which passes\\nthrough them may be inclined to the horizon, still it is\\ntheir angular distance measured on the horizon which\\ndetermines their difference of azimuth. Figure 13 rep-\\nresents an Altitude and Azimuth Instrument, several of\\nthe usual appendages and subordinate contrivances being\\nomitted for the sake of distinctness and simplicity. Here\\nabc is the vertical or altitude circle, and EFG the hori-\\nzontal or azimuth circle AB is a telescope mounted on\\nFier. 13.\\na horizontal axis and capable of two motions, one in al-\\ntitude parallel to the circle abc, and the other in azimuth\\nparallel 10 EFG. Hence it can be easily brought to\\n6", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0077.jp2"}, "76": {"fulltext": "62 THE EARTH.\\nbear upon any object. At m, under the eye glass of the\\ntelescope, is a small mirror placed at an angle of 45\u00c2\u00b0\\nwith the axis of the telescope, by means of which the\\nimage of the object is reflected upwards, so as to be\\nconveniently presented to the eye of the observer. At d\\nis represented a tangent screw, by which a slow motion\\nis given to the telescope at c. At h and g are seen two\\nspirit levels, at right angles to each other, which show\\nwhen the azimuth circle is truly horizontal. The in-\\nstrument is supported on a tripod, for the sake of greater\\nsteadiness, each foot being furnished with a screw for\\nlevelling.\\n95. The Sextant is an instrument used for taking the\\nangular distance between any two bodies on the surface\\nof the celestial sphere, by reflecting the image of one of\\nthe bodies so as to coincide with the other body as seen\\ndirectly. It is particularly valuable for measuring celes-\\ntial arcs at sea, because it is not, like most astronomical\\ninstruments, affected by the motion of the ship.\\nThis instrument (Fig 14,) is of a triangular shape,\\nand is made strong and firm by metallic crossbars. It\\nhas two reflectors, I and H, called, respectively, the Index\\nGlass, and the Horizon Glass, both of which are firmly\\nfixed perpendicular to the plane of the instrument. The\\nIndex Glass is attached to the movable arm ID and\\nturns as this is moved along the graduated limb EF.\\nThis arm also carries a Vernier at D, which enables us to\\ntake off minute parts of the spaces into which the limb\\nis divided. The Horizon Glass, H, consists of two\\nparts the upper being transparent or open, so that the\\neye, looking through the telescope T, can see through\\nit a distant body as a star at S, while the lower part is\\na reflector.\\n95. Define the Sextant For what is it particularly valu-\\nable Describe it from figure 14. Where is the Vernier and\\nwhat is its use Specify the manner in which the light comes\\nfrom the object to the eye. How can we measure the angulai\\ndistance between the raoon and a star 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0078.jp2"}, "77": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n63\\nSuppose it were required to measure the angular dis-\\ntance between the moon and a certain star, the moon\\nFig. 14.\\nbeing at M, and the star at S. The instrument is held\\nfirmly in the hand, so that the eye, looking through the\\ntelescope, sees the star S through the transparent part of\\nthe Horizon Glass. Then the movable arm ID is moved\\nfrom F towards E, until the image of M is carried down\\nto S, when the number of degrees and parts of a degree\\nreckoned on the limb from F to the index at D, will\\nshow the angular distance between the two bodies.\\nFIGURE AND DENSITY OP THE EARTH.\\n96. We have already shown, that the figure of the\\nearth is nearly globular but since the semi-diameter of\\nthe earth is taken as the base line in determining the\\nparallax of the heavenly bodies, and lies therefore at the\\nfoundation of all astronomical measurements, it is very", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0079.jp2"}, "78": {"fulltext": "64\\nTHE EARTH.\\nimportant that it should be ascertained with the greatest\\npossible exactness. Having now learned the use of as-\\ntronomical instruments, and the method of measuring\\narcs on the celestial sphere, we are prepared to under-\\nstand the methods employed to determine the exact fig-\\nure of the earth. This element is indeed ascertained\\nin different ways, each of which is independent of all\\nthe rest, namely, by investigating the effects of the cen-\\ntrifugal force arising from the revolution of the earth\\non its axis by measuring arcs of the meridian and by\\nexperiments with the pendulum.\\n97. First, the known effects of the centrifugal force,\\nwould give to the earth a spheroidal figure, elevated in\\nthe equatorial, and fattened in the polar regions.\\nBy the centrifugal force is meant, the tendency which\\nrevolving bodies exhibit to recede from the\\nFig. 15. center. Thus when a grindstone is turn-\\niiiiiiiiiiiiiiiininiiiiiiiiiiiiiil ed swiftly, water is thrown off from it in\\nstraight lines. The same effect is notic-\\ned when a carriage wheel is driven rapidly\\nthrough the water. If a pail, containing\\na little water, is whirled, the water rises\\non the sides of the pail in consequence of\\nthe centrifugal force. The same principle\\nis more strikingly illustrated by the annex-\\ned cut, (Fig. 15,) which represents an\\nopen glass vessel suspended by a cord at-\\ntached to its opposite sides, and passed\\nthrough a staple in the ceiling of the room.\\nA little water is introduced into the ves-\\nsel which is made to whirl rapidly by ap-\\nplying the hand to the opposite sides. As\\nit turns, the water rises on the sides of the\\nvessel, receding as far as possible from the\\n96. Why is it so necessary to ascertain accurately the semi-\\ndiameter of the earth 1 In how many different ways is this\\nelement ascertained 1 Specify them. What is meant by the\\ncentrifugal force 1 Give an illustration. Describe figure 15.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0080.jp2"}, "79": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 65\\ncenter. The same effect is produced by suffering the\\ncord to untwist freely, which gives a swift revolution\\nto the vessel. In like manner, a ball of soft clay when\\nmade to turn rapidly on its axis, swells out in the central\\nparts and becomes flattened at the ends, forming the fig-\\nure called an oblate spheroid.\\nHad the earth been originally constituted (as geolo-\\ngists suppose) of yielding materials, either fluid or semi-\\nfluid, so that its particles could obey their mutual at-\\ntraction, while the body remained at rest it would spon-\\ntaneously assume the figure of a perfect sphere as soon,\\nhowever, as it began to revolve on its axis, the greater\\nvelocity of the equatorial regions would give to them a\\ngreater centrifugal force, and cause the body to swell\\nout into the form of an oblate spheroid. Even had the\\nsolid part of the earth consisted of unyielding materials\\nand been created a perfect sphere, still the waters that\\ncovered it would have receded from the polar and have\\nbeen accumulated in the equatorial regions, leaving bare\\nextensive regions on the one side, and ascending to a\\nmountainous elevation on the other.\\nOn estimating, from the known dimensions of the\\nearth and the velocity of its rotation, the amount of the\\ncentrifugal force in different latitudes, and the figure of\\nequilibrium which would result, Newton inferred that\\nthe earth must have the form of an oblate spheroid be-\\nfore the fact had been established by observation and\\nhe assigned nearly the true ratio of the polar and equa-\\ntorial diameters.\\n97. What would be the figure of the earth derived from the\\ncentrifugal force What figure would the earth have assumed\\nif at rest 1 How would this figure be changed when it began to\\nrevolve Had the earth been originally a solid sphere covered\\nwith water, how would the water have disposed itself when the\\nearth was made to turn on its axis How was the spheroidal\\nfigure of the earth inferred before the fact was established bv\\nobservation\\n6*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0081.jp2"}, "80": {"fulltext": "66 THE EARTH.\\n98. Secondly, the spheroidal figure of the earth is\\nproved, by actually measuring the length of a degree on\\nthe meridian in different latitudes.\\nWere the earth a perfect sphere, the section of it made\\nby a plane passing through its center in any direction\\nwould be a perfect circle, whose curvature would be\\nequal in all parts but if we find by actual observation,\\nthat the curvature of the section is not uniform, we in-\\nfer a corresponding departure in the earth from the figure\\nof a perfect sphere. The task of measuring portions of\\nthe meridian, has been executed in different countries.\\nWe may know, in- each case, how far we advance on\\nthe meridian, because every step we take northward,\\nproduces a corresponding increase in the altitude of the\\nnorth star. That an increase of the length of the de\\ngrees of the meridian, as we advance from the equator\\ntowards the pole, really proves that the earth is flattened\\nat the poles, will be readily seen on a little reflection.\\nWe must bear in mind that a degree is not any certain\\nlength, but only the three hundred and sixtieth part of a\\ncircle, whether great or small. If, therefore, a degree is\\nlonger in one case than in another, we infer that it is the\\nthree hundred and sixtieth part of a larger circle and\\nsince we find that a degree towards the pole is longer\\nthan a degree towards the equator, we infer that the cur-\\nvature is less in the former case than in the latter.\\nThe result of all the measurements is, that the length\\nof a degree increases as we proceed from the equator\\ntowards the pole, as may be seen from the following\\ntable\\n98. By what measurements is the spheroidal figure of the\\nearth proved What would be the curvature in all parts were\\nthe earth a perfect sphere How may we know when we have\\nadvanced one degree northward in the meridian Explain how\\nan increase of the length of a degree proves that the earth is\\nflattened towards the poles In what places have arcs of the me-\\nridian been measured What is the mean diameter of the\\nearth I What is the difference between the two diameters\\nWhat fraction expresses the ellipticity of the earth", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0082.jp2"}, "81": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n67\\nPlaces of observation.\\nLatitude.\\nLength of a degree in miles\\nPeru,\\n00\u00c2\u00b0 00 00\\n68.732\\nPennsylvania,\\n30 12 00\\n68.896\\nItaly,\\n43 01 00\\n68.998\\nFrance,\\n46 12 00\\n69.054\\nEngland,\\n51 29 54J\\n69.164\\nSweden,\\n66 20 10\\n69.292\\nCombining the results of various estimates, the di-\\nmensions of the terrestrial spheroid are found to be as\\nfollows\\nEquatorial diameter, 7925.648\\nPolar diameter, 7899.170\\nMean diameter, 7912.409\\nThe difference between the greatest and the least, is\\n26.478 2 ^9 of the greatest. This fraction (^q) is de-\\nnominated the ellipticity of the earth, being the excess\\nof the longest over the shortest diameter.\\n99. Thirdly, the figure of the earth is shown to be\\nspheroidal, by observations with the pendulum.\\nIf a pendulum, like that of a clock, be suspended\\nand the number of its vibrations per hour be counted,\\nthey will be found to be different in different latitudes.\\nA pendulum that vibrates 3600 times per hour at the\\nequator, will vibrate 3605J times at London, and a still\\ngreater number of times nearer the north pole. Now the\\nvibrations of the pendulum are produced by the force of\\n96. Explain how we may ascertain the figure of the earth by\\nmeans of a pendulum How will the number of vibrations be\\nin different latitudes 1 How many times will a pendulum vi-\\nbrate in an hour at London, which vibrates 3600 times per hour\\nat the equator 1 How are the vibrations of the pendulum pro-\\nduced 1 Why are these comparative numbers at different\\nplaces measures of the relative distances from the center of the\\nearth What could we infer from two observations with the\\npendulum, one at the equator and the other at the north pole\\nTo what conclusions have pendulum observations, made in va-\\nrious parts of the earth, led", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0083.jp2"}, "82": {"fulltext": "68 THE EARTH.\\ngravity. Hence their comparative number at different\\nplaces is a measure of the relative forces of gravity at\\nthose places. But when we know the relative forces of\\ngravity at different places, we know their relative dis-\\ntances from the center of the earth, because the nearer a\\nplace is to the center of the earth, the greater is the force\\nof gravity. Suppose, for example, we should count the\\nnumber of vibrations of a pendulum at the equator, and\\nthen carry it to the north pole and count the number of\\nvibrations made there in the same time we should be\\nable from these two observations to estimate the relative\\nforces of gravity at these two points and having the rel-\\native forces of gravity, we can thence deduce their rela-\\ntive distances from the center of the earth, and thus ob-\\ntain the polar and equatorial diameters. Observations\\nof this kind have been taken with the greatest accuracy\\nin many places on the surface of the earth, at various\\ndistances from each other, and they lead to the same\\nconclusions respecting the figure of the earth, as those\\nderived from measuring arcs of the meridian.\\n100. The density of the earth compared with water,\\nthat is, its specific gravity, is 5^ c The density was first\\nestimated by Dr. Hutton, from observations made by D v\\nMaskelyne, Astronomer Royal, on Schehallien, a moun-\\ntain of Scotland, in the year 1774. Thus, let M (Fig.\\n16,) represent the mountain, D, B, two stations on op-\\nposite sides of the mountain, and I a star and let IE\\nand IG be the zenith distances as determined by the\\ndifference of latitude of the two stations. But the ap-\\nparent zenith distances as determined by the plumb line\\nare IE and IG The deviation towards the mountain\\non each side exceeded 7 The attraction of the moun-\\ntain being observed on both sides of it, and its mass be-\\ning computed from a number of sections taken in all di-\\n100 What is the specific gravity of the earth How was it\\nascertained? Explain figure 16. Why is the density of the\\nearth so important an element", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0084.jp2"}, "83": {"fulltext": "DENSITY OF THE EARTH.\\n69\\nrections, tnese data, when compared with the known\\nattraction and magnitude of the earth, led to a knowl-\\nedge of its mean density. According to Dr. Hutton\\nthis is to that of water as 9 to 2 but later and more ac-\\ncurate estimates have made the specific gravity of the\\nearth as stated above. But this density is nearly double\\nthe average density of the materials that compose the\\nexterior crust of the earth, showing a great increase of\\ndensity towards the center.\\nThe density of the earth is an important element, as\\nwe shall find that it helps us to a knowledge of the den-\\nsity of each of the other members of the solar system.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0085.jp2"}, "84": {"fulltext": "PART II. OF THE SOLAR SYSTEM.\\n101 Having considered the Earth, in its astronomical\\nrelations, and the Doctrine of the Sphere, we proceed\\nnow to a survey of the Solar System, and shall treat suc-\\ncessively of the Sun, Moon, Planets, and Comets.\\nCHAPTER I.\\nOF THE SUN SOLAR SPOTS\u00e2\u0080\u0094 ZODIACAL LIGHT.\\n102. Tun figure which the sun presents to us is that\\nof a perfect circle, whereas most of the planets exhibit a\\ndisk more or less elliptical, indicating that the true shape\\nof the body is an oblate spheroid. So great, however,\\nis the distance of the sun, that a line 400 miles long\\nwould subtend an angle of only l y/ at the eye, and would\\ntherefore be the least space that could be measured.\\nHence, were the difference between two conjugate di-\\nameters of the sun any quantity less than this, we could\\nnot determine by actual measurement that it existed at\\nall. Still we learn from theoretical considerations,\\nfounded upon the known effects of centrifugal force,\\narising from the sun s revolution on his axis, that his\\nfigure is not a perfect sphere, but is slightly spheroidal.\\n103. The distance of the sun from the earth, is nearly\\n95,000,000 miles. In order to form some faint concep-\\n101. What subjects are treated of in Part II\\n102. What figure does the sun present to us What angle\\nwould a line of 400 miles on the sun s disk subtend How is\\nit inferred that the figure of the sun is spheroidal 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0086.jp2"}, "85": {"fulltext": "DENSITY. 71\\ntion at least of this vast distance, let us reflect that a rail-\\nway car, moving at the rate of 20 miles per hour, would\\nrequire more than 500 years to reach the sun.\\nThe apparent diameter of the sun is a little more than\\nhalf a degree, (32 3 Its linear diameter is about\\n885,000 miles and since the diameter of the earth is\\nonly 7912 miles, the latter, number is contained in the\\nformer nearly 112 times; so that it would require one\\nhundred and twelve bodies like the earth, if laid side by\\nside, to reach across the diameter of the sun and a ship\\nsailing at the rate of ten miles an hour, would require\\nmore than ten years to sail across the solar disk.\\nThe sun is about 1,400,000 times as large as the earth.\\nThe distance of the moon from the earth being 238,000\\nmiles, were the center of the sun made to coincide with\\nthe center of the earth, the sun would extend every way\\nfrom the earth nearly twice as far as the moon.\\n1 04. In density, the sun is only one-fourth that of the\\nearth, being but a little heavier than water and the\\nquantity of matter in the. sun is three hundred and fifty\\nthousand times as great as in the earth. A body would\\nweigh nearly 28 times as much at the sun as at the\\nearth. A man weighing 200 lbs. would, if transported\\nto the surface of the sun, weigh 5,580 lbs., or nearly 2\\\\\\ntons. To lift one s limb, would, in such a case, be be-\\nyond the ordinary power of the muscles. At the surface\\nof the earth, a body falls through lGjLfeet in a second;\\n103. What is the distance of the sun from the earth 1 How\\nlong would a railway car, moving at the rate of 20 miles per\\nhour, require to reach the sun How many bodies equal to\\nthe earth could lie side by side across the sun 1 How long\\nwould a ship be in sailing across it at 10 miles an hour If\\nthe sun s center were made to coincide with the center of the\\nearth, how much farther would it reach than the moon What\\nis the sun s apparent diameter 1 What is its linear diameter 1\\n104. In density how does the sun compare with the earth?\\nHow in quantity of matter How much more would a body\\nweigh at the sun than at the earth How far would a body\\nfall in one second at the surface of the sun", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0087.jp2"}, "86": {"fulltext": "72 THE SUN.\\nbut a body would fall at the sun in one second through\\n448.7 feet.\\nSOLAR SPOTS.\\n105. The surface of the sun, when viewed with a\\ntelescope, usually exhibits dark spots, which vary much,\\nat different times, in number, figure, and extent. One\\nhundred or more, assembled in several distinct groups,\\nare sometimes visible at once on the solar disk. Tlje\\ngreatest part of the solar spots are commonly very small,\\nbut occasionally a spot of enormous size is seen occupy-\\ning an extent of 50,000 miles in diameter. They are\\nsometimes even visible to the naked eye, when the sun\\nis viewed through colored glass, or, when near the hori-\\nzon, it is seen through light clouds or vapours. When it\\nis recollected that 1 of the solar disk implies an extent\\nof 400 miles, it is evident that a space large enough to be\\nseen by the naked eye, must cover a very large extent.\\nA solar spot usually consists of two parts, the nucleus\\nand the umbra, (Fig. 17.) The nucleus is black, of a\\nFig. 17.\\n105. Solar spots. Are they constant or variable in number\\nand appearance How many are sometimes seen on the sun s\\ndisk at once Are they usually large or small 1 How many\\nmiles in diameter are the largest 1 Describe a spot. What\\nchanges occur in the nucleus What is the umbra In what\\npart of the sun do the spots mostly appear 1 What apparent\\nmotions have they What is the period of their revolution T", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0088.jp2"}, "87": {"fulltext": "SOLAR SPOTS.\\n73\\nvery irregular shape, and is subject to great and sudden\\nchanges, both in form and size. Spots have sometimes\\nseemed to burst asunder, and to project fragments in dif-\\nferent directions. The umbra is a wide margin of\\nlighter shade, and is often of greater extent than the\\nnucleus. The spots are usually confined to a zone ex-\\ntending across the central regions of the sun, not exceed-\\ning 60\u00c2\u00b0 in breadth. When the spots are observed from\\nday to day, they are seen to move across the disk of the\\nsun, occupying about two weeks in passing from one\\nlimb to the other. After an absence of about the same\\nperiod, the spot returns, having taken 27d. 7b. 37m. in\\nthe entire revolution.\\n106. The spots must be nearly\\nor quite in contact with the body\\nof the sun. Were they at any\\nconsiderable distance from it, the\\ntime during which they would/\\nbe seen on the solar disk, would/\\nbe less than that occupied in\\nthe remainder of the revolution.\\nThus, let S, (Fig. 18,) be the\\nsun, E the earth, and abc the path\\nof the body, revolving about\\nthe sun. Unless the spot were\\nnearly or quite in contact with\\nthe body of the sun, being pro-\\njected upon his disk only while\\npassing from b to c, and being\\ninvisible while describing the\\narc cab, it would of course be\\nout of sight longer than in sight,\\nwhereas the two periods are\\nfound to be equal. Moreover,\\nFig. 18\\n106. How are the spots known to be nearly or quite in con-\\ntact with the body of the sun 1 Illustrate by figure 18. What\\ncauses the motion of the spots What is the period of the sun s\\nrevolution on his axis Explain by figure 1 9.\\n7", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0089.jp2"}, "88": {"fulltext": "74\\nTHE SUN.\\nthe lines which all the solar spots describe on the disk\\nof the sun, are found to be parallel to each other, like\\nthe circles of diurnal revolution around the earth, and\\nhence it is inferred that they arise from a similar cause,\\nnamely, the revolution of the sun on its axis, a fact which\\nis thus made known to us.\\nBut although the spots occupy about 27-|- days in pass-\\ning from one limb of the sun around to the same limb\\nagain, yet this is not the period of the sun s revolution\\non his axis, but exceeds it by nearly two days. For,\\nlet AA B (Fig. 19,) represent the sun, and EE M the\\norbit of the earth. Thus, when the earth is at E, the\\nvisible disk of the sun will be\\nAA B and if the earth remain-\\ned stationary at E, the time oc-\\ncupied by a spot after leaving A\\nuntil it returned to A, would be\\nin st equal to the time of the\\nsun s revolution on his axis.\\nBut during the 27^ days in\\nwhich the spot has been per-\\nforming its apparent revolution,\\nthe earth has been advancing\\nin his orbit from E to E where\\nthe visible disk of the sun is\\nA B Consequently, before the spot can appear again\\non the limb from which it set out, it must describe so\\nmuch more than an entire revolution as equals the arc\\nAA and this occupies nearly two days, which sub-\\ntracted from 27-J days, makes the sun s revolution on\\nits axis about 25J days or more accurately, it is 25d.\\n9h. 56m.\\n107. A telescope of moderate powers is sufficient to\\nshow the spots on the sun, and it is earnestly recom-\\nmended to the learner to avail himself of the first oppor-\\n107. How large a telescope is sufficient to view the spots on\\nthe sun How is the eye protected from the glare of the sun s\\nlight How may these shades be made", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0090.jp2"}, "89": {"fulltext": "SOLAR SPOTS. 75\\ntunity he may have, to view them for himself. For ob-\\nservations on the sun, telescopes are usually furnished\\nwith colored glass shades, which are screwed upon the\\nend of the instrument to which the eye is applied, foi\\nthe purpose of protecting the eye from the glare of the\\nsun s light. Such screens may be easily made by hold-\\ning a small piece of window glass over the flame of a\\nlamp, the wick being raised higher than usual so as to\\nsmoke freely.\\n108. The cause of the solar spots is unknown. It is\\nnot easy to determine what it is that occasions such\\nchanges on the surface of the sun but various conjec-\\ntures have been proposed by different astronomers. Ga-\\nlileo supposed that the dark part of a spot is owing to\\nblack cinders which rise from the interior of the sun,\\nwhere they are formed by the action of heat, constitu-\\nting a kind of volcanic lava that floats upon the surface\\nof the fiery flood, which he supposed to constitute the\\nouter portion of the sun. But the vast extent which\\nthese spots occasionally assume is unfavourable to such a\\nsupposition. It is incredible that a quantity of volcanic\\nlava should suddenly rise to the surface of the sun, suffi-\\ncient to occupy (as a spot is sometimes found to do)\\n2000,000,000 square miles.\\nDr. Herschel proposed a theory respecting the nature\\nand constitution of the sun, which, more from respect\\nto his authority than on account of any evidence by\\nsvhich it is supported, has been generally received. Ac-\\ncording to him, the sun is itself an opake body like the\\nearth, but is enveloped at a considerable distance from\\nhis body by two different strata of clouds, the exterior\\n108. Is the cause of solar spots well known What was\\nGalileo s hypothesis 1 What objections are there against it\\nWhat is Herschel s theory of the nature and constitution of\\nthe sun What sort of a body does he consider the sun itself?\\nBy what is it encompassed Where is the repository of the\\nsun s light and heat How does he explain the spots What\\nobjections are there to this duwttv What are facula?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0091.jp2"}, "90": {"fulltext": "78 THE SUN.\\nstratum being the fountain from which emanates the\\nsun s light and heat. The solar spots arise from the oc-\\ncasional displacement of portions of this envelope of\\nclouds, disclosing to view tracts of the solid body of the\\nsun.\\nWe regard this view of the origin of the sun s light and\\nheat as unsubstantiated by any satisfactory proofs, and\\nas in itself highly improbable. Such a medium would\\nbe a very unsuitable repository for the intense heat oi\\nthe sun, which can arise only from fixed matter in a state\\nof high ignition. The most probable supposition is, that\\nthe surface of the sun consists of melted matter in such\\na state. We must confess our ignorance of any known\\ncause which is adequate to explain the sudden extinc-\\ntion and removal of so large portions of this fiery flood,\\nas is occupied by some of the solar spots.\\nBesides the dark spots on the sun, there aie also seen,\\nin different parts, places that are brighter than the neigh-\\nboring portions of the disk. These are called faculce.\\nOther inequalities are observable in powerful telescopes,\\nall indicating that the surface of the sun is in a state of\\nconstant and powerful agitation.\\nZODIACAL LIGHT.\\n109. The Zodiacal Light is a faint light resembling\\nthe tail of a comet, and is seen at certain seasons of the\\nyear following the course of the sun after evening twi-\\nlight, or preceding his approach in the morning sky.\\nFigure 20 represents its appearance as seen in the even-\\ning in March, 1838. The following are the leading facts\\nrespecting it.\\n1. Its form is that of a luminous pyramid, having its\\nbase towards the sun. It reaches to an immense dis-\\ntance from the sun, sometimes even beyond the orbit of\\nthe earth. It is brighter in the parts nearer the sun than\\nin those that are more remote, and terminates in an ob-\\ntuse apex, its light fading away by insensible gradations,\\nuntil it becomes too feeble for distinct vision. Hence\\nits limits are at the same time fixed at dhTerent dis-", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0092.jp2"}, "91": {"fulltext": "ZODIACAL LIGHT.\\n77\\nFiff. 23.\\ntances from the sun by different observers, according to\\ntheir respective powers of vision.\\n2. Its aspects vary very much with the different seasons\\nof the year. About the first of October, in our climate\\n(Lat. 41\u00c2\u00b0 18 it becomes visible before the dawn of day.\\nrising along north of the ecliptic, and terminating above\\nthe nebula of Cancer. About the middle of November,\\nits vertex is in the constellation Leo. At this time no\\ntraces of it are seen in the west after sunset, but about\\nthe first of December it becomes faintly visible in the\\nwest, crossing the Milky Way near the horizon, and\\nreaching from the sun to the head of Capricornus, form-\\ning, as its brightness increases, a counterpart to the Milky\\n109. Zodiacal Light. Describe it. When and where\\nseen What is its form How far does it reach Where\\nbrightest How do its aspects vary at different seasons of\\nthe year What motions has it Is it equally conspicuous\\nevery year 1 What was it formerly held to be W T ith what\\nphenomenon has it been supposed to be connected\\n7*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0093.jp2"}, "92": {"fulltext": "78 THE SUN.\\nWay, between which on the right, and the Zodiacal\\nLight on the left, lies a triangular space embracing the\\nDolphin. Through the month of December, the Zo-\\ndiacal Light is seen on both sides of the sun, namely,\\nbefore the morning and after the evening twilight, some-\\ntimes extending 50\u00c2\u00b0 westward, and 70\u00c2\u00b0 eastward of the\\nsun at the same time. After it begins to appear in the\\nwestern sky, it increases rapidly from night to night,\\nboth in length and brightness, and withdraws itself from\\nthe morning sky, where it is scarcely seen after the\\nmonth of December, until the next October.\\n3. The Zodiacal Light moves through the heavens in\\nthe order of the signs. It moves with unequal velocity,\\nbeing sometimes stationary and sometimes retrogade,\\nwhile at other times it advances much faster than the\\nsun. In February and March, it is very conspicuous in\\nthe west, reaching to the Pleiades and beyond but in\\nApril it becomes more faint, and nearly or quite disap-\\npears during the month of May. It is scarcely seen in\\nthis latitude during the summer months.\\n4. It is remarkably conspicuous at certain periods of\\na few years, and then for a long interval almost disap-\\npears.\\n5. The Zodiacal Light was formerly held to be the\\natmosphere of the sun. But La Place has shown that\\nthe solar atmosphere could never reach so far from the\\nsun as this light is seen to extend. It has been supposed\\nby others to be a nebulous body revolving around the\\nsun. The author of this work has ventured to suggest\\nthe idea, that the extraordinary Meteoric Showers, which\\nat different periods visit the earth, especially in the\\nmonth of November, may be derived from this body.\\nSee American Journal of Science, Vol. 29, p. 378.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0094.jp2"}, "93": {"fulltext": "79\\nCHAPTER II.\\nOF THE APPARENT ANNUAL MOTION OF THE SUN-\\nFIGURE OF THE EARTH S ORBIT.\\n-SEASONS\\n110. The revolution of the earth around the sun once\\na year, produces an apparent motion of the sun around\\nthe earth in the same period. When bodies are at such\\na distance from each other as the earth and the sun, a\\nspectator on either would project the other body upon\\nthe concave sphere of the heavens, always seeing it on\\nthe opposite side of a great circle, 180\u00c2\u00b0 from himself.\\nThus when the earth arrives at Libra (Fig. 21,) we see\\nFig. 21.\\nthe sun in the opposite sign Aries. When the earth\\nmoves from Libra to Scorpio, as we are unconscious of\\nour own motion, the sun it is that appears to move from\\nAries to Taurus, being always seen in the heavens, where", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0095.jp2"}, "94": {"fulltext": "80 THE SUN.\\na line drawn from the eye of the spectator through the\\nbody meets the concave sphere of the heavens. Hence\\nthe line of projection carries the sun forward on one\\nside of the ecliptic, at the same rate as the earth moves\\non the opposite side and therefore, although we are un-\\nconscious of our own motion, we can read it from day to\\nday in the motions of the sun. If we could see the stars\\nat the same time with the sun, we could actually observe\\nfrom day to day the sun s progress through them, as we\\nobserve the progress of the moon at night only the\\nsun s rate of motion would be nearly fourteen times\\nslower than that of the moon. Although we do not see\\nthe stars when the sun is present, yet after the sun is set,\\nwe can observe that it makes daily progress eastward,\\nas is apparent from the constellations of the Zodiac oc-\\ncupying, successively, the western sky after sunset, pro-\\nving that either all the stars have a common motion east-\\nward independent of their diurnal motion, or that the\\nsun has a motion past them, from west to east. We\\nshall see hereafter abundant evidence to prove, that this\\nchange in the relative position of the sun and stars, is\\nowing to a change in the apparent place of the sun,\\nand not to any change in the stars.\\n111. Although the apparent revolution of the sun is\\nin a direction opposite to the real motion of the earth, as\\nregards absolute space, yet both are nevertheless from\\nwest to east, since these terms do not refer to any direc-\\ntions in absolute space, but to the order in which certain\\nconstellations (the constellations of the Zodiac) succeed\\none another. The earth itself, on opposite sides of its\\norbit, does in fact move towards directly opposits points\\n110. What produces the apparent motion of the sun around\\nthe earth once a year How would a spectator on either body\\nsee the other 1 When the earth is at Libra, where does the\\nsun appear to be 1 Explain figure 21. If the stars were visi-\\nble in the day time, how could we determine the sun s path\\nWhat change do the constellations of the Zodiac undergo with\\nrespect to the sun", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0096.jp2"}, "95": {"fulltext": "ANNUAL MOTION. 81\\nof space but it is all the while pursuing its course in\\nthe order of the signs. In the same manner, although\\nthe earth turns on its axis from west to east, yet any\\nplace on the surface of the earth is moving in a direc-\\ntion in space exactly opposite to its direction twelve\\nhours before. If the sun left a visible trace on the face\\nof the sky, the ecliptic would of course be distinctly\\nmarked on the celestial sphere as it is on an artificial\\nglobe and were the equator delineated in a similar man-\\nner, (by any method like that supposed in Art. 33,) we\\nshould then see at a glance the relative position of these\\ntwo circles, the points where they intersect one another\\nconstituting the equinoxes, the points where they are at\\nthe greatest distance asunder, or the solstices, and vari-\\nous other particulars, which for want of such visible\\ntraces, we are now obliged to search for by indirect and\\ncircuitous methods. It will even aid the learner to have\\nconstantly before his mental vision, an imaginary delin-\\neation of these two important circles on the face of the\\nsky.\\n112. The equator makes an angle with the ecliptic of\\n23\u00c2\u00b0 28 This is called the obliquity of the ecliptic.\\nAs the sun and earth are both always in the ecliptic, and\\nas the motion of the earth in one part of it makes the\\nsun appear to move in the opposite part at the same rate,\\nthe sun apparently descends in the winter 23\u00c2\u00b0 28 to the\\nsouth of the equator, and ascends in the summer the\\nsame number of degrees to the north of it. We must\\nkeep in mind that the celestial equator and the celestial\\necliptic are here understood, and we may imagine them\\n111. In what sense are the motions of the sun and earth\\nopposite, and in what sense in the same direction 1 If the\\necliptic and equator were distinctly delineated on the face of\\nthe sky, what points in them could be easily observed 1\\n112. What angle does the equator make with the ecliptic?\\nIn what circle do the sun and earth always appear How far\\ndo they recede from the equator How does the obliquity of\\nthe ecliptic vary", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0097.jp2"}, "96": {"fulltext": "82 THE SUN.\\nto be two great circles distinctly delineated on the face\\nof the sky. On comparing observations made at differ-\\nent periods for more than two thousand years, it is found,\\nthat the obliquity of the ecliptic is not constant, but\\nthat it undergoes a slight diminution from age to age,\\namounting to 52 in a century, or about half a second\\nannually. We might apprehend that by successive ap-\\nproaches to each other the equator and ecliptic would\\nfinally coincide but astronomers have found by a most\\nprofound investigation, founded on the principles of\\nuniversal gravitation, that this variation is confined with-\\nin certain narrow limits, and that the obliquity, after di-\\nminishing for some thousands of years, will then in-\\ncrease for a similar period, and will thus vibrate for ever\\nabout a mean value.\\n113. Let us conceive of the sun as at that point of the\\necliptic where it crosses the equator, that is, at one of the\\nequinoxes, as the vernal equinox. Suppose he stands\\nstill then for twenty four hours. The revolution of the\\nearth on its axis from east to west during this twenty\\nfour hours, will make the sun appear to describe a great\\ncircle from east to west, coinciding with the equator.\\nAt the end of this period, suppose the sun to move\\nnorthward one degree and to remain there for the next\\ntwenty-four hours, in which time the revolution of the\\nearth will make the sun appear to describe another cir-\\ncle from east to west, parallel to the equator, but one\\ndegree north of it. Thus we may conceive of the sun\\nas moving one degree every day for about three months,\\nwhen it will reach the point of the ecliptic farthest\\nfrom the equator, which is called the tropic from a Greek\\n113. Suppose the sun to start from the equator and to ad-\\nvance one degree north daily, explain its apparent diurnal rev-\\nolutions. When is the sun at the northern tropic When is\\nhe at the southern tropic How are the respective meridian\\naltitudes of the sun at these periods How do we find from\\nthese observations, the obliquity of the ecliptic", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0098.jp2"}, "97": {"fulltext": "THE SEASONS.\\n66\\nword (igsnco) which signifies to turn, because when the\\nsun arrives at this point, his motion in his orbit carries\\nhim continually towards the equator, and therefore he\\nseems to turn about.\\nWhen the sun is at the northern tropic, which hap-\\npens about the 21st of June, his elevation above the\\nsouthern horizon at noon, is the greatest of the year\\nand when he is at the southern tropic, about the 21st\\nof December, his elevation at noon is the least in the\\nyear. The difference between these two meridian alti-\\ntudes, will give the whole distance from one tropic to\\nthe other, and consequently twice the distance from each\\ntropic to the equator. By this means we find how far\\nthe tropic is from the equator, and that gives us the in-\\nclination of the two circles to one another for the great-\\nest distance between any two great circles on the sphere,\\nis always equal to the angle which they make with each\\nother.\\n114. The dimensions of the earth s orbit, when com-\\npared with its own magnitude, are immense.\\nSince the distance of the earth from the sun is\\n95,000,000 miles, and the length of the entire orbit nearly\\n600,000,000 miles, it will be found, on calculation, that\\nthe earth moves 1,640,000 miles per day, 68,000 miles\\nper hour, 1,100 miles per minute, and nearly 19 miles\\nevery second, a velocity nearly sixty times as great as\\nthe maximum velocity of a cannon ball. A place on\\nthe earth s equator turns, in the diurnal revolution, at the\\nrate of about 1,000 miles an hour and of a mile per\\nsecond. The motion around the sun, therefore, is nearly\\nseventy times as swift as the greatest motion around the\\naxis.\\n114. What is said of the dimensions of the earth s orbit\\nAt what rate does the earth move in its orbit per day, hour,\\nminute, and second 1 How far does a place on the earth s\\nequator move per hour and second How much swifter is\\nthe motion in the orbit than on its axis", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0099.jp2"}, "98": {"fulltext": "84 THE SUN.\\nTHE SEASONS.\\n115. The change of seasons depends on two causes,\\n(1) the obliquity of the ecliptic, and (2) the earth s axis\\nalways remaining parallel to itself Had the earth s\\naxis been perpendicular to the plane of its orbit, the\\nequator would have coincided with the ecliptic, and the\\nsun would have constantly appeared in the equator\\nTo the inhabitants of the equatorial regions, the sun\\nwould always have appeared to move in the prime ver-\\ntical and to the inhabitants of either pole, he would\\nalways have been in the horizon. But the axis being\\nturned out of a perpendicular direction 23\u00c2\u00b0 28 the\\nequator is turned the same distance out of the ecliptic\\nand since the equator and ecliptic are two great circles\\nwhich cut each other in two opposite points, the sun,\\nwhile performing his circuit in the ecliptic, must evi-\\ndently be once a year in each of those points, and must\\ndepart from the equator of the heavens to a distance on\\neither side equal to the inclination of the two circles,\\nthat is, 23\u00c2\u00b0 28\\n116. The earth being a globe, the sun constantly en-\\nlightens the half next to him,* while the other half is in\\ndarkness. The boundary between the enlightened and\\nunenlightened part, is called the circle of illumination.\\nWhen the earth is at one of the equinoxes, the sun is at\\nthe other, and the circle of illumination passes through\\nboth the Doles. When the earth reaches one of the\\n115. The Seasons. On what two causes does the change\\nof seasons depend 1 Had the earth s axis been perpendicu-\\nlar to the plane of its orbit, in what great circle would the sun\\nalways have appeared to move 1\\nIn fact, the sun enlightens a little more than half the earth, since\\non account of his vast magnitude the tangents drawn from opposite\\nsides of the sun to opposite sides of the earth, converge to a point\\nbehind the earth, as will be seen by and by in the representation of\\neclipses", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0100.jp2"}, "99": {"fulltext": "THE SEASONS.\\n85\\ntropics, the sun being at the other, the circle of illumin-\\nation cuts the earth, so as to pass 23\u00c2\u00b0 28 beyond the\\nnearer, and the same distance short of the remoter pole.\\nThese results would not be uniform, were not the earth s\\naxis always to remain parallel to itself. The following\\nfigure will illustrate the foregoing statements.\\nFig. 22.\\nLet ABCD represent the earth s place in different\\nparts of its orbit, having the sun in the center. Let A,\\n116. How much of the earth does the sun enlighten at once\\nDefine the circle of illumination. How does it cut the earth at\\nthe equinoxes How at the solstices 1 Explain figure 22.\\nWhen the earth is at one of the tropics and the sun at the\\nother, where is it continual day and where continual night\\n8", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0101.jp2"}, "100": {"fulltext": "86 THE SUN.\\nC, be the positions of the earth at the equinoxes, and B,\\nD, its positions at the tropics, the axis ns being always\\nparallel to itself.* At A and C the sun shines on both\\nn and s and now let the globe be turned round on its\\naxis, and the learner will easily conceive that the sun\\nwill appear to describe the equator, which being bisected\\nby the horizon of every place, of course the day and\\nnight will be equal in all parts of the globe. f Again,\\nat B when the earth is at the southern tropic, the sun\\nshines 23J\u00c2\u00b0 beyond the north pole n, and falls the same\\ndistance short of the south pole s. The case is exactly\\nreversed when the earth is at the northern tropic and\\nthe sun at the southern. While the earth is at one of\\nthe tropics, at B for example, let us conceive of it as turn-\\ning on its axis, and we shall readily see that all that part\\nof the earth which lies within the north polar circle will\\ne-njoy continual day, while that within the south polar\\ncircle will have continual night, and that all other places\\nwill have their days longer as they are nearer to the en-\\nlightened pole, and shorter as they are nearer to the un-\\nenlightened pole. This figure likewise shows the suc-\\ncessive positions of the earth at different periods of the\\nyear, with respect to the signs, and what months corres-\\npond to particular signs. Thus the earth enters Libra\\nand the sun Aries on the 21st of March, and on the 21st\\nof June the earth is just entering Capricorn and the sun\\nCancer.\\n117. Had the axis of the earth been perpendicular\\nto the plane of the ecliptic, then the sun would always\\nhave appeared to move in the equator, the days would\\nevery where have been equal to the nights, and there\\ncould have been no change of seasons. On the other\\nhand, had the inclination of the ecliptic to the equator\\nThe learner will remark that the hemisphere towards n is above,\\nand that towards 5 is below the plane of the paper. It is important to\\nform a just conception of the position of the axis with respect to the\\nplane of its orbit.\\nt At the pole, the solar disk, at the time of the equinox, appears bis-\\nected by the horizon.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0102.jp2"}, "101": {"fulltext": "THE SEASONS. 87\\nbeen much greater than it is, the vicissitudes of the sea-\\nsons would have been proportionally greater than at pres-\\nent. Suppose, for instance, the equator had been at\\nright angles to the ecliptic, in which case the poles of\\nthe earth would have been situated in the ecliptic itself;\\nthen in different parts of the earth the appearances\\nwould have been as follows. To a spectator on the\\nequator, the sun as he left the vernal equinox would\\nevery day perform his diurnal revolution in a smaller\\nand smaller circle, until he reached the north pole, when\\nhe would halt for a moment, and then wheel about and\\nreturn to the equator in the reverse order. The pro-\\ngress of the sun through the southern signs, to the south\\npole, would be similar to that already described. Such\\nwould be the appearances to an inhabitant of the equa-\\ntorial regions. To a spectator living in an oblique\\nsphere, in our own latitude for example, the sun while\\nnorth of the equator would advance continually north-\\nward, making his diurnal circuits in parallels farther and\\nfarther distant from the equator, until he reached the\\ncircle of perpetual apparition, after which he would\\nclimb by a spiral course to the north star, and then as\\nrapidly return to the equator. By a similar progress\\nsouthward, the sun would at length pass the circle of\\nperpetual occultation, and for some time (which would\\nbe longer or shorter according to the latitude of the place\\nof observation) there would be continual night.\\nThe great vicissitudes of heat and cold which would\\nattend such a motion of the sun, would be wholly in-\\ncompatible with the existence of either the animal or\\nthe vegetable kingdoms, and all terrestrial nature would\\n117. Had the earth s axis been perpendicular to the plane\\nof the ecliptic, would there have been any change of seasons\\nWhat would have been the consequence had the equator been\\nat right angles to the ecliptic How would the sun appear to\\nmove to a person on the equator How to one situated at the\\npole 1 How to an inhabitant of an oblique sphere How\\nwould have been the vicissitudes of heat and cold", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0103.jp2"}, "102": {"fulltext": "88\\nTHE SUN.\\nbe doomed to perpetual sterility and desolation. The\\nhappy provision which the Creator has made against\\nsuch extreme vicissitudes, by confining the changes of\\nthe seasons within such narrow bounds, conspires with\\nmany other express arrangements in the economy of\\nnature to secure the safety and comfort of the human\\nrace.\\nFIGURE OF THE EARTHS ORBIT.\\n118. Thus far we have taken the earth s orbit as a\\ngreat circle, such being the projection of it on the celes-\\ntial sphere but we now proceed to investigate its actual\\nfigure.\\nFig. 23.\\nWere the earth s path a circle, having the sun in the\\ncenter, the sun would always appear to be at the same\\n118. Were the earth s path a circle, how would the distance\\nof the sun from us always appear Define the radius vector.\\nWhat do we infer from the fact that the radius vector is con-\\nstantly varying How do we learn the relative distances ot\\nthe earth How do we construct a figure representing the\\nearth s orbit Explain figure 23.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0104.jp2"}, "103": {"fulltext": "FTGURE OF THL EARTH S ORBIT. 89\\ndistance from us that is, the radius of its orbit, or ra-\\ndius vector, the name given to a line drawn from the\\ncenter of the sun to the orbit of any planet, would al-\\nways be of the same length. But the earth s distance\\nfrom the sun is constantly varying, which shows that\\nits orbit is not a circle. We learn the true figure of the\\norbit, by ascertaining the relative distances of the earth\\nfrom the sun at various periods of the year. These all\\nbeing laid down in a diagram, according to their respec-\\ntive lengths, the extremities, on being connected, give\\nus our first idea of the shape of the orbit, which appears\\nof an oval form, and at least resembles an ellipse and,\\non further trial, we find that it has the properties of an\\nellipse. Thus, let E (Fig. 23,) be the place of the\\nearth, and a, b, c, c. successive positions of the sun\\nthe relative lengths of the lines E#, Eft, c. being\\nknown on connecting the points, a, b, c, c. the result-\\ning figure indicates the true shape of the earth s orbit.\\n119. These relative distances are found in two differ-\\nent ways first, by changes in the sun s apparent diam-\\neter, and, secondly, by variations in his angular velo-\\ncity. The same object appears to us smaller in propor-\\ntion as it is more distant and if we see a heavenly body\\nvarying in size at different times, we infer that it is at\\ndifferent distances from us that when largest, it is near-\\nest to us, and when smallest, farthest off. Now when\\nthe sun s diameter is measured accurately by instru-\\nments, it is found to vary from day to day, being when\\ngreatest more than thirty-two minutes and a half, and\\nwhen smallest only thirty-one minutes and a half, differ-\\ning in all, about seventy-five seconds. When the diam-\\neter is greatest, which happens in January, we know\\n119. How does the same body appear when at different dis-\\ntances 1 What inferences do we make from its variations of\\nsize How much does the apparent diameter of the snn vary\\nin different parts of the year When is it greatest, and\\nwhen smallest Define the terms perihelion and aphelion.\\n8*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0105.jp2"}, "104": {"fulltext": "90 THE SUN\\nthat the sun is nearest to us and when the diameter is\\nleast, which occurs in July, we infer that the sun is at\\nthe greatest distance from us.\\nThe point where the earth or any planet, in its revo-\\nlution, is nearest the sun, is called its perihelion the\\npoint where it is farthest from the sun, its aphelion,\\n120. Similar conclusions may be drawn from obser-\\nvations on the sun s angular velocity. A body appears\\nto move most rapidly when nearest to us. Indeed the\\napparent velocity of the sun increases rapidly as it ap-\\nproaches us, and as rapidly diminishes when it recedes\\nfrom us. If it were to come twice as near as before it\\nwould appear, to move not merely twice as swift, but\\nfour times as swift if it came ten times nearer, its appa-\\nrent velocity would be one hundred times as great as\\nbefore. We say, therefore, that the velocity varies\\ninversely as the square of the distance, for as the dis-\\ntance is diminished ten times, the velocity is increased\\nthe square of ten, that is, one hundred times. Now by\\nnoting the time it takes the sun, from day to day, to re-\\nturn to the meridian, we learn the comparative veloci-\\nties with which it moves at different times, and from\\nthese we derive the comparative distances of the sun\\nat the corresponding times.\\nWhen by either of the foregoing methods, we have\\nlearned the relative distances of the sun from the earth\\nat various periods of the year, we may lay down, or plot\\nin a diagram like figure 23, a representation of the orbit\\nwhich the sun apparently describes about the earth, and\\nit will give us the figure of the orbit which the earth\\nreally describes about the sun, in its annual revolution.\\n120. What conclusions are drawn from the variations in\\nthe sun s angular velocity 1 According to what law does the\\nvelocity vary How may we ascertain the sun s daily rate\\nWhat great doctrine is it necessary to be acquainted with, in\\norder to understand the celestial motions", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0106.jp2"}, "105": {"fulltext": "UNIVERSAL GRAVITATION. 91\\nBut neither the revolution of the earth about the sun,\\nnor indeed that of any of the planets, can be well and\\nclearly understood, until we are acquainted with the\\nforces by which their motions are produced, especially\\nwith the doctrine of Universal Gravitation. To this\\nsubject, therefore, let us next apply our attention.\\nCHAPTER III.\\nOF UNIVERSAL GRAVITATION KEPLER S LAWS MOTION\\nIN AN ELLIPTICAL ORBIT PRECESSION OF THE EQUI-\\nNOXES.\\n121. We discover in nature a tendency of every por-\\ntion of matter towards every other. This tendency is\\ncalled gravitation. In obedience to this power, a stone\\nfalls to the ground and a planet revolves around the sun.\\nIt was once supposed that we could not reason from\\nthe phenomena of the earth to those of the heavens\\nsince it was held that the laws of motion might be\\nvery different among the heavenly bodies from what\\nwe find them to be on this globe but Galileo and New-\\nton in their researches into nature, proceeded on the\\nidea that nature is uniform in all her works, and that\\nevery where the same causes produces the same effects,\\nand that the same effects result from the same causes.\\nThat this is a sound principle of philosophy, is proved\\nby the fact, that all the conclusions derived from it in\\nthe interpretation of nature are found to be true. Hence\\nby studying the laws of motion as exhibited constantly\\nbefore our eyes in all terrestrial motions, we are learning\\n121. What force do we observe in nature What is this\\nforce called Can we reason from terrestrial to celestial phe-\\nnomena On what idea did Galileo and Newton proceed\\nHow is this proved to be a sound principle of philosophy I", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0107.jp2"}, "106": {"fulltext": "92 UNIVERSAL GRAVITATION\\nthe laws that govern the movements of the heavenly\\nbodies.\\n122. On the earth all bodies are seen to fall towards\\nits center. A stone let fall in any part of the earth, de-\\nscends immediately to the ground. This may seem to\\nthe young learner as so much a matter of course as to\\nrequire no explanation. But stones fall in exactly op-\\nposite directions on opposite sides of the earth, always\\nfalling towards the center of the earth from every part\\nexterior to its surface as when Fl S- 24\\nwe hold a small needle towards n^ ^dliillllSIIIlillllfiiilliiiiKy^\\na magnetic ball or load stone, the\\nneedle will fly towards the ball,\\nand cling to its surface, to which-\\never side of the ball it is present-\\ned. (Fig. 24.) From this uni-\\nversal descent of bodies near the y*\\nearth, we infer the existence of\\nsome force which draws or impels them, and this invisi-\\nble force we call the attraction of gravitation, or simply\\ngravity.\\n123. By the laws of gravity we mean the manner in\\nwhich it always acts. They are three in number, and\\nare comprehended in the following proposition\\nGravity acts on all matter alike, with a force propor-\\ntioned to the quantity of matter, and inversely as the\\nsquare of the distance.\\nFirst, gravity acts on all matter alike. Every body\\nin nature, whether great or small, whether solid, liquid,\\nor aeriform, exhibits the same tendency to fall towards\\nthe center of the earth. Some bodies, indeed, seem less\\nprone to fall than others, and some even appear to rise,\\nas smoke and light vapors. But this is because they are\\nsupported by the air when that is removed, they de-\\n122. In what directions do bodies fall in all parts of the\\nearth Illustrate by figure 24. What is gravity", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0108.jp2"}, "107": {"fulltext": "LAWS OF GRAVITY.\\n93\\nscend alike towards the earth a guinea and a feather,\\nthe lightest vapor and the heaviest rocks, fall with equal\\nvelocities.\\nSecondly, the force of gravity is proportioned to the\\nquantity of matter. A mass of lead contains perhaps\\nfifty times as much matter as an equal bulk of cotton\\nyet, if carried beyond the atmosphere, and let fall in ab-\\nsolute space, they would both descend towards the earth\\nwith equal speed, until they entered the atmosphere,\\nand were the atmosphere removed they would continue\\nto fall side by side until they reached the earth. Now\\nif the lead contains fifty times as much matter as the\\ncotton, it must take fifty times the force to make it move\\nwith equal velocity. If we double the load we must\\ndouble the team, if we would continue to travel at the\\nsame speed as before. Hence, from the fact that bodies\\nof various degrees of density descend alike towards the\\ncenter of the earth by the force of gravity, we infer\\nthat that force is always exerted upon bodies in exact\\nproportion to their quantity of matter.\\nThirdly, the force with which gravity acts upon bod-\\nies at different distances from the earth, is inversely as\\nthe square of the distance from the center of the earth.\\nIf a pound of lead were carried as far above the earth as\\nfrom the center to the surface of the earth, it would\\nweigh only one-fourth of a pound for being twice as\\nfar as before from the center of the earth, its weight\\nwould be diminished in the proportion of the square of\\ntwo, that is, four times.\\n123. What do we mean by the law of gravity 1 State the\\ngeneral proposition. Show that gravity acts on all matter alike\\nHow is this consistent with the fact, that some bodies appear to\\nrise How would all bodies fall in a vacuum 1 Explain how\\ngravity is proportioned to the quantity of matter. How would\\nequal masses of lead and cotton fall, if carried beyond the at-\\nmosphere 1 What do we infer from the fact, that all bodies fall\\ntowards the earth with equal velocities To what is gravity\\nacting at different distances proportioned How much would\\na pound of lead weigh, if carried as far above the earth as from\\nv .he surface to the center", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0109.jp2"}, "108": {"fulltext": "94 UNIVERSAL GRAVITATION.\\n124. Bodies falling to the earth by gravity have their\\nvelocity continually increased. For since they retain\\nwhat motion they have and constantly receive more\\nby the continued action of gravity, they must move\\nfaster and faster, as a wheel has its velocity constantly\\naccelerated when we continue to apply successive im-\\npulses to it.\\nThe spaces which bodies describe, when falling freely\\nby gravity, are as the squares of the times. It is found\\nby experiment, that a body will fall from a state of\\nrest 16 j2 feet in one second. In two seconds it will not\\nfall merely through double this space, but through four\\ntimes this space, that is, through a distance expressed\\nby the square of the time multiplied into ISy^- Conse-\\nquently, in two seconds the fall will be 64J, in three se-\\nconds 144J, and in ten seconds 1608J feet, that is,\\nthrough one hundred times 16^2 feet.\\nThe weight of a body is nothing more than the ac-\\ntion of gravity upon it tending to carry it towards the\\ncenter of the earth. The counterpoise which is placed\\nin the opposite scale by which its weight is estimated, is\\nthe force it takes to hold the body back, which must be\\njust equal to that by which it endeavors to descend.\\n125. There is another principle which it is necessary\\nclearly to comprehend before we can understand the mo-\\ntions of the heavenly bodies. It is commonly called the\\nFirst Law of Motion and is as follows\\nEvery body perseveres in a state of rest, or of uniform\\nmotion in a straight line, unless compelled by some force\\nto change its state. This law has been fully established\\nby experiment, and is conformable to all experience.\\nIt embraces several particulars. First, A body when at\\n124. When a body is falling towards the earth, how is its\\nvelocity affected To what are the spaces described by fall-\\ning bodies proportioned How far will a body fall from a state\\nof rest in one second 1 How far in two seconds What is\\nthe weight of a body", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0110.jp2"}, "109": {"fulltext": "LAWS OF MOTION. 95\\nrest remains so unless some force puts it in motion\\nand hence it is inferred, when a body is found in mo-\\ntion, that some force must have been applied to it suffi-\\ncient to have caused its motion. Thus, the fact that\\nthe earth is in motion around the sun and around its own\\naxis, is to be accounted for by assigning to each of these\\nmotions a force adequate, both in quantity and direction,\\nto produce these motions respectively.\\nSecondly, When a body is once in motion it will con-\\ntinue to move forever, unless something stops it. When\\na ball is struck on the surface of the earth, the friction\\nof the earth and the resistance of the air soon stop its\\nmotion when struck on smooth ice it will go much\\nfarther before it comes to a state of rest, because the ice\\nopposes much less resistance than the ground and were\\nthere no impediment to its motion it would, when once\\nset in motion, continue to move without end. The\\nheavenly bodies are actually in this condition they\\ncontinue to move, not because any new forces are ap-\\nplied to them, but, having been once set in motion, they\\ncontinue in motion because there is nothing to stop them.\\nThirdly, The motion to which a body naturally tends\\nis uniform that is, the body moves just as far the se-\\ncond minute as it did the first, and as far the third as\\nthe second, passing over equal spaces in equal times.\\nFourthly, A body in motion will move in a straight\\nline, unless diverted out of that line by some external\\nforce and the body will resume its straight forward mo-\\ntion, when ever the force that turns it aside is with-\\ndrawn. Every body that is revolving in an orbit, like\\nthe moon around the earth, or the earth around the sun,\\n125. Recite the first law of motion. How has this law been\\nestablished What does the fact, that the earth is in motion\\naround the sun imply? How would a ball when once struck\\ncontinue to move, if it met with no resistance Why do the\\nheavenly bodies continue to move What is meant by saying\\nthat motion is naturally uniform In what direction does\\nevery revolving bodv tend to move.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0111.jp2"}, "110": {"fulltext": "96 UNIVERSAL GRAVITATION.\\ntends to move in a straight line which is a tangent* to\\nits orbit.\\nLet us now see how the foregoing principles, which\\noperate upon bodies on the earth, are extended so as to\\nembrace all bodies in the universe, as in the doctrine of\\nUniversal Gravitation. This important principle is thus\\ndefined\\n126. Universal gravitation, is that influence by\\nwhich every body in the universe, whether great or small,\\ntends towards every other, with a force which is directly\\nas the quantity of matter, and inversely as the square of\\nthe distance.\\nAs this force acts as though bodies were drawn to-\\nwards each other by a mutual attraction, the force is de-\\nnominated attraction; but it must be borne in mind,\\nthat this term is figurative, and implies nothing respect-\\ning the nature of the force.\\nThe existence of such a force in nature was distinctly\\nasserted by several astronomers previous to the time of\\nSir Isaac Newton, but its laws were first promulgated\\nby this wonderful man in his Principia, in the year 1687.\\nIt is related, that while sitting in a garden, and musing\\non the cause of the falling of an apple, he reasoned\\nthus :f that, since bodies far removed from the earth fall\\ntowards it, as from the tops of towers, and the highest\\nmountains, why may not the same influence extend\\neven to the moon and if so, may not this be the reason\\nwhy the moon is made to revolve around the earth, as\\nwould be the case with a cannon ball were it projected\\nhorizontally near the earth with a certain velocity. Ac-\\ncording to the first law of motion, the moon, if not con-\\ntinually drawn or impelled towards the earth by some\\nforce, would not revolve around it, but would proceed\\non in a straight line. But going around the earth as she\\ndoes, in an orbit that is nearly circular, she must be\\nA tangent is a straight line which touches a curve. Thus AB (Fig.\\n25,) is a tangent to the circle at\u00c2\u00abA.\\nt Pemberton s View of Newton s Philosophy.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0112.jp2"}, "111": {"fulltext": "UNIVERSAL KRAVITATION.\\n97\\nurged towards the earth by some force, which diverts\\nher from a straight course. For let the earth (Fig. 25.)\\nbe at E, and let the arc described by the moon in one\\nsecond of time be Ab. Were the moon influenced by\\nno extraneous force, to turn aside, she would have de-\\nscribed, not the arc Ab, but the straight line AB, and\\nwould have been found at the end of the given time at\\nB instead of b. She therefore departs from the line in\\nwhich she tends naturally to move, by the line B\\nwhich in small angles may be taken as equal to Aa.\\nFig. 25.\\nThis deviation from the tangent must be owing to some\\nextraneous force. Does this force correspond to what\\nthe force of gravity exerted by the earth, would be at\\nthe distance of the moon The question resolves itself\\ninto this Would the force of gravity exerted by the\\nearth upon the moon, cause the moon to deviate from\\nher straight forward course towards the earth just as\\nmuch as she is actually found to deviate Now we\\n126. Universal Gravitation. Define it. Why called at-\\ntraction State the historical facts connected with its discov-\\nery. How did Sir Isaac Newton reason from the falling of an\\napple Explain by figure 25. How is it proved that gravity\\nand no other force causes the moon to revolve about the earth\\n9", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0113.jp2"}, "112": {"fulltext": "98 UNIVERSAL GRAVITATION.\\nknow how far the moon is from the earth, namely sixty\\ntimes as far as it is from the center to the surface of the\\nearth and since the force of gravity decreases in pro-\\nportion to the square of the distance, this force must be\\n3600 times (which equals the square of 60,) less than at\\nthe surface of the earth. This is found, on computa-\\ntion, to be exactly the force required to make the moon\\ndeviate to the amount she does from the straight line in\\nwhich she constantly tends to move and hence it is\\ninferred that gravity, and no other force than gravity,\\ncauses the moon to circulate around the earth.\\nBy this process it was discovered that the law of grav-\\nitation extends to the moon. By subsequent inquiries\\nit was found to extend in like manner to all the planets,\\nand to every member of the solar system and, finally,\\nrecent investigations have shown that it extends to the\\nfixed stars. The law of gravitation, therefore, is now\\nestablished as the grand principle which governs all the\\nmotions of the heavenly bodies.\\n127. There are three great principles, according to\\nwhich the motions of the earth and all the planets\\naround the sun are regulated, called Kepler s Laws, hav-\\ning been first discovered by the great astronomer whose\\nname they bear. They may appear to the young learner,\\nwhen he first reads them, dry and obscure yet they\\nwill be easily understood from the explanations that fol-\\nlow and so important have they proved in astronomical\\ninquiries, that they have acquired for their renowned\\ndiscoverer the exalted appellation of the legislator of the\\nskies.\\nWe will consider each of these laws separately.\\n127. Kepler s Laws. Why so called What appellation\\nhas been given to Kepler", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0114.jp2"}, "113": {"fulltext": "KEPLER S LAWS.\\n99\\n128. First law. The orbits of the earth and all the\\nplanets are ellipses, having the sun in the common\\nfocus.\\nIn a circle all the diameters are equal to each other\\nbut if we take a metallic wire or hoop and draw it out on\\nopposite sides, we elongate it into an ellipse, of which the\\ndifferent diameters are very unequal. That which con-\\nnects the two points most distant from each other is called\\nthe transverse, and that which is at right angles to this\\nis called the conjugate axis. Thus AB (Fig. 26) is the\\ntransverse axis and CD the conjugate of the ellipse AB.\\nBy such a process of elongating the circle into an el-\\nlipse, the center of the circle may be conceived of as\\ndrawn opposite ways to E and F, each of which be-\\ncomes a focus, and both together are called the foci of the\\nellipse. The distance GE or GF of the focus from the\\n128. Recite the first law. In a circle, how are all the diam-\\neters How are. they in an ellipse What is the longest di-\\nameter called 1 What is the shortest called Explain by figure\\n26. What is the eccentricity of the ellipse How many el-\\nlipses may there be having a common focus 1 Explain figure\\n26 How eccentric is the earth s orbit", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0115.jp2"}, "114": {"fulltext": "100\\nUNIVERSAL GRAVITATION.\\ncenter is called the eccentricity of the ellipse and the\\nellipse is said to be more or less eccentric, as the distance\\nof the focus from the center is greater or less.\\nNow there may be an indefinite number of ellipses\\nhaving one common focus, but varying greatly in ec-\\ncentricity. Figure 27 represents such a collection of\\nellipses around the common focus F, the innermost AGD\\nhaving a small eccentricity or varying little from a cir-\\ncle, while the outermost ACB is a very eccentric ellipse.\\nThe orbits of all the bodies that revolve about the sun,\\nboth planets and comets, have, in like manner, a com-\\nmon focus in which the sun is situated, but they differ\\nin eccentricity.\\nMost of the planets have orbits of very little eccen-\\ntricity, differing little from circles, but comets move in\\nvery eccentric ellipses.\\nThe earth s path around the sun varies so little from\\na circle, that a diagram representing it truly would\\nscarcely be distinguished from a perfect circle yet\\nwhen the comparative distances of the sun from the\\nearth are taken at different seasons of the year, as is ex-\\nplained in Art. 118, we find that the difference between", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0116.jp2"}, "115": {"fulltext": "kepler s laws. 101\\nthe greatest and least distances is no less than 3,000,000\\nmiles.\\n129. Second law. The radius vector of the earth,\\nor of any planet, describes equal areas in equal times.\\nIt will be recollected that the radius vector is a line\\ndrawn from the center of the sun to a planet revolving\\nabout the sun, (Art. 118.) Thus Ea, Eb, Ec, (Fig. 23,)\\nc. are successive representations of the radius vector.\\nNow if a planet sets out from a and travels round the sun\\nin the direction of abc, it will move faster when nearer the\\nsun, as at a, than when more remote from it, as at m\\nyet if ab and mn be arcs described in equal times, then,\\naccording to the foregoing law, the space Eab will be\\nequal to the space Emn and the same is true of all the\\nother spaces described in equal times. Although the\\nfigure Eab is much shorter than Emn, yet its greater\\nbreadth exactly counterbalances the greater length of\\nthose figures which are described by the radius vector\\nwhere it is longer.\\ni30. Third law. The squares of the periodical times\\nare as the cubes of the mean distances from the sun.\\nThe periodical time of a body is the time it takes to\\ncomplete its orbit in its revolution about the sun. Thus\\nthe earth s periodic time is one year, and that of the\\nplanet Jupiter is about twelve years. As Jupiter takes\\nso much longer time to travel round the sun than the\\nearth does, we might suspect that his orbit was larger\\nthan that of the earth, and of course that he was at\\na greater distance from the sun, and our first thought\\nmight be that he was probably twelve times as far off;\\nbut Kepler discovered that the distances did not increase\\nas fast as the times increased, but that the planets which\\n129. State Kepler s second law. Explain by figure 23, p. 88.\\n130. State Kepler s third law. What is meant by the peri-\\nodical time of a body Do planets move faster or slower as\\nthey are more distant from the sun Explain the law.\\n9*", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0117.jp2"}, "116": {"fulltext": "102 UNIVERSAL GRAVITATION.\\nare more distant from the sun actually move slower than\\nthose which are nearer. After trying a great many pro-\\nportions, he at length found that if we take the squares\\nof the periodic times of two planets, the greater square\\ncontains the less, just as often as the cube of the dis-\\ntance of the greater contains that of the less. This fact\\nis expressed by saying, that the squares of the periodic\\ntimes are to one another as the cubes of the distances.\\nThis law is of great use in determining the distances\\nof all the planets from the sun, as we shall see more fully\\nhereafter.\\nMOTION IN AN ELLIPTICAL ORBIT.\\n131. Let us now endeavor to gain a just conception\\nof the forces by which the earth and all the planets are\\nmade to revolve about the sun.\\nIn obedience to the first law of motion, every moving\\nbody tends to move in a straight line and were not the\\nplanets deflected continually towards the sun by the\\nforce of attraction, these bodies as well as others would\\nmove forward in a rectilineal direction. We call the force\\nby which they tend to such a direction the projectile\\nforce, because its effects are the same as though the body\\nwere originally projected from a certain point in a certain\\ndirection. It is an interesting problem for mechanics to\\nsolve, what was the nature of the impulse originally\\ngiven to the earth, in order to impress upon it its two\\nmotions, the one around its own axis, the other around\\nthe sun. If struck in the direction of its center of\\ngravity it might receive a forward motion, but no rota-\\ntion on its axis. It must, therefore, have been impelled\\nby a force, whose direction did not pass through its\\n131. Explain how a body is made to revolve in an orbit,\\nunder the action of two forces. What is meant by the projec-\\ntile force How must the earth have been impelled in order\\nto receive its present motions How illustrated by the mo-\\ntions of a top 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0118.jp2"}, "117": {"fulltext": "MOTION IN AN ELLIPTICAL ORBIT. 103\\ncenter of gravity. Bernouilli, a celebrated mathemati-\\ncian, has calculated that the impulse must have been\\ngiven very nearly in the direction of the center, the\\npoint of projection being only the 165th part of the\\nearth s radius from the center. This impulse alone\\nwould cause the earth to move in a right line gravita-\\ntion towards the sun causes it to describe an orbit.\\nThus a top spinning on a smooth plane, as that of glass\\nor ice, impelled in a direction not coinciding with that\\nof the center of gravity, may be made to imitate the two\\nmotions of the earth, especially if the experiment is tried\\nin a concave surface like that of a large bowl. The re-\\nsistance occasioned by the surface on which the top\\nmoves, and that of the air, will gradually destroy the\\nforce of projection and cause the top to revolve in a\\nsmaller and smaller orbit but the earth meets with no\\nsuch resistance, and therefore makes both her days and\\nyears of the same length from age to age. A body,\\ntherefore, revolving in an orbit about a center of attrac-\\ntion, is constantly under the influence of two forces,\\nthe projectile force, which tends to carry it forward in a\\nstraight line which is a tangent to its orbit, and the cen-\\ntripetal force, by which it tends towards the center.\\n132. At an example of a body revolving in an orbit\\nunder the influence of two forces, suppose a body pla-\\nced at any point P (Fig. 28,) above the surface of the\\nearth, and let PA be the direction of the earth s center.\\nIf the body were allowed to move without receiving\\nany impulse, it would descend to the earth in the direc-\\ntion PA with an accelerated motion. But suppose that\\nat the moment of its departure from P, it receives an\\nimpulse in the direction PB, which would carry it to B\\nin the time the body would fail from P to A then un-\\nder the influence of both forces it would descend along\\nthe curve PD. If a stronger impulse were given it in\\n132. Explain figure 28. How might a body be made to\\ncirculate quite around the earth?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0119.jp2"}, "118": {"fulltext": "104\\nUNIVERSAL GRAVITATION.\\nthe direction PB, it would describe a larger curve PE,\\nor PF, or finally, it would go quite round the earth and\\nreturn again to P.\\n133. The most simple example we have of the com-\\nbined action of these two forces, is the motion of a mis-\\nsile thrown from the hand, or of a ball fired from a can-\\nnon. It is well known that the particular form of the\\ncurve described by the projectile, in either case, will de-\\npend upon the velocity with which it is thrown. In\\neach case the body will begin to move in the line of di-\\nrection in which it is projected, but it will soon be de-\\nflected from that line towards the earth. It will how-\\never continue nearer to the line of projection as the ve-\\nFig. 29.\\n-B\\nW\\nlocity of projection is greater.\\nThus let AB (Fig. 29,)\\n133. When a cannon ball is fired with different velocities,\\nwhen is its motion nearest to the line of projection?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0120.jp2"}, "119": {"fulltext": "MOTION IN AN ELLIPTICAL ORBIT.\\n105\\nperpendicular to AC represent the line of projection.\\nThe body will, in every case, commence its motion in\\nthe line AB, which will therefore be the tangent to the\\ncurve it describes but if it be thrown with a small ve-\\nocity, it will soon depart from the tangent, describing\\nthe line AD with a greater velocity it will describe a\\ncurve nearer to the tangent, as AE and with a still\\ngreater velocity it will describe the curve AF.\\n134. In figure 30, suppose the planet to have passed\\nthe point C with so small a velocity,- that the attraction\\nof the sun bends its path very much, and causes it im-\\nmediately to begin to approach towards the sun the\\nsun s attraction will increase its velocity as it moves\\nthrough D, E, and F. For the sun s attractive force on\\nthe planet, when at D, is acting in the direction DS,\\nand, on account of the small inclination of DE to DS,\\nthe force acting in the line DS helps the planet forward\\nin the path DE, and thus increases its velocity. In like\\nmanner, the velocity of the planet will be continually\\nincreasing as it passes through E, and F and though\\n134. Explain the motion of a planet in an elliptical orbit,\\nfrom figure 30.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0121.jp2"}, "120": {"fulltext": "106 UNIVERSAL GRAVITATION.\\nthe attractive force, on account of the planet s nearness,\\nis much increased, and tends therefore to make the\\norbit more curved, yet the velocity is also so much in-\\ncreased that the orbit is not more curved than before.\\nThe same increase of velocity occasioned by the planet s\\napproach to the sun, produces a greater increase of cen-\\ntrifugal force which carries it off again. We may see\\nalso why, when the planet has reached the most distant\\nparts of its orbit, it does not entirely fly off, and never\\nreturn to the sun. For when the planet passes along\\nH, K, A, the sun s attraction retards the planet, just as\\ngravity retards a ball rolled up hill and when it has\\nreached C, its velocity is very small, and the attraction\\nat the center of force causes a great deflection from the\\ntangent, sufficient to give its orbit a great curvature,\\nand the planet turns about, returns to the sun, and goes\\nover the same orbit again. As the planet recedes from\\nthe sun, its centrifugal force diminishes faster than the\\nforce of gravity, so that the latter finally preponderates.\\n135. We may imitate the motion of a body in its orbit\\nby suspending a small ball from the ceiling by a long string.\\nThe ball being drawn out of its place of rest, (which is\\ndirectly under the point of suspension,) it will tend con-\\nstantly towards the same place by a force which corres-\\nponds to the force of attraction of a central body. If\\nan assistant stands under the point of suspension, his\\nhead occupying the place of the ball when at rest, the\\nball may be made to revolve about his head as the earth\\nor any planet revolves about the sun. By projecting the\\nball in different directions, and with different degrees of\\nvelocity, we may make it describe different orbits, ex-\\nemplifying principles which have been explained in the\\nforegoing articles.\\n135. How may we imitate the motion of a body in its or-\\nbit 1 How may we make the bail describe different orbits", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0122.jp2"}, "121": {"fulltext": "PRECESSION OF THE EQUINOXES. 107\\nPRECESSION OF THE EQUINOXES.\\n136 The Precession of the equinoxes, is a slow\\nbut continual shifting of the equinoctial points from east\\nto west.\\nSuppose that we mark the exact place in the heavens\\nwhere, during the present year, the sun crosses the equa-\\ntor, and that this point is close to a certain star next\\nyear the sun will cross the equator a little way west-\\nward of that star, and thus every year a little farther west-\\nward, so that in a long course of ages, the place of the\\nequinox will occupy successively every part of the eclip-\\ntic, until we come round to the same star again. As,\\ntherefore, the sun, revolving from west to east in his ap-\\nparent orbit, comes round towards the point where it\\nleft the equinox, it meecs the equinox before it reaches\\nthat point. The appearance is as though the equinox\\ngoes forward to meet the sun, and hence the phenome-\\nnon is called the Precession of the Equinoxes, and the\\nfact is expressed by saying that the equinoxes retrograde\\non the ecliptic, until the line of the equinoxes makes a\\ncomplete revolution from east to west. The equator is\\nconceived as sliding westward on the ecliptic, always\\npreserving the same inclination to it, as a ring placed at\\na small angle with another of nearly the same size,\\nwhich remains fixed, may be slid quite around it, giving\\na corresponding motion to the two points of intersec-\\ntion. It must be observed, however, that this mode of\\nconceiving of the precession of the equinoxes is purely\\nimaginary, and is employed merely for the convenience\\nof representation.\\n137. The amount of precession annually is 50. 1\\nwhence, since there are 3600 in a degree, and 360\u00c2\u00b0 in\\n136. Precession of the Equinoxes. Define it. If the son\\ncrosses the equator near a certain star this year, where will it\\ncross it next year 1 Why s the fact called the precession of\\nthe equinoxes 1 How is the equator conceived as moving\\nwith regard to the ecliptic", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0123.jp2"}, "122": {"fulltext": "108 UNIVERSAL GRAVITATION.\\nthe whole circumference, and consequently, 1296000\\nthis sum divided by 50.1 gives 25868 years for the pe-\\nriod of a complete revolution of the equinoxes.\\n138. Suppose now we fix to the center of each of the\\ntwo rings, (Art. 136,) a wire representing its axis, one\\ncorresponding to the axis of the ecliptic, the other to\\nthat of the equator, the extremity of each being the pole\\nof its circle. As the ring denoting the equator turns\\nround on the ecliptic, which with its axis remains fixed,\\nit is easy to conceive that the axis of the equator re-\\nvolves around that of the ecliptic, and the pole of the\\nequator around the pole of the ecliptic, and constantly at\\na distance equal to the inclination of the two circles. To\\ntransfer our conceptions to the celestial sphere, we may\\neasily see that the axis of the diurnal sphere, (that of\\nthe earth produced, Art. 15,) would not have its pole\\nconstantly in the same place among the stars, but that\\nthis pole would perform a slow revolution around the\\npole of the ecliptic from east to west, completing the cir-\\ncuit in about 26,000 years. Hence the star which we\\nnow call the pole star, has not always enjoyed that dis-\\ntinction, nor will it always enjoy it hereafter. When\\nthe earliest catalogues of the stars were made, this star\\nwas 12\u00c2\u00b0 from the pole. It is now 1\u00c2\u00b0 33 and will ap-\\nproach still nearer or to speak more accurately, the pole\\nwill come still nearer to this star, after which it will\\nleave it, and successively pass by others. In about\\n13,000 years, the bright star Lyree, which lies on the\\ncircle of revolution opposite to the present pole star,\\n137. What is the amount of precession annually? In what\\ntime will the equinoxes perform a complete revolution\\n138. Illustrate the precession of the equinoxes by an appa-\\nratus of wires. How is the pole of the earth situated with\\nrespect to the stars at different times 1 Has the present pole\\nstar always been such What will be the pole star 13,000\\nyears hence Will this cause affect the elevation of tho\\nnorth pole above the horizon", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0126.jp2"}, "123": {"fulltext": "r\\nPRECESSION OF THE EQUINOXES. 109\\nwill be within 5\u00c2\u00b0 of the pole, and will constitute the\\nPole Star. As a Lyrse now passes near our zenith, the\\nlearner might suppose that the change of position of the\\npole among the stars, would be attended with a change\\nof altitude of the north pole above the horizon. This\\nmistaken idea is one of the many misapprehensions\\nwhich result from the habit of considering the horizon\\nas a fixed circle in space. However the pole might\\nshift its position in space, we should still be at the\\nsame distance from it, and our horizon would always\\nreach the same distance beyond it.\\n139. The time occupied by the sun in passing from\\nthe equinoctial point round to the same point again, is\\ncalled the tropical year. As the sun does not perform\\na complete revolution in this interval but falls short of it\\n50. 1, the tropical year is shorter than the sidereal by\\n20m. 20s. in mean solar time, this being the time of de-\\nscribing an arc of 5\u00c2\u00ae. in the annual revolution.* The\\nchanges produced by the precession of the equinoxes in\\nthe apparent places of the circumpolar stars, have led to\\nsome interesting results in chronology. In consequence\\nof the retrograde motion of the equinoctial points, the\\nsigns of the ecliptic, do not correspond at present to\\nthe constellations which bear the same names, but lie\\nabout one whole sign or 30\u00c2\u00b0 westward of them. Thus,\\nthat division of the ecliptic which is called the sign\\nTaurus, lies in the constellation Aries, and the sign\\nGemini in the constellation Taurus. Undoubtedly how-\\never when the ecliptic was thus first divided, and the\\ndivisions named, the several constellations lay in the re-\\nspective divisions which bear their names. How long\\nis it, then, since our zodiac was formed\\n139. Define the tropical year. How much shorter is the\\ntropical than the sidereal year 1 How has the precession of the\\nequinoxes been applied in Chronology\\n59 8. 3 24h 50. 1 20m. 20s.\\n10", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0127.jp2"}, "124": {"fulltext": "110 THE MOON.\\n50. 1 1 year: :30\u00c2\u00b0( 108000 2155.G years.\\nThe result indicates that the present divisions of the\\nzodiac, were made soon after the establishment of the\\nAlexandrian school of astronomy.\\nCHAPTER IV.\\nOF THE MOON PHASES REVOLUTIONS.\\n140. Next to the Sun the Moon naturally claims our\\nattention. She is an attendant or satellite to the earth,\\naround which she revolves at the distance of nearly\\n240,000 miles, or more exactly 238,545 miles. Her\\nangular diameter is about half a degree, and her real diam-\\neter 2160 miles. She is therefore a comparatively small\\nbody, being only one forty-ninth part as large as the\\nearth.\\nThe moon shines by reflected light borrowed from\\nthe sun, and when full exhibits a disk of silvery bright-\\nness, diversified by extensive portions partially shaded.\\nThese dusky spots are generally said to be land, and the\\nbrighter parts water but astronomers tell us that if ei-\\nther are water, it must be the darker portions. Land by\\nscattering the rays of the sun s light would appear more\\nluminous than the ocean which reflects the light like a\\nmirror. By the aid of the telescope, we see undoubted\\nsigns of a varied surface, in some parts composed of ex-\\ntensive tracts of level country, and in others exceedingly\\nbroken by mountains and valleys.\\n141. The line which separates the enlightened from\\nthe dark portions of the moon s disk, is called the Ter-\\n140. The Moon. What relation has the moon to the earth\\nState her distance, diameter and bulk. Is her light direct or\\nreflected What are the dark places in the moon generally un-\\nderstood to be Why would water appear darker than land\\nWhat does the telescope reveal to us respecting the moon", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0128.jp2"}, "125": {"fulltext": "LUNAR GEOGRAPHY. Ill\\nminator. (See Frontispiece.) As the terminator traver-\\nses the disk from new to full moon, it appears through the\\ntelescope exceedingly broken in some parts, but smooth\\nin others, indicating that portions of the lunar surface are\\nuneven while others are level. The broken regions ap-\\npear brighter than the smooth tracts. The latter have\\nbeen taken for seas, but it is supposed with more prob-\\nability that they are extensive plains, since they are still\\ntoo uneven for the perfect level assumed by bodies of\\nwater. That there are mountains in the moon, is known\\nby several distinct indications. First, when the moon\\nis increasing, certain spots are illuminated sooner than\\nthe neighboring places, appearing like bright points be-\\nyond the terminator, within the dark part of the disk,\\nin the same manner as the tops of mountains on the\\nearth are tipped with the light of the sun, in the morn-\\ning, while the regions below are still dark. Secondly,\\nafter the terminator has passed over them, they project\\nshadows upon the illuminated part of the disk, always\\nopposite to the sun, corresponding in shape to the form\\nof the mountain, and undergoing changes in length from\\nnight to night, according as the sun shines upon that\\npart of the moon more or less obliquely. Many indi-\\nvidual mountains rise to a great height in the midst of\\nplains, and there are several very remarkable mountain-\\nous groups, extending from a common center in long\\nchains.\\n142. That there are also valleys in the moon, is\\nequally evident. The valleys are known to be truly\\nsuch, particularly by the manner in which the light of\\nthe sun falls upon them, illuminating the part opposite\\nto the sun while the part adjacent is dark, as is the case\\nwhen the light of a lamp shines obliquely into a china\\n141. Define the terminator. What do we learn from its rug-\\nged appearance State the proofs of mountains in the moon.\\n142. State the proofs of valleys in the moon. When is the\\nbest time for viewing the mountains and valleys of the moon.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0129.jp2"}, "126": {"fulltext": "112 THE MOON.\\ncup. These valleys are often remarkably regular, and\\nsome of them almost perfect circles. In several instan-\\nces, a circular chain of mountains surrounds an exten-\\nsive valley, which appears nearly level, except that a\\nsharp mountain sometimes rises from the center. The\\nbest time for observing these appearances is near the\\nfirst quarter of the moon, when half the disk is en-\\nlightened but in studying the lunar geography, it is\\nexpedient to observe the moon every evening from new\\nto full, or rather through her entire series of changes.\\n143. The various places on the moon s disk have re-\\nceived appropriate names. The dusky regions, being\\nformerly supposed to be seas, were named accordingly\\nand other remarkable places have each two names, one\\nderived from some well known spot on the earth, and\\nthe other from some distinguished personage. Thus\\nthe same bright spot on the surface of the moon is\\ncalled Mount Sinai or Tycho, and another, Mount Et-\\nna or Copernicus. The names of individuals, how-\\never, are more used than the others. The frontispiece\\nexhibits the telescopic appearance of the full moon. A\\nfew of the most remarkable points have the following\\nnames, corresponding to the numbers and letters on the\\nmap. (See Fig. p. 113.)\\n1. Tycno,\\nA. Mare Humorum,\\n2. Kepler,\\nB. Mare Nubium,\\n3. Copernicus,\\nC. Mare Imbrium,\\n4. Aristarchus,\\nD. Mare Nectaris,\\n5. Helicon,\\nE. Mare Tranquilitatis,\\n6. Eratosthenes,\\nF. Mare Serenitatis,\\n7. Plato,\\nG. Mare Fecunditatis,\\n8. Archimedes,\\nH. Mare Crisium.\\n9. Eudoxus,\\n10. Aristotle,\\nIt is earnestly recommended to the student of astronomy, to exam-\\nine the moon repeatedly with the hest telescope he can commajad, using\\nlow powers at first, for the sake of a better light.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0130.jp2"}, "127": {"fulltext": "TU", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0131.jp2"}, "128": {"fulltext": "Telescopic view of the Moon.\\nTelescDpic view of the Moon when five days old.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0132.jp2"}, "129": {"fulltext": "LUNAR GEOGRAPHY. 113\\nThe figure represents the appearance of the moon\\nin the telescope when Ml and when five days old.\\nIn the latter cut, the learner will remark the rough,\\nrugged appearance of the terminator the illuminated\\npoints beyond the terminator within the dark part of the\\nmoon, which are the tops of mountains; and the nu-\\nmerous circular spaces, which exhibit valleys or caverns\\nsurrounded by mountainous chains. Those circles which\\nare near the terminator into which the suns light shines\\nvery obliquely, cast deep shadows on the sides opposite\\nthe sun. Those more remote from the terminator, and\\nfarther within the illuminated part of the moon, into\\nwhich the sun shines more directly, have a greater por-\\ntion illuminated, with shorter shadows and those which\\nlie near the edge of the moon, most distant from the ter-\\nminator, are of an oval figure, being presented obliquely\\nto the eye.\\n144. The heights of the lunar mountains, and the\\ndepths of the valleys, can be estimated with a considera-\\nble degree of accuracy. Some of the mountains are as\\nhigh as five miles, and the valleys in some instances\\nare four miles deep. Hence it is inferred that the sur-\\nface of the moon is more broken and irregular than that\\nof the earth, its mountains being higher and its valleys\\ndeeper in proportion to its magnitude than that of the\\nearth. The lunar mountains in general, exhibit an ar-\\n143. How are places in the moon named Point out the\\nmost remarkable places on the map of the full moon. Point\\nout the mountains, valleys, and craters, on the cut, which rep-\\nresents the moon five days old.\\n144. Specify the heights of some of the lunar mountains.\\nIs the surface of the moon more or less broken than that of the\\nearth 1 Are the mountains like or unlike ours What is the\\nfirst variety What is the shape of the insulated mountains\\nHow can their heights be calculated 1 What is said of the\\nsecond variety, the mountain ranges 1 What is said of the\\ncircular ranges What is said of the central mountains\\n10*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0133.jp2"}, "130": {"fulltext": "114 THE MOON.\\nrangement and an aspect very different from the moun-\\ntain scenery of our globe. They may be arranged un-\\nder the four following varieties.\\nFirst, Insulated Mountains, which rise from plains\\nnearly level, shaped like a sugar loaf, which may be\\nsupposed to present an appearance somewhat similar to\\nMount Etna, or the Peak of Teneriffe. The shadows\\nof these mountains, in certain phases of the moon, are\\nas distinctly perceived, as the shadow of an upright staff,\\nwhen placed opposite to the sun and these heights can\\nbe calculated from the length of their shadows. Some\\nof these mountains being elevated in the midst of exten-\\nsive plains, would present to a spectator on their sum-\\nmits, magnificent views of the surrounding regions.\\nSecondly, Mountain Ranges, extending in length two\\nor three hundred miles. These ranges bear a distant re-\\nsemblance to our Alps, Appenines, and Andes but they\\nare much less in extent. Some of them appear very\\nrugged and precipitous, and the highest ranges are in\\nsome places more than four miles in perpendicular alti-\\ntude. In some instances, they are nearly in a straight\\nline from northeast to southwest, as in that range called\\nthe Appenines in other cases they assume the form of\\na semicircle or crescent.\\nThirdly, Circular Ranges, which appear on almost\\nevery part of the moon s surface, particularly in its south-\\nern regions. This is one grand peculiarity of the lunar\\nranges, to which we have nothing similar on the earth.\\nA plain, and sometimes a large cavity, is surrounded\\nwith a circular ridge of mountains, which encompasses\\nit like a mighty rampart. These annular ridges and\\nplains are of all dimensions, from a mile to forty or fifty\\nmiles in diameter, and are to be seen in great numbers\\nover every region of the moon s surface they are most\\nconspicuous, however, near the upper and lower limbs\\nabout the time of half moon.\\nThe mountains which form these circular ridges are\\nof different elevations, from one fifth of a mile to three\\nand a half miles, and their shadows cover one half of\\nthe plain at the base. These plains are sometimes on", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0134.jp2"}, "131": {"fulltext": "LUNAR GEOGRAPHY. 115\\na level with the general surface of the moon, and in\\nother cases they are sunk a mile or more below the level\\nof the ground, which surrounds the exterior circle of the\\nmountains.\\nFourthly, Central Mountains, or those which are\\nplaced in the middle of circular plains. In many of the\\nplains and cavities surrounded by circular ranges of\\nmountains there stands a single insulated mountain,\\nwhich rises from the center of the plain, and whose\\nshadow sometimes extends in the form of a pyramid\\nhalf across the plain or more to the opposite ridges.\\nThese central mountains are generally from half a mile\\nto a mile and a half in perpendicular altitude. In some\\ninstances they have two and sometimes three different\\ntops, whose shadows can be easily distinguished from\\neach other. Sometimes they are situated towards one\\nside of the plain or cavity, but, in the great majority\\nof instances, their position is nearly or exactly central.\\nThe lengths of their bases vary from five to about fifteen\\nor sixteen miles.\\n145. The Lunar Caverns form a very peculiar and\\nprominent feature of the moon s surface, and are to\\nbe seen throughout almost every region, but are most\\nnumerous in the southwest part of the moon. Nearly a\\nhundred of them, great and small, may be distinguished\\nin that quarter. They are all nearly of a circular shape,\\nand appear like a very shallow egg-cup. The smaller\\ncavities appear within almost like a hollow cone, with\\nthe sides tapering towards the center but the larger\\nones have for the most part, flat bottoms, from the cen-\\nter of which there frequently rises a small steep conical\\nhill, which gives them a resemblance to the circular\\nridges and central mountains before described. In some\\ninstances their margins are level with the general sur-\\nface of the moon, but in most cases they are encircled\\n145. Lunar Caverns. What is said of their number, shape\\nand appearances", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0135.jp2"}, "132": {"fulltext": "116 THE MOON.\\nwith a high annular ridge of mountains, marked with\\nlofty peaks. Some of the larger of these cavities con\\ntain smaller cavities of the same kind and form, particu-\\nlarly in their sides. The mountainous ridges which sur-\\nround these cavities, reflect the greatest quantity of\\nlight and hence that region of the moon in which they\\nabound, appears brighter than any other. From their\\nlying in every possible direction, they appear at and\\nnear the time of full moon, like a number of brilliant\\nstreaks or radiations. These radiations appear to con-\\nverge towards a large brilliant spot, surrounded by a\\nfaint shade, near the lower part of the moon which is\\nnamed Tycho, (Frontispiece, 1,) which may be easily dis-\\ntinguished even by a small telescope. The spots named\\nKepler and Copernicus, are each composed of a central\\nspot with luminous radiations.*\\n146. Dr. Herschel is supposed also to have obtained\\ndecisive evidence of the existence of volcanoes in the\\nmoon, not only from the light afforded by their fires,\\nbut also from the formation of new mountains by the\\naccumulation of matter where fires had been seen to\\nexist, and which remained after the fires were extinct.\\n147. Some indications of an atmosphere about the\\nmoon have been obtained, the most decisive of which\\nare derived from appearances of twilight, a phenomenon\\nthat implies the presence of an atmosphere. Similar in-\\ndications have been detected, it is supposed, in eclipses\\nof the sun, denoting a transparent refracting medium\\nencompassing the moon.\\n146. Volcanoes. What proofs are there of their having ex-\\nisted in the moon\\n147. What evidence is there of a lunar atmosphere\\nThe foregoing accurate description of the lunar mountains and cav-\\nerns is from Dick s Celestial Scenery.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0136.jp2"}, "133": {"fulltext": "LUNAR GEOGRAPHI. 117\\n148. It has been a question with astronomers, whether\\nthere is water in the moon The general opinion is\\nthat there is none. If there were any, we should ex-\\npect to see clouds or at least we should expect to find\\nthe face of the moon occasionally obscured by clouds\\nbut this is not the case, since the spots on the moon s\\ndisk, when our sky is clear, are always in full view.\\nThe deep caverns, moreover, seen in those dusky spots\\nwhich were supposed to be seas, are unfavorable to the\\nsupposition, that they are surrounded by water and the\\nterminator when it passes over these places is, as already\\nremarked, too uneven to permit us to suppose that these\\ntracts are seas.\\n149. The improbability of our ever identifying arti-\\nficial structures in the moon, may be inferred from the\\nfact that a line one mile in length in the moon subtends\\nan angle at the eye of only about one second. If, there-\\nfore, works of art were to have a sufficient horizontal\\nextent to become visible, they can hardly be supposed\\nto attain the necessary elevation, when we reflect that\\nwhe height of the great pyramid of Egypt is less than\\nthe sixth part of a mile. Still less probable is it that we\\nshall ever discover any inhabitants in the moon. The\\ngreatest magnifying power that has ever been applied\\nwith distinctness, to the moon, does not much exceed a\\nthousand times, bringing the moon apparently a thou-\\nsand times nearer to us than when seen by the naked\\neye. But this implies a distance still of 240 miles and\\n148. Is there water in the moon What proofs arc there\\nto the contrary 1\\n149. Is it probable that artificial structures in the moon will\\never be identified How high must they be, in order to be\\nseen distinct from the surface Is it probable that we shall\\never be able to recognize inhabitants in the moon What is\\nthe greatest magnifying power of the telescope that has ever\\nbeen applied to the moon If we could magnify the moon\\n1 0,000 times what would still be her apparent distance What\\ninherent difficulty is there in employing very great magnifiers", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0137.jp2"}, "134": {"fulltext": "118 THE MOON.\\ncould we magnify the moon ten thousand times, her ap-\\nparent distance would still be twenty-four miles, a dis-\\ntance too great to distinguish living beings. Moreover,\\nwhen we use such high magnifiers in the telescope, our\\nfield of view is necessarily exceedingly small, so that it\\nwould be a mere point that we could view at a time.\\nThis difficulty is inherent in the very nature of tele-\\nscopes, namely, that the field of view is reduced as the\\nmagnifying power is increased and we magnify the\\nvapors and the undulations of the atmosphere, as well\\nas the moon, and by this means impair the medium so\\nmuch that we should not be able to see anything with\\ndistinctness. It is only to such minute objects as a star,\\nthat very high powers of the telescope can ever be ap-\\nplied.\\n150. Some writers, however, suppose that possibly\\nwe may trace indications of lunar inhabitants in their\\nworks, and that they may, in like manner, recognize the\\nexistence of the inhabitants of our planet. An author\\nwho has reflected much on subjects of this kind, rea-\\nsons as follows A navigator who approaches within a\\ncertain distance of a small island, although he perceives\\nno human being upon it, can judge with certainty, that\\nit is inhabited, if he perceives human habitations, villa-\\nges, cornfields, or other traces of cultivation. In like\\nmanner, if we could perceive changes or operations in\\nthe moon, which could be traced to the agency of intel-\\nligent beings, we should then obtain satisfactory evi-\\ndence, that such beings exist on that planet and it is\\nthought possible that such operations may be traced.\\nA telescope which magnifies 1200 times, will enable us\\nto perceive, as a visible point on the surface of the moon,\\nan object whose diameter is only about 300 feet. Such\\n150. What have some writers supposed with respect to the\\nprobability of our tracing marks of living beings on the moon\\nHow is it proposed to ha^e thfl moon examined for this pur-\\npose I", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0138.jp2"}, "135": {"fulltext": "LUNAR GEOGRAPHY. 119\\nan object is not larger than many of our public edifices\\nand, therefore, were any such edifices rearing in the\\nmoon, or were a town or city extending its boundaries,\\nor were operations of this description carrying on in a\\ndistrict where no such edifices had previously been\\nerected, such objects and operations might probably be\\ndetected by a minute inspection. Were a multitude of\\nliving creatures moving from place to place in a body,\\nor were they even encamping in an extensive plain, like\\na large army, or like a tribe of Arabs in the desert, and\\nafterwards removing, it is possible that such changes\\nmight be traced by the difference of shade or color,\\nwhich such movements would produce. In order to de-\\ntect such minute objects and operations, it would be\\nrequisite that the surface of the moon should be distrib-\\nuted among at least a hundred astronomers, each having\\na spot or two allotted to him, as the object of his more\\nparticular investigation, and that the observations be\\ncontinued for a period of at least thirty or forty years,\\nduring which time certain changes would probably be\\nperceived, arising either from physical causes, or from\\nthe operations of living agents.*\\n151. It has sometimes been a subject of speculation,\\nwhether it might be possible, by any symbols, to cor-\\nrespond with the inhabitants of the moon. It has been\\nsuggested, that if some vast geometrical figure, as a\\nsquare or a triangle, were erected on the plains of Siberia,\\nit might be recognized by the lunarians, and answered\\nby some corresponding signal. Some geometrical figure\\nwould be peculiarly appropriate for such a telegraphic\\ncommerce with the inhabitants of another sphere, since\\nthese are simple ideas common to all minds.\\n151. How is it proposed to carry on a telegraphic communi-\\ncation with the lunarians\\nDick s Celestial Scenery, Ch. iv.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0139.jp2"}, "136": {"fulltext": "r20 THE MOON.\\nPHASES OF THE MOON.\\n152. The changes of the moon, commonly called her\\nPhases, arise from different portions of her illuminated\\nside being turned towards the earth at different times.\\nWhen the moon is first seen after the setting sun, her\\nform is thit of a bright crescent, on the side of the disk\\nnext to the sun, while the other portions of the disk\\nshine with a feeble light, reflected to the moon from the\\nearth. Every night we observe the moon to be farther\\nand farther eastward of the sun, and at the same time\\nthe crescent enlarges, until, when the moon has reached\\nan elongation from the sun of 90\u00c2\u00b0, half her visible disk\\nis enlightened, and she is said to be in her first quarter.\\nThe terminator, or line which separates the illuminated\\nfrom the dark part of the moon, is convex towards the\\nsun from the new moon to the first quarter, and the\\nmoon is said to be horned. The extremities of the\\ncrescent are called cusps. At the first quarter, the ter-\\nminator becomes a straight line, coinciding with a di-\\nameter of the disk but after passing this point, the ter-\\nminator becomes concave towards the sun, bounding\\nthat side of the moon by an elliptical curve, when the\\nmoon is said to be gibbous. When the moon arrives at\\nthe distance of 180\u00c2\u00b0 from the sun, the entire circle is\\nilluminated, and the moon is full. She is then in oppo-\\nsition to the sun, rising about the time the sun sets. For\\na week after the full, the moon appears gibbous again,\\nuntil, having arrived within 90\u00c2\u00b0 of the sun, she re-\\nsumes the same form as at the first quarter, being then\\nat her third quarter. From this time until new moon,\\nshe exhibits again the form of a crescent before the ri-\\nsing sun, until, approaching her conjunction with the\\n152. Phases of the Moon. Whence do they rise State\\nthe successive appearances of the moon from new to full. In\\nwhat parts of her revolution is she horned, and in what parts\\ngibbons When is she said to be in conjunction, and when in\\nopposition What are the syzigies, quadratures, and octants\\nDefine the circle of illumination, and the ciicle of the disk.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0140.jp2"}, "137": {"fulltext": "PHASES. 121\\nsun, her narrow thread of light is lost in the solar blaze\\nand finally, at the moment of passing the sun, the dark\\nside is wholly turned towards us, and for some time we\\nlose sight of the moon.\\nThe two points in the orbit corresponding to new and\\nfull moon respectively, are called by the common name\\nof syzigies those which are 90\u00c2\u00b0 from the sun are\\ncalled quadratures and the points half way between\\nthe syzigies and quadratures are called octants. The\\ncircle which divides the enlightened from the unen-\\nlightened hemisphere of the moon, is called the circle of\\nillumination: that which divides the hemisphere that\\nis turned towards us from the hemisphere that is turn-\\ned from us, is called the circle of the disk.\\n153. As the moon is an opake body of a spherical\\nfigure, and borrows her light from the sun, it is obvious\\nFig. 31\\nthat that half only which is towards the sun can be il-\\nluminated. More or less of this side is turned towards\\nthe earth, according as the moon is at a greater or less\\nelongation from the sun. The reason of the different\\nphases will be best understood from a diagram. There-\\nfore let T (Fig. 31.) represent the earth, and S the sun.\\n11", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0141.jp2"}, "138": {"fulltext": "122 THE MOON.\\nLet A, B, C, c. be successive positions of the moon.\\nAt A the entire dark side of the moon being turned to-\\nwards the earth, the disk would be wholly invisible. Al\\nB, the circle of the disk cuts of a small part of the en\\nlightened hemisphere, which appears in the heavens at\\nb, under the form of a crescent. At C, the first quarter\\nthe circle of the disk cuts off half the enlightened hem-\\nisphere, and a half moon is seen at c. In like manner it\\nwill be seen that the appearances presented at D, E, F,\\nc. must be those represented at d, e,f. If a round\\nbody, as an apple, suspended by a string, be carried\\naround a lamp, the eye remaining fixed opposite to it at\\nthe same level, the various phases of the moon will be\\nexhibited.\\nREVOLUTIONS OF THE MOON.\\n154. The moon revolves around the earth from west\\nto east, making the entire circuit of the heavens in about\\n27} days.\\nThe period of the moon s revolution from any point\\nin the heavens round to the same point again, is called\\na month. A sidereal month is the time of the moon s\\npassing from any star, until it returns to the same star\\nagain. A synodical month, so called from two Greek\\nwords implying that at the end of this period the two\\nbodies (the sun and moon) come together, is the time\\nfrom one conjunction or new moon to another. The\\nsynodical month is about 29J days, or more exactly,\\n29d. 12h. 44m. 2s.8 =29.53 days. The sidereal month\\nis about two days shorter, being 27d. 7h. 43m. lls.5.\\nor 27.32 days. As the sun and moon are both revolv-\\ning in the same direction, and the sun is moving nearly\\n153. How much of the moon is illuminated at once? Ex-\\nplain the phases of the moon from figure 31.\\n154. Define a month. Define a sidereal month. Also a sy-\\nnodical month. Why so called What is the length of the\\nsynodical month Also of the sidereal month 1 What is the\\nmoon s daily motion", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0142.jp2"}, "139": {"fulltext": "REVOLUTIONS. 123\\na degree a day, during the 27 days of the moon s revo-\\nlution, the sun must have moved 27\u00c2\u00b0. Now since the\\nmoon passes over 360\u00c2\u00b0 in 27.32 days, her daily motion\\nmust be 13\u00c2\u00b0 17 It must therefore evidently take about\\ntwo days for the moon to overtake the sun.\\n155. The moon s orbit is inclined to the ecliptic in an\\nangle of about 5\u00c2\u00b0 (5\u00c2\u00b0 8 48 The moon crosses the\\necliptic in two opposite points called her nodes. That\\nwhich the moon crosses from south to north, is called\\nher ascending node, that which she crosses from north\\nto south, her descending node. The moon, therefore, is\\nnever seen far from the ecliptic, but the path she pur-\\nsues through the skies, is very nearly the same as that\\nof the sun in his annular revolution around the earth.\\n156. The moon, at the same age, crosses the meridian\\nat different altitudes at different seasons of the year and\\naccordingly it is said to run sometimes high and some-\\ntimes low. The full moon, for example, will appear\\nmuch farther in the south when on the meridian at one\\nperiod of the year than at another. The reason of this\\nmay be explained as follows. When the sun is in the\\npart of the ecliptic south of the equator, the earth and\\nof course the moon, which always keeps near to the\\nearth, is in the part north of the equator. At such\\ntimes, therefore, the new moons, which are always\\nseen in the part of the heavens where the sun is, will\\nrun far south, while the full moons, which are always in\\nthe opposite part of the heavens from the sun, will run\\nhigh. Such is the case during the winter months but.\\n1 55. How much is the moon s orbit inclined to the ecliptic\\nDefine the nodes. What is the ascending and Avhat the de-\\nscending node\\n156. Why does the moon run high and low At what sea-\\nson of the year are the full moons longest above the horizon\\nExplain how this operates favorably to those who are near\\nthe pole.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0143.jp2"}, "140": {"fulltext": "124 THE MOON.\\nin the summer, when the sun is towards the northern\\ntropic and the earth towards the southern, the new\\nmoons run high and the full moons low. This arrange-\\nment gives us a great advantage in respect to the amount\\nof light received from the moon since the full moon\\nis longest above the horizon during the long nights of\\nwinter, when her presence is most needed, This cir-\\ncumstance is especially favorable to the inhabitants of\\nthe polar regions, the moon, when full, traversing that\\npart of her orbit which lies north of the equator, and of\\ncourse above the horizon of the north pole, and traver-\\nsing the portion that lies south of the equator, and be-\\nlow the polar horizon, when new. During the polar\\nwinter, therefore, the moon, during her second and third\\nquarters, when she gives most light, is commonly above\\nthe horizon, while the sun is absent whereas, during\\nsummer, while the sun is present and the light is not\\nneeded, during her second and third quarters, she is be-\\nlow the horizon.\\n157. About the time of the autumnal equinox, the\\nmoon when near the full, rises about sunset for a num-\\nber of nights in succession and as this is, in England,\\nthe period of harvest, the phenomenon is called the\\nHarvest Moon. To understand the reason of this, since\\nthe moon is never far from the ecliptic, we will suppose\\nher progress to be in the ecliptic. If the moon moved\\nin the equator, then, since this great circle is at right\\nangles to the axis of the earth, all parts of it, as the\\nearth revolves, cut the horizon at the same constant\\nangle. But the moon s orbit, or the ecliptic, which is\\nhere taken to represent it, being oblique to the equator,\\ncuts the horizon at different angles in different parts, as\\nwill easily be seen by reference to an artificial globe.\\nWhen the first of Aries, or vernal equinox, is in the\\n157. Why is the harvest moon so called Explain its cause.\\nHow is the moon s orbit inclined to the horizon at different\\ntimes", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0144.jp2"}, "141": {"fulltext": "REVOLUTIONS. 125\\neastern horizon, it will be seen that the ecliptic, (and\\nconsequently the moon s orbit,) makes its least angle\\nwith the horizon. Now, at the autumnal equinox, the\\nsun being in Libra, the moon at the full, when she is\\nalways opposite to the sun, is in Aries, and rises when\\nthe sun sets. On the following evening, although she\\nhas advanced in her orbit about 13\u00c2\u00b0, yet her progress be-\\ning oblique to the horizon, and at a small angle with it,\\nshe will be found at this time but a little w T ay below the\\nhorizon, compared with the point where she was at sun-\\nset the preceding evening. She therefore rises but little\\nlater, and so for a week only a little later each evening\\nthan she did the preceding night.\\n1 58. The moon turns on its axis in the same time in\\nwhich it revolves around the earth.\\nThis is known by the moon s always keeping nearly\\nthe same face towards us, as is indicated by the tele-\\nscope, which could not happen unless her revolution on\\nher axis kept pace with her motion in her orbit. Thus\\nit will be seen by inspecting figure 22, that the earth\\nturns different faces towards the sun at different times\\nand if a ball having one hemisphere white and the\\nother black be carried around a lamp, it will easily be\\nseen that it cannot present the same face constantly to-\\nwards the lamp unless it turns once on its axis while\\nperforming its revolution. The same thing will be ob-\\nserved when a man walks around a tree, keeping his face\\nconstantly towards it. Since however the motion of\\nthe moon on its axis is uniform, while the motion in its\\norbit is unequal, the moon does in fact reveal to us a lit-\\ntle sometimes of one side and sometimes of the other.\\nThus when the ball above mentioned is placed before\\nthe eye with its light side towards us, on carrying it\\nround, if it is moved faster than it is turned on its axis,\\n]58. In what time does the moon turn on its axis Illus-\\ntrate by the motion of a ball around a lamp. Is the same side\\nof the moon ahravs turned exactly towards us 1\\n11*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0145.jp2"}, "142": {"fulltext": "126 1HE MOON.\\na portion of the dark hemisphere is brought into view\\non one side or if it is moved forward slower than it is\\nturned on its axis, a portion of the dark hemisphere\\ncomes into view on the other side.\\n159, These appearances are called the moon s libra-\\ntions in longitude. The moon has also a libration in\\nlatitude, so called, because in one part of her revolution,\\nmore of the region around one of the poles comes into\\nview, and in another part of the revolution, more of the\\nregion around the other pole which gives the appear-\\nance of a tilting motion to the moon s axis. This has\\nnearly the same cause with that which occasions our\\nchange of seasons. The moon s axis being inclined to\\nthe plane of her orbit, and always remaining parallel to\\nitself, the circle which divides the visible from the in-\\nvisible part of the moon, will pass in such a way as to\\nthrow sometimes more of one pole into view, and some-\\ntimes more of the other, as would be the case with the\\nearth if seen from the sun. (See Fig. 22.)\\nThe moon exhibits another phenomenon of this kind\\ncalled her diurnal libration, depending on the daily ro-\\ntation of the spectator. She turns the same face to-\\nwards the center of the earth only, whereas we view\\nher from the surface. When she is on the meridian, we\\nsee her disk nearly as though we viewed it from the\\ncenter of the earth, and hence in this situation it is sub-\\nject to little change but when near the horizon, our\\ncircle of vision takes in more of the upper limb than\\nwould be presented to a spectator at the center of the\\nearth. Hence, from this cause, we see a portion of one\\nlimb while the moon is rising, which is gradually lost\\nsight of, and we see a portion of the opposite limb as\\nthe moon declines to the west. It will be remarked\\nthat neither of the foregoing changes implies any actual\\nmotion in the moon, but that each arises from a change\\nof position in the spectator.\\n159. Explain -he librations in longitude. Ditto in latilado\\nDitto the diurnal librations.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0146.jp2"}, "143": {"fulltext": "REVOLUTIONS. 127\\n160. Since the succession of day and night depends\\non the revolution of a planet on its own axis, an inhab-\\nitant of the moon would have but one day and one night\\nduring the whole lunar month of 29^- days. One of its\\ndays, therefore, is equal to nearly 15 of ours. So pro-\\ntracted an exposure to the sun s rays, especially in the\\nequatorial regions of the moon, must occasion an exces-\\nsive accumulation of heat and so long an absence of\\nthe sun must occasion a corresponding degree of cold.\\nEach day would be a wearisome summer each night a\\nsevere winter.* A spectator on the side of the moon\\nwhich is opposite to us would never see the earth but\\none on the side next to us would see the earth present-\\ning a gradual succession of changes during his long\\nnight of 380 hours. Soon after the earth s conjunction\\nwith the sun, he would have the light of the earth re-\\nflected to him, presenting at first a crescent, but enlarg-\\ning as the earth approaches its opposition, to a great orb,\\n13 times as large as the full moon appears to us, and af-\\nfording nearly 13 times as much light. Our seas, our\\nplains, our mountains, our volcanoes, and our clouds,\\nwould produce very diversified appearances, as would\\nthe various parts of the earth brought successively into\\nview by its diurnal rotation. The earth while in view\\nto an inhabitant of the moon, would remain immovably\\nfixed in the same part of the heavens. For being un-\\nconscious of his own motion around the earth, as we are\\nof our motion around the sun, the earth would seem to\\nrevolve around his own planet from west to east, just as\\nthe moon appears to us to revolve about the earth but,\\nmeanwhile, his rotation along with the moon on her\\naxis, would cause the earth to have an apparent motion\\n160. How many days would an inhabitant of the moon have\\nin a lunar month What vicissitudes of temperature would\\noccur in a single day Would a spectator on the side of the\\nmoon opposite to us, ever see the earth How wouldthe earth\\nappear to a spectator on the side of the moon next to us\\nFrancoeur, Uratiog. p. 91.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0147.jp2"}, "144": {"fulltext": "128 THE MOON.\\nwestward at the same rate. The two motions, there-\\nfore, would exactly balance each other, and the earth\\nwould appear all the while at rest.\\n161. We have thus far contemplated the revolution\\nof the moon around the earth as though the earth were\\nat rest. But, in order to have just ideas respecting the\\nmoon s motions, we must recollect that the moon like-\\nwise revolves along with the earth around the sun. It\\nis sometimes said that the earth carries the moon along\\nwith her in her annual revolution. This language may\\nconvey an erroneous idea for the moon, as well as the\\nearth, revolves around the sun under the influence of\\ntwo forces, and would continue her motion around the\\nsun were the earth removed out of the way. Indeed,\\nthe moon is attracted towards the sun 2J times more\\nthan towards the earth, and would abandon the earth\\nwere not the latter also carried along with her by the\\nsame forces. So far as the sun acts equally on both\\nbodies, their motion with respect to each other would\\nnot be disturbed. Because the gravity of the moon to-\\nwards the sun is found to be greater, at the conjunction,\\nthan her gravity towards the earth, some have appre-\\nhended that, if the doctrine of universal gravitation is\\ntrue, the moon ought necessarily to abandon the earth.\\nIn order to understand the reason why it does not do\\nthus, we must reflect, that when a body is revolving in\\nits orbit under the action of the projectile force and\\ngravity, whatever diminishes the force of gravity while\\nthat of projection remains the same, causes the body to\\napproach nearer to the tangent of her orbit, and of course\\nto recede from the center and whatever increases the\\namount of gravity carries the body towards the center.\\n161. Can it be said that the earth carries the moon around\\nthe sun How much more is the moon attracted towards the\\nsun than towards the earth Why does not the moon abandon\\nthe earth When the sun acts equally on both bodies, does it\\ndisturb their relative places? How does the sun act upon\\nthese bodies at the conjunctions and oppositions", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0148.jp2"}, "145": {"fulltext": "REVOLUTIONS. 129\\nNow, when the moon is in conjunction, her gravity to-\\nwards the earth acts in opposition to that towards the\\nsun, while her velocity remains too great to carry her,\\nwith what force remains, in a circle about the sun, and\\nshe therefore recedes from the sun, and commences her\\nrevolution around the earth. On arriving at the opposi-\\ntion, the gravity of the earth conspires with that of the\\nsun, and the moon s projectile force being less than that\\nrequired to make her revolve in a circular orbit, when\\nattracted towards the sun by the sum of these forces, she\\naccordingly begins to approach the sun and descends\\nagain to the conjunction.\\n162. The attraction of the sun, however, being every\\nwhere greater than that of the earth, the actual path of\\nthe moon around the sun is every where concave to-\\nwards the latter. Still the elliptical path of the moon\\naround the earth, is to be conceived of in the same way\\nas though both bodies were at rest with respect to the\\nsun. Thus, while a steamboat is passing swiftly around\\nan island, and a man is walking slowly around a post in\\nthe cabin, the line which he describes in space between\\nthe forward motion of the boat and his circular motion\\naround the post, may be every where concave towards\\nthe island, while his path around the post will still be\\nthe same as though both were at rest. A nail in the rim\\nof a coach wheel, will turn around the axis of the wheel,\\nwhen the coach has a forward motion in the same man-\\nner as when the coach is at rest, although the line ac-\\ntually described by the nail will be the resultant of both\\nmotions, and very different from either.\\n163. We have hitherto regarded the moon as descri-\\nbing a great circle on the face of the sky, such being the\\n162. How is the moon s path in space with respect to the\\nsun How is the elliptical path of the moon around the earth\\nto be conceived of 1 How is this illustrated by the motions of\\na man in a steamboat Also by the motions of a nail in the\\nrim of a coach wheel", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0149.jp2"}, "146": {"fulltext": "130 THE MOON.\\nvisible orbit as seen by projection. But, on more exact\\ninvestigation, it is found that her orbit is not a circle,\\nand that her motions are subject to very numerous ir-\\nregularities. These will be best understood in connec-\\ntion with the causes on which they depend. The law\\nof universal gravitation has been applied with wonder-\\nful success to their investigation, and its results have\\nconspired with those of long continued observation, to\\nfurnish the means of ascertaining with great exactness\\nthe place of the moon in the heavens at any given in-\\nstant of time, past or future, and thus to enable astrono-\\nmers to determine longitudes, to calculate eclipses, and\\nto solve various other problems of the highest interest.\\nA complete understanding of all the irregularities of the\\nmoon s motions, must be sought for in more extensive\\ntreatises of astronomy than the present but some gen-\\neral acquaintance with the subject, clear and intelligible\\nas far as it goes, may be acquired by first gaining a dis-\\ntinct idea of the mutual actions of the sun, the moon,\\nand the earth.\\n164. The irregularities of the moon s motions, are\\ndue chiefly to the disturbing influence of the sun, which\\noperates in two ways first, by acting unequally on the\\nearth and moon, and, secondly, by acting obliquely on\\nthe moon, on account of the inclination of her orbit to\\nthe ecliptic.\\nIf the sun acted equally on the earth and moon, and\\nalways in parallel lines, this action would serve only to\\nrestrain them in their annual motions round the sun, and\\nwould not affect their actions on each other, or their\\nmotions about their common center of gravity. In that\\ncase, if they were allowed to fall directly towards the\\nsun, they would fall equally, and their respective situa-\\ntions would not be affected by their descending equally\\ntowards it. We might then conceive them as in a\\nplane, every part of which being equally acted on by\\n163. Are the motions of the moon regular or irregular By\\nwhat, general law are they explained 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0150.jp2"}, "147": {"fulltext": "REVOLUTIONS. 131\\nthe sun, the whole plane would descend towards the\\nsun, but the respective motions of the earth and the\\nmoon in this plane, would be the same as if it were\\nquiescent. Supposing then this plane and all in it,\\nto have an annual motion imprinted on it, it would\\nmove regularly around the sun, while the earth and moon\\nwould move in it with respect to each other, as if the\\nplane were at rest, without any irregularities. But be-\\ncause the moon is nearer the sun in one half of her orbit\\nthan the earth is, and in the other half of her orbit is at\\na greater distance than the earth from the sun, while the\\npower of gravity is always greater at a less distance it\\nfollows, that in one half of her orbit the moon is more\\nattracted than the earth towards the sun, and in the other\\nhalf less attracted than the earth. The excess of the\\nattraction, in the first case, and the defect in the second,\\nconstitutes a disturbing force, to which we may add an-\\nother, namely, that arising from the oblique action of the\\nsolar force, since this action is not directed in parallel\\nlines, but in lines that meet in the center of the sun.\\n165. To see the effects of this process, let us suppose\\nthat the projectile motions of the earth and moon were\\ndestroyed, and that they were allowed to fall freely to-\\nwards the sun. If the moon was in conjunction with\\nthe sun, or in that part of her orbit which is nearest to\\nhim, the moon would be more attracted than the earth,\\nand fall with greater velocity towards the sun so that\\nthe distance of the moon from the earth w T ould be in-\\ncreased in the fall. If the moon was in opposition, or\\n164. To what cause are the inequalities of the moons mo-\\ntions chiefly due If the sun acted equally on the earth and\\nmoon, and in parallel lines, would it disturb their motions If\\nallowed to fair towards the sun, how would they fall? How\\nmight we conceive them as situated in a plane When is the\\nmoon more attracted than the earth When is the earth more\\nattracted than the moon 1 What constitutes the disturbing face.\\n165. Trace the effects of the sun, if the projectile force were\\ndestroyed, at conjunction, at opposition, and at quadrature.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0151.jp2"}, "148": {"fulltext": "132 THE MOON.\\nin the part of her orbit which is farthest from the sun,\\nshe would be less attracted than the earth by the sun,\\nand would fall with a less velocity towards the sun, and\\nwould be left behind so that the distance of the moon\\nfrom the earth would be increased in this case also. If\\nthe moon was in one of the quarters, then the earth and\\nmoon being both attracted towards the center of the\\nsun, they would both descend directly towards that cen-\\nter, 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\\nwhenever the action of the sun would increase their dis-\\ntance, if they were allowed to fall towards the sun,\\nthen the sun s action, by endeavouring to separate them,\\ndiminishes their gravity to each other whenever the\\nsun s action would diminish the distance, then it in-\\ncreases their mutual gravitation. Hence, in the con-\\njunction and opposition, that is, in the syzigies, their\\ngravity towards each other is diminished by the action\\nof the sun, while in the quadratures it is increased.\\nBut it must be remembered that it is not the total action\\nof the sun on them that disturbs their motions, but only\\nthat part of it which tends at one time to separate them,\\nand at another time to bring them nearer together. The\\nother and far greater part, has no other effect than to\\nretain them in their annual course around the sun.\\n166. The figure of the moon s orbit is an ellipse, hav-\\ning the earth in one of the foci.\\nThe greatest and least distances of the moon from the\\nearth, are nearly 64 and 56, the radius of the earth being\\ntaken for unity. Hence, taking the arithmetical mean,\\nwe find that the mean distance of the moon from the\\n166. What is the figure of the moon s orbit What are the\\ngreatest and least distances of the moon from the earth De-\\nfine the terms perigee and apogee. What numbers express the\\ngreatest and least distance of the sun from the earth 1 How\\ndoes the eccentricity of the lunar orbit, compare with that of\\nthe solar 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0152.jp2"}, "149": {"fulltext": "REVOLUTIONS. 133\\nearth is very nearly 60 times the radius of the earth.\\nThe point in the moon s orbit nearest the earth, is\\ncalled her perigee the point farthest from the earth,\\nher apogee.\\nThe greatest and least distances of the sun are re-\\nspectively as the numbers 32.583, and 31.51 7. By com-\\nparing this ratio with that of the distances of the moon,\\nit will be seen that the latter vary much more than the\\nformer, and consequently that the lunar orbit is much\\nmore eccentric than the solar. The eccentricity of the\\nmoon s orbit is in fact of its mean distance from the\\nearth, while that of the earth is only of its mean dis-\\ntance from the sun,\\n167. The mooits nodes constantly shift their positions\\nin the ecliptic from east to west, at the rate of 19\u00c2\u00b0 3d per\\nannum, returning to the same points in 18.6 years.\\nSuppose the great circle of the ecliptic marked out on\\nthe face of the sky in a distinct line, and let us observe,\\nat any given time, the exact point where the moon\\ncrosses this line, which w T e will suppose to be close to a\\ncertain star then, on its next return to that part of the\\nheavens, we shall find that it crosses the ecliptic sensi-\\nbly to the westward of that star, and so on, farther and\\nfarther to the westward every time it crosses the ecliptic\\nat either node. This fact is expressed by saying that\\nthe nodes retrograde on the ecliptic, and that the line\\nwhich joins them, or the line of the nodes, revolves from\\neast to west.\\n1 68. The period occupied by the sun in passing from\\none of the moon s nodes until it comes round to the\\nsame node again, is called the synodical revolution of the\\nnode. This period is shorter than the sidereal year, be-\\ning only about 346^ days. For since the node shifts its\\n167. How do the moon s nodes shift their position In\\nwhat time do they make a complete revolutin in the ecliptic 1\\nExplain what is mean* hy saying that the nodes retrogade.\\n12", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0153.jp2"}, "150": {"fulltext": "134 THE MOON.\\nplace to the westward 19\u00c2\u00b0 35 per annum, the sun, in\\nhis annual revolution, comes to it so much before he\\ncompletes his entire circuit and since the sun moves\\nabout a degree a day, the synodical revolution of the\\nnode is 365 19=346, or more exactly, 346.619851.\\nThe time from one new moon, or from one full moon,\\nto another, is 29.5305887 days. Now 19 synodical rev-\\nolutions of the nodes contain very nearly 223 of these\\nperiods.\\nFor 346.619851 x 19 6585.78.\\nAnd 29.5305887x223 6585.32.\\nHence, if the sun and moon were to leave the moon s\\nnode together, after the sun had been round to the same\\nnode 19 times, the moon would have made very nearly\\n223 conjunctions with the sun, and would therefore, at\\nthe end of this period meet at the same node, to repeat\\nthe same circuit. And since eclipses of the sun and\\nmoon depend upon the relative position of the sun, the\\nmoon, and node, these phenomena are repeated in nearly\\nthe same order, in each of those periods. Hence, this\\nperiod, consisting of about 18 years and 10 days, under\\nthe name of the Saros, was used by the Chaldeans and\\nother ancient nations in predicting eclipses.\\n169. The Metonic Cycle is not the same with the Sa-\\nros, but consists of 19 tropical years. During this pe-\\nriod the moon makes very nearly 235 synodical revolu-\\ntions, and hence the new and full moons, if reckoned\\nby periods of 19 years, recur at the same dates. If, for\\nexample, a new moon fell on the fiftieth day of one\\ncycle, it would also fall on the fiftieth day of each suc-\\n168. What is meant by the synodical revolution of the node 1\\nHow many new moons occur in 19 synodical revolutions of the\\nnode 1 Why was this period used in predicting eclipses What\\nwas it called\\n169. What is the period of the Metonic Cycle 1 How many\\nconjunctions of the moon with the sun occur during this pe-\\nriod What us$ did the Athenians make of this lunar cycle 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0154.jp2"}, "151": {"fulltext": "REVOLUTIONS. 135\\nceeding cycle and, since the regulation of games,\\nfeasts, and fasts, has been made very extensively ac-\\ncording to new or full moons, hence this lunar cycle has\\nbeen much used both in ancient and modern times.\\nThe Athenians adopted it 433 years before the Christian\\nera, for the regulation of their calendar, and had it in-\\nscribed in letters of gold on the walls of the temple of\\nMinerva. Hence the term Golden Number, which de-\\nnotes the year of the lunar cycle.\\n170. The line of the apsides of the moon s orbit re-\\nvolves from west to east through her whole orbit in about\\nnine years.\\nIf, in any revolution of the moon, we should accu-\\nrately mark the place in the heavens where the moon\\ncomes to its perigee, (which would be known by the\\nmoon s apparent diameter being then greatest,) we should\\nfind, that at the next revolution, it would come to its\\nperigee at a point a little farther eastward than before,\\nand so on at every revolution, until, after nine years, it\\nwould come to its perigee at nearly the same point as at\\nfirst. This fact is expressed by saying that the perigee\\nand of course the apogee, revolves, and that the line\\nwhich joins these two points, or the line of the apsides,\\nfdso revolves.\\n171. The inequalities of the moon s motions are di-\\nvided into periodical and secular. Periodical inequal-\\nities are those which are completed in comparatively\\nshort periods. Secular inequalities are those which\\nare completed only in very long periods, such as cen-\\nturies or ages. Hence the corresponding terms peri-\\nodical equations and secular equations. As an exam-\\nple of a secular inequality, we may mention the ac-\\nceleration of the moon s mean motion. It is discov-\\nered, that the moon actually revolves around the earth\\n170. In what period does the line of the apsides revolve?\\nExplain what is meant by this.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0155.jp2"}, "152": {"fulltext": "136 THE MOON.\\nin less time now than she did in ancient times. The\\ndifference however is exceedingly small, being only\\nabout 10 in a century, but increases from century to\\ncentury as the square of the number of centuries. This\\nremarkable fact was discovered by Dr. Halley,* In a\\nlunar eclipse the moon s longitude differs from that of\\nthe sun, at the middle of the eclipse, by exactly 180\u00c2\u00b0\\nand since the sun s longitude at any given time of the\\nyear is known, if we can learn the day and hour when\\nan eclipse occurs, we shall of course know the longitude\\nof the sun and moon. Now in the year 721 before the\\nChristian era, on a specified day and hour, Ptolemy re-\\ncords a lunar eclipse to have happened, and to have been\\nobserved by the Chaldeans. The moon s longitude,\\ntherefore, for that time is known and as we know the\\nmean motions of the moon at present, starting from that\\nepoch, and computing, as may easily be done, the place\\nwhich the moon ought to occupy at present at any given\\ntime, she is found to be actually nearly a degree and a\\nhalf in advance of that place. Moreover, the same con-\\nclusion is derived from a comparison of the Chaldean\\nobservations with those made by an Arabian astronomer\\nof the tenth century.\\nThis phenomenon at first led astronomers to appre-\\nhend that the moon encountered a resisting medium,\\nwhich, by destroying at every revolution a small portion\\nof her projectile force, would have the effect to bring\\nher nearer and nearer to the earth and thus to augment\\nher velocity. But in 1786, La Place demonstrated that\\n171 How are the inequalities of the moon s motions divided?\\nWhat are periodical inequalities 1 What are secular inequali-\\nties Give an example of a secular inequality. How is it\\nknown that the moon s motions are accelerated What is the\\namount of the acceleration per century Will they always\\ncontinue to be accelerated\\nAstronomer Royal of Great Britain, and cotemporary with Sir Isaac\\nNewton.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0156.jp2"}, "153": {"fulltext": "ECLIPSES. 137\\nthis acceleration is one of the legitimate effects of the\\nsun s disturbing force, and is so connected with changes\\nin the eccentricity of the earth s orbit, that the moon\\n\\\\vill continue to be accelerated while that eccentricity\\ndiminishes, but when the eccentricity has reached its\\nminimum (as it will do after many ages) and begins to\\nincrease, then the moon s motion will begin to be re-\\ntarded, and thus her motions will oscillate forever about\\na mean value.\\nCHAPTER V.\\nOF ECLIPSES.\\n172. An Eclipse of the moon happens when the moon\\nin its revolution around the earth, falls into the earth s\\nshadow. An Eclipse of the sun happens when the\\nmoon coming between the earth and the sun, covers\\neither a part or the whole of the solar disk.\\nThe earth and the moon being both opake globular\\nbodies exposed to the sun s light, they cast shadows op-\\nposite to the sun like any other bodies on which the\\nsun shines. Were the sun of the same size with the\\nearth and the moon, then the lines drawn touching the\\nsurface of the sun, and the surface of the earth or moon\\n(which lines form the boundaries of the shadow) would\\nbe parallel to each other, and the shadow would be a\\ncylinder infinite in length and were the sun less than\\nthe earth or the moon, the shadow would be an increas-\\ning cone, its narrower end resting on the earth but as\\n172. When does an eclipse of the moon happen When\\ndoes an eclipse of the sun happen Were the sun of the same\\nsize with the earth and moon, how would their shadows be\\nHow if less than these bodies How are they in fact? Ex-\\nplain by figure 32\\n12", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0157.jp2"}, "154": {"fulltext": "138\\nTHE MOON.\\nthe sun is vastly greater than either of these bodies*\\nthe shadow of each is a cone, whose base rests on the\\nbody itself, and which comes to a point or vertex at a\\ncertain distance behind the body. These several cases\\nare represented in the following diagrams.\\nFig. 32.\\n173. It is found by calculation, that the length of the\\nmoon s shadow is, on an average, just about sufficient to\\nreach to the earth, but the moon is sometimes farther\\nfrom the earth than at others. (Art. 166.) When she is\\nnearer than usual, the shadow reaches considerably be-\\nyond the surface of the earth. Also the moon as well\\nas the earth, is at different distances from the sun at dif-\\nferent times, and its shadow is longest when it is far-\\nthest from the sun. Now when both these circumstan-\\nces conspire, that is, when the moon is in her perigee\\nand in her aphelion, her shadow extends nearly 15000\\nmiles beyond the center of the earth, and covers a space\\n173. How does the moon s shadow compare with her dis-\\ntance from the earth When does her shadow extend farthest\\nbeyond the center of the earth What is the greatest breadth\\nof her shadow where it falls on the surface of the earth What\\nis the length of the earth s shadow Whenonlycan an eclipse\\nof the sun take place When only can an eclipse of the moon\\noccur Explain from figure 33. What is the moon s Pen-\\numbra 1", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0158.jp2"}, "155": {"fulltext": "ECLIPSES.\\n139\\non the surface of the earth 170 miles broad. The\\nearth s shadow is towards a million of miles in length,\\nand more than three and a half times as long as the dis-\\ntance from the earth to the moon and it is also at the\\ndistance of the moon three times as broad as the moon\\nitself. An eclipse of the sun can take place only at new\\nmoon, when the sun and moon meet in the same part of\\nthe heavens, for then only can the moon come between\\nus and the sun and an eclipse of the moon can occur\\nonly when the sun and moon are in opposite parts of\\nthe heavens, or at full moon, for then only can the moon\\nfall into the shadow of the earth.\\nThe nature of eclipses will be clearly understood from\\nthe following representation. This figure exhibits the\\nFig. 33.\\nrelative position of the sun, the earth, and the moon,\\nboth in a solar and in a lunar eclipse. It is evident from\\nthe figure, that if a spectator were situated where the\\nmoon s shadow strikes the earth, the moon would cut oft*\\nfrom him the view of the sun, or the sun would be to-\\ntally eclipsed. Or, if he were within a certain distance\\nof the shadow on either side, the moon would be partly\\nbetween him and the sun, and would intercept from\\nhim more or less of the sun s light, according as he was\\nnearer to the shadow or farther from it. If he were at\\nc, or a, he would just see the moon entering upon the", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0159.jp2"}, "156": {"fulltext": "140 THE MOON.\\nsun s disk if he were nearer the shadow than either of\\nthese points, he would have a portion of the sun s light\\ncut off from his view, and the moment he entered the\\nshadow itself, he would lose sight of the sun. To all\\nplaces between c or d and the shadow, the sun would\\ncast a partial shadow of the moon, growing deeper and\\ndeeper as it approached the true shadow. This partial\\nshadow is called the moon s Penumbra. In like man-\\nner, as the moon approaches the earth s shadow in a lu-\\nnar eclipse, as soon as she arrives at a, the earth begins\\nto intercept from her a portion of the sun s light, or she\\nfalls into the earth s penumbra. She continues to lose\\nmore and more of the sun s light as she draws near to\\nthe shadow, and hence her disk becomes gradually ob-\\nscured, until it enters the shadow, where the sun s light\\nis entirely lost.\\n174. As the sun and earth are both situated in the\\nplane of the ecliptic, if the moon also revolved around\\nthe earth in this plane, we should have a solar eclipse at\\nevery new moon, and a lunar eclipse at every full\\nmoon for in the former case the moon would come di-\\nrectly between us and the sun, and in the latter case,\\nthe earth would come directly between the sun and the\\nmoon. But the moon s path is inclined to the ecliptic\\nabout 5\u00c2\u00b0, and the center of the moon may be all this\\ndistance from the center of the sun, at new moon, and\\nthe same distance from the center of the earth s shadow\\nat full moon. It is true the moon extends across her\\npath, one half her breadth lying on each side of it, and\\nthe sun likewise reaches from the ecliptic a distance\\nequal to half his breadth. But these luminaries to-\\ngether make but little more than a degree, and conse-\\nquently their two semi-diameters would occupy only\\n174. Why do we not have a solar eclipse every new moon,\\nand a lunar eclipse every full moon Explain how eclipses\\noccur only when the sun is near one of the moon s nodes, by\\nfiffure 34.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0160.jp2"}, "157": {"fulltext": "ECLIPSES.\\n141\\nabout half a degree of the five degrees from one orbit\\nto the other. Also the earth s shadow where the moon\\ncrosses it extends from the ecliptic less than three\\nfourths of a degree, so that the semi-diameter of the\\nmoon and of the earth s shadow, would together reach\\nbut little way across the space that may in certain cases\\nseparate the two luminaries from each other when they\\nare in opposition. Thus suppose we could take hold\\nof the circle in the figure that represents the moon s\\norbit, (Fig. 31,) and lift the moon up five degrees above\\nthe plane of the paper, it is evident that the moon\\nas seen from the earth, would appear in the heavens\\nfive degreess above the sun, and of course would cut off\\nnone of his light, and that the moon at the full would\\npass the shadow of the earth five degrees below it, and\\nwould suffer no eclipse. But in the course of the sun s\\napparent revolution around the earth once a year, he is\\nsuccessively in every part of the ecliptic consequently,\\nthe conjunctions and oppositions of the sun and moon\\nmay occur at any part of the ecliptic, and of course at\\nthe two points where the moon s orbit crosses the eclip-\\ntic, that is, at the nodes, for the sun must necessarily\\ncome to each of these nodes once a year. If then the\\nmoon overtakes the sun just as she is crossing his path,\\nFig. 34.\\nshe will hide more or less of his disk from us. Since,\\nalso, the earth s shadow is always directly opposite to\\nthe sun, if the sun is at one of the nodes, the shadow", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0161.jp2"}, "158": {"fulltext": "142 THE MOON.\\nmust extend in the direction of the other node, so as to\\nlie directly across the moon s path, and if the moon over-\\ntakes it there, she will pass through it and be eclipsed.\\nThus in figure 34, let BN represent the sun s path, and\\nAN the moon s, N being the place of the node then it is\\nevident that if the two luminaries at new moon be so\\nfar from the node, that the distance between their centers\\nis greater than their semi-diameters, no eclipse can hap-\\npen but if that distance is less than this sum as at\\nE, F, then an eclipse will take place, but if the position\\nDe as at C, D, the two bodies will just touch one another.\\nIf A denote the earth s shadow instead of the sun, the\\nsame illustration will apply to an eclipse of the moon.\\n175. Since bodies are defined to be in conjunction\\nwhen they are in the same part of the heavens, and to\\nbe in opposition when they are in opposite parts of the\\nheavens, it may not appear how the sun and moon can\\nbe in conjunction as at A and B, when they are still at\\nsome distance from each other. But it must be recol-\\nlected that bodies are in conjunction when they have the\\nsame longitude, in which case they are both situated in\\nthe same great circle perpendicular to the ecliptic, that\\nis, in the same secondary to the ecliptic. One of the\\nbodies may be much farther from the ecliptic than the\\nother still, if the same secondary to the ecliptic passes\\nthrough them both, they will be in conjunction or oppo-\\nsition.\\n176. In a total eclipse of the moon, its disk is still\\nvisible, shining with a dull red light. This light cannot\\nbe derived directly from the sun, since the view of the\\nsun is completely hidden from the moon nor by reflex-\\nion from the earth, since the illuminated side of the\\n175. Is it necessary for two bodies to be precisely together\\nin order to be in conjunction\\n176. Why is the disk of the moon still visible in a total\\neclipse of the moon", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0162.jp2"}, "159": {"fulltext": "ECLIPSES. 143\\nearth is wholly turned from the moon but it is owing\\nto refraction from the earth s atmosphere, by which a\\nfew scattered rays of the sun are bent round into the\\nearth s shadow and conveyed to the moon, sufficient in\\nnumber to afford the feeble light in question.\\n177. It is impossible fully to understand the method\\nof calculating eclipses, without a knowledge of trigo-\\nnometry still it is not difficult to form some general no-\\ntion of the process. It may be readily conceived that,\\nby long continued observations on the sun and moon,\\nthe exact places which they will occupy in the heavens\\nat any future times, may be forseen and laid down in\\ntables of the sun and moon s motions that we may thus\\nascertain by inspecting the tables the exact instant when\\nthese two bodies will appear together in the heavens, or\\nbe in conjunction, and when they will be 180\u00c2\u00b0 apart,\\nor in opposition. Moreover, since the exact place of the\\nmoon s node among the stars at any particular time is\\nknown to astronomers, it cannot be difficult to determine\\nwhen the new or full moon occurs in the same part of\\nthe heavens as that where the node is projected as seen\\nfrom the earth. In short, as astronomers can easily de-\\ntermine what will be the relative position of the sun,\\nthe moon, and the moon s nodes for any given time,\\nthey can tell when these luminaries will meet so near\\nthe node as to produce an eclipse of the sun, or when\\nthey will be in opposition so near the node as to produce\\nan eclipse of the moon.\\n178. Let us endeavor to form a just conception of the\\nmanner in which these three bodies, the sun, the earth,\\nand the moon, are situated with respect to each other at\\nthe time of a solar eclipse. First, suppose the conjunction\\nto take place at. the node. Then the straight line which\\nconnects the center of the sun and the earth, also passes\\n177. What science must be known in order fully to under-\\nstand the mode of calculating eclipses Explain the general\\nprinciples of the calculation.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0163.jp2"}, "160": {"fulltext": "144 THE MOON.\\nthrough the center of the moon, and coincides with the\\naxis of its shadow and, since the earth is bisected by\\nthe plane of the ecliptic, the shadow would traverse the\\nearth in the direction of the terrestrial ecliptic, from\\nwest to east, passing over the middle regions of the\\nearth. Here the diurnal motion of the earth being in\\nthe same direction with the shadow, but with a less ve-\\nlocity, the shadow will appear to move with a speed\\nequal only to the difference between the two. Secondly,\\nsuppose the moon is on the north side of the ecliptic at\\nthe time of conjunction, and moving towards her de-\\nscending node, and that the conjunction takes place\\nas far from the node as an eclipse can happen. The\\nshadow will not fall in the plane of the ecliptic, but\\na little northward of it, so as just to graze the earth\\nnear the pole of the ecliptic. The nearer the conjunc-\\ntion comes to the node, the farther the shadow will fall\\nfrom the pole of the ecliptic towards the equatorial re-\\ngions.\\n179. The leading particulars respecting an eclipse\\nof the sun, are ascertained very nearly like those of a\\nlunar eclipse. The shadow of the moon travels over a\\nportion of the earth, as the shadow of a small cloud, seen\\nfrom an eminence in a clear day, rides along over hills\\nand plains. Let us imagine ourselves standing on the\\nmoon then we shall see the earth partially eclipsed by\\nthe shadow of the moon, in the same manner as we\\nnow see the moon eclipsed by the earth s shadow.\\nBut, although the general characters of a solar eclipse\\nmight be investigated on these principles, so far as re-\\nspects the earth at large, yet as the appearances of the\\nsame eclipse of the sun are very different at different\\nplaces on the earth s surface, it is necessary to calculate\\n1 78. Explain the relative position of the sun, the earth, and\\nthe moon, in a solar eclipse. Explain the circumstances when\\nthe conjunction takes place at the node, and when it occurs at\\na distance from the node.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0164.jp2"}, "161": {"fulltext": "ECLIPSES. 145\\nits peculiar aspects for each place separately, a circum-\\nstance which makes the calculation of a solar eclipse\\nmuch more complicated and tedious than of an eclipse\\nof the moon. The moon, when she enters the shadow\\nof the earth, is deprived of the light of the part immer-\\nsed, and that part appears black alike to all places where\\nthe moon is above the horizon. But it is not so with a\\nsolar eclipse. We do not see this by the shadow cast\\non the earth, as we should do if we stood on the moon,\\nbut by the interposition of the moon between us and the\\nsun and the sun may be hidden from one observer\\nwhile he is in full view of another only a few miles dis-\\ntant. Thus, a small insulated cloud sailing in a clear\\nsky, will, for a few moments, hide the sun from us, and\\nfrom a certain space near us, while all the region around\\nis illuminated.\\nWe have compared the motion of the moon s shadow\\nover the surface of the earth to that of a cloud but its\\nvelocity is incomparably greater. The mean motion of\\nthe moon around the earth is about 33 per hour but\\n33 of the moon s orbit is 2280 miles, and the shadow\\nmoves of course at the same rate, or 2280 miles per\\nhour, traversing the entire disk of the earth in less than\\nfour hours.\\n180. The diameter of the moon s shadow where it\\neclipses the earth can never exceed 170 miles, and com-\\nmonly falls much short of that and the greatest por-\\ntion of the earth s surface ever covered by the moon s\\npenumbra is about 4393 miles.\\n181. The apparent diameter of the moon is sometimes\\nlarger than that of the sun, sometimes smaller, and\\n179. Hcnr are theleadingparticulars of an eclipse of the sun\\nascertained 1 How illustrated by the motion of a cloud In\\nwhat respects does the calculation of a solar differ from that of\\na lunar eclipse How does the shadow of the moon compare\\nwith that of a cloud in velocity\\n13", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0165.jp2"}, "162": {"fulltext": "146\\nTHE MOON.\\nsometimes exactly equal to it. Suppose an observer\\nplaced on the right line which joins the centers of the\\nsun and moon if the apparent diameter of the moon is\\ngreater than that of the sun, the eclipse will be total. If\\nthe two diameters are equal, the moon s shadow jusl\\nreaches the earth, and the sun is hidden but for a mo-\\nment from the view of spectators situated in the line\\nwhich the vertex of the shadow describes on the surface\\nof the earth. But if, as happens when the moon comes\\nto her conjunction in that part of her orbit which is to-\\nwards her apogee, the moon s diameter is less than the\\nsun s, then the observer will see a ring of the sun en-\\ncircling the moon, constituting an Annular Eclipse, as in\\nfigure 35.\\nFig. 35.\\n180. What cannot the diameter of the moon s shadow\\nwhere it eclipses the earth, exceed What is the greatest\\nportion of the earth s surface ever covered by the moon s pe-\\nnumbra\\n181. How does the moon s apparent diameter compare with\\nthe sun s 1 When will the eclipse be total, and when annular", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0166.jp2"}, "163": {"fulltext": "ECLIPSES. 147\\n182. Eclipses of the sun are modified by the eleva-\\ntion of the moon above the horizon, since its apparent\\ndiameter is augmented as its altitude is increased. This\\naffect, combined with that of parallax, may so increase\\nor diminish the apparent distance between the centers of\\nthe sun and moon, that from this cause alone, of two\\nobservers at a distance from each other, one might see\\non eclipse which was not visible to the other. If the\\nhorizontal diameter of the moon differs but little from\\nthe apparent diameter of the sun, the case might occur\\nwhere the eclipse would be annular over the places\\nwhere it was observed morning and evening, but total\\nwhere it was observed at mid-day.\\nThe earth in its diurnal revolution and the moons\\nshadow both move from west to east, but the shadow\\nmoves faster than the earth hence the moon overtakes\\nthe sun on its western limb and crosses it from west to\\neast. The excess of the apparent diameter of the moon\\nabove that of the sun in a total eclipse is so small, that\\ntotal darkness seldom continues longer than four minutes,\\nand can never continue so long as eight minuutes. An\\nannular eclipse may last 12m. 24s.\\n183. Eclipses of the sun are more frequent than those\\nof the moon. Yet lunar eclipses being visible to every\\npart of the terrestrial hemisphere opposite to the sun,\\nwhile those of the sun are visible only to the small por-\\ntion of the hemisphere on which the moon s shadow\\nfalls, it happens that for any particular place on the\\nearth, lunar eclipses are more frequently visible than\\nsolar. In any year, the number of eclipses of both lu-\\n182. Ifow are eclipses of the sun modified by the elevation\\nof the moon above the horizon How might the same eclipse\\nappear total to one observer and annular to another How\\nlong can total darkness continue in a solar eclipse 1 How long\\nmay an annular eclipse last\\n183. Which are most frequent, solar or lunar eclipses Why\\ndoes an eclipse of the moon sometimes happen at the next full\\nmoon after an eclipse of the sun", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0167.jp2"}, "164": {"fulltext": "148 REVOLUTIONS.\\nminaries cannot be less than two nor more than seven\\nthe most usual number is four, and it is very rare to\\nhave more than six. A total eclipse of the moon fre-\\nquently happens at the next full moon after an eclipse\\nof the sun. For since, in an eclipse of the sun, the sun\\nis at or near one of the moon s nodes, the earth s shadow\\nmust be at or near the other node, and may not have\\npassed far from the node before the moon overtakes it.\\n184. In total eclipses of the sun, there has sometimes\\nbeen observed a remarkable radiation of light from the\\nmargin of the sun. This has been ascribed to an illu-\\nmination of the solar atmosphere, but it is with more\\nprobability owing to the zodiacal light, which at that\\ntime is projected around the sun, and which is of such\\ndimensions as to extend far beyond the solar orb.*\\nA total eclipse of the sun is one of the most sublime\\nand impressive phenomena of nature. Among barbarous\\ntribes it is ever contemplated with fear and astonish-\\nment, while among cultivated nations it is recognized,\\nfrom the exactness with which the time of occurrence\\nand the various appearances answer to the prediction, as\\naffording one of the proudest triumphs of astronomy.\\nBy astronomers themselves it is of course viewed with\\nthe highest interest, not only as verifying their calcula-\\ntions, but as contributing to establish beyond all doubt\\nthe certainty of those grand laws, the truth of which is\\ninvolved in the result. During the eclipse of June,\\n1806, which was one of the most remarkable on record,\\nthe time of total darkness, as seen by the author of this\\nwork, was about mid-day. The sky was entirely eloud-\\n1 84. How is the radiation of light around the margin of the\\nsun in a total eclipse of the sun, accounted for How have\\neclipses of the sun been regarded among barbarous tribes\\nHow among civilized nations 1 How by astronomers Give\\nsome account of the great eclipse of 1806.\\nSee an excellent description and delineation of this appearance as\\nit was exhibited in the eclipse of 1806, in the Transactions of the Al-\\nbany Institute, by the late Chancellor De Witt.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0168.jp2"}, "165": {"fulltext": "ECLIPSES 149\\nless, but as the period of total obscuration approached, a\\ngloom pervaded all nature. When the sun was wholly\\nlost sight of, planets and stars came into view a fearful\\npall hung upon the sky, unlike both to night and to\\ntwilight and, the temperature of the air rapidly de-\\nclining, a sudden chill came over the earth. Even the\\nanimal tribes exhibited tokens of fear and agitation.\\n185. The word Eclipse is derived from a Greek word,\\n(exleufjig,) which signifies to fail, to faint, or swoon\\naway, since the moon at the period of her greatest\\nbrightness falling into the shadow of the earth, was im-\\nagined by the ancients to sicken and swoon, as if she\\nwere going to die. By some very ancient nations she\\nwas supposed at such times to be in pain, and hence\\nlunar eclipses were called the labors of the moon, (lunae\\nlabores and, in order to relieve her fancied distress, they\\nlifted torches high in the atmosphere, blew horns and\\ntrumpets, beat upon brazen vessels, and even, after the\\neclipse was over, they offered sacrifices to the moon.\\nThe opinion also extensively prevailed, that it was in\\nthe power of witches, by their spells and charms, not\\nonly to darken the moon, but to bring her down from\\nher orbit, and to compel her to shed her baleful influences\\nupon the earth. In a solar eclipse also, especially when\\ntotal, the sun was supposed to turn away his face in ab-\\nhorrence of some atrocious crime, that either had been\\nperpetrated or was about to be perpetrated, and to\\nthreaten mankind with everlasting night, and the de-\\nstruction of the world.\\nThe Chinese, who from a very high period of anti-\\nquity have been great observers of eclipses, although\\nthey did not take much notice of those of the moon, re-\\ngarded eclipses of the sun in general as unfortunate, but\\nespecially such as occurred on the first day of the year.\\n185. From what is the word eclipse derived 1 What ideas\\nhad certain ancient nations respecting eclipses With what\\nceremonies did they observe them How were eclipses re-\\ngarded among the Chinese 1\\n13*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0169.jp2"}, "166": {"fulltext": "150 THE MOON.\\nThese were thought to forbode the greatest calamities\\nto the emperor, who on such occasions did not receive\\nthe usual compliments of the season. When an eclipse\\nof the sun was expected from the predictions of their as-\\ntronomers, they made great preparation at court for ob-\\nserving it and as soon as it commenced, a blind man\\nbeat a drum and a great concourse assembled, and the\\nMandarins, or nobility, appeared in state.\\n186. From 1831 to 1838, was a period distinguished\\nfor great eclipses of the sun, in which time there were no\\nless than five, of the most remarkable character. The\\nnext total eclipse of the sun, visible in the United States,\\nwill occur on the 7th of August, 1869.\\nCHAPTER VI.\\nOF LONGITUDE. TIDES.\\n187. As eclipses of the sun afford one of the most\\napproved methods of finding the longitude of places, our\\nattention is naturally turned next towards that subject.\\nThe ancients studied astronomy in order that they\\nmight read their destinies in the stars the moderns that\\nthey may securely navigate the ocean. A large portion\\nof the refined labors of modern astronomy, has been di-\\nrected towards perfecting the astronomical tables with\\nthe view of finding the longitude at sea, an object\\nmanifestly worthy of the highest efforts of science, con-\\nsidering the vast amount of property and of human life\\ninvolved in navigation.\\n188. The difference of longitude between two places,\\nmay be found by any method by which we can ascertain\\n1S6. What recent period has abounded with great eclipses\\nof the sun When will the next total eclipse of the sun occur\\n187. For what purpose did the ancients study astronomy\\nFor what purpose do the moderns study it", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0170.jp2"}, "167": {"fulltext": "LONGITUDE. 151\\nthe difference of their local times, at the same instant of\\nabsolute time.\\nAs the earth turns on its axis from west to east, any\\nplace that lies eastward of another will come sooner un-\\nder the sun, or will have the sun earlier on the meridian,\\nand consequently, in respect to the hour of the day, will\\nbe in advance of the other at the rate of one hour for\\nevery 15\u00c2\u00b0, or four minutes of time for each degree. Thus,\\nto a place 15\u00c2\u00b0 east of Greenwich, it is 1 o clock, P. M.\\nwhen it is noon at Greenwich; and to a place 15\u00c2\u00b0 west\\nof that meridian, it is 11 o clock, A. M. at the same in-\\nstant. Hence the difference of time at any two places,\\nindicates their difference of longitude.\\n189. The easiest method of finding the longitude is\\nby means of an accurate time piece, or chronometer. Let\\nus set out from London with a chronometer accurately\\nadjusted to Greenwich time, and travel eastward to a\\ncertain place, where the time is accurately kept, or may\\nbe ascertained by observation. We find, for example,\\nthat it is 1 o clock by our chronometer, when it is 2\\no clock and 30 minutes at the place of observation.\\nHence the longitude is 15 x 1.5=22J\u00c2\u00b0 E. Had we trav-\\nelled westward until our chronometer was an hour and\\na half in advance of the time at the place of observa-\\ntion, (that is, so much later in the day,) our longitude\\nwould have been 22^\u00c2\u00b0 W. But it would not be neces-\\nsary to repair to London in order to set our chronometer\\nto Greenwich time. This might be done at any obser-\\nvatory, or any place whose longitude has been accu-\\n188. How may the difference of longitude between two pla-\\nces be found How many degrees of longitude, correspond to\\none hour in time How many minutes to one degree\\n189. Explain the method of finding the longitude by the\\nchronometer. To what time is it set l How do we ascertain\\ndie longitude of a place by it 1 Would it be necessary to re-\\npair to Greenwich to regulate our chronometer What is said\\nof the accuracy of some chronometers Why is not this\\nmethod adapted to general use", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0171.jp2"}, "168": {"fulltext": "152 THE MOON.\\nrately determined. For example, the time at New York\\nis 4h. 56m. 4s. 5 behind that of Greenwich. If, there-\\nfore, we set our chronometer so much before the true\\ntime at New York, it will indicate the time at Green-\\nwich. Moreover, on arriving at different places any\\nwhere on the earth, whose longitude is accurately known,\\nwe may learn whether our chronometer keeps accurate\\ntime or not, and if not, the amount of its error. Chro-\\nnometers have been constructed of such an astonishing\\ndegree of accuracy, as to deviate but a few seconds in a\\nvoyage from London to Baffin s Bay and back, during an\\nabsence of several years. But chronometers which are\\nsufficiently accurate to be depended on for long voya-\\nges, are too expensive for general use, and the means of\\nverifying their accuracy are not sufficiently easy. More-\\nover, chronometers, by being transported from one place\\nto another, change their daily rate, or depart from that\\nmean rate which they preserve at a fixed station, A\\nchronometer, therefore, cannot be relied on for determin-\\ning the longitudes of places where the greatest degree of\\naccuracy is required, especially where the instrument is\\nconveyed over land, although the uncertainty attendant\\non one instrument may be nearly obviated by employing\\nseveral and taking their mean results.\\n190. Eclipses of the sun and moon are sometimes\\nused for determining the longitude. The exact instant\\nof immersion or of emersion, or any other definite mo-\\nment of the eclipse which presents itself to two distant\\nobservers, affords the means of comparing their difference\\nof time, and hence of determining their difference of\\nlongitude. Since the entrance of the moon into the\\nearth s shadow, in a lunar eclipse, is seen at the same\\ninstant of absolute time at all places where the eclipse\\nis visible, this observation would be a very suitable one\\nfor finding the longitude were it not that, on account of\\n190. Explain how to find the longitude by eclipses of the sun\\nand moon. What objections are there to this method, both in\\nlunar and solar eclipses", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0172.jp2"}, "169": {"fulltext": "LONGITUDE. 153\\nthe increasing darkness of the penumbra near the boun-\\ndaries of the shadow, it is difficult to determine the pre-\\ncise instant when the moon enters the shadow. By\\ntaking observations on the immersions of known spots\\non the lunar disk, a mean result may be obtained which\\nwill give the longitude with tolerable accuracy. In an\\neclipse of the sun, the instants of immersion and emer-\\nsion may be observed with greater accuracy, although,\\nsince these do not take place at the same instant of ab-\\nsolute time, the calculation of the longitude from obser-\\nvations on a solar eclipse are complicated and laborious.\\n191. The lunar method of finding the longitude, at\\nsea, is in many respects preferable to every other. It\\nconsists in measuring (with a sextant) the angular dis-\\ntance between the moon and the sun, or between the\\nmoon and a star, and then turning to the Nautical Alma-\\nnac,* and finding what time it was at Greenwich when\\nthat distance was the same. The moon moves so rap-\\nidly, that this distance will not be the same except at\\nvery nearly the same instant of absolute time. For ex-\\nample, 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\\nand, on looking into the Nautical Almanac, we find that\\nthe time when this distance was the same for the me-\\nridian of Greenwich was 1 o clock, P. M. hence we\\ninfer that the longitude of the place is four hours, or 00\u00c2\u00b0\\nwest.\\n191. Explain the lunar method of finding the longitude.\\nWhat measurements are made How do we find the corres-\\nponding time at Greenwich\\nThe Nautical Almanac, is a bock published annually by the British\\nBoard of Longitude, containing various tables and astronomical infor-\\nmation for the use of navigators. The American Almanac also con-\\ntains a variety of astronomical information, peculiarly interesting to the\\npeople of the United States, in connexion with a vast amount of\\nstatistical matter. It is well deserving of a place in the library of the\\nstudent.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0173.jp2"}, "170": {"fulltext": "154 THE MOON.\\nThe Nautical Almanac contains the true angular dis-\\ntance of the moon from the sun, from the four large\\nplanets, (Venus, Mars, Jupiter, and Saturn,) and from\\nnine bright fixed stars, for the beginning of every third\\nhour of mean time for the meridian of Greenwich and\\nthe mean time corresponding to any intermediate hour,\\nmay be found by proportional parts.*\\n192. It would be a very simple operation to determine\\nthe longitude by Lunar Distances, if the process as de-\\nscribed in the preceding article were all that is neces-\\nsary but the various circumstances of parallax, refrac-\\ntion, and dip of the horizon, would differ more or less at\\nthe two places, even were the bodies, whose distances\\nwere taken, in view from both, which is not necessarily\\nthe case. The observations, therefore, require to be\\nreduced to the center of the earth, being cleared of the\\neffects of parallax and refraction. Hence, three obser-\\nvers are necessary in order to take a lunar distance in\\nthe most exact manner, viz. two to measure the altitudes\\nof the two bodies respectively, at the same time that\\nthe third takes the angular distance between them.\\nThe altitudes of the two luminaries at the time of ob-\\nservation must be known, in order to estimate the effects\\nof parallax and refraction.\\n193. Although the lunar method of finding the longi-\\ntude at sea has many advantages over the other meth-\\nods in use, yet it also has its disadvantages. One is, the\\ngreat exactness requisite in observing the distance of\\nthe moon from the sun or star, as a small error in the\\ndistance makes a considerable error in the longitude.\\nThe moon moves at the rate of about a degree in two\\n192. What difficulties are there in this method Why are\\nthree observers necessary\\n193. What are the objections to this method What is the\\nerror of the best tables now in use 1\\nSee Bowditch s Navigator, Tenth Ed. p. 226.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0174.jp2"}, "171": {"fulltext": "LONGITUDE. 155\\nhours, or one minute of space in two minutes of time.\\nTherefore, if we make an error of one minute in ob-\\nserving the distance, we make an error of two minutes\\nin time, or 30 miles of longitude at the equator. A sin-\\ngle observation with the best sextant, may be liable to\\nan error of more than half a minute but the accuracy\\nof the result may be much increased by a mean of sev-\\neral observations taken to the east and west of the moon.\\nThe imperfection of the lunar tables was until recently\\nconsidered as an objection to this method. Until within a\\nfew years, the best lunar tables were frequently errone-\\nous to the amount of one minute, occasioning an error\\nof 30 miles. The error of the best tables now m use\\nwill rarely exceed 7 or 8 seconds.\\nTIDES.\\n194. The tides are an alternate rising and falling of\\nthe waters of the ocean, at regular intervals. They have\\na maximum and a minimum twice a day, twice a month,\\nand twice a year. Of the daily tide, the maximum is\\ncalled High tide, and the minimum Low tide. The\\nmaximum for the month is called Spring tide, and the\\nminimum Neap tide. The rising of the tide is called\\nFlood and its falling Ebb tide.\\nSimilar tides, whether high or low, occur on opposite\\nsides of the earth at once. Thus at the same time that it\\nis high tide at any given place, it is also high tide on the\\ninferior meridian, and the same is true of the low tides.\\nThe interval between two successive high tides is\\n12h. 25m.; or, if the same tide be considered as return-\\ning to the meridian, after having gone around the globe,\\n194. What are the tides 1 When have they a maximum and\\na minimum Define the terms High and Low, Spring and\\nNeap, Flood and Ebb tides. What two tides occur at the same\\ntime 1 What is the interval between two successive high tides\\nHow rmieh later is the tide of to-day than the same tide of\\nyesterday What is the average height of the tide for the\\nwhole globe To what extreme height does it sometimes rise\\nHave inland lakes and seas any tides", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0175.jp2"}, "172": {"fulltext": "156 /HE MOON\\nits return is about 50 minutes later than it occurred on\\nthe preceding day. In this respect, as well as in various\\nothers, it corresponds very nearly to the motions of the\\nmoon.\\nThe average height for the whole globe is about 2^\\nfeet or, if the earth were covered uniformly with a\\nstratum of water, the difference between the two diam-\\neters of the oval would be 5 feet, or more exactly 5 feet\\nand 8 inches but its actual height at various places is\\nvery various, sometimes rising to 60 or 70 feet, and\\nsometimes being scarcely perceptible. At the same\\nplace also, the phenomena of the tides are very different\\nat different times.\\nInland lakes and seas, even those of the largest class,\\nas Lake Superior, or the Caspian, have no perceptible\\ntide.\\n195. Tides are caused by the unequal attraction of\\nthe sun and moon upon different parts of the earth.\\nSuppose the projectile force by which the earth is car-\\nried forward in her orbit, to be suspended, and the earth\\nto fall towards one of these bodies, the moon, for exam-\\nple, in consequence of their mutual attraction. Then,\\nif all parts of the earth fell equally towards the moon,\\nno derangement of its different parts would result, any\\nmore than of the particles of a drop of water in its de-\\nscent to the ground. But if one part fell faster than an-\\nother, the different portions would evidently be separa-\\nted from each other. Now this is precisely what takes\\nplace with respect to the earth in its fall towards the\\nmoon. The portions of the earth in the hemisphere\\nnext to the moon, on account of being nearer to the\\ncenter of attraction, fall faster than those in the oppo-\\nsite hemisphere, and consequently leave them behind.\\nThe solid earth, on account of its cohesion, cannot obey\\n195. State the cause of the tides. What would be the con-\\nsequence were the earth abandoned to the force exerted by\\nthe moon alone", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0176.jp2"}, "173": {"fulltext": "TIDES.\\n157\\nthis impulse, since all its different portions constitute\\none mass, which is acted on in the same manner as\\nthough it were all collected in the center but the wa-\\nters on the surface, moving freely under this impulse,\\nendeavor to desert the solid mass and fall towards the\\nmoon. For a similar reason the waters in the opposite\\nhemisphere falling less towards the moon than the solid\\nearth are left behind, or appear to rise from the center\\nof the earth.\\n196. Let DEFG (Fig. 36,) represent the globe and,\\nfor the sake of illustrating the principle, we will sup-\\npose the waters entirely to cover the globe at a uniform\\ndepth. Let defg represent the solid globe, and the cir-\\ncular ring exterior to it, the covering of waters. Let C\\nbe the center of gravity of the solid mass, A that of the\\nhemisphere next to the moon, (for the center of gravity\\nof a ring is within the ring,) and B that of the remoter\\nhemisphere. Now the force of attraction exerted by\\nthe moon, acts in the same manner as though the solid\\nmass were all concentrated in C, and the waters of each\\nhemisphere at A and B respectively and (the moon be-\\n196. Explain the tides upon the doctrine of the center of\\ngravity. Where would the tide-wave always be seen were it\\nnot for impediments What are these\\n14", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0177.jp2"}, "174": {"fulltext": "158 THE MOON.\\ning supposed above E) it is evident that A will tend to\\nleave C, and C to leave B behind. The same must evi-\\ndently be true of the respective portions of matter, of\\nwhich these points are the centers of gravity. The wa-\\nters of the globe will thus be reduced to an oval shape,\\nbeing elongated in the direction of that meridian which\\nis under the moon, and flattened in the intermediate\\nparts, and most of all at points ninety degrees distant\\nfrom that meridian.\\nWere it not, therefore, for impediments which prevent\\nthe force from producing its full effects, we might expect\\nto see the great tide-wave, as the elevated crest is called,\\nalways directly beneath the moon, attending it regularly\\naround the globe. But the inertia of the waters pre-\\nvents their instantly obeying the moon s attraction, and\\nthe friction of the waters on the bottom of the ocean,\\nstill farther retards its progress. It is not therefore until\\nseveral hours (differing at different places) after the\\nmoon has passed the meridian of a place, that it is high\\ntide at that place.\\n197. The sun has a similar action to the moon, but\\nonly one third as great. On account of the great mass\\nof the sun compared with that of the moon, we might\\nsuppose that his action in raising the tides would be\\ngreater than that of the moon but the nearness of the\\nmoon to the earth more than compensates for the sun s\\ngreater quantity of matter. Let us, however, form a just\\nconception of the advantage which the moon derives\\nfrom her proximity. It is not that her actual amount of\\nattraction is thus rendered greater than that of the sun\\nbut it is that her attraction for the different parts of the\\nearth is very unequal, while that of the sun is nearly\\nuniform. It is the inequality of this action, and not the\\nabsolute force, that produces the tides. The diameter of\\nthe earth is of the distance of the moon, while it is\\nless than -3-0^00 \u00c2\u00b0f tne distance of the sun.\\n197. Explain the action of the sun in raising the tide Why\\nis its efFect less than that of the moon", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0178.jp2"}, "175": {"fulltext": "TIDES. 159\\n198. Having now learned the general cause of the\\ntides, we will next attend to the explanation of -particu-\\nlar phenomena.\\nThe Spring tides, or those which rise to an unusual\\nheight twice a month, are produced by the sun and\\nmoon s acting together and the Neap tides, or those\\nwhich are unusually low twice a month, are produced\\nby the sun and moon s acting in opposition to each\\nother. The Spring tides occur at the syzigies the\\nNeap tides at the quadratures. At the time of new moon,\\nthe sun and moon both being on the same side of the\\nearth, and acting upon it in the same line, their actions\\nconspire, and the sun may be considered as adding so\\nmuch to the force of the moon. We have already ex-\\nplained how the moon contributes to raise a tide on the\\nopposite side of the earth. But the sun as well as the\\nmoon raises its own tide-wave, which, at new moon,\\ncoincides with the lunar tide-wave. At full moon, also,\\nthe two luminaries conspire in the same way to raise\\nthe tide for we must recollect that each body contri-\\nbutes to raise the tide on the opposite side of the earth\\nas well as on the side nearest to it. At both the con-\\njunctions and oppositions, therefore, that is, at the syzi-\\ngies, we have unusually high tides. But here also the\\nmaximum effect is not at the moment of the syzigies,\\nbut 36 hours afterwards.\\nAt the quadratures, the solar wave is lowest where the\\nlunar wave is highest hence the low tide produced by\\nthe sun is subtracted from high water and produces the\\nNeap tides. Moreover, at the quadratures the solar\\nwave is highest where the lunar wave is lowest, and\\nhence is to be added to the height of low water at the\\ntime of Neap tides. Therefore the difference between\\nhigh and low water is only about half as great at Neap\\ntide as at Spring tide.\\n198. What is the cause of the Springtides 1 Also of the\\nNeap.tides? How long after the syzigies does the highest\\ntide occur 1", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0179.jp2"}, "176": {"fulltext": "160\\nTHE MOON\\n199. The variations of distance in the sun are not\\ngreat enough to influence the tides very materially, but\\nthe variations in the moon s distance have a striking\\neffect. The tides which happen when the moon is in\\nperigee, are considerably greater than when she is in\\napogee and if she happens to be in perigee at the time\\nof the syzigies, the Spring tide is unusually high.\\nWhen this happens at the equinoxes, the highest tides\\nof the year are produced.\\n200. The declinations of the sun and moon have a\\nconsiderable influence on the height of the tide. When\\nthe moon, for example, has no declination, or is in the\\nFig. 37.\\nequator, as in figure 37,* the two tides will be exactly\\nequal on opposite sides of the meridian in the same\\nparallel. Thus a place in the parallel TT will have\\n199. How do the variations in the moon s distance from the\\nearth affect the tides How are the tides when the moon is in\\nperigee How when she in apogee When are the highest\\ntides of the year produced 1\\nDiagrams like these are apt to mislead the learner, by exhibiting the\\nprotuberance occasioned by the tides as much greater than the reality.\\nWe must recollect that it amounts, at the highest, to only a very few\\nfeet in eight thousand miles. Were the diagram, therefore, drawn in\\njust proportions, the alteration of figure produced by the tides would\\nbe wholly insensible.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0180.jp2"}, "177": {"fulltext": "TIDES.\\n161\\nthe height of one tide T2 and the other tide T 3.\\nThe tides are in this case greatest at the equator, and\\ndiminish gradually to the poles, where it will be low\\nwater during the whole day. When the moon is\\non the north side of the equator, as in figure 38, at\\nher greatest northern declination, a place describing\\nthe parallel TT will have T 3 for the height of the\\nFig. 38.\\ntide when the moon is on the superior meridian, and T2\\nfor the height at the same time on the inferior me-\\nridian. Therefore, all places north of the equator will\\nhave the highest tide when the moon is above the hor-\\nizon, and the lowest when she is below it the differ-\\nence of the tides diminishing towards the equator, where\\nthey are equal. In like manner, (the moon being still\\nat M, Fig. 38, that is, having northern declination,)\\nplaces south of the equator have the highest tides when\\nthe moon is below the horizon, and the lowest when she\\nis above it. The circumstances are all reversed when\\nthe moon is south of the equator.\\n201. The motion of the tide- wave, it should be re-\\nmarked, is not a. progressive motion, but a mere undula-\\ntion, and is to be carefully distinguished from the cur-\\n200 Explain the effect of the declinations of the sun and\\nmoon upon the tides. How will the upper and lower tides cor-\\nrespond when the moon is in the equator 1 How when the\\nmoon is north of the equator Explain by figures 37, 38\\n14", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0181.jp2"}, "178": {"fulltext": "162 THE MOON.\\nrents to which it gives rise. If the ocean completely\\ncovered the earth, the sun and moon being in the equa-\\ntor, the tide-wave would travel at the same rate as the\\nearth on its axis. Indeed, the correct way of conceiv-\\ning of the tide- wave, is to consider the moon at rest,\\nand the earth in its rotation from west to east, as bringing\\nsuccessive portions of water under the moon, which\\nportions being elevated successively at the same rate as\\nthe earth revolves on its axis, have a relative motion\\nwestward in the same degree.\\n202. The tides of rivers, narrow bays, and shores\\nfor from the main body of the ocean, are not produced\\nin those places by the direct action of the sun and moon,\\nbut are subordinate waves propagated from the great\\ntide-wave.\\nLines drawn through all the adjacent parts of any\\ntract of water, which have high water at the same time,\\nare called cotidal lines. We may, for instance, draw a\\nline through all places in the Atlantic Ocean which\\nhave high tide in a given day at 1 o clock, and another\\nthrough all places which have high tide at 2 o clock.\\nThe cotidal line for any hour may be considered as rep-\\nresenting the summit or ridge of the tide-wave at that\\ntime and could the spectator, detached from the earth,\\nperceive the summit of the wave, he would see it travel-\\ning round the earth in the open ocean once in twenty-\\nfour hours, followed by another twelve hours distant,\\nand both sending branches into rivers, bays, and other\\nopenings into the main land. These latter are called\\nDerivative tides, while those raised directly by the ac-\\ntion of the sun and moon, are called Primitive tides.\\n201. Is the motion of the tide-wave progressive? if the\\nocean completely covered the earth and the sun and moon were\\nin the equator, how would the tide-wave travel 1 What is the\\nmost correct way of conceiving of the tide-wave\\n202. How are the tides of rivers, c. produced? Define\\ncotidal lines. What does the cotidal line for any hour repre-\\nsent Distinguish between Primitive and Derivative tides.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0182.jp2"}, "179": {"fulltext": "TIDES\\n163\\n203. The velocity with which the wave moves, will\\ndepend on various circumstances, but principally on the\\ndepth, and probably on the regularity of the channel.\\nIf the depth be nearly uniform, the cotidal lines will be\\nnearly straight and parallel. But if some parts of the\\nchannel are deep while others are shallow, the tide will\\nbe detained by the greater friction of the shallow places,\\nand the cotidal lines will be irregular. The direction\\nalso of the derivative tide, may be totally different from\\nthat of the primative. Thus, (Fig, 39,) if the great\\nFig. 39.\\ntide-wave, moving from east to west, be represented by\\nthe lines 1, 2, 3, 4, the derivative tide which is propa-\\ngated up a river or bay, will be represented by the co-\\ntidal lines 3. 4, 5, 6, 7. Advancing faster in the channel\\nthan next the bank, the tides will lag behind towards\\nthe shores, and the cotidal lines will take the form of\\ncurves as represented in the diagram.\\n203- On what will the velocity of the tide-wave depend]\\nWhat circumstances will retard it Explain figure 39.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0183.jp2"}, "180": {"fulltext": "164 THE MOON.\\n204. On account of the retarding influence of shoals,\\nand an uneven, indented coast, the tide-wave travels\\nmore slowly along the shores of an island than in the\\nneighbouring sea, assuming convex figures at a little dis-\\ntance from the island and on opposite sides of it. These\\nconvex lines sometimes meet and become blended in\\nsuch a manner as to create singular anomalies in a sea\\nmuch broken by islands, as well as on coasts indented\\nwith numerous bays and rivers. Peculiar phenomena\\nare also produced, when the tide flows in at opposite\\nextremities of a reef or island, as into the two opposite\\nends of Long Island Sound. In certain cases a tide-\\nwave is forced into a narrow arm of the sea, and pro-\\nduces very remarkable tides. The tides of the Bay of\\nFundy (the highest in the world) sometimes rise to\\nthe height of 60 or 70 feet and the tides of the rivei\\nSevern, near Bristol in England, rise to the height of 40\\nfeet.\\n205. The Unit of Altitude of any place, is the height\\nof the maximum tide after the syzigies, 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\\nthe sun and moon from the earth, and by their declina-\\ntions, these distances are taken at their mean value, and\\nthe luminaries are supposed to be in the equator the\\nobservations being so reduced as to conform to these cir-\\ncumstances. The unit of altitude can be ascertained\\nby observation only. The actual rise of the tide de-\\npends much on the strength and direction of the wind.\\nWhen high winds conspire with a high flood tide, as is\\nfrequently the case near the equinoxes, the tide often\\n204. How does the tide-wave travel along the shores of an\\nisland How are the great tides of the Bay of Fundy accounted\\nfor? How high do they rise there, and at Bristol in England\\n205. Define the unit of altitude. By what circumstances is\\nthe unit of altitude affected How is it ascertained State\\nit for several places.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0184.jp2"}, "181": {"fulltext": "TIDES. 165\\nrises to a very unusual height. We subjoin from the\\nAmerican Almanac a few examples of the unit of alti-\\ntude for different places.\\nFeet.\\nCumberland, head of the Bay of Fundy, 71\\nBoston, 11|\\nNew Haven, 8\\nNew York, 5\\nCharleston, S. C, 6\\n206. The Establishment of any port is the mean in-\\nterval between noon and the time of high water, on the\\nday of new or full moon. As the interval for any given\\nplace is always nearly the same, it becomes a criterion\\nof the retardation of the tides at that place. On ac-\\ncount of the importance to navigation of a correct\\nknowledge of the tides, the British Board of Admiralty,\\nat the suggestion of the Royal Society, recently issued\\norders to their agents in various important naval stations,\\nto have accurate observations made on the tides, with\\nthe view of ascertaining the establishment and various\\nother particulars respecting each station and the gov-\\nernment of the United States is prosecuting similar in-\\nvestigations respecting our own ports.\\n207. According to Professor Whewell, the tides on\\nthe coast of North America are derived from the great\\ntide-wave of the South Atlantic, which runs steadily\\nnorthward along the coast to the mouth of the Bay of\\nFundy, where it meets the northern tide-wave flowing\\nin the opposite direction. Hence he accounts for the\\nhigh tides of the Bay of Fundy.\\n208. The largest lakes and inland seas have no per-\\nceptible tides. This is asserted by all writers respect-\\n206. What is the establishment of a port What efforts\\nhave been made to obtain accurate observations on the tides", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0185.jp2"}, "182": {"fulltext": "166 THE MOON.\\ning the Caspian and Euxine, and the same is found to\\nbe true of the largest of the North American lakes,\\nLake Superior.\\nAlthough these several tracts of water appear large\\nwhen taken by themselves, yet they occupy but small\\nportions of the surface of the globe, as will appear ev-\\nident from the delineation of them on an artificial globe.\\nNow we must recollect that the primitive tides are pro-\\nduced by the unequal action of the sun and moon upon\\nthe different parts of the .earth and that it is only at\\npoints whose distance from each other bears a consider-\\nable ratio to the whole distance of the sun or the moon,\\nthat the inequality of action becomes manifest. The\\nspace required is larger than either of these tracts of\\nwater. It is obvious also that they have no opportunity\\nto be subject to a derivative tide.\\n209. To apply the theory of universal gravitation to\\nall the varying circumstances that influence the tides,\\nbecomes a matter of such intricacy, that La Place pro-\\nnounces the problem of the tides the most difficult\\nproblem of celestial mechanics.\\n210. The Atmosphere that envelops the earth, must\\nevidently be subject to the action of the same forces as\\nthe covering of waters, and hence we might expect a\\nrise and fall of the barometer, indicating an atmospheric\\ntide corresponding to the tide of the ocean. La Place\\nhas calculated the amount of this aerial tide. It is too\\ninconsiderable to be detected by changes in the barom-\\neter, unless by the most refined observations. Hence it\\nis concluded, that the fluctuations produced by this cause\\nare too slight to affect meteorological phenomena in any\\nappreciable degree.\\n207. How are the tides on the coast of North America de-\\nrived\\n208. Why have lakes and seas no tides 1\\n209. What is said of the difficulty of applying the principle\\nof universal gravitation to all the circumstances of the tides", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0186.jp2"}, "183": {"fulltext": "167\\nCHAPTER VII.\\nOF THE PLANETS THE INFERIOR PLANETS, MERCURY\\nAND VENUS.\\n211. The name planet signifies a loanderer* and is\\napplied to this class of bodies because they shift their\\npositions in the heavens, whereas the fixed stars con-\\nstantly maintain the same places with respect to each\\nother. The planets known from a high antiquity, are\\nMercury, Yenus, Earth, Mars, Jupiter, and Saturn. To\\nthese, in 1781, was added Uranus, f (or Herschel, as it\\nis sometimes called, from the name of its discoverer,)\\nand, as late as 1816, another large planet, Neptune,\\nwas added to the list, making eight in all of the regular\\nseries. Besides these, there are found between Mars\\nand Jupiter, a remarkable group of small planets, called\\nAsteroids, numbering over thirty. Of these, four\\nCeres, Pallas, Juno, and Yesta were discovered near\\nthe commencement of the present century; and the\\nremainder have been brought to light since 1845, and\\nnew ones are still very frequently announced.\\nThe planets, with the exception of the new-discovered\\nAsteroids, are designated by the following characters\\n1. Mercury 7. Ceres\\n2. Venus 9 8. Pallas\\n3. Earth 9. Jupiter U\\n4. Mars 10. Saturn\\n5. Vesta fi 11. Uranus Jff\\n6. Juno 12. Neptune f\\nThe foregoing are called the primary planets. Sev-\\neral of these have one or more attendants, or satellites,\\nwhich revolve around them, as they revolve around\\n210. Has the atmosphere any tide? Is it sufficient to influ-\\nence meteorological phenomena\\n211. Whence is the name planet derived? Which of the\\nFrom the Greek TrXav^r??; -j- From Ovpavos.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0187.jp2"}, "184": {"fulltext": "168 THE PLANETS.\\nthe sun. The earth has one satellite, namely, the moon\\nJnpiter has four; Saturn, eight; Uranus, six; and\\nNeptune, one. These bodies also are planets, but in\\ndistinction from the others they are called secondary\\nplanets. Hence the whole number of planetary bodies\\nin the solar system is 61 namely, 8 large primaries,\\n20 secondaries, and 33 Asteroids.\\n212. With the exception of the Asteroids, the primary\\nplanets have their orbits nearly in the same plane, and\\nare never seen far from the ecliptic. Mercury, whose\\norbit is most inclined of all, never departs further from\\nthe ecliptic than about 7\u00c2\u00b0, while most of the other\\nplanets pursue very nearly the same path with the earth,\\nin their annual revolutions around the sun. The new\\nplanets, however, make wider excursions from the plane\\nof the ecliptic, amounting, in the case of Pallas, to 34J\u00c2\u00b0.\\n213. Mercury and Yenus are called inferior planets,\\nbecause they have their orbits nearer to the sun than\\nthat of the earth while all the others, being more dis-\\ntant from the sun than the earth, are called superior\\nplanets. The planets present great diversity among\\nthemselves in respect to distance from the sun, magni-\\ntude, time of revolution, and density. They differ also\\nin regard to satellites, of which, as we have seen, three\\nhave respectively four, six, and eight, while more than\\nhalf have none at all. It will aid the memory, and ren-\\nder our view of the planetary system more clear and com-\\nplanets have been long known Which have been added in\\nmodern times? Mark on paper or on the black-board, the\\nseveral characters by which the planets are designated. Dis-\\ntinguish between the primary and the secondary planets. What\\nis said of the Asteroids What bodies have satellites State\\nthe whole number of planets.\\n212. Near what great circle are the orbits of all the planets?\\nHow far does Pallas deviate from the ecliptic\\n213. Why are Mercury and Venus called inferior planets?\\nWhy are the other planets called superior? What diversities\\ndo the planets exhibit among themselves", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0188.jp2"}, "185": {"fulltext": "DISTANCES FROM THE SUN. 169\\nprehensive, if we classify, as far as possible, the various\\nparticulars comprehended under the foregoing heads.\\n214. DISTANCES FROM THE SUX.\\n1. Mercury, 37,000,000\\n2. Venus, 68,000,000\\n3. Earth, 95,000,000\\n4. Mars, 145,000,000\\n5. Asteroids, 250,000,000\\n6. Jupiter, 495,000,000\\n1 Saturn, 900,000,000\\n8. Uranus, 1800,000,000\\n9. Neptune, 2800,000,000\\nThe dimensions of the planetary system are seen from\\nthis table to be vast, comprehending a circular space\\ntowards six thousand millions of miles in diameter. A\\nrailway car, travelling at the rate of 20 miles an hour,\\nand of course making 480 miles a day, would require\\nabout 50 days to travel round the earth on a great-circle,\\nand about 500 days to reach the moon but it will give\\nsome idea of the vastnesss of the planetary spaces to\\nreflect that, setting out from the sun and travelling from\\nplanet to planet at the same rate, to reach Mercury\\nwould require about 200 years Yenus, nearly 400 the\\nEarth, 542; Mars, more than 800; Jupiter, towards\\n3000 Saturn, above 5000 Uranus, 10,000 Neptune,\\nmore than 16,000 and to cross the entire orbit of\\nNeptune (the present boundary of the planetary system),\\nwould require upwards of 32,000 years.\\nDiagrams and orreries, as usually constructed, wholly\\nfail of giving any just conceptions of the distances of\\nthe planets from the Sun and from each other. If we\\n214. State the distance of each of the planets from the sun.\\nWhat is said of the dimensions of the planetary system How\\ndo the distances of those planets which are nearest the sun in-\\ncrease Also those which are more distant How may the\\nmean distances of the planets from the sun he determined?\\nGive an example in computing the distance of Jupiter. What\\nis said of diagrams and orreries\\n15", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0189.jp2"}, "186": {"fulltext": "170 THE PLANETS.\\nrepresent, for instance, the distance of the Earth by\\n1 loot, we shall require 30 feet in order to reach the\\nplace of Neptune; and when we have constructed a\\ndiagram on so large a scale, we must still recollect that\\neach foot represents a space of nearly 100 millions\\nof miles.\\nIt may aid the memory to remark, that in regard to\\nthe planets nearest the sun, the distances increase in an\\narithmetical ratio, while those most remote, increase in\\na geometrical ratio. Thus, if we add 30 to the distance\\nof Mercury, it gives us nearly that of Yenus 30 more\\ngives that of the Earth while Saturn is nearly twice\\nthe distance of Jupiter, and Uranus twice the distance\\nof Saturn. Between the orbits of Mars and Jupiter, a\\ngreat chasm appeared, which broke the continuity of\\nthe series but the discovery of the new planets has\\nfilled the void.\\nThe mean distances of the planets from the sun, may\\nbe determined by means of Kepler s law, that the squares\\nof the periodical times are as the cubes of the distances.\\nThus the earth s distance being previously ascertained\\nbj means of the sun s horizontal parallax, and the pe-\\nriod of any other planet, as Jupiter, being learned from\\nobservation, we say as 365.256 2 4332.585 2 l 3\\n5.202 3 which equals the cube of Jupiter s distance from\\nthe sun, and its root equals that distance itself.\\n215. MAGNITUDES.\\nMercury,\\nVenus,\\nEarth,\\nMars,\\nCeres,\\nJupiter,\\nSaturn,\\nUranus,\\nNeptune,\\nDiam. in Miles.\\nVolume.\\n2950\\n1\\nT9\\n7800\\n9\\nTo\\n7912\\n1\\n4500\\n1\\n160\\n89000\\n1400\\n79000\\n1000\\n35000\\n86\\n31000\\n60\\nThis is the number of days in one revolution of Jupiter.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0190.jp2"}, "187": {"fulltext": "PERIODIC TIMES.\\n171\\nWe remark here a great diversity in regard to magni-\\ntude, a diversity which does not appear to be subject to\\nany definite law. While Venus, an inferior planet, is\\nT as large as the earth, Mars, a superior planet, is only\\nJ, while Jupiter is 1400 times as large. Although several\\nof the planets, when nearest to us, appear brilliant and\\nlarge when compared with the fixed stars, yet the angle\\nwhich they subtend is very small, that of Venus, the\\ngreatest of all, never exceeding about 1 or more exact-\\nly 61 .9, and that of Jupiter being when greatest only\\nabout of a minute.\\n216.\\nPERIODIC\\nTIMES.\\nKevolution in its orbit\\nMean daily motion\\nMercury, 3 months\\nor 88\\ndays,\\n4\u00c2\u00b0 5 32 .6\\nVenus, 7J\\n224\\n1\u00c2\u00b0 36 7 .8\\nEarth, 1 year,\\n365\\n0\u00c2\u00b0 59 8 .3\\nMars, 2 years,\\n687\\n0\u00c2\u00b0 31 26 .7\\nCeres, 4-J\\n1687\\na\\n0\u00c2\u00b0 12 50 .9\\nJupiter, 12\\n4332\\na\\n0\u00c2\u00b0 4 59 .3\\nSaturn, 29\\n10759\\na\\n0\u00c2\u00b0 2 0 .6\\nUranus, 84\\n30686\\nU\\n0\u00c2\u00b0 0 42 .4\\nNeptune, 164\u00c2\u00b1-\\n60127\\n0\u00c2\u00b0 0 21 .5\\nFrom this view, it appears that the planets nearest\\nthe sun move most rapidly. Thus Mercury performs\\nnearly 350 revolutions while Uranus performs one.\\nThis is evidently not owing merely to the greater dimen-\\nsions of the orbit of Uranus, for the length of its orbit\\nis not 50 times that of the orbit of Mercury, While the\\n215. State the diameter of each of the planets. What diver-\\nsities occur in regard to their magnitudes How great angles\\ndo Venus and Jupiter subtend\\n216. State the periodic time of each of the planets. Which\\nplanets move most rapidly How many revolutions does Mer-\\ncury perform while Uranus performs one What is the daily\\nrate of Uranus", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0191.jp2"}, "188": {"fulltext": "172 THE PLANETS.\\ntime employed in describing it is 350 times that of\\nMercury. Indeed this ought to follow from Kepler s\\nlaw, that the squares of the periodical times are as the\\ncubes of the distances from which it is manifest that\\nthe times of revolution increase faster than the dimen-\\nsions of the orbit. Accordingly, the apparent progress\\nof the most distant planets is exceedingly slow, the\\ndaily rate of Uranus being only 42 .4 per day so that\\nfor weeks and months, and even years, this planet but\\nslightly changes its place among the stars.\\nTHE INFERIOR PLANETS, MERCURY AND VENUS.\\n217. The inferior planets, Mercury and Yenus, hav-\\ning their orbits so far within that of the earth, appear\\nto us as attendants upon the sun. Mercury never ap-\\npears further from the sun than 29\u00c2\u00b0 (28\u00c2\u00b0 48 and seldom\\nso far and Yenus never more than about 47\u00c2\u00b0 (47\u00c2\u00b0 12\\nBoth planets, therefore, appear either in the west soon\\nafter sunset, or in the east a little before sunrise. In\\nhigh latitudes, where the twilight is prolonged, Mercury\\ncan seldom be seen with the naked eye, and then only\\nat the periods of its greatest elongation.* The reason\\nof this will readily appear from the following diagram.\\nLet S (Fig. 40) represent the sun, ADB the orbit of\\nMercury, and E the place of the Earth. Each of the\\nplanets is seen at its greatest elongation, when a line,\\nEA or EB in the figure, is a tangent to its orbit. Then\\nthe sun being at S in the heavens, the planet will be\\nseen at A and B when at its greatest elongations, and\\nwill appear no further from the sun than the arc S A\\nor S B respectively.\\n217. What is Mercury s greatest elongation from the sun?\\nWhat is Vemis s What is said respecting the difficulty of\\nseeing Mercury Explain by figure 40.\\nCopernicus is said to have lamented on his death-bed that he had\\nnever been able to obtain a sight of Mercury, and Delambre saw it\\nbut twice.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0192.jp2"}, "189": {"fulltext": "MERCURY AND VENUS.\\nm\\nFig. 40.\\n218. A planet is said to be in conjunction with the\\nsun, when it is seen in the same part of the heavens\\nwith the sun, or when it has the same longitude. Mer-\\ncury and Yenus have each two conjunctions, the infe-\\nrior and the superior. The inferior conjunction is its\\nposition when in conjunction on the same side of the\\nsun with the earth, as at C in the figure the superior\\nconjunction is its position when on the side of the sun\\nmost distant from the earth, as at D.\\n219. The period occupied by a planet between two\\nsuccessive conjunctions with the earth, is called its sy-\\nnodical revolution. Both the planet and the earth be-\\n218. When is a planet said to be in conjunction with the\\nsun What conjunctions have the inferior planets\\n219. Define the synodical revolution. How does this period\\ncompare with the sidereal revolution Explain by figure 40.\\nWhat is the synodical period of Mercury and Venus respectively\\n15*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0193.jp2"}, "190": {"fulltext": "1*74 THE PLANETS.\\ning in motion, the time of the synodical revolution ex-\\nceeds that of the sidereal revolution of Mercury or\\nYenus for when the planet comes round to the place\\nwhere it before overtook the earth, it does not find the\\nearth at that point, but far in advance of it. Thus, let\\nMercury come into inferior conjunction with the earth\\nat C, (Fig. 40.) In about 88 days the planet will come\\nround to the same point again but meanwhile the\\nearth has moved forward through the arc EE and will\\ncontinue to move while the planet is moving more\\nrapidly to overtake her, the case being analogous to\\nthat of the hour and minute hand of a clock.\\nThe synodical period of Mercury is 116, and of Ye-\\nnus 584 days.\\n220. TJie motion of an inferior planet is direct in\\npassing through its superior conjunction, and retrograde\\nin passing through its inferior conjunction. Thus Ye-\\nnus, while going from B through D to A, (Fig. 40,)\\nmoves in the order of the signs, or from west to east,\\nand would appear to traverse the celestial vault B S A\\nfrom right to left but in passing from A through C to\\nB, her course would be retrograde, returning on the\\nsame arc from left to right. If the earth were at rest,\\ntherefore, (and the sun, of course, at rest,) the inferior\\nplanets would appear to oscillate backwards and for-\\nwards across the sun. But, it must be recollected, that\\nthe earth is moving in the same direction with the\\nplanet, as respects the signs, but with a slower motion.\\nThis modifies the motions of the planet, accelerating it\\nin the superior and retarding it in the inferior conjunc-\\ntion. Thus in figure 40, Yenus while moving through\\nBDA would seem to move in the heavens from B to\\n220. When is the motion of an inferior planet direct and\\nwhen retrograde Explain by figure 40. If the earth were at\\nrest, how would the inferior planets appear to move Show\\nhow the earth s motion modifies the apparent motions.", "height": "3584", "width": "2132", "jp2-path": "compendiumofast00olm_0194.jp2"}, "191": {"fulltext": "MERCURY AND VENUS. 175\\nA were the earth at rest but meanwhile the earth\\nchanges its position from E to E by which means the\\nplanet is not seen at A but at A being accelerated\\nby the arc A A in consequence of the earth s motion.\\nOn the other hand, when the planet is passing through\\nits inferior conjunction ACB, it appears to move back-\\nwards in the heavens from A to B if the earth is at\\nrest, but from A to B if the earth has in the mean\\ntime moved from E to E being retarded by the arc\\nB B Although the motions of the earth have the\\neffect to accelerate the planet in the superior conjunc-\\ntion, and to retard it in the inferior, yet, on account of\\nthe greater distance, the apparent motion of the planet\\nis much slower in the superior than in the inferior con-\\njunction.\\n221. When passing from the superior to the inferior\\nconjunction, or from the inferior to the superior con-\\njunction, through the greatest elongations, the inferior\\nplanets are stationary.\\nIf the earth were at rest, the stationary points would\\nbe at the greatest elongations, as at A and B, for then the\\nplanet would be moving directly towards or from the\\nearth, and would be seen for some time in the same\\nplace in the heavens but the earth itself is moving\\nnearly at right angles to the line of the planet s motion,\\nthat is, the line which is drawn from the earth to the\\nplanet through the point of greatest elongation hence a\\ndirect motion is given to the planet by this cause. When\\nthe planet, however, has passed this line, by its superior\\nvelocity it soon overcomes this tendency of the earth\\nto give it a relative motion eastward, and becomes\\nretrograde as it approaches the inferior conjunction.\\n221. When are the inferior planets stationary Why are\\nthey not stationary at the points of greatest elongation At\\nwhat elongation are Mercury and Venus stationary respect-\\nively", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0195.jp2"}, "192": {"fulltext": "176 THE PLANETS.\\nIts stationary point obviously lies between its place of\\ngreatest elongation and the place where its motion be-\\ncomes retrograde. Mercury is stationary at an elon-\\ngation of from 15\u00c2\u00b0 to 20\u00c2\u00b0 from the sun and Venus at\\nabout 29\u00c2\u00b0.\\n222. Mercury and Venus exhibit to the telescope pha-\\nses similar to those of the moon.\\nWhen on the side of their inferior conjunction, these\\nplanets appear horned, like the moon in her first and\\nlast quarters and when on the side of their superior\\nconjunctions they appear gibbous. At the moment of\\nsuperior conjunction, the whole enlightened orb of the\\nplanet is turned towards the earth, and the appearance\\nwould be that of the full moon, but the planet is too\\nnear the sun to be commonly visible.\\nThese different phases show that these bodies are opake,\\nand shine only as they reflect to us the light of the sun\\nand the same remark applies to all the planets.\\n223. The orbit of Mercury is the most eccentric, and\\nthe most inclined of all the planets while that of Ve-\\nnus varies but little from a circle, and lies much nearer\\nto the ecliptic.\\nThe eccentricity of the orbit of Mercury is nearly\\nits semi-major axis, while thatofYenus is only T J 3-;\\nthe inclination of Mercury s orbit is 7\u00c2\u00b0, while that of\\nYenus is less than 3J\u00c2\u00b0. Mercury, on account of his dif-\\nferent distances from the earth, varies much in his ap-\\n222. What phases do Mercury and Venus exhibit? Explain\\nby figure 40. Whence do these bodies derive their light Is\\nthe same true of the other planets\\n223. What is said of the eccentricity and inclination of the\\norbit of Mercury How does the apparent diameter of Mer-\\ncury vary How are his changes of seasons\\nThe new planets of course excepted.", "height": "3584", "width": "2132", "jp2-path": "compendiumofast00olm_0196.jp2"}, "193": {"fulltext": "MERCURY AND VENUS. 177\\nparent diameter, which is only 5 in the apogee, but\\n12 in the perigee. The inclination of his orbit to his\\nequator being very great, the changes of his seasons\\nmust be proportionally great.\\nThese different aspects of an inferior planet will be\\neasily understood from Fig. 41, where the earth is at E,\\nand the planet is represented in various positions in its\\nrevolutions around the sun. When at A, in the supe-\\nrior conjunction, the whole enlightened disk is turned\\ntowards us at D, in the inferior conjunction, the en-\\nlightened side is turned entirely from us and at the\\nquadratures B and C half the disk is in view. Between\\nA and B and A and C the planet is gibbous, like the\\nmoon in her second and third quarters and between B\\nand D and C and D the planet is horned, like the moon\\nin her first and last quarters.\\n224. An inferior planet is brightest at a certain\\npoint between its greatest elongation and inferior con-\\njunction.\\nIts maximum brilliancy would happen at the inferior\\nconjunction, (being then nearest to us,) if it shinecl by\\n224. When is an inferior planet brightest? Why not when,\\nnearest to us Why not when most of the illuminated side is\\nturned towards us", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0197.jp2"}, "194": {"fulltext": "1?8\\nTHE PLANETS.\\nits own light; but in that position its dark side is\\nturned towards us. Still, its maximum cannot be when\\nmost of the illuminated side is towards us for then,\\nbeing at the superior conjunction, it is at its greatest\\ndistance from us. The maximum must therefore be\\nsomewhere between the two. Yenus gives her greatest\\nlight when about 40\u00c2\u00b0 from the sun.\\n225. Mercury and Yenus loth revolve on their axes^\\nin nearly the same time with the earth.\\nThe diurnal period of Mercury is 24h. 5m. 28s., and\\nthat of Yenus 23h. 21m. 7s. The revolutions on their\\naxes have been determined by means of some spot or\\nmark seen by the telescope, as the revolution of the sun\\non his axis is ascertained by means of his spots.\\n226. Yenus is regarded as the most beautiful of the\\nplanets, and is well known as the morning and evening\\nstar. The most ancient nations did not, indeed, recog-\\nnize the evening and morning star as one and the same\\nbody, but supposed they were different planets, and\\naccordingly gave them different names, calling the\\nmorning star Lucifer, and the evening star Hesperus.\\nAt her period of greatest splendor, Yenns casts a\\nshadow, and is sometimes visible in broad daylight.\\nHer light is then estimated as equal to that of twenty\\nstars of the first magnitude. At her period of greatest\\nelongation, Yenus is visible from three to four hours\\nafter the setting or before the rising of the sun.\\n227. Every eight years Yenus forms her conjunctions\\nwith the sun in the same part of the heavens.\\n225. In what time do Mercury and Venus, respectively, re-\\nvolve on their axes How are these periods ascertained\\n226. What erroneous notions had the ancients respecting the.\\nmorning and evening star What is said of the brilliancy of\\nVenus at her greatest splendor How long may Venus be in\\nsight after sunset", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0198.jp2"}, "195": {"fulltext": "MERCURY AND VENUS. 1*79\\nFor, since the synodical period of Venus is 584 days,\\nand her sidereal period 224.7,\\n224.7 360\u00c2\u00b0 584 935.6 the arc of longitude de-\\nscribed by Verms between the first and second conjunc-\\ntions. Deducting 720\u00c2\u00b0, or two entire circumferences,\\nthe remainder, 2 15\u00c2\u00b0. 6, shows how far the place of the\\nsecond conjunction is in advance of the first. Hence,\\nin five synodical revolutions, or 2920 days, the same\\npoint must have advanced 215\u00c2\u00b0.6 x5= 1078\u00c2\u00b0, which is\\nnearly three entire circumferences, so that at the end of\\nfive synodical revolutions, occupying 2920 days, or 8\\nyears, the conjunction of Venus takes place nearly in\\nthe same place in the heavens as at first.\\nWhatever appearances of this planet, therefore, arise\\nfrom its position with respect to the earth and the sun,\\nthey are repeated every eight years in nearly the same\\nform.\\nTRANSITS OF THE INFERIOR PLANETS.\\n228. The Transit of Mercury or Venus, is its pas-\\nsage across the surfs disk, as the moon passes over it in\\na solar eclipse.\\nAs a transit takes place only when the planet is in\\ninferior conjunction, at which time her motion is retro-\\ngrade, it is always from left to right, and the planet is\\nseen projected on the solar disk in a black round spot.\\nWere the orbits of the inferior planets coincident with\\nthe plane of the earth s orbit, a transit would occur to\\nsome part of the earth at every inferior conjunction.\\nBut the orbit of Venus makes an angle of 3 J\u00c2\u00b0 with the\\necliptic, and Mercury an angle of 7\u00c2\u00b0 and, moreover,\\nthe apparent diameter of each of these bodies is very\\n227. What happens to Venus every eight years?\\n228. What is meant by the transit of Mercury or Venus\\nWhen only can a transit take place What angles do the or-\\nbits of Venus and Mercury respectively make with the ecliptic\\nIn what months does the sun pass through the nodes of each of\\nthese planets", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0199.jp2"}, "196": {"fulltext": "180 THE PLANETS.\\nsmall, both of which circumstances conspire to render a\\ntransit a comparatively rare occurrence, since it can\\nhappen only when the sun, at the time of an inferior\\nconjunction, chances to be at or extremely near the\\nplanet s node. The nodes of Mercury lie in that part\\nof the earth s orbit which the sun passes through in\\nMay and November. It is only in these months, there-\\nfore, that transits of Mercury can occur. For a similar\\nreason, those of Venus occur only in June and Decem-\\nber. Since, however, the nodes of both planets have a\\nsmall retrograde motion, the months in which transits\\noccur will change in the course of ages.\\n229. Transits of Mercury occur more frequently than\\nthose of Yenus. The periodic times of Mercury and\\nthe earth are so adjusted to each other, that Mercury\\nperforms nearly 29 revolutions while the earth per-\\nforms 7. If, therefore, the two bodies meet at the node\\nin any given year, seven years afterwards they will\\nmeet nearly at the same node, and a transit may take\\nplace, accordingly, at intervals of 7 years. But 54:\\nrevolutions of Mercury correspond still nearer to 13\\nrevolutions of the earth, and therefore a transit is still\\nmore probable after intervals of 13 years. At intervals\\nof 33 years, transits of Mercury are exceedingly proba-\\nble, because in that time Mercury makes almost exactly\\n137 revolutions. Intermediate transits however may\\noccur at the other node, these intervals having reference\\nmerely to the same node. Thus transits of Mercury\\nhappened at the ascending node in 1815, and 1822, at\\nintervals of 7 years and at the descending node in\\n1832, which returned in 1815, after an interval of 13\\n229. Which planet lias the most frequent transits? What\\nis the shortest interval of the transits of Mercury What are\\nthe longer intervals When will the next occur What are\\nintervals of the transits of Venus When was the last transit of\\nVenus, and when will the next occur", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0200.jp2"}, "197": {"fulltext": "3LERCURY AND VENUS. 181\\nyears. Transits of Venus are much more unfrequent\\nthan those of Mercury. Eight revolutions of the earth\\nare completed in nearly the same time as thirteen revo-\\nlutions of Venus, and hence two transits of Venus may\\noccur at an interval of 8 years, as was the case at the\\nlast return of this phenomenon, one transit having oc-\\ncurred in 1761, and another in 1769. But if a transit\\ndoes not happen after 8 years, it will not happen, at the\\nsame node, until an interval of 235 years but inter-\\nmediate transits may occur at the other node. The\\nnext transit of Venus will take place in 1874, being 235\\nyears after the first that was ever observed, which oc-\\ncurred in the year 1639. In the mean time, as already\\nmentioned, two transits have occurred at the other node,\\nat intervals of 8 years.\\n230. The great interest attached by astronomers to a\\ntransit of Venus, arises from its furnishing the most ac-\\ncurate means in our power of determining the surfs\\nhorizontal parallax an element of great importance,\\nsince it leads us to a knowledge of the distance of the\\nearth from the sun, and, consequently, by the applica-\\ntion of Kepler s law, (Art. 130,) of the distances of all\\nthe other planets. Hence, in 1769, great efforts were\\nmade throughout the civilized world, under the patron-\\nage of different governments, to observe this phenome-\\nnon under circumstances the most favorable for deter-\\nmining the parallax of the sun.\\nThe common methods of finding the parallax of a\\nheavenly body cannot be relied on to a greater degree\\nof accuracy than 4 In the case of the moon, whose\\ngreatest parallax amounts to about 1\u00c2\u00b0, this deviation\\nfrom absolute accuracy is not material but it amounts\\nto nearly half the entire parallax of the sun.\\n230. Why is so much interest attached to the transits of\\nVenus What efforts were made to observe it in 1769 Why\\ncannot we ascertain the horizontal parallax of the sun in the\\nsame way as we do that of the moon\\n16", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0201.jp2"}, "198": {"fulltext": "182 THE PLANETS.\\n231. If the sun and Yenus were equally distant from\\nus, they would be equally affected by parallax as view-\\ned by spectators in different parts of the earth, and\\nhence their relative situation would not be altered by\\nit; but since Yenus, at the inferior conjunction is only\\nabout one third as far off as the sun, her parallax is pro-\\nportionally greater, and therefore spectators at distant\\npoints will see Yenus projected on different parts of the\\nsolar disk, as the planet traverses the disk. Astron-\\nomers avail themselves of this circumstance to ascer-\\ntain the sun s horizontal parallax. In order to make\\nthe difference as large as possible, very distant places\\nare selected for observation. Thus in the transit of\\n1769, among the places selected, two of the most favor-\\nable were Wardhuz in Lapland, and Tahiti, one of\\nthe South Sea Islands.\\nThe appearance of Yenus on the sun s disk being\\nthat of a well-defined black spot, and the exactness with\\nwhich the moment of external or internal contact may\\nbe determined, are circumstances favorable to the ex-\\nactness of the result and astronomers repose so much\\nconfidence in the estimation of the sun s horizontal\\nparallax as derived from the observations on the transit\\nof 1769, that this important element is thought to be\\nascertained within of a second. The general result\\nof all these observations gives the sun s horizontal\\nparallax 8 .6, or more exactly, 8 .5776.\\n232. The elder astronomers imagined they had dis-\\ncovered a satellite accompanying Yenus in her transit.\\nIf Yenus had in reality any satellite, the fact would be\\nobvious at her transits, as the satellite would be pro-\\njected near the primary on the sun s disk; but later\\n231. How is Yenus projected on the sun to spectators in\\ndifferent parts of the earth What places were selected for\\nobserving the transit of 1769\\n232, Has Venus any Satellite?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0202.jp2"}, "199": {"fulltext": "SUPERIOR PLANETS. 183\\nastronomers have searched in vain for any appearances\\nof the kind, and the inference is, that former astronomers\\nwere deceived by some optical illusion.\\nCHAPTER VIII.\\nOF THE SUPERIOR PLANETS MARS, JUPITER, SATURN,\\nURANUS, AND NEPTUNE ASTEROIDS.\\n233. The Superior planets are distinguished from the\\nInferior, by being seen at all distances from the sun\\nfrom 0\u00c2\u00b0 to 180\u00c2\u00b0. Having their orbits exterior to that\\nof the earth, they of course never come between us and\\nthe sun, that is, they never have any inferior conjunction\\nlike Mercury and Yenus, but they are sometimes seen in\\nsuperior conjunction, and sometimes in opposition. Nor\\ndo they, like the inferior planets, exhibit to the telescope\\ndifferent phases, but, with a single exception, they al-\\nways present the side that is turned towards the earth\\nfully enlightened. This is owing to their great distance\\nfrom the earth for were the spectator to stand upon the\\nsun, he would of course always have the illuminated\\nside of each of the planets turned towards him but, so\\ndistant are all the superior planets except Mars, that\\nthey are viewed by us very nearly in the same manner\\nas they would be if we actually stood on the sun.\\n234. Mars is a small planet, his diameter being only\\nabout half of that of the earth, or 4500 miles. He also,\\nat times, comes nearer to the earth than any other planet\\n233. Name the Superior Planets. How are they distin-\\nguished from the Inferior? Which of them exhibit phases?\\nWhy do not the rest\\n234. Mars. State his diameter mean distance from the\\nsun inclination of his orbit. How distinguished from the\\nother planets Why do his brightness and apparent magnitude\\nvary so much Illustrate by figure 42.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0203.jp2"}, "200": {"fulltext": "184\\nTHE PLANETS.\\nexcept Venus. His mean distance from the sun is\\n14:5,000,000 miles; but his orbit is so eccentric that his\\ndistance varies much in different parts of his revolution,\\nMars is always very near the ecliptic, never varying from\\nit 2\u00c2\u00b0. Pie is distinguished from all the planets by his\\ndeep red color, and hery aspect but his brightness and\\napparent magnitude vary much at different times, being\\nsometimes nearer to us than at others, by the whole di-\\nameter of the earth s orbit, that is, by about 190,000,000\\nof miles. When Mars is on the same side of the sun\\nwith the earth, or at his opposition, he comes within\\n47,000,000 miles of the earth, and rising about the time\\nthe sun sets, surprises us by his magnitude and splendor\\nbut when he passes to the other side of the sun to his\\nsuperior conjunction, he dwindles to the appearance of\\na small star, being then 237,000,000 miles from us. Thus,\\nlet M (Fig. 42) represent Mars in opposition, and M\\nin the superior conjunction, while E represents the earth.\\nIt is obvious that in the former situation, the planet\\nmust be nearer to the earth than in the latter by the\\nwhole diameter of the earth s orbit.\\nFig. 42.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0204.jp2"}, "201": {"fulltext": "MARS. 185\\n235. Mars is the only one of the superior planets\\nwhich exhibits phases. When he is towards the quad-\\nratures at Q or Q it is evident from the figure that\\nonly a part of the circle of illumination is turned towards\\nthe earth, such a portion of the remoter part of it being\\nconcealed from our view as to render the form more or\\nless gibbous.\\n236. When viewed with a powerful telescope, the\\nsurface of Mars appears diversified with numerous vari-\\neties of light and shade. The region around the poles\\nis marked by white spots, which vary their appearance\\nwith the changes of seasons in the planets. Hence Dr.\\nHerschel conjectured that they were owing to ice and\\nsnow, which alternately accumulates and melts, according\\nto the position of each pole with respect to the sun. It\\nhas been common to ascribe the ruddy light of this plan-\\net to an extensive and dense atmosphere, which was said\\nto be distinctly indicated by the gradual diminution of\\nlight observed in a star as it approached very near to the\\nplanet in undergoing an occultation; but more recent\\nobservations afford no such evidence of an atmosphere.\\n237. By observations on the spots, we learn that Mars\\nrevolves on his axis in very nearly the same time with\\nthe earth, (24h. 39m. 21s.3 and that the inclination\\nof his axis to that of his orbit is also nearly the same,\\nbeing 28\u00c2\u00b0 42\\nAs the diurnal rotation of Mars is nearly the same as\\nthat of the earth, we might expect a similar flattening at\\nthe poles, giving to the planet a spheroidal figure. In-\\n235. Show why Mars should exhibit phases.\\n236. How is the surface of Mars diversified? What is seen\\naround the poles What indications are there of ice and snow\\nTo what is the ruddy hue of Mars ascribed\\n237. How do we learn his revolution on his axis? In what\\ntime does it take place What is the figure of Mars How\\ndoes its ellipticity compare with that of the earth\\n16*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0205.jp2"}, "202": {"fulltext": "186 THE PLACETS.\\ndeed the compression or ellipticity of Mars is six times\\nthat of the earth. This remarkable flattening of the\\n23oles of Mars has been supposed to arise from a great\\nvariation of density in the planet in different parts.\\n238. Jupiter is distinguished from all the other plan-\\nets by his vast magnitude. His diameter is more than\\n11 times, and his volume is 1400 times that of the earth.\\nHis figure is strikingly spheroidal, the equatorial being\\nlarger than the polar diameter in the proportion of 107\\nto 100. Such a figure might naturally be expected\\nfrom the rapidity of his diurnal rotation, which is ac-\\ncomplished in about 10 hours. A place on the equator\\nof Jupiter must turn 27 times as fast as on the terrestrial\\nequator. The distance of Jupiter from the sun is\\n495,000,000 miles, and his revolution around the sun\\noccupies nearly 12 years.\\n239. The view of Jupiter through a good telescope,\\n(Fig. 43,) is one of the most magnificent and interesting\\nFig. 43.\\nspectacles in astronomy. The disk expands into a large\\nand bright orb like the full moon the spheroidal figure\\n238. Jupiter. State his diameter, volume, figure, revolution\\non his axis, velocity of his equator, distance from the sun, periodic\\ntime.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0206.jp2"}, "203": {"fulltext": "JUPITER. 187\\nwhich theory assigns to revolving spheres, is here pal-\\npably exhibited to the eye across the disk 5 arranged\\nin parallel stripes, are discerned several dusky bands,\\ncalled belts; and four bright satellites, always in at-\\ntendance, and ever varying their positions, compose a\\nsplendid retinue. Indeed, astronomers gaze with eeuliar\\ninterest on Jupiter and his moons, as affording a minia-\\nture representation of the whole solar system, repeating\\non a smaller scale, the same revolutions, and exemplify-\\ning, in a manner more within the compass of our ob-\\nservation, the same laws as regulate the entire assem-\\nblage of sun and planets.\\n240. The Belts of Jupiter, are variable in their num-\\nber and dimensions. With the smaller telescopes, only\\none or two are seen across the equatorial regions; but\\nwith more powerful instruments, the number is in-\\ncreased, covering a great part of the whole disk. Dif-\\nferent opinions have been entertained by astronomers\\nrespecting the cause of the belts but they have gen-\\nerally been regarded as clouds formed in the atmosphere\\nof the planet, agitated by winds, as is indicated by their\\nfrequent changes, and made to assume the form of belts\\nparallel to the equator by currents that circulate around\\nthe planet like the trade winds and other currents that\\ncirculate around our globe. Sir John Herschel supposes\\nthat the belts are not ranges of clouds, but portions of\\nthe planet itself brought into view by the removal of\\nclouds and mists, that exist in the atmosphere of the\\nplanet through which are openings made by currents\\ncirculating around Jupiter.\\n241. The Satellites of Jupiter may be seen with a\\ntelescope of very moderate powers. Even a common\\nspy-glass will enable us to discern them. Indeed, one\\n239. What does the telescopic view of Jupiter exhibit Why\\ndo astronomers regard it with so much interest\\n240. Describe Jupiter s Belts to what are they ascribed", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0207.jp2"}, "204": {"fulltext": "188\\nTHE PLANETS.\\nor two of them have been occasionally seen with the\\nnaked eye. In the largest telescopes, they severally\\nappear as bright as Sirins. With such an instrument,\\nthe view of Jupiter with his moons and belts is truly a\\nmagnificent spectacle, a world within itself. As the\\norbits of the satellites do not deviate far from the plane\\nof the ecliptic, and but little from the equator of the\\nplanet, they are usually seen in nearly a straight line with\\neach other, extending across the central part of the disk.\\n242. Jupiter s satellites are distinguished from one\\nanother by the denominations of first, second, third, and\\nfourth* according to their relative distances from Jupi-\\nter, the first being that which is nearest to him. Their\\napparent motion is oscillatory, like that of a pendulum,\\ngoing alternately from their greatest elongation on one\\nside to their greatest elongation on the other, sometimes\\nin a straight line, and sometimes in an elliptical curve,\\naccording to the different points of view in which we\\nobserve them from the earth. They are sometimes sta-\\ntionary their motion is alternately direct and retro-\\ngrade and, in short, they exhibit in miniature all the\\nphenomena of the planetary system. Various partic-\\nulars of the system are exhibited in the following table.\\nThe diameters and distances are given in miles.\\nSatellites.\\nDiameter.\\nDistances.\\nSidereal Kevolution.\\n1\\n2\\n3\\n4\\n2440\\n2190\\n3580\\n3060\\n278,500\\n443,300\\n707,000\\n1,243,000\\nId. 18h. 28m.\\n3 13 15\\n7 3 43\\n16 16 32\\nHence, it appears, first, that Jupiter s satellites are all,\\n241. How do the satellites appear to the telescope?\\n242. Describe the motions of the satellites magnitudes\\ndistances periods of revolution.\\nThe classical names of Jupiter s satellites, are Io, Europa, Gany-\\nmede, Calisto.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0208.jp2"}, "205": {"fulltext": "JUPITER. 189\\nexcept the second, somewhat larger than the moon, but\\nthat the second satellite is the smallest, and the third the\\nlargest of the whole, although the diameter of the latter\\nis only about -j-j part of that of the primary secondly,\\nthat the distance of the innermost satellite from the\\nplanet is 40,000 miles further than that of the moon\\nfrom the earth, while that of the outermost satellite\\nstretches off to the distance of a million and a quarter\\nmiles; thirdly, that the first satellite completes his\\nrevolution around the primary in one day and three\\nfourths, while the fourth satellite requires nearly sixteen\\nand three fourths days.\\n243. The orbits of the satellites are nearly or quite\\ncircular, and deviate but little from the plane of the\\nplanet s equator, and of course are but slightly inclined\\nto the plane of its orbit. They are, therefore, in a sim-\\nilar situation with respect to Jupiter as the moon would\\nbe with respect to the earth if her orbit nearly coincided\\nwith the ecliptic, in which case she would undergo an\\neclipse at -every opposition.\\n244. The eclipses of Jupiter s satellites, in their gen-\\neral conception, are perfectly analogous to those of the\\nmoon, but in their detail they differ in several particulars.\\nOwing to the much greater distance of Jupiter from the\\nsun, and its greater magnitude, the cone of its shadow is\\nmuch longer and larger than that of the earth. On this\\naccount, as well as on account of the little inclination of\\ntheir orbits to that of their primary, the three inner sat-\\nellites of Jupiter pass through the shadow, and are totally\\neclipsed at every revolution. The fourth satellite, owing\\nto the greater inclination of its orbit, sometimes though\\n243. What is the shape of their orbits How situated with\\nregard to the plane of the planet s orbit\\n244. Describe the phenomena of their eclipses. Which of\\nthem escapes an eclipse Are these eclipses seen in different\\nparts of the earth at the same moment of absolute time?", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0209.jp2"}, "206": {"fulltext": "190 THE PLANETS.\\nrarely escapes eclipse, and sometimes merely grazes the\\nlimits of the shadow or suffers a partial eclipse. These\\neclipses, moreover, are not seen, as is the case with\\nthose of the moon, from the center of their motion, but\\nfrom a remote station, and one whose situation with\\nrespect to the line of the shadow is variable. This, of\\ncourse, makes no difference in the times of the eclipses,\\nbut a very great one in their visibility, and in their\\napparent situations with respect to the planet at the\\nmoment of their entering or quitting the shadow.\\n245. The eclipses of Jupiter s satellites present some\\ncurious phenomena, which will be understood from the\\nfollowing diagrams.\\nFig. 44.\\nLet A, B, C, D, (Fig. 44,) represent the earth in dif-\\nferent parts of its orbit J, Jupiter in his orbit sur-\\nrounded by his four satellites, the orbits of which are\\nmarked 1, 2, 3, 4. At a the first satellite enters the\\nshadow of the planet, and emerges from it at 5, and ad-\\nvances to its greatest elongation at c. The other satellites\\n245. Describe the phenomena of the eclipses from figure 44.\\nWill these appearances be affected by the relative position of\\nthe earth, with respect to the planet? Does the shadow of a\\nsatellite or the satellite itself ever make a transit across the disk\\nof the planet", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0210.jp2"}, "207": {"fulltext": "JUPITER. 191\\ntraverse the shadow in a similar manner. These ap-\\n23earances will be modified by the place the earth hap-\\npens to occupy in its orbit, being greatly altered by per-\\nspective but their appearances for any given night as\\nexhibited at Greenwich, are calculated and accurately\\nlaid down in the Nautical Almanac.\\nWhen one of the satellites is passing between Jupi-\\nter and the sun, it casts its shadow on the primary as the\\nmoon casts its shadow on the earth in a solar eclipse.\\nWe see with the telescope, the shadow traversing the\\ndisk. Sometimes the satellite itself is seen projected on\\nthe disk but being illuminated as well as the primary,\\nit is not so easily distinguished as Yenus or Mercury\\nwhen seen on the sun s disk, since, at the time of their\\ntransits, their dark sides are turned towards us. The\\nmanner in which these phenomena take place, as seen\\nfrom the earth in the several positions, A, B, C, D, may\\nbe conceived by attentively inspecting the figure. It\\nwill be seen, that when the earth is at A or C, the im-\\nmersions and emersions must take place close to the disk\\nof the planet, but that, in other positions of the earth,\\nas at B or D, the satellite will be seen to enter and leave\\nthe shadow at some distance from the primary.\\n246. The eclipses of Jupiter s satellites have been\\nstudied with great attention by astronomers, on account\\nof their affording one of the easiest methods of deter-\\nmining the longitude. On this subject Sir J. Herschel\\nremarks The discovery of Jupiter s satellites by Galileo,\\nwhich was one of the first fruits of the invention of the\\ntelescope, forms one of the most memorable epochs in\\nthe history of astronomy. The first astronomical solution\\nof the great problem of the longitude, the most\\nimportant problem for the interests of mankind, that has\\n246. Why have the eclipses of Jupiter s satellites been studied\\nwith so much attention Who first discovered these eclipses\\nWhat bearing has the system of Jupiter and his satellites upon\\nthe Copernican system of astronomy", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0211.jp2"}, "208": {"fulltext": "192 THE PLANETS.\\never been brought under the dominion of strict scientific\\nprinciples, dates immediately from their discovery. The\\nfinal and conclusive establishment of the Copernican\\nsystem of astronomy, may also be considered as refer-\\nable to the discovery and study of this exquisite minia-\\nture system, in which the laws of the planetary motions,\\nas ascertained by Kepler, and especially that which\\nconnects their periods and distances, were speedily\\ntraced, and found to be satisfactorily maintained.\\n247. The entrance of one of Jupiter s satellites into\\nthe shadow of the primary being seen like the entrance\\nof the moon into the earth s shadow, at the same mo-\\nment of absolute time, at all places where the planet is\\nvisible, and being wholly independent of parallax be-\\ning, moreover, predicted beforehand with great accuracy\\nfor the instant of its occurrence at Greenwich, and given\\nin the Nautical Almanac this would seem to be one of\\nthose events (Art. 188) which are peculiarly adapted\\nfor finding the longitude. It must be remarked, how-\\never, that the extinction of light in the satellite at its\\nimmersion, and the recovery of its light at its emersion,\\nare not instantaneous but gradual for the satellite, like\\nthe moon, occupies some time in entering into the\\nshadow or in emerging from it, which occasions a pro-\\ngressive diminution or increase of light. The better the\\nlight afforded by the telescope with which the observa-\\ntion is made, the later the satellite will be seen at its\\nimmersion, and the sooner at its emersion.* In noting\\nthe eclipses even of the first satellite, the time must be\\nconsidered as uncertain to the amount of 20 or 30 sec-\\n247. Explain how these eclipses are used in finding the lon-\\ngitude. What imperfections attend this method Is this method\\nmuch employed at present Why can it not be used at sea\\nThis is the reason why observers are directed in the Nautical Al-\\nmanac to use telescopes of a certain power.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0212.jp2"}, "209": {"fulltext": "SATURN. 193\\nonds; and those of the other satellites involve still\\ngreater uncertainty. Two observers, in the same room,\\nobserving with different telescopes the same eclipse,\\nwill frequently disagree in noting its time to the amount\\nof 15 or 20 seconds and the difference will be always\\nthe same way.\\nBetter methods, therefore, of finding the longitude are\\nnow employed, although the facility with which the\\nnecessary observations can be made, and the little calcu-\\nlation required, still render this method eligible in many\\ncases where extreme accuracy is not important. As a\\ntelescope is essential for observing an eclipse of one of\\nthe satellites, it is obvious that this method cannot be\\npracticed at sea.\\n248. The grand discovery of the progressive motion\\nof light, was first made by observations on the eclipses\\nof Jupiter s satellites. In the year 1675, it was remarked\\nby Koemer, a Danish astronomer, on comparing together\\nobservations of these eclipses during many successive\\nyears, that they take place sooner by about sixteen min-\\nutes, (16m. 26s.6) when the earth is on the same side of\\nthe sun with the planet, than when she is on the oppo-\\nsite side. This difference he ascribed to the progressive\\nmotion of light, which takes that time to pass through\\nthe diameter of the earth s orbit, making the velocity of\\nlight about 192,000 miles per second. So great a velocity\\nstartled astronomers at first, and produced some degree\\nof distrust of this explanation of the phenomenon but\\nthe subsequent discovery of what is called the aberration\\nof light, led to an independent estimation of the velocity\\nof light with almost precisely the same result.\\n248. How was the progressive motion of light first discovered\\nExplain the manner of the discovery. How long is light in trav-\\nersing the diameter of the earth s orbit What is its velocity\\nper second How does this agree with that derived from the\\naberration of light\\n17", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0213.jp2"}, "210": {"fulltext": "194 THE PLANETS.\\n249. Satuen comes next in the series as we recede\\nfrom the sun, and has, like Jupiter, a system within it-\\nself, on a scale of great magnificence. In size it is, next\\nto Jupiter, the largest of the planets, being 79,000 miles\\nin diameter, or about 1,000 times as large as the earth.\\nIt has likewise belts on its surface and is attended by\\neight satellites. But a still more wonderful appendage\\nis its Ring, a broad wheel encompassing the planet at\\na great distance from it. We have already intimated\\nthat Saturn s system is on a grand scale. As, however,\\nSaturn is distant from us nearly 900,000,000 miles, we\\nare unable to obtain the same clear and striking views of\\nhis phenomena as we do of the phenomena of Jupiter, al-\\nthough they really present a more wonderful mechanism.\\n250. Saturn s ring, when viewed with telescopes of a\\nhigh power, is found to consist of two concentric rings,\\nseparated from each other by a dark space.* Although\\nthis division of the rings appears to us, on account of\\nour immense distance, as only a fine line, yet it is in\\nreality an interval of not less than about 1800 miles.\\nThe dimensions of the whole system are in round num-\\nbers 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, 1*76,000\\nThe figure represents Saturn as it appears to a power-\\nful telescope, surrounded by its rings, and having its\\nbody striped with dark belts, somewhat similar but\\n249. Saturn. State his diameter and volume, number of\\nsatellites, ring, distance from the sun.\\nA third ring, less luminous than the other two, has recently been\\ndiscovered.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0214.jp2"}, "211": {"fulltext": "broader and less strongly marked than those of Jupiter,\\nand owing doubtless to a similar cause. That the ring\\nis a solid opake substance, is shown by its throwing its\\nshadow on the body of the planet on the side nearest\\nthe sun, and on the other side receiving that of the body.\\nFrom the parallelism of the belts with the plane of the\\nring, it may be conjectured that the axis of rotation of\\nthe planet is perpendicular to that plane and this con-\\njecture is confirmed by the occasional appearance of\\nextensive dusky spots on its surface, which when watch-\\ned indicate a rotation parallel to the ring in lOh. 29m. 17s.\\nThis motion, it will be remarked, is nearly the same with\\nthe diurnal motion of Jupiter, subjecting places on the\\nequator of the planet to a very swift revolution, and\\noccasioning a high degree of compression at the poles,\\nthe equatorial being to the polar diameter in the high\\nratio of 11 to 10. It requires a telescope of high mag-\\nnifying powers and a strong light, to give a full and\\n250. How is the ring divided by large telescopes State the\\nseveral dimensions of Saturn and his rings. Describe the figure.\\nHow is the ring inferred to be a solid opake substance In what\\ntime does Saturn revolve on his axis What figure does this\\ngive to the planet What kind of telescope is required to see\\nthe phenomena of Saturn to advantage", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0215.jp2"}, "212": {"fulltext": "196 THE PLANETS.\\nstriking view of Saturn with his rings, and belts, and\\nsatellites; for we must bear in mind, that in the dis-\\ntance of Saturn, one second of angular measurement\\ncorresponds to 4,000 miles, a space equal to the semi-\\ndiameter of our globe. But with a telescope of moderate\\npowers, the leading phenomena of the ring itself may\\nbe observed.\\n251. Saturn s ring, in its revolution around the sun,\\nalways remains parallel to itself.\\nIf we hold opposite to the eye a circular ring or disk\\nlike a piece of coin, it will appear as a complete circle\\nwhen it is at right angles to the axis of vision, but when\\noblique to that axis it will be projected into an ellipse\\nmore and more flattened as its obliquity is increased,\\nuntil, when its plane coincides with the axis of vision,\\nit is projected into a straight line. Let us place on the\\ntable a lamp to represent the sun, and holding the ring\\nat a certain distance inclined a little towards the lamp,\\nlet us carry it round the lamp, always keeping it parallel\\nto itself. During its revolution it will twice present its\\nedge to the lamp at opposite points, and twice at places\\n90\u00c2\u00b0 distant from those points, it will present its broadest\\nface towards the lamp. At intermediate points, it will\\nexhibit an ellipse more or less open, according as it is\\nnearer one or the other of the preceding positions. It\\nw T ill be seen also that in one half of the revolution the\\nlamp shines on one side of the ring, and in the other\\nhalf of the revolution on the other side. Such would\\nbe the successive appearances of Saturn s ring to a spec-\\ntator on the sun and since the earth is, in respect to so\\ndistant a body as Saturn, very near the sun, these ap-\\npearances are presented to us in nearly the same manner\\nas though we viewed them from the sun. Accordingly,\\nwe sometimes see Saturn s rina under the form of a\\n251. How is the position of the ring with respect to itself in\\nall parts of its revolution How may the various appearances\\nof the ring be represented", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0216.jp2"}, "213": {"fulltext": "SATURN.\\n197\\nbroad ellipse, which grows continually more and more\\nacute until it passes into a line, and we either lose sight\\nof it altogether, or by the aid of the most powerful\\ntelescopes, we see it as a fine thread of light drawn\\nacross the disk and projecting out from it on each side.\\nAs the whole revolution occupies 30 years, and the edge\\nis presented to the sun twice in the revolution, this last\\nphenomenon, namely, the disappearance of the ring,\\ntakes place every 15 years.\\n252. The learner may perhaps gain a clearer idea of\\nthe foregoing appearances from the following diagram\\nFig. 46.\\nLet A, B, C, c. represent successive positions of\\nSaturn and his ring in different parts of his orbit, while\\nabc represents the orbit of the earth.* Were the ring\\nwhen at and G perpendicular to the line of vision,\\nit would be seen by a spectator situated at a or d a\\nperfect circle, but being inclined to that line 28\u00c2\u00b0 4 it\\nis projected into an ellipse. This ellipse contracts in\\nbreadth as the ring passes towards its nodes at A and\\nE, where, being seen edgewise, it dwindles into a straight\\n252. Explain the revolution of the ring by figure 46.\\nIt may be remarked by the learner, that these orbits are made so\\nelliptical, not to represent the eccentricity of either the earth s or Sat-\\nurn s orbit, bnt merely as the projection of circles seen very obliquely.\\n11*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0217.jp2"}, "214": {"fulltext": "108 THE PLANETS.\\nline. From E to G the ring opens again, becomes broad-\\nest at G, and again contracts till it becomes a straight\\nline at A, and from this point expands till it recovers\\nits original breadth at C. These successive appearances\\nare all exhibited to a telescope of moderate powers.\\nThe ring is extremely thin, since the smallest satellite,\\nwhen projected on it, more than covers it. The thick-\\nness is estimated at 100 miles.\\n253. Saturn s ring shines wholly by reflected light\\nderived from the sun. This is evident from the fact,\\nthat that side only which is turned towards the snn is\\nenlightened and it is remarkable, that the illumination\\nof the ring is greater than that of the planet itself, but\\nthe outer ring is less bright than the inner. Although,\\nas we have already remarked, we view Saturn s ring\\nnearly as though we saw it from the sun, yet the plane of\\nthe ring produced may pass between the earth and the\\nsun, in which case also the ring becomes invisible, the\\nilluminated side being wholly turned from us. Thus when\\nthe ring is approaching its node at E, a spectator at a\\nwould have the dark side of the ring presented to him.\\nIt appears, therefore, that there are three causes for\\nthe disappearance of Saturn s ring first, when the edge\\nof the ring is presented to the sun secondly, when the\\nedge is presented to the earth and thirdly, when the\\nunilluminated side is towards the earth.\\n254. /Saturn s ring revolves in its own plane in about\\n10^ hours, (lOh. 32 m. 15s.4.) La Place inferred this\\nfrom the doctrine of universal gravitation. He proved\\nthat such a rotation was necessary, otherwise the matter\\n253. Whence does the ring derive its light? What causes\\noccasion the disappearance of the ring At what intervals do\\nthese disappearances occur\\n254. In what time does the ring revolve in its own plane\\nHow was this revolution inferred to exist before it was actually\\nobserved", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0218.jp2"}, "215": {"fulltext": "SATURN. 199\\nof which the ring is composed would be precipitated\\nupon its primary. He showed that in order to sustain\\nitself, its period of rotation must be equal to the time of\\nrevolution of a satellite, circulating around Saturn at a\\ndistance from it equal to that of the middle of the ring,\\nwhich period would be about 10| hours. By means of\\nspots in the ring, Dr. Herschel followed the ring in its\\nrotation, and actually found its period to be the same as\\nassigned by La Place, a coincidence which beautifully\\nexemplifies the harmony of truth.\\n255. Although the rings are very nearly concentric\\nwith the planet, yet recent measurements of extreme\\ndelicacy have demonstrated, that the coincidence is not\\nmathematically exact, but that the center of gravity of\\nthe rings describes around that of the body a very\\nminute orbit. This fact, unimportant as it may seem, is\\nof the utmost consequence to the stability of the system\\nof rings. Supposing them mathematically perfect in\\ntheir circular form, and exactly concentric with the plan-\\net, it is demonstrable that they would form (in spite of\\ntheir centrifugal force) a system in a state of unstable\\nequilibrium, which the slightest external power would\\nsubvert not by causing a rupture in the substance of\\nthe rings but by precipitating them unbroken on the\\nsurface of the planet. The ring may be supposed of an\\nunequal breadth in its different parts, and as consisting\\nof irregular solids, whose common center of gravity does\\nnot coincide with the center of the figure. Were it not\\nfor this distribution of matter, its equilibrium would be\\ndestroyed by the slightest force, such as the attraction\\nof a satellite, and the ring would finally precipitate it-\\nself upon the planet.\\nAs the smallest difference of velocity between the\\nplanet and its rings must infallibly precipitate the rings\\n255. Are the rings concentric with the planet? What ad-\\nvantage results from this arrangement? How must the rings\\nappear when seen from the planets", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0219.jp2"}, "216": {"fulltext": "200 THE PLANETS.\\nupon the planet, never more to separate, it follows either\\nthat their motions in their common orbit round the sun,\\nmust have been adjusted to each other by an external\\npower, with the minutest precision, or that the rings\\nmust have been formed about the planet while subject\\nto their common orbitual motion, and under the full and\\nfree influence of all the acting forces.\\nThe rings of Saturn must present a magnificent spec-\\ntacle from those regions of the planet which lie on their\\nenlightened sides, appearing as vast arches spanning the\\nsky from horizon to horizon, and holding an invariable\\nsituation among the stars. On the other hand, in the\\nregion beneath the dark side, a solar eclipse of 15 years\\nin duration, under their shadow, must afford (to our\\nideas) an inhospitable abode to animated beings, but ill\\ncompensated by the full light of its satellites. But we\\nshall do wrong to judge of the fitness or unfitness of\\ntheir condition from what we see around us, when, per-\\nhaps, the very combinations which convey to our minds\\nonly images of horror may be in reality theatres of the\\nmost striking and glorious displays of beneficent con-\\ntrivance. (Sir J. Herschel.)\\n256. Saturn is attended by eight satellites, one having\\nbeen recently added to the seven before known Al-\\nthough bodies of considerable size, their great distance\\nprevents their being visible to any telescopes but such\\nas afford a strong light and high magnifying powers.\\nThe outermost satellite is distant from the planet more\\nthan thirty times the planet s diameter, and is by far\\n256. What is the number of Saturn s satellites? How far\\ndistant from the planet is the outermost satellite Do the sat-\\nellites follow Kepler s third law? Which of the satellites are\\neasily seen Do they undergo eclipses\\nThe names of the satellites of Saturn, proceeding outwards, are\\nMimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, and Japetus.\\nHyperion is the one recentlj T discovered.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0220.jp2"}, "217": {"fulltext": "URANUS. 201\\nthe largest of the whole. It is the only one of the series\\nwhose theory has been investigated further than suffices\\nto verify Kepler s law of the periodic times, which is\\nfound to hold good here as well as in the system of Ju-\\npiter. It exhibits, like the satellites of Jupiter, periodic\\nvariations of light, which prove its revolution on its axis\\nin the time of a sidereal revolution about Saturn. The\\nnext satellite in order, proceeding inwards, is the one\\nrecently discovered the next is tolerably conspicuous\\nthe three next are very minute, and require pretty power-\\nful telescopes to see them while the two interior satel-\\nlites, which just skirt the edge of the ring, and move\\nexactly in its plane, have never been discovered but\\nwith the most powerful telescopes which human art has\\nyet constructed, and then only under peculiar circum-\\nstances. At the time of the disappearance of the rings\\n(to ordinary telescopes) they were seen by Sir William\\nHerschel with his great telescope, projected along the\\nedge of the ring, and threading like beads the thin fibre\\nof light to which the ring is then reduced. Owing to\\nthe obliquity of the ring, and of the orbits of the satel-\\nlites to that of their primary, there are no eclipses of\\nthe satellites, the two interior ones excepted, until near\\nthe time when the ring is seen edgewise.\\n257. Uranus is rarely visible except to the telescope.\\nAlthough his diameter is more than four times that of\\nthe earth, (35,112 miles,) yet his distance from the sun\\nis likewise nineteen times as great as the earth s distance,\\nor about 1,800,000,000 miles. His revolution around\\nthe sun occupies nearly 84 years, so that his position in\\nthe heavens for several years in succession is nearly\\nstationary. His path lies very nearly in the ecliptic,\\nbeing inclined to it less than one degree, (W 28 .44.)\\n257. Uranus. State liis diameter distance from the sun\\nperiodic time inclination of his orbit. How would the sun\\nappear from Uranus State the history of his discovery. By", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0221.jp2"}, "218": {"fulltext": "202 THE PLANETS.\\nThe sun himself when seen from Uranus dwindles al-\\nmost to a star, subtending as it does an angle of only\\n1 40 so that the surface of the sun would appear there\\n400 times less than it does to us.\\nThis planet was discovered by Sir William Herschel\\non the 13th of March, 1781. His attention was attracted\\nto it by the largeness of its disk in the telescope and\\nfinding that it shifted its place among the stars, he at\\nfirst took it for a comet, but soon perceived that its orbit\\nwas not eccentric like the orbits of comets, but nearly\\ncircular like those of the planets. It was then recog-\\nnized as a new member of the planetary system, a con-\\nclusion which has been justified by all succeeding ob-\\nservations.\\nThe satellites of Uranus are exceedingly minute ob-\\njects, and visible only to the most powerful telescopes.\\nAlthough the discoverer assigned six satellites to this\\nplanet, yet only two of the number have, until quite\\nrecently, been seen by other astronomers. Two more\\nhave of late been added, and an increasing confidence\\nis beginning to be felt that the entire number given by\\nHerschel will be identified. These satellites offer re-\\nmarkable, and indeed quite unexpected and unexampled\\npeculiarities. Contrary to the unbroken analogy of the\\nwhole planetary system, the planes of their orbits are\\nnearly perpendicular to the ecliptic, being inclined no\\nless than 78\u00c2\u00b0 58 to that plane, and in these orbits their\\nmotions are retrograde that is, instead of advancing\\nfrom west to east around their primary, as is the case\\nwith all the other planets and satellites, they move in\\nthe opposite direction. With this exception, all the\\nmotions of the planets, whether around their own axes,\\nor around the sun, are from west to east. The sun, him-\\nhow many satellites is Uranus attended What is said of their\\nminuteness? What remarkable peculiarities have they? In\\nwhat direction are the motions of all the bodies in the solar\\nsystem What does this fact indicate with respect to their origin", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0222.jp2"}, "219": {"fulltext": "NEPTUNE. 203\\nself, turns on his axis from west to east all the primary\\nplanets revolve around the sun from west to east their\\nrevolutions on their own axes are also in the same direc-\\ntion; all the secondaries, with the single exception\\nabove mentioned, move about their primaries from west\\nto east and, finally, such of the secondaries as have\\nbeen discovered to have a diurnal revolution, follow the\\nsame course. Such uniformity among so many motions,\\ncould have resulted only from forces impressed upon\\nthem by the same omnipotent hand and few things in\\nthe creation more distinctly proclaim that God made\\nthe world.\\n258. Neptune is (so far as is known) the last planet\\nof the series, being removed from the sun to the im-\\nmense distance of nearly 3000 millions of miles. Its\\ndiameter is a little less than that of Uranus, being\\n31,000 miles. It is nearly 60 times as large as the earth.\\nIt takes 164^ years to go round the sun, or about twice\\nas long as Uranus.\\nThe discovery of this planet (so late as the year 1846)\\nwas the most remarkable ever made in astronomy. Al-\\nthough a comparatively large planet, yet it is so far\\nfrom us as to be wholly invisible to the naked eye; and\\nyet its existence, the place among the stars where it lay\\nhidden, and various other particulars respecting it, were\\ndetermined by Leverrier, a distinguished French astron-\\nomer, before it was actually seen. Indeed, he directed,\\nfrom the result of his calculations, to what spot in the\\nstarry heavens the telescope must be pointed in order to\\nsee it, and thus it was found. This wonderful result was\\nreached in the following manner: It had been observed\\nthat some unknown cause disturbed the motions of Ura-\\nnus, which led astronomers to suspect the existence of a\\nplanet outside of it. The problem then was to find a\\nplanet so situated, and of such a size, as would produce\\nthe effect in question. The principle of gravitation would\\nlead to an estimate of the nature, duration, and amount of\\nthe disturbing force, and this would reveal the position", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0223.jp2"}, "220": {"fulltext": "204 THE PLANETS.\\nand magnitude of the body. To make the estimates so\\naccurately as to be able to point the telescope among the\\nstars to the precise point where the hidden body lay,\\nrequired great genius and great skill in mathematical\\ncalculations. The success that crowned the undertaking\\nshowed that these qualifications were possessed in the\\nhighest degree by the discoverer, and at the same time\\ndisplayed the wonderful reach of the principle of uni-\\nversal gravitation, as well as the boundless resources of\\nthe higher mathematics.\\nTHE NEW PLANETS, OR ASTEKOIDS.\\n259. The commencement of the present century was\\nrendered memorable in the annals of astronomy, by- the\\ndiscovery of four new planets between Mars and Jupiter.\\nKepler, from some analogy which he found to subsist\\namong the distances of the planets from the sun, had\\nlong before suspected the existence of one at this dis-\\ntance and his conjecture was rendered more probable\\nby the discovery of Uranus, which follows the analogy\\nof the other planets. So strongly, indeed, were astrono-\\nmers impressed with the idea that a planet would be\\nfound between Mars and Jupiter, that, in the hope of\\ndiscovering it, an association was formed on the conti-\\nnent of Europe of twenty-four observers, who divided\\nthe sky into as many zones, one of which was allotted\\nto each member of the association. The discovery of\\nthe first of these bodies was however made accidentally\\nby Piazzi, an astronomer of Palermo, on the first of Jan-\\nuary, 1801. It was shortly afterwards lost sight of on\\naccount of its proximity to the sun, and was not seen\\nagain until the close of the year, when it was rediscov-\\nered in Germany. Piazzi called it Ceres, in honor of\\nthe tutelary goddess of Sicily; and her emblem, the\\nhas been adopted as its appropriate symbol.\\n258. Neptune. State his distance from the sun diameter\\nperiodic time. Relate the historv of his discovery.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0224.jp2"}, "221": {"fulltext": "NEW PLANETS. 205\\nThe difficulty of finding Ceres induced Dr. Olbers, of\\nBremen, to examine with particular care all the small\\nstars that lie near her path, as seen from the earth and\\nwhile prosecuting these observations, in March, 1802, he\\ndiscovered another similar body, very nearly at the same\\ndistance from the sun, and resembling the former in\\nmany other particulars. The discoverer gave to this\\nsecond planet the name of Pallas, choosing for its symbol\\nthe lance the characteristic of Minerva.\\n260. The most surprising circumstance connected\\nwith the discovery of Pallas, was the existence of two\\nplanets at nearly the same distance from the sun, and\\napparently having a common node. On account of this\\nsingularity, Dr. Olbers was led to conjecture that Ceres\\nand Pallas are only fragments of a larger planet, which\\nhad formerly circulated at the same distance, and been\\nshattered by some internal convulsion. The hypothesis\\nsuggested the probability that there might be other frag-\\nments, whose orbits, however they might differ in ec-\\ncentricity and inclination, might be expected to cross\\nthe ecliptic at a common point, or to have the same node.\\nDr. Olbers, therefore, proposed to examine carefully\\nevery month the two opposite parts of the heavens in\\nwhich the orbits of Ceres and Pallas intersect one an-\\nother, with a view to the discovery of other planets,\\nwhich might be sought for in those parts with greater\\nchance of success than in a wider zone, embracing the\\nentire limits of these orbits. Accordingly, in 1804, near\\none of the nodes of Ceres and Pallas, a third planet was\\ndiscovered. This was called Juno, and the character\\nwas adopted for its symbol, representing the starry\\nsceptre of the queen of Olympus. Pursuing the same\\n259. Name the New Planets. When were they discovered\\nWhat had been conjectured previous to their discovery? Who\\ndiscovered the first What is its name How was Pallas dis-\\ncovered\\n18", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0225.jp2"}, "222": {"fulltext": "206 THE PLANETS.\\nresearches, in 1807, a fourth planet was discovered, to\\nwhich was given the name of Vesta, and for its symbol\\nthe character was chosen an altar surmounted with\\na censer holding the sacred fire.\\nSince 1845 to the present time, (Nov. 1854,) no fewer\\nthan 29 more Asteroids have been discovered, making\\nthe entire number at present 33. Their names are Ceres,\\nPallas, Juno, and Yesta; Astrea, Hebe, Iris, Flora,\\nMetis, Hygeia, Parthenope, Victoria, Egeria, Irene,\\nEunomia, Psyche, Thetis, Melpomene, Fortuna, Massa-\\nlia, Lutetia, Calliope, Thalia, Themis, Phocea, Proser-\\npina, Euterpe, Bellona, Amphytrite, Urania, Euphro-\\nsyne, Pomona, Polymnia.\\n261. The average distance of these bodies from the\\nsun is 261,000,000 miles and it is remarkable that their\\norbits are very near together. Taking the distance of\\nthe earth from the sun for unity, their respective dis-\\ntances are 2.77, 2.77, 2.67, 2.37.\\nAs they are found to be governed, like the other mem-\\nbers of the solar system, by Kepler s law, that regulates\\nthe distances and times of revolution, their periodical\\ntimes are of course pretty nearly equal, averaging about\\n4i years.\\nIn respect to the inclination of their orbits, there is\\nconsiderable diversity. The orbit of Yesta is inclined\\nto the ecliptic only about 7\u00c2\u00b0, while that of Pallas is more\\nthan 34\u00c2\u00b0. They all therefore have a higher inclination\\nthan the orbits of the old planets, and of course make\\nexcursions from the ecliptic beyond the limits of the\\nZodiac.\\nThe eccentricity of their orbits is also, in general,\\ngreater than that of the old planets and the eccentrici-\\n260. How do Ceres and Pallas compare in distance from the\\nsun and the place of their nodes What hypothesis did Olbers\\nadopt State the circumstances connected with the discovery of\\nJuno and Yesta. What additional asteroids have been discovered\\nsince 3 845", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0226.jp2"}, "223": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 207\\nties of the orbits of Pallas and Juno exceed that of the\\norbit of Mercury.\\nTheir small size constitutes one of their most remark-\\nable peculiarities. The difficulty of estimating the ap-\\nparent diameters of bodies at once so very small and so\\nfar off, would lead us to expect different results in the\\nactual estimates. Accordingly, while Dr. Herschel es-\\ntimates the diameter of Pallas at only 80 miles, Schroe-\\nter places it as high as 2,000 miles, or about the size of\\nthe moon. The volume of Yesta is estimated at only\\none fifteen thousandth part of the earth s, and her sur-\\nface is only about equal to that of the kingdom of Spain.\\nThese little bodies are surrounded by atmospheres of\\ngreat extent, some of which are uncommonly luminous,\\nand others appear to consist of nebulous or vapory mat-\\nter. These planets in general shine with a more vivid\\nlight than might be expected from their great distance\\nand diminutive size.\\nCHAPTER IX.\\nMOTIONS OF THE PLANETARY SYSTEM QUANTITY OF MAT-\\nTER IN THE SUN AND PLANETS STABILITY OF THE SO-\\nLAR SYSTEM.\\n262. We have waited until the learner may be sup-\\nposed to be familiar with the contemplation of the heav-\\nenly bodies, individually, before inviting his attention to\\na systematic view of the planets, and of their motions\\naround the sun. The time has now arrived for entering\\nmore advantageously upon this subject than could have\\nbeen done at an earlier period.\\n261. What is the average distance of the New Planets from\\nthe sun How do these orbits lie with respect to each other\\nAre they subject to Kepler s third law What is their average\\nperiodical time What is said of the inclination of their orbits\\nAlso, of the eccentricity What is their size", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0227.jp2"}, "224": {"fulltext": "208 THE PLANETS.\\nThere are two methods of arriving at a knowledge of\\nthe motions of the heavenly bodies. One is to begin\\nwith the apparent, and from these to deduce the real\\nmotions the other is, to begin with considering things\\nas they really are in nature, and then to inquire why\\nthey appear as they do. The latter of these methods is\\nby far the more eligible it is much easier than the\\nother, and proceeding from the less difficult to that which\\nis more difficult, from motions that are very simple to\\nsuch as are complicated, it finally puts the learner in\\npossession of the whole machinery of the heavens. We\\nshall, in the first place, therefore, endeavor to introduce\\nthe learner to an acquaintance with the simplest motions\\nof the planetary system, and afterwards to conduct him\\ngradually through such as are more complicated and\\ndifficult.\\n263. Let us first of all endeavor to acquire an adequate\\nidea of absolute space, such as existed before the crea-\\ntion of the world. We shall find it no easy matter to\\nform a correct notion of infinite space but let us fix our\\nattention, for some time, upon extension alone, devoid\\nof every thing material, without light or life, and with-\\nout bounds. Of such a space we could not predicate\\nthe ideas of up or down, east, west, north, or south, but\\nall reference to our own horizon (which habit is the most\\ndifficult of all to eradicate from the mind) must be com-\\npletely set aside. Into such a void we would introduce\\nthe Sun. We would contemplate this body alone, in\\nthe midst of boundless space, and continue to fix the at-\\ntention upon this subject, until we had fully settled its\\nrelations to the surrounding void. The ideas of up and\\ndown would now present themselves, but as yet there\\nwould be nothing to suggest any notion of the cardinal\\n262. What are the two methods of studying the motions of\\nthe heavenly bodies Which method is best What motions\\nwill be first considered", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0228.jp2"}, "225": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 209\\npoints. We suppose ourselves next to be placed on the\\nsurface of the sun, and the firmament of stars to be\\nlighted np. The slow revolution of the sun on his axis,\\nwould be indicated by a corresponding movement of\\nthe stars in the opposite direction; and in a period equal\\nto more than 25 of our days, the spectator would see\\nthe heavens perform a complete revolution around the\\nsun, as he now sees them revolve around the earth once\\nin 21 hours. The point of the firmament where no mo-\\ntion appeared, would indicate the position of one of the\\npoles, which being called North, the other cardinal\\npoints would be immediately suggested.\\nThus prepared, we may now enter upon the consider-\\nation of the planetary motions.\\n264:. Standing on the sun, we see all the planets mo-\\nving slowly around the celestial sphere, nearly in the\\nsame great highway, and in the same direction from\\nwest to east. They move, however, with very unequal\\nvelocities. Mercury makes very perceptible progress\\nfrom night to night, like the moon revolving about the\\nearth, his daily progress eastward being one third as\\ngreat as that of the moon, since he completes his entire\\nrevolution in about three months.. If we watch the\\ncourse of this planet from night to night, we observe it,\\nin its revolution, to cross the ecliptic in two opposite\\npoints of the heavens, and wander about 7\u00c2\u00b0 from that\\nplane at its greatest distance from it. Knowing the po-\\nsition of the orbit of Mercury with respect to the ecliptic,\\nwe may now, in imagination, represent that orbit by a\\ngreat circle passing through the center of the planet and\\nthe center of the sun, and cutting the plane of the eclip-\\ntic in two opposite points at an angle of 7\u00c2\u00b0. We may\\n263. How can we form a correct idea of absolute space?\\nWhat can we predicate of such a space If the sun were placed\\nin such a void, what new ideas would present themselves How\\nshould we get a knowledge of the cardinal points\\n18*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0229.jp2"}, "226": {"fulltext": "210 THE PLANETS.\\nimagine the intersection of these two great circles with\\nthe celestial vault to be marked out in plain and palpa-\\nble lines on the face of the sky but we must bear in\\nmind that these orbits are mere mathematical planes,\\nhaving no permanent existence in nature, any more than\\nthe path of an eagle flying through the sky and if we\\nconceive of their orbits marked on the celestial vault,\\nwe must be careful to attach to the representation the\\nsame notion as to a thread or wire, carried round to\\ntrace out the course pursued by a horse in a race-ground.*\\nThe planes of both the ecliptic and the orbit of Mer-\\ncury, may be conceived of as indefinitely extended to a\\ngreat distance until they meet the sphere of the stars\\nbut the lines which the earth and Mercury describe in\\nthose planes, that is, their orbits, may be conceived of as\\ncomparatively near to the sun. Could we now for a\\nmoment be permitted to imagine that the planes of the\\necliptic, and of the orbit of Mercury, were made of thin\\nplates of glass, and that the paths of the respective plan-\\nets were marked out on their planes in distinct lines, we\\nshould perceive the orbit of the earth to be almost a per-\\nfect circle, while that of Mercury would appear distinctly\\nelliptical. But having once made use of a palpable sur-\\nface and visible lines to aid us in giving position and\\n264. Where must the spectator be placed in order to see the\\nreal motions of the planets? How would the motions of the\\nseveral planets appear from this station? State the particular\\nmovements of Mercury. How may we imagine the ecliptic and\\nthe orbit of Mercury to be represented on the sky How shall\\nwe conceive of the planes of these orbits as distinguished from\\nthe orbit itself?\\nIt would seem superfluous to caution the reader on so plain a point,\\ndid not the experience of the instructor constantly show that young\\nlearners, from the habit of seeing the celestial motions represented in\\norreries and diagrams, almost always fall into the absurd notion of con-\\nsidering the orbits of the planets as having a distinct and independent\\nexistence.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0230.jp2"}, "227": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 211\\nfigure to the planetary orbits, let us now throw aside\\nthese devices, and hereafter conceive of these planes\\nand orbits as they are in nature, and learn to refer a\\nbody to a mere mathematical plane, and to trace its\\npath in that plane through absolute space.\\n265. A clear understanding of the motions of Mer-\\ncury and of the relation of its orbit to the plane of the\\necliptic, will render it easy to understand the same -par-\\nticulars in regard to each of the other planets. Standing\\non the sun, we should see each of the planets pursuing a\\nsimilar course to that of Mercury, all moving from west\\nto east, with motions differing from each other chiefly\\nin two respects, namely, in their velocities, and in the\\ndistances to which they ever recede from the ecliptic.\\nThe earth revolves about the sun very much like Ve-\\nnus, and to a spectator on the sun, the motions of these\\ntwo planets would exhibit much the same appearances.\\nWe have supposed the observer to select the plane of\\nthe earth s orbit as his standard of reference, and to see\\nhow each of the other orbits is related to it but such a\\nselection of the ecliptic is entirely arbitrary the spec-\\ntator on the sun, who views the motions of the planets\\nas they actually exist in nature, would make no such\\ndistinction between the different orbits, but merely in-\\nquire how they were mutually related to each other.\\nTaking, however, the ecliptic as the plane to which all\\nthe others are referred, we do not, as in the case of the\\nother planets, inquire how its plane is inclined, nor\\nwhat are its nodes, since it has neither inclination nor\\nnode.\\n266. The attempt to exhibit the motions of the solar\\nsystem, and the positions of the planetary orbits by\\n265. If we stood on the sun, how should we see each of the\\nplanets revolve Why is the earth s orbit selected as the stan-\\ndard of reference Would the spectator on the sun make any\\nsuch distinction", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0231.jp2"}, "228": {"fulltext": "212 THE PLANETS.\\nmeans of diagrams, or even orreries, is usually a failure.\\nThe student who relies exclusively on such aids as these,\\nwill acquire ideas on this subject that are both inade-\\nquate and erroneous. They may aid reflection, but can\\nnever supply its place. The impossibility of represent-\\ning things in their just proportions will be evident wdien\\nwe reflect, that to do this, if, in an orrery, we make\\nMercury as large as a cherry, we should require to re-\\npresent the sun by a globe six feet in diameter. If w T e\\npreserve the same proportions in regard to distance, we\\nmust place Mercury 250 feet, and Neptune more than\\nfive miles from the sun. The mind of the student of\\nastronomy must, therefore, raise itself from such imper-\\nfect representations of celestial phenomena as are afford-\\ned by artificial mechanism, and, transferring his contem-\\nplations to the celestial regions themselves, he must con-\\nceive of the sun and planets as bodies that bear an in-\\nsignificant ratio to the immense spaces in which they\\ncirculate, resembling more a few little birds flying in\\nthe open sky, than they do the crowded machinery of\\nan orrery.\\n267. Having acquired as correct an idea as we are\\nable of the planetary system, and of the positions of the\\norbits with respect to the ecliptic, let us next inquire\\ninto the nature and causes of the apparent motions.\\nThe apparent motions of the planets are exceedingly\\nunlike the real motions, a fact which is owing to two\\ncauses first, we mew them out of the center of their Dr-\\noits secondly, we are ourselves in motion. From the\\nfirst cause, the apparent places of the planets are greatly\\nchanged by perspective and from the second cause,\\nw j e attribute to the planets changes of place which arise\\nfrom our own motions, of which we are unconscious.\\n266. What is said of the attempt to represent the positions\\nand motions of the solar system by diagrams and orreries Give\\nexamples.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0232.jp2"}, "229": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 213\\nThe situation of a heavenly body as seen from the\\ncenter of the sim is called its heliocentric place; as seen\\nfrom the center of the earth, its geocentric place. The\\ngeocentric motions of the planets must, according to\\nwhat has just been said, be far more irregular and com-\\nplicated than the heliocentric.\\n268. The apparent motions of the Inferior Planets as\\nseen from the earth, have been already explained in ar-\\nticles 216 and 217 from which it appeared, that Mer-\\ncury and Yenus move backwards and forwards across\\nthe sun, the former never being seen farther than 29\u00c2\u00b0,\\nand the latter never more than 47\u00c2\u00b0 from that luminary.\\nIt was also shown that while passing from the greatest\\nelongation on one side to the greatest elongation on the\\nother side, through the superior conjunction, the appa-\\nrent motions of these planets are accelerated by the mo-\\ntion of the earth but that while moving through the\\ninferior conjunction, at which time their motions are\\nretrograde, they are apparently retarded by the earth s\\nmotion. Let us now see what are the geocentric mo-\\ntions of the Superior Planets.\\n269. Let A, B, C, (Fig. 47), represent the earth in\\ndifferent positions in its orbit, and M a superior planet\\nas Mars, and NR, an arc of the concave sphere of the\\nheavens. First, suppose the planet to remain at rest in\\nM, and let us see what apparent motions it will receive\\nfrom the real motions of the earth. When the earth is\\nat B, it will see the planet in the heavens at N and as\\nthe earth moves successively through C, D, E, F, the\\nplanet will appear to move through O, P, Q, R. B and\\n267. Are the apparent motions of the planets like the real\\nmotions What- makes them different How does each cause\\noperate What is the heliocentric place, and what the geocen-\\ntric place of a planet\\n268. Describe the apparent motions of Mercury and Venus\\nfrom figure 40.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0233.jp2"}, "230": {"fulltext": "214\\nTHE PLANETS.\\nF are the two points of greatest elongation of the earth\\nfrom the sun as seen from the planet hence between\\nthese two points, while passing through the part of her\\norbit most remote from the planet, (when the planet is\\nseen in superior conjunction,) the earth by her own mo-\\nFig. 47.\\ntion gives an apparent motion to the planet in the order\\nof the signs that is, the apparent motion given by the\\nearth is direct. But in passing from F to B through A,\\nwhen the planet is seen in opposition, the apparent mo-\\ntion given to the planet by the earth s motion is from\\nR to S and is therefore retrograde. As the arc described\\n269. Describe the motions of the Superior Planets from fig-\\nure 47. The planet remaining at rest, what apparent motions\\nwill the motion of the earth impart to it, when in opposition\\nWhat when in superior conjunction", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0234.jp2"}, "231": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 215\\nby the earth, when the motion is direct, is much greater\\nthan when the motion is retrograde, while the apparent\\narc of the heavens described by the planet from N to E\\nin the one case, and from K to N in the other, is the same\\nin both cases, the retrograde motion is much swifter\\nthan the direct, being performed in much less time.\\n270. But the superior planet is not in fact at rest, as\\nwe have supposed, but is all the while moving east-\\nward, though with a slower motion than the earth. In-\\ndeed, with respect to the remotest planets, as Saturn and\\nUranus, the forward motion is so exceedingly slow that\\nthe above representation is nearly true for a single year.\\nStill, the effect of the real motions of all the superior\\nplanets eastward, is to increase the direct apparent mo-\\ntion communicated by the earth and to diminish the\\nretrograde motion.\\nIf Mars stood still while the earth went round the\\nsun, then a second opposition as at A, would occur at\\nthe end of one year from the first but while the earth\\nis performing this circuit, Mars is also moving the same\\nway, more than half as fast, so that when the earth re-\\nturns to A, the planet has already performed more than\\nhalf the same circuit, and will have completed its whole\\nrevolution before the earth comes up with it. Indeed,\\nMars, after having been once seen in opposition, does\\nnot come into opposition again until after two years and\\nfifty days. And since the planet is then comparatively\\nvery near to us, and appears very large and bright, rising\\nunexpectedly about the time the sun sets, he surprises\\nthe world as though it were some new celestial body.\\nBut on account of the slow progress of Saturn and Ura-\\nnus, we find, after having performed one circuit around\\nthe sun, that they are but little advanced beyond where\\nwe left them at. the last opposition. The time between\\none opposition of Saturn and another is only a year and\\nthirteen days.\\nIt appears, therefore, that the superior planets steadily\\npursue their course around the sun, but that their appa-", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0235.jp2"}, "232": {"fulltext": "216 THE PLANETS.\\nrent retrograde motion when in opposition is occasioned\\nby our passing by them with a swifter motion, like the\\napparent backward motion of a vessel when we over-\\ntake it and pass rapidly by it in a steamboat.\\nQUANTITY OF MATTER IN THE SUN AND PLANETS.\\n271. It would seem at first view very improbable that\\nan inhabitant of this earth should be able to weigh the\\nsun and planets, and estimate the exact quantity of mat-\\nter which they severally contain. But the principles of\\nUniversal Gravitation conduct us to this result, by a\\nprocess remarkable for its simplicity. By comparing the\\nrelations of a few elements that are known to us, we\\nascend to the knowledge of such as appeared to be be-\\nyond the pale of human investigation. We learn the\\nquantity of matter in a body from the force of gravity it\\nexerts, and this force is estimated by its effects. Hence\\nworlds are weighed with as much ease as a pebble or an\\narticle of merchandise.\\n272. The sun contains about 355,000 times as much\\nmatter as the earth, and 800 times as much matter as\\nall the planets. This, however, is owing rather to its\\ngreat size than to the specific gravity of its materials,\\nfor the density of the sun is only one fourth as great as\\nthat of the earth. The earth is nearly 5 times as heavy\\nas water, but the sun is only a little heavier than that\\nfluid. The planets near the sun are in general more\\ndense than those more remote Mercury being as heavy\\n270. How does the real motion of the planet modify the fore-\\ngoing results How in respect to the remotest planets, as Ura-\\nnus, and how in respect to a nearer planet, as Mars How often\\nis Mars in opposition What is his appearance then\\n271. What is said of the apparent difficulty of weighing the\\nsun and planets What great principles lead us to this result\\nHow do we learn the quantity of matter in the bodies of the\\nsolar system", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0236.jp2"}, "233": {"fulltext": "STABILITY OF THE SOLAR SYSTEM. 21*7\\nas iron ore, while Saturn is as light as cork. The de-\\ncrease in density, however, is not entirely regular, since\\nVenus is a little lighter than the earth, while Jupiter is\\nheavier than Mars, and Uranus than Saturn.\\nSTABILITY OF THE SOLAR SYSTEM.\\n273. The perturbations or irregularities occasioned in\\nthe motions of the planets by their action on each other,\\nare very numerous, since every body in the system ex-\\nerts an attraction on every other, in conformity with the\\nlaw of Universal Gravitation. Yenus and Mars, ap-\\nproaching as they do at times comparatively near to the\\nEarth, sensibly disturb its motions and Jupiter and\\nSaturn, although very far asunder, still, in consequence\\nof their great masses, exert on each other, when on the\\nsame side of the heavens especially, a decided influence.\\nMoreover the Sun, by his unequal action on the several\\nplanets, in consequence of the peculiar figure of each,\\nproduces various irregularities in their motions. These\\nperturbations are divided into periodical and secular:\\nperiodical, when completed in comparatively short\\nperiods, as those for example which undergo all their\\nchanges during one revolution of the planet and secu-\\nlar, when completed only in very long periods, as those\\nwhich affect the form and inclination of the orbits.\\n274. If the only bodies in the system were a central\\n272. How much more matter does the sun contain than the\\nearth? How much more than all the planets? What is the\\ndensity of the sun compared with that of the earth How much\\nheavier is the earth than water? How much heavier is the sun\\nthan water Which of the planets have the greatest density\\nHow heavy is Mercury How heavy is Saturn\\n273. To what extent do perturbations exist among the planets\\nWhat is their cause? What planets in particular disturb the\\nmotions of the earth In what way does the sun disturb the sev-\\neral planets State the distinction between periodical and secu-\\nlar perturbations.\\n19", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0237.jp2"}, "234": {"fulltext": "218 THE PLANETS.\\nbody like the Sun, and a revolving body like Venus,\\nthen when the planet was once pnt in motion with such\\na projectile force as to make it describe an ellipse, it\\nwould forever continue to describe the same figure with-\\nout the least variation but now introduce a third body\\nso near as to exert on it a decided attraction, and its\\nmotions no longer retain their simplicity, but become\\ncomplicated by the conflicting influences of the two at-\\ntracting bodies. The Sun, however, in consequence of\\nits mass, which is eight hundred times as great as that\\nof all the planets, and of course vastly greater than any\\none of them, exerts a force so much superior to that of\\nany or all the other disturbing bodies, that the elliptical\\nfigure of the orbit is nearly maintained, and a mere ap-\\nproximation to the place of the planet is obtained, by\\nneglecting all those minor forces, and simply contem-\\nplating it as revolving in an elliptical orbit. Still it is\\ne c sential, in order to find the exact place of a planet at\\nany given time, that all these irregularities, minute as\\nthey may be, should be carefully summed up, and their\\nresultant applied to the elliptical motion. To inves-\\ntigate these perturbations, to estimate their precise\\namount, and to register them in tables, for the use of\\nthe practical astronomer, have constituted a large part\\nof the labors of modern astronomy. The knowledge\\ngained by astronomers of the planetary motions, con-\\nsidering the very numerous irregularities, both perio-\\ndical and secular, to which they are subject, is truly\\nwonderful. The motion of Jupiter, for instance, is so\\nperfectly calculated, that astronomers have computed,\\nten. years beforehand, the time at which it will pass\\nthe meridian of different places, and the result does not\\nvary half a second from the prediction. The more ob-\\nvious irregularities have been detected by observation\\nthe more minute, by following out the consequences of\\nuniversal gravitation. Even those at first revealed to\\nthe instruments of the astronomer, have been confirmed\\nand estimated with greater accuracy, by the same far-\\nreaching principle and many of the irregularities have", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0238.jp2"}, "235": {"fulltext": "STABILITY OF THE SOLAR SI STEM. 219\\nbeen first brought to light by this theory, which had\\nbefore eluded observation although when once pointed\\nout as a result of the principle of gravitation, careful\\ninstrumental measurements have confirmed them, ex-\\ncept in cases where the force was too minute to be\\nreached by the most refined observation. Periodical\\nperturbations among the bodies of the solar system, may\\nbe compared to the regular flux and reflux of the tides,\\nby which the ocean daily oscillates about its mean level\\nwhile secular perturbations would resemble any slow\\nchanges of level, which, accumulating from time to\\ntime, might finally become obvious to measures of the\\ndepth of the ocean, as recorded from age to age. As an\\nexample of the extreme minuteness of some of these\\nsecular perturbations, we may instance the changes in\\nthe eccentricity of the Earth s orbit. The entire eccen-\\ntricity is so small, that the figure when drawn on paper\\nin just proportions, can scarcely be distinguished from\\na circle, the focus of the ellipse being distant from the\\ncenter only about V part of the semi-major axis; but\\nthe change of eccentricity in a century is only one\\ntwenty-five thousandth part of this small quantity.\\n275. But although the secular inequalities of the\\nplanetary motions are exceedingly slow, yet may they\\nnot in time accumulate so as to derange the whole sys-\\ntem and do they not at least indicate that the system\\n274. If there were only a central body, as the Sun, and revolv-\\ning body, as Yenus, how would the planet move Consequence\\nof introducing a third body What effect has the greater mass\\nof the sun in preserving the stability of the planetary motions\\nAVhat is necessary in order to find the exact place of a planet\\nWhat has constituted a large part of the labors of modern astro-\\nnomers What is said of the accuracy to which astronomical\\ncalculations are brought How were these irregularities detect-\\ned To what are periodical and secular perturbations respective-\\nly compared What is said of the change of eccentricity in the\\nearth s orbit", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0239.jp2"}, "236": {"fulltext": "220 THE PLANETS.\\ncarries within it the seeds of its own dissolution So\\nfar is this from being the case, that the stability of the\\nsolar system is a fact established on the most unques-\\ntionable evidence. Even a superficial view of the sys-\\ntem, will convince us that care has been bestowed on\\nthis point by several obvious arrangements. One is,\\nthat the planets have severally so small masses com-\\npared with the sun, as to interfere but little with his\\nsupremacy over the planetary motions. Another is,\\nthat the planets are placed at such great distances from\\neach other a distance which is greater among the\\nlarger bodies, as Jupiter and Saturn, than among the\\nsmaller, as the Earth and Yenus and another still, that\\nthe orbits are less eccentric when the masses are greater,\\nby which provision they are always maintained at a\\nremote distance from the sun. Were the orbit of Jupi-\\nter as eccentric as that of Mars, he would approach so\\nnear the earth at his perihelion, as greatly to endanger\\nits stability. The major axes of the planetary orbits\\nremain from year to year constantly of the same length,\\nby which means the periodic times (which are always\\nin a fixed mathematical ratio to the major axes), remain\\ninvariable, else we should have years of different lengths\\nbut the nicest observations can detect no difference in\\nthe times in which the planets severally perform their\\nrevolutions about the sun.\\n276. It is worthy of remark, as evincing the super-\\nintending care of Providence, that those perturbations,\\nsuch as changes in the place of the perihelion, affecting\\na change of direction in space of the major axis of the\\norbit, or in the place of the nodes, which, by accumu-\\nlating do not endanger the stability of the system, pro-\\nceed onward through the entire circuit of the heavens,\\nwhile perturbations which, by indefinite accumulation,\\n275. What planets have orbits of small eccentricity? How\\ndoes this fact contribute to the stability of the system State\\nthe conditions necessary to the stability of the system.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0240.jp2"}, "237": {"fulltext": "COMETS. 221\\nwould bring ruin to the system, such as variations of\\neccentricity and of inclination, are not progressive but\\noscillatory, waving to and fro within the limits of entire\\nsafety. These ends would not have been secured, had\\nthe system been constructed differently from what it is.\\nNumerous conditions must concur in order to produce\\nthese results the mass of the sun must have greatly ex-\\nceeded that of any or all of the planets the eccentrici-\\nties of the orbits, and their inclinations, must have been\\nsmall and the planets must all have revolved around\\nthe sun in the same direction. So perfectly, indeed, are\\nthe planets adjusted to each other, and so beautiful and\\nharmonious an order pervades the solar system, that the\\nvelocities, distances, periodic times, and force of attrac-\\ntion towards the slid, of the entire collection of bodies,\\nconstitute a series in geometrical progression of which\\nthe first term is the ratio. Thus the comparative dis-\\ntance is the square of the velocity, the periodic time is\\nthe cube, and the attraction towards the sun is the biquad-\\nrate. If, for example, we observe that a new-discovered\\nbody moves 6 times as slow as the earth, we know at\\nonce that it is 36 times as far from the sun, revolves in\\nits orbit in 216 years, and is attracted towards the sun\\n1296 times less than the earth is and if any one of these\\nparticulars be given, all the others may in like manner\\nbe readily found.\\nCHAPTER X.\\nOF COMETS AND METEORIC SHOWERS.\\n277. A Comet, when perfectly formed, consists of\\nthree parts, the ISTucleus, the Envelope, and the Tail.\\nThe Nucleus^ or body of the comet, is generally distin-\\nguished by its forming a bright point in the center of\\nthe head, conveying the idea of a solid, or at least of a\\nvery dense portion of matter. Though it is usually ex-\\n19*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0241.jp2"}, "238": {"fulltext": "222 co me is.\\nceedingly small when compared with the other parts of\\nthe comet, yet it sometimes subtends an angle capable\\nof being measured by the telescope. The Envelope\\n(sometimes called the coma) is a dense nebulous cover-\\ning, which frequently renders the edge of the nucleus\\nso indistinct, that it is extremely difficult to ascertain its\\ndiameter with any degree of precision. Many comets\\nhave no nucleus, but present only a nebulous mass ex-\\ntremely attenuated on the confines, but gradually in-\\ncreasing in density towards the center. Indeed, there\\nis a regular gradation of comets, from such as are com-\\nposed merely of a gaseous or vapory medium, to those\\nwhich have a well-defined nucleus. In some instances\\non record, astronomers have detected with their tele-\\nscopes small stars through the densest part of a comet.\\nThe Tail is regarded as an expansion or prolongation\\nof the coma and presenting, as it sometimes does, a\\ntrain of appalling magnitude, and of a pale, disastrous\\nlight, it confers on this class of bodies their peculiar\\ncelebrity.\\nFig. 48.\\nThese several parts are exhibited in figure 48, which\\nrepresents the appearance of the comet of 1680.\\n2*1*1. Of what three parts does a comet consist Describe each.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0242.jp2"}, "239": {"fulltext": "COMETS, 223\\n278. The number of comets belonging to the solar\\nsystem, is probably very great. Many, no doubt, escape\\nobservation by being above the horizon in the daytime.\\nSeneca mentions, that during a total eclipse of the sun,\\nwhich happened 60 years before the Christian era, a\\nlarge and splendid comet suddenly made its appearance,\\nbeing very near the sun. The elements of at least\\n180 comets have been computed, and arranged in a cat-\\nalogue for comparison. Of these, six are particularly\\nremarkable, viz. the comets of 1680, 1770, and 1843;\\nand those which bear the names of ITalley, Encke, and\\nBiela. The comet of 1680 was distinguished not only\\nfor its astonishing size and splendor, but is remarkable\\nfor having been the first comet whose elements were\\ndetermined on the sure basis of mathematics, as was\\ndone by Sir Isaac ]N ewton, it having appeared in his\\ntime. The comet of 1770 is memorable for the changes\\nits orbit has undergone by the action of Jupiter, and for\\nhaving approached very near to the earth. The comet\\nof 1843 was the most remarkable in its appearance of\\nall that have been seen in modern times, having been\\nvisible at noon-day. ITalley s comet (the same which\\nreappeared in 1835) is distinguished as that whose re-\\nturn was first successfully predicted, and whose orbit\\nwas first accurately determined and Biela s and\\nEncke s comets are well known for their short periods\\nof revolution, which subject them frequently to the view\\nof astronomers. Biela s comet, at its return in 1846,\\ndisplayed another remarkable feature a separation into\\ntwo distinct parts. At one time the distance of one nu-\\ncleus from the other, was estimated at 157,000 miles.\\n279. In magnitude and brightness comets exhibit a\\ngreat diversity. History informs us of comets so bright\\n278. What is said of the number of comets How many have\\nbeen arranged in a table Specify the six that are most remark-\\nable. State particulars respecting each.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0243.jp2"}, "240": {"fulltext": "224 COMETS.\\nas to be distinctly visible in the daytime, even at noon\\nand in the brightest sunshine, a fact regarded as almost\\nincredible, until verified in the great comet of 1843.\\nSuch was the comet seen at Rome a little before the\\nassassination of Julius Csesar. The comet of 1680 cover-\\ned an arc of the heavens of 97\u00c2\u00b0, and its length was esti-\\nmated at 123,000,000 miles. That of 1811 had a nucleus\\nof only 428 miles in diameter, but a tail 132,000,000 miles\\nlong. Had it been coiled around the earth like a serpent,\\nit would have reached round more than 5,000 times.\\nOther comets are of exceedingly small dimensions, the\\nnucleus being estimated at only 25 miles and some\\nwhich are destitute of any perceptible nucleus, appear\\nto the largest telescopes, even when nearest to us, only\\nas a small speck of fog, or as a tuft of down. The ma-\\njority of comets can be seen only by the aid of the tel-\\nescope.\\nThe same comet, indeed, has often very different as-\\npects at its different returns. Halley s comet in 1305\\nwas described by the historians of that age, as the comet\\nof terrific magnitude, (cometa horrendm magnitudinis\\nin 1456 its tail reached from the horizon to the zenith,\\nand inspired such terror, that by a decree of the Pope\\nof Rome, public prayers were offered up at noon-day in\\nall the Catholic Churches to deprecate the wrath of\\nheaven, while in 1682, its tail was only 30\u00c2\u00b0 in length,\\nand in 1759 it was visible only to the telescope, until\\nafter it had passed the perihelion. At its recent return\\nin 1835, the greatest length of the tail was about 12\u00c2\u00b0.\\nThese changes in the appearance of the same comet,\\nare partly owing to the different positions of the earth\\nwith respect to them, being sometimes much nearer to\\nthem when they cross its track than at others also one\\n279. What is said of the magnitude and brightness of comets 1\\nWhat was the length of the comet of 1680? Ditto of 1811\\nHas the same comet different aspects at different returns Ex-\\nample in Halley s comet.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0244.jp2"}, "241": {"fulltext": "COMETS. 225\\nspectator so situated as to see the coma at a higher angle\\nof elevation or in a purer sky than another, will see the\\ntrain longer than it appears to another less favorably\\nsituated but the extent of the changes are such as indi-\\ncate also a real change in magnitude and brightness.\\n280. The periods of comets in their revolutions around\\nthe sun are equally various. Encke s comet, which has\\nthe shortest known period, completes its revolution in\\n3^- years, or more accurately, in 1208 days while that\\nof 1811 is estimated to have a period of 3383 years.\\n281. The distances to which different comets recede\\nfrom the sun, are also very various. While Encke s\\ncomet performs its entire revolution within the orbit of\\nJupiter, Halley s comet recedes from the sun to twice\\nthe distance of Uranus, or nearly 3600,000,000 miles.\\nSome comets, indeed, are thought to go to a much\\ngreater distance from the sun than this, while some even\\nare supposed to pass into parabolic or hyperbolic orbits,\\nand never to return.\\n282. Comets shine hy reflecting the light of the sun.\\nIn one or two instances they have exhibited distinct\\nphases, although the nebulous matter with which the\\nnucleus is surrounded, would commonly prevent such\\nphases from being distinctly visible, even when they\\nwould otherwise be apparent. Moreover, certain quali-\\nties of polarized light enable the optician to decide\\nwhether the light of a given body is direct or reflected\\nand M. Arago, of Paris, by experiments of this kind on\\n280. How are the periods of comets What is that of Encke s\\ncomet, and that of the comet of 1811\\n281. How are the distances of comets from the sun Compai e\\nEncke s and Halley s. Do comets always return to the sun\\n282. Do comets shine by direct or by reflected light? Do\\nthey exhibit phases How is it known that their light is reflect-\\ned and not direct light", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0245.jp2"}, "242": {"fulltext": "226 COMETS.\\nthe light of the comet of 1819, ascertained it to be re-\\nflected light.\\n283. The tail of a comet usually increases very much\\nas it approaches the sun and it frequently does not\\nreach its maximum until after the perihelion passage.\\nIn receding from the sun, the tail again contracts, and\\nnearly or quite disappears before the body of the comet\\nis entirely out of sight. The tail is frequently divided\\ninto two portions, the central parts, in the direction of\\nthe axis, being less bright than the marginal parts. In\\n1744, a comet appeared which had six tails, spread out\\nlike a fan.\\nThe tails of comets extend in a direct line from the\\nsun, although more or less curved, like a long quill or\\nfeather, being convex on the side next to the direction\\nin which they are moving, a figure which may result\\nfrom the less velocity of the portions most remote from\\nthe sun. Expansions of the Envelope have also been\\nat times observed on the side next the sun, but these\\nseldom attain any considerable length.\\n284. The quantity of matter in comets is exceedingly\\nsmall. Their tails consist of matter of such tenuity that\\nthe smallest stars are visible through them. They can\\nonly be regarded as great masses of thin vapor, suscep-\\ntible of being penetrated through their whole substance\\nby the sunbeams, and reflecting them alike from their\\ninterior parts and from their surfaces. It appears, per-\\nhaps, incredible that so thin a substance should be visi-\\nble by reflected light, and some astronomers have held\\nthat the matter of comets is self-luminous but it re-\\nquires but very little light to render an object visible\\nin the night, and a light vapor may be visible when\\nilluminated throughout an immense stratum, which\\n283. How are the tails of comets affected by being near the\\nsun How many tails have some comets In what direction is\\nthe tail in respect to the sun", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0246.jp2"}, "243": {"fulltext": "COMETS. 227\\ncould not be seen if spread over the face of the sky like\\na thin cloud. From the extremely small quantity of\\nmatter of these bodies, compared with the vast spaces\\nthey cover, Newton calculated that if all the matter con-\\nstituting the largest tail of a comet, were to be com-\\npressed to the same density with atmospheric air, it\\nwould occupy no more than a cubic inch. This is in-\\ncredible, but still the highest clouds that float in our\\natmosphere, must be looked upon as dense and massive\\nbodies, compared with the filmy and all but spiritual\\ntexture of a comet.\\n285. The small quantity of matter in comets is proved\\nby the fact, that they have sometimes passed very near\\nto some of the planets, without disturbing their motions\\nin any appreciable degree. Thus the comet of 1770, in\\nits way to the sun, got entangled among the satellites of\\nJupiter, and remained near them four months, yet it\\ndid not perceptibly change their motions. The same\\ncomet also came very near the earth so near, that had\\nits mass been equal to that of the earth, it would have\\ncaused the earth to revolve in an orbit so much larger\\nthan at present, as to have increased the length of the\\nyear 2h. 47m. Yet it produced no sensible effect on\\nthe length of the year, and therefore its mass, as is shown\\nby La Place, could not have exceeded ^Vo \u00c2\u00b0f that of\\nthe earth, and might have been less than this to any ex-\\ntent. It may indeed be asked, what proof we have that\\ncomets have any matter, and are not mere reflections of\\nlight. The answer is, that, although they are not able\\nby their own force of attraction to disturb the motions\\nof the planets, yet they are themselves exceedingly dis-\\nturbed by the action of the planets, and in exact con-\\n284. How is the quantity of matter in comets? Of what do\\nthe tails consist Can a substance so thin shine by reflected light\\nWhat opinion had Newton of the extreme tenuity of the material\\nof comets tails?", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0247.jp2"}, "244": {"fulltext": "228 COMETS.\\nformity with the law of universal gravitation. A deli-\\ncate compass may be greatly agitated by the vicinity\\nof a mass of iron, while the iron is not sensibly affected\\nby the attraction of the needle.\\n286. By approaching very near to a large planet, a\\ncomet may have its orbit entirely changed. This fact\\nis strikingly exemplified in the history of the comet of\\n1770. At its appearance in 1770, its orbit was found\\nto be an ellipse, requiring for a complete revolution only\\n5\u00c2\u00a7 years and the wonder was, that it had not been seen\\nbefore, since it was a very large and bright comet. As-\\ntronomers suspected that its path had been changed, and\\nthat it had been recently compelled to move in this short\\nellipse, by the disturbing force of Jupiter and his satel-\\nlites. The French Institute, therefore, offered a high\\nprize for the most complete investigation of the elements\\nof this comet, taking into account any circumstances\\nwhich could possibly have produced an alteration in its\\ncourse. By tracing back the movements of this comet\\nfor some years previous to 1770, it was found that, at\\nthe beginning of 1767, it had entered considerably\\nwithin the sphere of Jupiter s attraction. Calculating\\nthe amount of this attraction from the known proximity\\nof the two bodies, it was found what must have been its\\norbit previous to the time when it became subject to\\nthe disturbing action of Jupiter. The result showed\\nthat it then moved in an ellipse of greater extent, having\\na period of 50 years, and having its perihelion instead\\nits aphelion near Jupiter. It was therefore evident why,\\nas long as it continued to circulate in an orbit so far\\nfrom the center of the system, it was never visible from\\nthe earth. In January, 1767, Jupiter and the comet\\n285. How is the small quantity of matter in comets proved\\nHow was this indicated by the comet of 1770? What did its\\nquantity of matter not exceed as compared with the earth s\\nMay we not infer that they have no matter?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0248.jp2"}, "245": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 229\\nhappened to be very near one another, and as both were\\nmoving in the same direction, and nearly in the same\\nplane, they remained in the neighborhood of each other\\nfor several months, the planet being between the comet\\nand the snn. The consequence was, that the comet s\\norbit was changed into a smaller ellipse, in which its\\nrevolution was accomplished in 5-J- years. But as it was\\napproaching the sun in 1779, it happened again to fall\\nin with Jupiter. It was in the month of June, that the\\nattraction of the planet began to have a sensible effect\\nand it was not until the month of October following,\\nthat they were finally separated.\\nAt the time of their nearest approach, in August, Ju-\\npiter was distant from the comet only T T of its distance\\nfrom the sun, and exerted an attraction upon it 225\\ntimes greater than that of the sun. By reason of this\\npowerful attraction, Jupiter being farther from the sun\\nthan the comet, the latter was drawn out into a new\\norbit, w T hich even at its perihelion came no nearer to\\nthe sun than the planet Ceres. In this third orbit, the\\ncomet requires about 20 years to accomplish its revolu-\\ntion and being at so great a distance from the earth, it\\nis invisible, and will forever remain so, unless, in the\\ncourse of ages, it may undergo new perturbations, and\\nmove again in some smaller orbit as before.\\nORBITS AND MOTIONS OF COMETS.\\n287. The planets, as we have seen (with the excep-\\ntion of the four new ones, which seem to be an inter-\\nmediate class of bodies between planets and comets),\\n286. How may a comet have its orbit changed? How was\\nthe orbit of the comet of 17*70 changed? How was this fact\\nascertained? What action did Jupiter exert upon it in 1767,\\nand again in 1779? How far was Jupiter from the comet at\\nthe time of their nearest approach How many years does it\\nnow require to perform its revolution\\n20", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0249.jp2"}, "246": {"fulltext": "230 COMETS.\\nmove in orbits which are nearly circular, and all very\\nnear to the plane of the ecliptic, and all move in the\\nsame direction, from west to east. But the orbits of\\ncomets are far more eccentric than those of the planets\\nthey are inclined to the ecliptic at various angles, being\\nsometimes even nearly perpendicular to it and the mo-\\ntions of comets are sometimes retrograde.\\n288. The Elements of a comet are five, viz. (1) The\\nperihelion distance (2) longitude of the perihelion\\n(3) longitude of the node (4) inclination of the orbit\\n(5) time of the perihelion passage.\\nThe investigation of these elements is a problem ex-\\ntremely intricate, requiring for its solution, a skilful and\\nlaborious application of the most refined analysis. This\\ndifficulty arises from several circumstances peculiar to\\ncomets. In the first place, from the elongated form of\\nthe orbits which these bodies describe, it is during only\\na very small portion of their course that they are visible\\nfrom the earth, and the observations made in that short\\nperiod cannot afterwards be verified on more convenient\\noccasions whereas in the case of the planets, whose or-\\nbits are nearly circular, and whose movements may be\\nfollowed uninterruptedly throughout a complete revolu-\\ntion, no such impediments to the determination of their\\norbits occur. In the second place, there are many com-\\nets which move in a direction opposite to the order of\\nthe signs in the zodiac, and sometimes nearly perpen-\\ndicular to the plane of the ecliptic so that their appa-\\nrent course through the heavens is rendered extremely\\ncomplicated, on account of the contrary motion of the\\nearth. In the third place, as there may be a multitude\\nof elliptic orbits, whose perihelion distances are equal\\n(see p. 100), it is obvious that, in the case of very eccen-\\ntric orbits, the slightest change in the position of the\\ncurve near the vertex, where alone the comet can be ob-\\n287. How do the orbits of comets differ from those of planets", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0250.jp2"}, "247": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 231\\nserved, must occasion a very sensible difference in the\\nlength of the orbit and therefore, though a small error\\nproduces no perceptible discrepancy between the ob-\\nserved and the calculated course, while the comet re-\\nmains visible from the earth, its effect, when diffused\\nover the whole extent of the orbit, may acquire a most\\nmaterial or even a fatal importance.\\n289. On account of these circumstances, it is found\\nexceedingly difficult to lay down the path which a comet\\nactually follows through the whole system, and least of\\nall, possible to ascertain with accuracy the length of\\nthe major axis of the ellipse, and consequently the peri-\\nodical revolution.* An error of only a few seconds may\\ncause a difference of many hundred years. In this\\nmanner, though Bessel determined the revolution of the\\ncomet of 1769 to be 2089 years, it was found that an\\nerror of no more than 5 in observation, would alter the\\nperiod either to 2678 years, or to 1692. Some astrono-\\nmers, in calculating the orbit of the great comet of 1680,\\nhave found the length of its greater axis 426 times the\\nearth s distance from the sun, and consequently its pe-\\nriod 8792 years whilst others estimate the greater axis\\n430 times the earth s distance, which alters the period\\nto 8916 years. JSTewton and Halley, however, judged\\nthat this comet accomplished its revolution in only\\n570 years.\\n288. What particulars are called the elements of a comet?\\nWhat is said of the difficulty of determining these elements\\nSpecify the several reasons of this difficulty.\\n289. Is it easy to ascertain the major axis of a comet s orbit,\\nand its periodic time What difference would an error of a few\\nseconds occasion? Give examples of this.\\nFor when we know the length of the major axis, we can find the\\nperiodic time by Kepler s law, which applies as well to comets as to\\nplanets.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0251.jp2"}, "248": {"fulltext": "232\\nCOMETS.\\n290. The appearances of the same comet at different\\nperiods of its return are so various, that we can never\\npronounce a given comet to be the same with one that\\nhas appeared before, from any peculiarities in its phy-\\nsical aspect. The identity of a comet with one already\\non record, is determined by the identity of the elements.\\nIt was by this means that H alley first established the\\nidentity of the comet which bears his name, with one\\nthat had appeared at several preceding ages of the world,\\nof which so many particulars were left on record, as to\\nenable him to calculate the elements at each period.\\nThese were as in the following table.\\nTime of appear.\\n1456\\nInclin. of the orbit. Lon. of Node.\\nLon. of Per.\\nPer. Dist.\\nCourse.\\n17\u00c2\u00b0 56\\n48\u00c2\u00b0 30\\n301\u00c2\u00b0 00\\n0.58\\nEetrograde\\n1531\\n17 56\\n49 25\\n301 38\\n0.57\\n1607\\n17 02\\n50 21\\n302 16\\n0.58\\n1682\\n17 42\\n50 48\\n301 36\\n0.58\\nOn comparing these elements, no doubt could be en-\\ntertained that they belonged to one and the same body\\nand since the interval between the successive returns\\nwas seen to be 75 or 76 years, Halley ventured to pre-\\ndict that it would again return in 1758. Accordingly,\\nthe astronomers who lived at that period, looked for its\\nreturn with the greatest interest. It was found, how-\\never, that on its way towards the sun it would pass very\\nnear to Jupiter and Saturn, and by their action on it, it\\nwould be retarded for a long time. Clairaut, a distin-\\nguished French mathematician, undertook the laborious\\ntask of estimating the exact amount of this retardation,\\nand found it to be no less than 618 days, namely, 100\\ndays by the action of Jupiter, and 518 days by that of\\nSaturn. This would delay its appearance until early in\\n290. Can we identify a comet with one that has been seen\\nbefore, by its appearance? How is this identity determined?\\nHow was Halley s comet proved to be the same with one that\\nhad appeared before? How was its return predicted? What\\ncauses alter the periods of its return", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0252.jp2"}, "249": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 233\\nthe year 1759, and Clairaut fixed its arrival at the peri-\\nhelion within a month of April 13th. It came to the\\nperihelion on the 12th of March.\\n291. The return of Halley s comet in 1835, was looked\\nfor with no less interest than in 1759. Several of the\\nmost accurate mathematicians of that age had calculated\\nits elements with inconceivable labor. Their zeal was\\nrewarded by the appearance of the expected visitant at\\nthe time and place assigned it travelled the northern\\nsky, presenting the very appearances, in most respects,\\nthat had been^anticipated and came to its perihelion\\non the 16th of November, within two clays of the time\\npredicted by Pontecoulant, a French mathematician\\nwho had, it appeared, made the most successful calcu-\\nlation.* On its previous return, it was deemed an ex-\\ntraordinary achievement to have brought the prediction\\nwithin a month of the actual time.\\nMany circumstances conspired to render this return\\nof Halley s comet an astronomical event of transcendent\\ninterest. Of all the celestial bodies, its history was the\\nmost remarkable it afforded most triumphant evidence\\nof the truth of the doctrine of universal gravitation, and\\nof course of the received laws of astronomy and it in-\\nspired new confidence in the power of that instrument\\n(the Calculus) by means of which its elements had been\\ninvestigated.\\n292. Encke s comet, by its frequent returns (once in\\n3J years), affords peculiar facilities for ascertaining the\\nlaws of its revolution and it has kept the appointments\\n291. How was the return of Halley s comet in 1835 regarded\\nby astronomers What circumstances conspired to produce this\\nfeeling\\nSee Professor Looinis s Observations on Hallev s Comet. Amer.\\nJour. Science, 30, 209.\\n20*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0253.jp2"}, "250": {"fulltext": "234 COMETS.\\nmade for it with great exactness. On its return in\\n1839 it exhibited to the telescope a globular mass of\\nnebulous matter, resembling fog, and moved towards\\nits perihelion with great rapidity.\\nBut what has made Encke s comet particularly fa-\\nmous, is its having first revealed to us the existence of a\\nResisting Medium in the planetary spaces. It has long\\nbeen a question, whether the earth and planets revolve\\nin a perfect void, or whether a fluid of extreme rarity\\nmay not be diffused through space. A perfect vacuum\\nwas deemed most probable, because no such effects on\\nthe motions of the planets could be detected as indicated\\nthat they encountered a resisting medium. But a feather\\nor a lock of cotton propelled with great velocity, might\\nrender obvious the resistance of a medium which would\\nnot be perceptible in the motions of a cannon ball. Ac-\\ncordingly, Encke s comet is thought to have plainly suf-\\nfered a retardation from encountering a resisting medium\\nin the planetary regions. The effect of this resistance,\\nfrom the first discovery of the comet to the present time,\\nhas been to diminish the time of its revolution about\\ntwo days. Such a resistance, by destroying a part of the\\nprojectile force, would cause the comet to approach\\nnearer to the sun, and thus to have its periodic time\\nshortened. The ultimate effect of this cause will be to\\nbring the comet nearer to the sun at every revolution,\\nuntil it finally falls into that luminary, although many\\nthousand years will be required to produce this catas-\\ntrophe. It is conceivable, indeed, that the effects of\\nsuch a resistance may be counteracted by the attraction\\nof one or more of the planets, near which it may pass\\nin its successive returns to the sun.\\nIt is peculiarly interesting to see a portion of matter,\\nof a tenuity exceeding the thinnest fog, pursuing its\\npath in space, in obedience to the same laws as those\\nwhich regulate such large and heavy bodies as Jupiter\\nor Saturn. In a perfect void, a speck of fog, if propelled\\nby a suitable projectile force, would revolve around the\\nsun, and hold on its way through the widest orbit, with", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0254.jp2"}, "251": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 235\\nas sure and steady a pace as the heaviest and largest\\nbodies in the system.\\n293. The most remarkable comet of the present cen-\\ntury hitherto observed, was the great comet of 1843.\\nFig. 49.\\nOn the 28th of February of that year, the attention of\\nnumerous observers, in various parts of the world, was\\narrested by a comet seen in the broad light of day, a\\nlittle eastward of the sun. The comet resembled a white\\ncloud of great density, being nearly equally shining\\nthroughout, with a nucleus as bright as the full moon at\\nmidnight in a clear sky. During the first week in March,\\nthe appearance of this body, as seen in the torrid zone,\\nwas splendid and magnificent, enhanced in both re-\\nspects by the transparency of a tropical sky, and the\\nhigher angle of elevation above that at which it was\\n292. Are trie elements of Encke s comet calculated with ex-\\nactness What was its appearance in 1839 What has made\\nit peculiarly famous Why should it be so favorable for detect-\\ning a resisting medium What has been its effect on the mo-\\ntions of the comet What will be its ultimate effect Does the\\nextreme tenuity of this body prevent its moving in obedience to\\nthe laws that regulate the motions of the largest bodies in the\\nsystem", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0255.jp2"}, "252": {"fulltext": "236 COMETS.\\nseen by northern observers. As seen at New Haven,\\non the evening of the 17th of March, soon after sunset,\\nit extended along the southern sky, below the feet of\\nOrion, reaching nearly to the bright star Sirins, being\\nabout 40\u00c2\u00b0 in length, although in the tropical regions its\\napparent length, at the maximum, w r as nearly 70\u00c2\u00b0. It\\nwas curved a little like a goose-quill, and colored with\\na slight tinge of rose-red, which in a few evenings dis-\\nappeared and left it nearly a pearly white. Although\\nastronomers have differed in their decisions respecting\\nits periodic time, yet it is generally believed to be\\n175 years. Of all the comets on record this approached\\nnearest to the sun. It almost grazed his luminous sur-\\nface, which it swept round with a velocity, at the point\\nof nearest approach, of more than one and a quarter\\nmillion of miles per hour, a velocity sufficient to carry\\nit half round the sun in two hours while it required\\n175 years to complete the other half, through a journey\\nextending to the distance from that luminary of more\\nthan 6000 millions of miles. The heat of the sun when\\nthe comet was passing its perihelion, was 47,000 greater\\nthan what falls on the earth.\\n294. Of the physical nature of comets, little is under-\\nstood. It is usual to account for the variations which\\ntheir tails undergo, by referring them to the agencies of\\nheat and cold. The intense heat to which they are\\nsubject in approaching so near the sun as some of them\\ndo, is alleged as a sufficient reason for the great expan-\\nsion of thin nebulous atmospheres forming their tails\\nand the inconceivable cold to which they are subject in\\nreceding to such a distance from the sun, is supposed to\\naccount for the condensation of the same matter until it\\nreturns to its original dimensions. Thus the great comet\\nof 1680, at its perihelion, approached 166 times nearer\\nthe sun than the earth, being only 130,000 miles from\\n293. Give an account of the great comet of 1843.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0256.jp2"}, "253": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 237\\nthe surface of the sun. The heat which, it must have\\nreceived, was estimated to be equal to 28,000 times that\\nwhich the earth receives in the same time, and 2000\\ntimes hotter than red-hot iron. This temperature would\\nbe sufficient to volatilize the most obdurate substances,\\nand to expand the vapor to vast dimensions and the\\nopposite effects of the extreme cold to which it would\\nbe subject in the regions remote from the sun, would be\\nadequate to condense it into its former volume.\\nThis explanation, however, does not account for the\\ndirection of the tail, extending, as it usually does, only\\nin a line opposite to the sun. Some writers therefore, as\\nDelambre, suppose that the nebulous matter of the comet,\\nafter being expanded to such a volume that the par-\\nticles are no longer attracted to the nucleus unless by\\nthe slightest conceivable force, are carried off in a direc-\\ntion from the sun by the impulse of the solar rays them-\\nselves. But to assign such a power of communicating\\nmotion to the sun s rays while they have never been\\nproved to have any momentum, is unphilosophical and\\nwe are compelled to place the phenomena of comets\\ntails among the points of astronomy yet to be explained.\\n295. Since those comets which have their perihelion\\nvery near the sun, like the comet of 1680, cross the or-\\nbits of all the planets, the possibility that one of them\\nmay strike the earth, has frequently been suggested.\\nStill, it may quiet our apprehensions on this subject, to\\nreflect on the vast extent of the planetary spaces, in\\nwhich these bodies are not crowded together as we see\\nthem erroneously represented in orreries and diagrams,\\nbut are sparsely scattered at immense distances from\\n294. Is the physical nature of comets well understood? How\\nare the variations in the lengths of their tails accounted for?\\nHow near did the comet of 1680 approach to the sun? What\\nheat did it acquire Does this account for the direction of the\\ntail How is that accounted for bv some writers", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0257.jp2"}, "254": {"fulltext": "238 METEORIC SHOWERS.\\neach other. They are like insects flying in the expanse\\nof heaven. If a comet s tail lay with its axis in the\\nplane of the ecliptic when it was near the sun, we can\\nimagine that the tail might sweep over the earth but\\nthe tail may be situated at any angle with the ecliptic\\nas well as in the same plane with it, and the chances\\nthat it will not be in the same plane are almost infinite.\\nIt is also extremely improbable that a comet w T ill cross\\nthe plane of the ecliptic precisely at the earth s path in\\nthat plane, since it may as probably cross it at any other\\npoint, nearer or more remote from the sun. Still, some\\ncomets have occasionally approached near to the earth.\\nThus Biela s comet, in returning to the sun in 1832,\\ncrossed the ecliptic very near to the earth s track, and\\nhad the earth been then at that point of its orbit, it\\nmight have passed through a portion of the nebulous\\natmosphere of the comet. The earth was within a\\nmonth of reaching that point. This might at first view\\nseem to involve some hazard yet we must consider that\\na month short, imolied a distance of nearly 50,000,000\\nmiles.\\nMETEORIC SHOWERS.\\n296. The remarkable exhibitions of shooting stars\\nwhich have occurred within a few years past, have ex-\\ncited great interest among astronomers. Their atten-\\ntion was first turned towards the subject by the great\\nmeteoric shower of November 13th, 1833. On that\\nmorning, from 2 o clock until broad daylight, the sky\\nbeing perfectly serene and cloudless, the whole heavens\\n295. What is said respecting the possibility of a comet s stri-\\nking the earth What considerations may quiet our apprehen-\\nsions How might the case be if the tail Jay in the plane of\\nthe ecliptic Is it probable that a comet will cross the ecliptic\\nprecisely at the place of the earth s path Have comets actually\\napproached near to the earth", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0258.jp2"}, "255": {"fulltext": "METEORIC SHOWERS. 239\\nwere lighted up with a magnificent display of celestial\\nfireworks. At times the air was filled with streaks of\\nlight, occasioned by fiery particles darting down so\\nswiftly as to leave their impression of light on the eye\\n(like a match ignited and whirled before the face), and\\ndrifting to the northwest like flakes of snow driven by\\nthe wind while, at short intervals, balls of fire, vary-\\ning in size from minute points to bodies as large as Ju-\\npiter or Yenus, and in a few instances as large as the\\nfull moon, descended more slowly along the arch of the\\nsky, often leaving after them long trains of light, which\\nwere in some cases variegated with different prismatic\\ncolore. On tracing back the lines of direction in which\\nthe meteors moved, it was found that they all appeared\\nto radiate from the same point, wmich was situated near\\none of the stars of the constellation Leo, named Gamma\\nLeonis and in every repetition of the meteoric shower\\nof November, the meteors have appeared to radiate\\nfrorn nearly the same place.\\n297. This shower pervaded nearly the whole of North\\nAmerica, having appeared in almost equal splendor from\\nthe British possessions on the north, to the West India\\nislands and Mexico on the south. Throughout this im-\\nmense region, the duration w r as nearly the same. The\\nmeteors began to attract attention by their unusual fre-\\nquency and brilliancy from nine to tvjelve o clock in the\\nevening w T ere most striking in their appearance from\\ntwo to four arrived at their maximum, in many places,\\nabout four o clock and continued until rendered invisi-\\nble bv the light of clay.\\n296. What first turned the attention of astronomers to the\\nsubject of shooting stars? Describe the meteoric shower of\\nNovember 13th, 1833. From what point among the stars did\\nthe meteors appear to come\\n297. Over what countries did this shower prevail At what\\ntime of night did the display commence At what hour was it\\ngreatest", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0259.jp2"}, "256": {"fulltext": "240 METEORIC SHOWERS.\\n298. Soon after this occurrence, it was ascertained\\nthat a similar meteoric shower had appeared in 1799,\\nand, what was remarkable, almost exactly at the same\\ntime of the year, namely, on the morning of the 12th of\\nNovember and it soon appeared by accounts received\\nfrom different parts of the world, that this phenomenon\\nhad occurred on the same 13th of November, in 1830,\\n1831, and 1832. Hence, this was evidently independent\\nof the casual changes of the atmosphere for, having a\\nperiodical return, it was undoubtedly to be referred to\\nastronomical causes, and its recurrence at a certain de-\\nfinite period of the year, plainly indicated some relation\\nto the revolution of the earth around the sun. The fol-\\nlowing conclusions respecting the meteoric shower of\\nNovember are believed to be well established, and\\nmost of them (which were first suggested by the author\\nof this work*) are now generally admitted by astron-\\nomers, though we cannot here exhibit the evidence on\\nwhich they are founded. It is considered then as esta-\\nblished, that the periodical meteors of November have\\ntheir origin beyond the atmosphere, descending to us\\nfrom some body (which from the known constitution of\\nthe meteors may be called a nebulous body) with which\\nthe earth falls in, near or through the borders of which\\nit passes that this body has an independent existence\\nas a member of the solar system, its periodic time being\\neither a year or half a year, so that for a number of years\\nin succession the two bodies meet near the same part of\\nthe earth s orbit. It is further established, that the me-\\nteors consist of light combustible matter that they move\\nwith great velocities, amounting in some instances to a\\n298. On what previous years did similar meteoric showers\\nappear What was the origin of the meteors From what kind\\nof body did they proceed What sort of bodies were the me-\\nteors With what velocity did they move How were they\\nSee American Journal of Science. Vols. xxy. and xxvi.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0260.jp2"}, "257": {"fulltext": "METEORIC SHOWERS. 241\\nvelocity not less than that of the earth in its orbit, or\\n19 miles per second, or 68,000 miles per hour; that\\nsome of them are bodies of large size, sometimes nearly\\nor quite a mile in diameter that when they enter the\\natmosphere, they rapidly and powerfully condense the\\nair before them, and thus elicit the heat which sets them\\non fire, as a spark is elicited in an air-match, by being\\nsuddenly condensed by means of a piston and cylinder\\nand that they are burned up at a considerable height\\nabove the earth, sometimes not less than 30 miles. On\\ninquiring further into the relations which this nebu-\\nlous body sustains to the solar system, it was inferred\\nto be, like comets, a regular member of the system, re-\\nvolving around the sun like them, but between the earth\\nand the sun and there are many reasons for believing\\nthat it is identical with the nebulous body long known\\nunder the name of the Zodiacal Light, and that it is in\\nfact from the outer extremities of this singular Light\\nthat the meteors are derived, being attracted down to\\nthe earth at that point where the earth in its annual re-\\nvolution approaches nearest, or perhaps passes through\\nthe extremities of the Zodiacal Light.*\\nset on fire What relations did this nebulous body sustain to the\\nsolar system? With what known body is it supposed to be\\nidentified\\nSee a paper on this subject by the author of the present work, in\\nthe Transactions of the American Association for the Advancement of\\nScience, for 1851 or American Journal of Science for November, 1851.\\n21", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0261.jp2"}, "258": {"fulltext": "l\u00c2\u00bbABT III.\u00e2\u0080\u0094 OF THE FIXED STARS.\\nCHAPTER I.\\nOF TEE CONSTELLATIONS.\\n299. Tee Fixed Stars are so called, because, to com-\\nmon observation, they always maintain the same situa-\\ntions with respect to one another.\\nThe stars are classed by their apparent magnitudes.\\nThe whole number of magnitudes recorded are sixteen,\\nof which the first six only are visible to the naked eye\\nthe rest are telescopic stars. As the stars which are\\nnow grouped together under one of the first six magni-\\ntudes are very unequal among themselves, it has recently\\nbeen proposed to subdivide each class into three, making\\nin all eighteen instead of six magnitudes visible to the\\nnaked eye. These magnitudes are not determined by\\nany very definite scale, but are merely ranked according\\nto their relative degrees of brightness, and this is left in\\na great measure to the decision of the eye alone, al-\\nthough it would appear easy to measure the compara-\\ntive degree of light in a star by a photometer, and upon\\nsuch measurement to ground a more scientific classifica-\\ntion of the stars. The brightest stars, to the number of\\n15 or 20, are considered as stars of the first magnitude\\nthe 50 or 60 next brightest, of the second magnitude\\n299. Why are the fixed stars so called? How are they\\nclassed? What is*tke whole number of magnitudes How\\nmany of these are visible to the naked eye How many of the\\nfirst, second, and the third magnitude respectively", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0262.jp2"}, "259": {"fulltext": "CONSTELLATIONS. 243\\nthe next 200 of the third magnitude and thus the num-\\nber of each class increases rapidly as we descend the\\nscale, so that no less than fifteen or twenty thousand are\\nincluded within the first seven magnitudes.\\n300. The stars have been grouped in Constellations\\nfrom the most remote antiquity a few, as Orion, Bootes,\\nand Ursa Major, are mentioned in the most ancient\\nwritings under the same names as they bear at present.\\nThe names of the constellations are sometimes founded\\non a supposed resemblance to the objects to which the\\nnames belong as the Swan and the Scorpion were\\nevidently so denominated from their likeness to those\\nanimals but in most cases it is impossible for us to\\nfind any reason for designating a constellation by the\\nfigure of the animal or the hero which is employed to\\nrepresent it. These representations were probably once\\nblended with the fables of pagan mythology. The\\nsame figures, absurd as they appear, are still retained\\nfor the convenience of reference since it is easy to\\nfind any particular star, by specifying the part of the\\nfigure to which it belongs, as when we say a star is in\\nthe neck of Taurus, in the knee of Hercules, or in the\\ntail of the Great Bear. This method furnishes a general\\nclue to its position but the stars belonging to any con-\\nstellation are distinguished according to their apparent\\nmagnitudes, as follows first, by the Greek letters,\\nAlpha, Beta, Gamma, c. Thus Alpha Orionis, de-\\nnotes the largest star in Orion, Beta A.?idromedce, the\\nsecond star in Andromeda, and Gamma Leonis, the\\nthird brightest star in the Lion. Where the number of\\nthe Greek letters is insufficient to include all the stars\\nin a constellation, recourse is had to the letters of the\\nRoman alphabet, a, b, c, c. and, in cases where\\n300. What constellations have been known from antiquity?\\nWhy are the ancient names preserved How are the individual\\nstars of a constellation named", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0263.jp2"}, "260": {"fulltext": "244 CONSTELLATIONS.\\nthese are exhausted, the final resort is to numbers.\\nThis is evidently necessary, since the largest constel-\\nlations contain many hundreds or even thousands of\\nstars.\\n301. The earliest catalogue of the stars was made by\\nITipparchus, of the Alexandrian School, about 140\\nyears before the Christian era. A new star appearing\\nin the firmament, he was induced to count the stars and\\nto record their positions, in order that posterity might\\nbe able to judge of the permanency of the constella-\\ntions. His catalogue contains all that were conspicuous\\nto the naked eye in the latitude of Alexandria, being\\n1022. Most persons unacquainted with the actual num-\\nber of the stars which compose the visible firmament,\\nwould suppose it to be much greater than this but it\\nis found that the catalogue of Hipparchus embraces\\nnearly all that can now be seen in the same latitude,\\nand that on the equator, where the spectator has the\\nnorthern and southern hemispheres both in view, the\\nnumber of stars that can be counted does not exceed\\n3000. A careless view of the firmament in a clear\\nnight, gives us the impression of an infinite multitude\\nof stars but when we begin to count them, they ap-\\npear much more sparsely distributed than we supposed,\\nand large portions of the sky appear almost destitute\\nof stars.\\nBy the aid of the telescope, new fields of stars pre-\\nsent themselves of boundless extent the number con-\\ntinually augmenting as the powers of the telescope are\\nincreased. Lalancle, in his Histoire Celeste, has re-\\ngistered the positions of no less than 50,000 and the\\nwhole number visible in the largest telescopes amount\\nto many millions.\\n301. Who made the earliest catalogue of stars How many\\ndid it contain How many can be seen with the naked eye\\nflow many by the telescope", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0264.jp2"}, "261": {"fulltext": "CONSTELLATIONS. 245\\n302. It is strongly recommended to the learner to\\nacquaint himself with the leading constellations at\\nleast, and with a few of the most remarkable individual\\nstars. The task of learning them is comparatively easy,\\nwhen they are taken up at suitable intervals throughout\\nthe year, the moon being absent and the sky clear.\\nAfter becoming familiar with such constellations as are\\nvisible on any given evening (suppose the first of Jan-\\nuary), these may be carefully reviewed after an interval\\nof a month, and the several new ones added which have\\nin the mean time risen above the eastern horizon. By\\nrepeating this process near the beginning of every\\nmonth of the year, the learner will acquire a competent\\nknowledge of the whole that are visible in his latitude,\\nand with a small expenditure of time. It may at first\\nbe advisable to obtain, for an evening or two, the assist-\\nance of some one who is acquainted with the constel-\\nlations, to point out such as are then visible in .the\\nevening sky. Then, by the aid of a celestial map, or,\\nwhat is better, a celestial globe, the learner will pursue\\nthe study without difficulty. We begin by rectifying\\nthe globe for the time, according to the directions given\\nin Article 61.\\nIn the following sketch of the leading constellations,\\nwe will point out a few of the marks by which they\\nmay be severally recognized, adding occasionally a few\\nparticulars, and leaving it to the learner to fill up the\\noutline by the aid of his map or globe, one of which,\\nindeed, is presumed to be before him.* But, by way\\nof giving a lead, we will indicate by diagrams the rel-\\native positions of a few of the principal stars of the\\nmost conspicuous constellations, especially of such as\\nhave remarkable figures. Our diagrams, being neces-\\nsarily small, do not represent the relative sizes of the\\nA celestial globe, sufficient for studying the constellations, may be\\npurchased for a small sum, and is, in other respects, a valuable posses-\\ndon to the astronomical student but even cheap maps of the stars,\\nlike those of Burritt or Kendal, will answer for beginners; and the\\n21*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0265.jp2"}, "262": {"fulltext": "246 CONSTELLATIONS.\\nconstellations. Those may be learned from globes or\\nmaps.\\nLet ns begin with the constellations of the Zodiac,\\nwhich, succeeding each other as they do in a known\\norder, are most easily found AEmg\\nAries (The Ram) the first constella-\\ntion of the Zodiac, is known by two d^ n^,\\nbright stars, Alpha on the northeast, p\\nand Beta on the southwest, 4\u00c2\u00b0f apart,\\nforming the head. South of Beta, at\\nthe distance of 2\u00c2\u00b0, is a smaller star, Gamma. The\\nnext brightest star of the Earn, Delta, is in the tail, 15\u00c2\u00b0\\nsoutheast of Alpha. The feet of the figure rest on the\\nhead of the Whale.\\nTaurus (The Bull) will be readily found by the seven\\nstars, or Pleiades, which lie in the neck, 24\u00c2\u00b0 eastward\\nof Arietis. The largest star in Taurus is Aldebaran,\\nof the first magnitude, in the Bull s eye, 10\u00c2\u00b0 southeast\\nof the Pleiades. It has a reddish color, and resembles\\nthe planet Mars. The other eye of the figure is Epsi-\\nlon, 3\u00c2\u00b0 northwest of Aldebaran. Five small stars,\\nCelestial Atlas, published by the Society for the Diffusion of Useful\\nKnowledge, which is suitable for the more advanced student, may be\\nprocured at a moderate expense. Those who have not studied Greek\\nmay easily learn the characters denoting the Greek letters.\\nIt will be expedient, where it is practicable, for the learner to\\nstudy the constellations in separate portions, at different seasons of the\\nyear, as at the equinoxes and at the solstices, according to the direc-\\ntions given in the closing article of this chapter. A3 the astronomer is\\nsupposed to face the south, the right side becomes west, and the left\\nside east.\\nThese measures are not intended to be stated with minute accu-\\nracy, but only with such a degree of exactness as may serve for a\\ngeneral guide. The learner will find it greatly for his advantage to\\naccustom himself to make an accurate estimate with the eye of dis-\\ntances in degrees on the celestial sphere and he may, at the outset,\\nfix on the distance between Alpha and Beta Arietis as a standard\\nmeasure (4\u00c2\u00b0) by which to estimate other angular distances among the\\nstars. Thus, half this length applied from Beta to Gamma, indicates\\nthat the two latter stars are 2\u00c2\u00b0 apart and two and a half times the\\nsame measure (10\u00c2\u00b0) will reach from the Pleiades to Aldebaran. Or the\\nPointers in the Great Bear will furnish a measure of 5\u00c2\u00b0.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0266.jp2"}, "263": {"fulltext": "CONSTELLATIOXS. 247\\nsituated a little west of Aldebaran, in the face of the\\nBull, constitute the Hyades. Although the Pleiades\\nTaurus. Pleiades.\\nare usually denominated the seven stars, yet it has\\nbeen remarked, from a high antiquity, that only six are\\npresent.*\\nSome persons, however, of remarkable powers of\\nvision, are still able to recognize seven, and even a\\ngreater number, f With a moderate telescope, not less\\nthan 50 or 60 stars, of considerable brightness, may be\\ncounted in this group, and a much larger number of\\nvery small stars are revealed to the more powerful\\ntelescopes. The beautiful allusion, in the Book of Job,\\nto the sweet influences of the Pleiades, and the\\nspecial mention made of this group by Homer and\\nHesiod, show how early it had attracted the attention of\\nmankind. The horns of the Bull are two stars, Beta\\nand Zeta, situated 25\u00c2\u00b0 east of the Pleiades, being 8\u00c2\u00b0\\napart. The northern horn, Beta, also forms one of the\\nfeet of Auriga, the Charioteer.\\nGemini (The Twins) is represented by two well-known\\nstars, Castor and Pollux, in the head of the figure, 5\u00c2\u00b0\\nasunder. Castor, the northern, is of the first, and\\nPollux of the second magnitude. Four conspicuous\\nstars, extending in a line from south to north, 25\u00c2\u00b0 S. W.\\nof Castor, form the feet, and two others parallel to these,\\nTheir names were Eleetra, Maia, Taygeta, Alcyone, Celseno, As-\\nterope, and Merope, the last being the Lost Pleiad of the poets.\\nAlcyone, according to a recent celebrated hypothesis, is distinguished\\nas the center around which the starry host revolve.\\nf Smyth s Cycle, II. 86.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0267.jp2"}, "264": {"fulltext": "248 CONSTELLATIONS.\\nat the distance of six or seven degrees E Twl!?s\\nnortheastward, are in the knees. p\\nCancer (The Crab). There are no\\nlarge stars in this constellation, and\\nit is regarded as less remarkable than\\nany other in the Zodiac. The two\\nmost conspicuous stars, Alpha and\\nBeta, are in the southern claws of 6\\nthe figure; and in its body are the\\nnorthern and southern Asellus, which\\nmay be readily found on a celestial\\nglobe. But the most remarkable 7\\nobject in this constellation, is a misty\\ngroup of very small stars, so close together when seen\\nby the naked eye as to resemble a comet, but easily\\nseparated by the telescope into a beautiful collection of\\nbrilliant points. It is called Prcesepe, or the Beehive.\\nLeo (The Lion) is a very large constellation, and has\\nmany interesting members. Megulus (a Leonis) is a star\\nThe Liox,\\nft\\np\\nof the first magnitude, which lies very near the ecliptic,\\nand is much used in astronomical observations. North\\nof Regulus lies a semicircle of five bright stars, arranged\\nin the form of a sickle, of which Regulus is the handle,\\nand extending over the shoulder and neck of the Lion.*\\nAs the Meteors of November always appear to radiate from a point\\nin the bend of the sickle, near the star Gamma, it may be noted that\\nthe names of the six stars composing this figure, beginning with Kegu-\\nius, are a, v, y, I, p,", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0268.jp2"}, "265": {"fulltext": "CONSTELLATIONS. 249\\nDenebola, a conspicuous star in the Lion s tail, lies 25\u00c2\u00b0\\neast of Kegulus. Twenty bright stars in all help to\\ncompose this beautiful constellation. It ranges from\\nwest to east along the Zodiac, over more than 40\u00c2\u00b0 of\\nlongitude, all parts of the figure excepting the feet lying\\nnorth of the ecliptic.\\nVirgo (The Virgin) extends along the Zodiac east-\\nward from the Lion, covering an equally wide region\\nof the heavens, although less distinguished by brilliant\\nstars. Spica, however, is a star of the first magnitude,\\nand lies a little east of the vernal equinox. Vindemi-\\natrix, in the arm of Virgo, 18\u00c2\u00b0 east of Denebola, and\\n23\u00c2\u00b0 north of Spica, is easily found and directly south\\nof Denebola 13\u00c2\u00b0, is Beta Virginis while four other-con-\\nspicuous stars, in the form of a trapezium, between this\\nand Vindemiatrix, lie in the wing and shoulders of the\\nfigure. The feet are near the Balance.\\nLibra (The Balance) is composed of a few scattered\\nmembers situated between the feet of Virgo and the\\nhead of Scorpio, but has no very distinctive marks.\\nTwo stars of the second magnitude, Alpha on the south,\\nand Beta 8\u00c2\u00b0 northeast of Alpha, together with a few\\nsmaller stars, form the scales.\\nScorpio (The Scorpion) is one of the finest of the con-\\nstellations of the Zodiac, and is manifestly so called\\nfrom its resemblance to the animal whose name it bears.\\nThe head is composed of five stars, arranged in a line\\nslightly curved, which is crossed in the center by the eclip-\\ntic, nearly at right angles, a degree south of the bright-\\nest of the group Beta Scorpionis. Nine degrees south-\\neast of this is a remarkable star of the first magnitude,\\ncalled Antares, and sometimes the Seccrt of the Scor-\\npion. It is of a red color, resembling the planet Mars.\\nISouth and east of this, a succession of not less than\\nnine bright stars sweep round in a semicircle, termina-\\nting in several small stars forming the sting of the Scor-\\npion. The tail of the figure extends into the Milky\\nWay.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0269.jp2"}, "266": {"fulltext": "250 CONSTELLATIONS.\\nThb Scorpion.\\n%V\\nSagittarius (The Archer). Ten degrees eastward\\nof the Scorpion s tail, on the eastern margin of the\\nMilky Way, we come to the bow of Sagittarius, con-\\nsisting of three stars about 6\u00c2\u00b0 apart, the middle one\\nbeing the brightest, and situated in the bend of the bow,\\nwhile a fourth star, 4\u00c2\u00b0 westward of it, constitutes the\\narrow. The archer is represented by the figure of a\\nCentaur (half horse and half man), and proceeding\\nabout ten degrees east from the bow, we come to a\\ncollection of seven or eight stars of the second and third\\nmagnitudes, which lie in the human or upper part of\\nthe figure.\\nCapricornus (The Goat), represented with the head\\nof a goat and the tail of a fish, comes next to Sagitta-\\nrius, about 20\u00c2\u00b0 eastward of the group that form the\\nupper portions of that constellation. Two stars of the\\nsecond magnitude, Alpha on the north, and Beta on\\nthe south, 3\u00c2\u00b0 apart, constitute the head of Capricornus,\\nwhile a collection of stars of the third magnitude, lying\\n20\u00c2\u00b0 southeast of these, form the tail.\\nAquarius (The Water Bearer) is closely in contact\\nwith the tail of Capricornus, immediately north of\\nwhich, at the distance of 10\u00c2\u00b0, is the western shoulder", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0270.jp2"}, "267": {"fulltext": "CONSTELLATIONS. 251\\n(Beta), and 10\u00c2\u00b0 further east is the eastern shoulder,\\n(Alpha) of Aquarius. About 3\u00c2\u00b0 southeast of Alpha is\\nGamma Aquarii, which, together with the other two,\\nmakes an acute triangle, of which Beta forms the ver-\\ntex. In the eastern arm of Aquarius are found four\\nstars, which together make the figure Y, the open part\\nbeing westward, or towards the shoulders of the con-\\nstellation. Aquarius ranges nearly 30\u00c2\u00b0 from north to\\nsouth, being nearly bisected by the ecliptic.\\nPisces (The Fishes). Three figures of this kind, at a\\ngreat distance apart, two north and one south of the\\necliptic, compose this constellation. The southern Fish,\\nPiscis Australia, otherwise called Pomalhaut, lies\\ndirectly below the feet of Aquarius, and being the only\\nconspicuous star in that part of the heavens, is much\\nused in astronomical measurements. It is 30\u00c2\u00b0 south of\\nthe equator.\\nAbout 12\u00c2\u00b0 east of the figure Y in the arm of Aqua-\\nrius, is an assemblage of five stars, forming a pretty\\nregular pentagon, which is one of the northern mem-\\nbers of the Constellation Pisces and far to the north-\\neast of this figure, north of the head of Aries, lies the\\nthird member, the three being represented as connected\\ntogether by a ribbon, or wavy band, composed of minute\\nstars.\\n303. The Constellations of the Zodiac, being first well\\nlearned, so as to be readily recognized, will facilitate\\nthe learning of others that lie north and south of them.\\nLet us therefore next review the principal Northern\\nConstellations, beginning at the North Pole.\\nUrsa Minor (The Little Bear). The Pole-star\\n(Polaris) is in the extremity of the tail of the Little\\nBear. It is of the third magnitude, and being within\\n302. What directions are given for learning the constellations\\nDescribe successively the constellations Aries, Taurus, Gemini,\\nCancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus,\\nAquarius, Pisces.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0271.jp2"}, "268": {"fulltext": "252 CONSTELLATIONS.\\nless than a degree and a half of the North. Pole of the\\nheavens, it serves at present to indicate the position of\\nThe Little Beab.\\nYf\\n7#\\nthe pole. It will be recollected, however, that on ac-\\ncount of the precession of the equinoxes, the pole of\\nthe heavens is constantly shifting its place from east to\\nwest, revolving about the pole of the ecliptic, and will\\nin time recede so far from the pole-star, that this will\\nno longer retain its present distinction (Art. 138). Three\\nstars in a straight line, 4\u00c2\u00b0 or 5\u00c2\u00b0 apart, commencing with\\nPolaris, lead to a trapezium of four stars, the whole\\nseven together forming the figure of a dipper, the tra-\\npezium being the body, and the three first-mentioned\\nstars being the handle.\\nUrsa Major (The Great Bear) is one of the largest\\nand most celebrated of the constellations. It is usuallv\\nThe Ore at Bea.e.\\nP\\nrecognized by the figure of a larger and more perfect\\ndipper than the one in the Little Bear three stars, as\\nbefore, constituting the handle, and four others, in the\\nform of a trapezium, the body of the figure. The two\\nwestern stars of the trapezium, ranging nearly with the\\nNorth Star, are called the Pointers and beginning\\n\u00e2\u0096\u00a0M", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0272.jp2"}, "269": {"fulltext": "CONSTELLATIONS. 253\\nwith the northern of these two, and following round from\\nleft to right through the whole seven, they correspond\\nin rank to the succession of the first seven letters of the\\nGreek alphabet, Alpha, Beta, Gamma, Delta, Epsilon,\\nZeta, Eta. Several of them also are known by their\\nArabic names. Thus, the first in the tail, corresponding\\nto Epsilon, is Aliotli, the next (Zeta) Mizar, and the\\nlast (Eta) Benetnasch. These are all bright and beauti-\\nful stars, Alpha being of the first magnitude, Beta,\\nGamma, Delta, of the second, and the three forming\\nthe tail, of the third. But it must be remarked that\\nthis very remarkable figure of a dipper or ladle com-\\nposes but a small part of the entire constellation, being\\nmerely the hinder half of the body and the tail of the\\nBear. The head and breast of the figure, lying about\\nten or twelve degrees west of the Pointers, contain a\\ngreat number of minute stars in a triangular group.\\nOne of the fourth magnitude, Omicron, is in the mouth\\nof the Bear. The feet of the figure may be looked for\\nabout 15\u00c2\u00b0 south of those already described, the two\\nhinder paws consisting each of two stars very similar\\nin appearance, and only a degree and a half apart.\\nThe two paws are distant from each other about 18\u00c2\u00b0\\nand following westward about the same number of de-\\ngrees, we come to another very similar pair of stars, which\\nconstitute one of the fore paws, the other foot being with-\\nout any corresponding pair.\\nIn a clear winter s night, when the whole constella-\\ntion is above the pole, these various parts may be easily\\nrecognized, and the entire figure will be seen to resem-\\nble a large animal, readily accounting for the name\\ngiven to this constellation from the earliest ages.\\nDraco (The Dragon) is also a very large constella-\\ntion, extending for a great length from east to west.\\nBeginning at the tail, which lies half way between the\\nPointers and the Pole-star, and winding round between\\nthe Great and the Little Bear, by a continued succession\\nof bright stars from 5\u00c2\u00b0 to 10\u00c2\u00b0 asunder, it coils around\\nunder the feet of the Little Bear, sweeps round the pole", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0273.jp2"}, "270": {"fulltext": "254 CONSTELLATIONS.\\nof the ecliptic, and terminates in a trapezium formed\\nby four conspicuous stars, from thirty to thirty-five de-\\ngrees from the North Pole. A few of the members of\\nthis constellation are of the second, but the greater part\\nof the third magnitude, and below it.\\n304. With the constellations already described as\\ngeneral landmarks, we may now proceed with each of\\nthe principal remaining ones, by stating its boundaries,\\nas we do those of countries in geography their relative\\nsituations being thus first learned from a map, or (what\\nis better) from a celestial globe, and then being severally\\ntraced out on the sky itself. We will begin with those\\nwhich surround the North Pole.\\nCepheus (The King) is bounded ~N. by the Little Bear,\\nE. by Cassiopeia, S. by the Lizard, and W. by the\\nDragon. The head lies in the Milky Way, and the feet\\nextend towards the pole. It contains no stars above the\\nthird magnitude.\\nCassiopeia.\\ni\\nCassiopeia is bounded E and W. by Cepheus, E. by\\nCamelopardalus, and S. by Andromeda, and is one of\\nthe constellations of the Milky Way. It is readily dis-\\ntinguished by the figure of a chair inverted, of which\\ntwo stars constitute the back, and four, in the form of a\\nsquare, the body of the chair. It is on the opposite side\\nof the pole from the Great Bear, and nearly at the same\\ndistance from it.\\n303. Describe the Northern Constellations, Ursa Minor, Ursa\\nMajor, Draco.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0274.jp2"}, "271": {"fulltext": "CONSTELLATIONS. 255\\nCamelopardaltjs (The Giraffe) is bounded N. by the\\nLittle Bear, E. by the head of the Great Bear, S. by\\nAuriga and Perseus, and W. by Cassiopeia. Although\\nthis constellation occupies a large space, yet it has no\\nconspicuous stars.\\nAndromeda is bounded 1ST. by Cassiopeia, E. by Per-\\nseus, S. by Pegasus, and W by the Lizard. The direc-\\ntion of the figure is from S. W. to N E., the head coming\\ndown within 30\u00c2\u00b0 of the equator, and being recognized\\nby a star of the second magnitude, which forms the\\nnortheastern corner of the great square in Pegasus, to\\nbe described hereafter. At the distance of six or seven\\ndegrees from the head, are three conspicuous stars in a\\nrow, ranging from north to south, which lie in the\\nbreast of the figure and about the same distance from\\nthese, and parallel to them, three more, which consti-\\ntute the girdle of Andromeda. Near the northernmost\\nof the three, is a faint, misty object, often mistaken for\\na comet, but is a nebula, and one of the most remarka-\\nble in the heavens.\\nPerseus is bounded 1ST. by Cassiopeia, E. by Auriga,\\nS. by Taurus, and W. by Andromeda. The figure ex-\\ntends from north to south, and is represented by a giant\\nholding aloft a sword in his right hand, while his left\\ngrasps the head of Medusa, a group of stars on the\\nwestern side of the figure, embracing the celebrated\\nstar Algol. A series of bright stars descend along the\\nshoulders and the waist, and there divide into the two\\nlegs. The western foot is 8\u00c2\u00b0 north of the Pleiades.\\nThe eastern leg is bent at the knee, which is distin-\\nguished by a group of small stars. Near the sword\\nhandle, under Cassiopeia s chair, is a fine cluster of stars,\\nso close together as scarcely to be separable by the eye.\\nAuriga (The Wagoner) is bounded ~N. by Camelo-\\npardalus, E. by the Lynx, S. by Taurus, and W. by\\nPerseus. He is represented as bearing on his left\\nshoulder the little Goat Capella, a white and beautiful\\nstar of the first magnitude, while Beta forms the\\nvight shoulder, 8\u00c2\u00b0 east of Capella. These two bright", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0275.jp2"}, "272": {"fulltext": "256 CONSTELLATIONS.\\nstars form, with tlie northern horn of the Bull, at the\\ndistance of 18\u00c2\u00b0, an isosceles triangle.\\nLeo Minor (The Lesser Lion) is bounded !N by Ursa\\nMajor, E. by Coma Berenices, S. by Leo, and W. by\\nthe Lynx. It lies directly under the hind feet of the\\nGreat Bear, and over the sickle in Leo, and is easily\\ndistinguished. Four stars in the central part of the\\nfigure, from 4\u00c2\u00b0 to 5\u00c2\u00b0 apart, form a pretty regular par-\\nallelogram.\\nCanes Yenatici (The Greyhounds). This constella-\\ntion lies between the hind legs of the Great Bear on\\nthe west, and Bootes on the east Cor Caroli, a soli-\\ntary star of the third magnitude, 18\u00c2\u00b0 south of Alioth,\\nin the tail of the Great Bear, will serve to mark this\\nconstellation.\\nComa Berenices (Berenice s Hair) is a cluster of\\nsmall stars, composing a rich group, 15\u00c2\u00b0 !N E. of Dene-\\nbola, in the Lion s tail, in a line between this star and\\nCor Caroli, and half way between the two.\\nBootes is bounded by Draco, E. by the Crown\\nand the head of Serpentarius, S. by Virgo, and W. by\\nComa Berenices and the Hounds. It reaches for a great\\ndistance from north to south, the head being within 20\u00c2\u00b0\\nof the Dragon, and the feet extending to the Zodiac. In\\nthe knee of Bootes is Arcturus, a star of the first mag-\\nnitude. The next brightest star, Beta, is in the head of\\nBootes, 23\u00c2\u00b0 north of Arcturus, and 15\u00c2\u00b0 east of the last\\nstar in the tail of the Great Bear. e thbCrown.\\nCorona Borealis (The North-\\nern Crown) is bounded 1ST. and\\nE. by Hercules, S. by the head of\\nSerpentarius, and W. by Bootes. %p\\nIt is formed of a semicircle of\\nbright stare, six in number, of which Gamma, near the\\ncenter of the curve, is of the second magnitude.\\nHercules is bounded E by Draco, E. by Lyra, S.\\nby Ophiuchus, and W. by Corona Borealis. It is a\\nvery large constellation, and contains some brilliant\\nobjects for the telescope, although its components are", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0276.jp2"}, "273": {"fulltext": "CONSTELLATIONS.\\n257\\ngenerally very small. The figure lies north and south,\\nwith the head near the head of Ophiuchus, and the\\nfeet under the head of Draco. Being between the\\nCrown and the Lyre, its locality is easily determined.\\nThe eastern foot of Hercules forms an isosceles triangle\\nwith the two southern stars of the trapezium in the head\\nof Draco while the head of Hercules is far in the\\nsouth, within 15\u00c2\u00b0 of the equator, being 6\u00c2\u00b0 west of a\\nsimilar star which constitutes the head of Ophiuchus.\\nLtea (The Lyke) is bounded N. by the head of Draco,\\nE. by the Swan, S. and W. by Hercules. Alpha Lyrse,\\nor Vega, is of the first magnitude. It is accompanied\\nby a small acute triangle of stars. Its color is a shining\\nwhite, resembling Capella and the Eagle.\\nCygnus (The Swan) extends along the Milky Way,\\nbelow Cepheus, and immediately eastward of the Lyre,\\nThe Swan.\\n%5\\nand has the figure of a large bird flying along the Milky\\nWay from north to south, with outstretched wings and\\nlong neck. Commencing with the tail, 25\u00c2\u00b0 east of Lyra,\\nand following down the Milky Way, we pass along a\\nline of conspicuous stars which form the body and neck\\nof the figure and then returning to the second of the\\nseries, we see two bright stars at eight or nine degrees\\non the right and left (the three together ranging across\\nthe Milky Way), which form the wings of the Swan.\\nThis constellation is among the few which exhibit\\nsome resemblance to the animals whose names they\\nbear.\\n22*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0277.jp2"}, "274": {"fulltext": "258 CONSTELLATIONS.\\nVulpecula (The Little Fox) is a small constellation,\\nin which a fox is represented as holding a goose in\\nhis mouth. It lies in the Milky Way, between the\\nSwan on the north and the Dolphin and the Arrow on\\nthe south.\\nAquila (The Eagle) stretches across the Milky Way,\\nand is bounded N. by Sagitta, a small constellation\\nwhich separates it from the Fox, E. by the Dolphin,\\nS. by Antinous, and W. by Taurus Poniatowski (the\\nPolish Bull), which separates it from Ophiuchus. It is\\ndistinguished by three bright stars in the neck, known\\nas the three stars, which lie in a straight line about\\n2\u00c2\u00b0 apart, on the eastern margin of the Milky Way.\\nThe central star is of the first magnitude. Its Arabic\\nname is Altair.\\nAntinous lies across the equator, between the Eagle\\non the north, and the head of- Capricorn on the south.\\nDelphlnus (The Dolphin) is situated east and north\\nof Altair, and is composed of five stars of the third\\nmagnitude, of which four, in the form of a rhombus,\\ncompose the head, and the fifth forms the tail.\\nPegasus (The Flying Hoese) is a very large constel-\\nlation, and is bounded !N by the Lizard and Andromeda,\\nE. and S. by Pisces, W. by the Dolphin. The head is near\\nthe Dolphin, while the back rests on Pisces, and the feet\\nextend towards Andromeda.\\nA large sqiiare, composed of four conspicuous mem-\\nbers, one (Markah) of the first, and three others of the\\nsecond magnitude, distinguish this constellation. The\\ncorners of the square are about 15\u00c2\u00b0 apart, the north-\\neastern corner being in the head of Andromeda.\\nOphiuchus is another very large constellation, the\\nhead being near the head of Hercules, and the feet\\n304. Bound and describe the following constellations, Ce-\\npheus, Cassiopeia, Camelopardalus, Andromeda, Perseus, Leo\\nMinor, Canes Venatici, Coma Berenices, Bootes, Corona Bore-\\nalis, Hercules, Lyra, Cygnus, Vulpecula, Aquila, Antinous, Del-\\nphi nus, Pegasus, Ophiuchus.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0278.jp2"}, "275": {"fulltext": "CONSTELLATIONS. 259\\nreaching to Scorpio, the western foot being almost in\\ncontact with Antares. The figure is that of a giant\\nholding a serpent in his hands. The head of the serpent\\nis a little south of the Crown, and the tail reaches far\\neastward towards the Eagle.\\n305. Of the constellations which lie south of the\\nZodiac, we shall notice only Cetns, Orion, Lepus, Mon-\\noceros, Canis Major, Canis Minor, Hydra, Crater, and\\nCorvus.\\nCetus (The Whale) is distinguished rather for its\\nextent than its brillancy, occupying a large tract of the\\nsky south of the constellations Pisces and Aries. The\\nhead is directly below the head of Aries, and the tail\\nreaches westward 45\u00c2\u00b0, being about 10\u00c2\u00b0 south of the\\nvernal equinox. Menkar (a Ceti), the largest of its com-\\nponents, is situated in the mouth, 25\u00c2\u00b0 southeast of a Arie-\\ntis and Mira (o Ceti), in the neck, 14\u00c2\u00b0 west of Menkar,\\nis celebrated as a variable star, which exhibits different\\nmagnitudes at different times.\\nOeion is one of the most magnificent of the constel-\\nlations, and one of those that have longest attracted the\\nadmiration of mankind, being alluded, to in the Book\\nof Job, and mentioned by Homer. The head of Orion\\nlies southeast of Taurus,. 15\u00c2\u00b0 from Aldebaran, and is\\ncomposed of a cluster of small stars. Two very bright\\nstars, Betelgeuse of the first, and Bellairrix of the second\\nmagnitude, form the shoulders three more, resembling\\nthe three stars of the Eagle, compose the girdle and\\nthree smaller stars, in a line inclined to the girdle, form\\nthe sword. Rigel, of the first magnitude, makes the west\\nfoot, but the corresponding star, 9\u00c2\u00b0 southeast of this,\\nwhich is sometimes taken for the other foot, is above\\nthe knee, this foot being concealed behind the Hare.\\nOrion s club is marked by three stars of the fifth mag-\\nnitude, close together, in the Milky Way, just below\\nthe southern horn of the Bull. Orion is a favorite con-\\nstellation with the practical astronomer, abounding, as\\nit does, in addition to the splendor of its components,", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0279.jp2"}, "276": {"fulltext": "260 CONSTELLATIONS.\\nwith fine nebulse, double stars, and other objects of\\npeculiar interest when viewed with the telescope. It\\nOrion.\\na%.\\n7-\\nm\\nembraces 70 stars, plainly visible to the naked eye, in-\\ncluding two of the first, four of the second, and three\\nof the third magnitude.\\nLepus (The Hare). Below Rigel, the western foot\\nof Orion, is a small trapezium of stars, which forms the\\nears of the Hare and an assemblage of nine stars, of\\nthe third and fourth magnitudes, south and east of these,\\nmake up the remaining parts of the figure.\\nCanis Major (The Greater Dog) lies directly east of\\nthe Hare, and is highly distinguished by containing\\nSirius, the most splendid of all the fixed stars, which\\nlies in the mouth of the figure. In the fore paw, 6\u00c2\u00b0\\nwest of Sirius, is a star of the second magnitude\\n((3 Canis Mag oris), and from 10\u00c2\u00b0 to 15\u00c2\u00b0 south of Sirius,\\nis a collection of stars of the second and third magni-\\ntudes, which make up the hinder portions of the figure.\\nThe Egyptians, who anticipated the rising of the Nile\\nby the appearance of Sirius in the morning sky, repre-\\nsented the constellation by the figure of a dog, the\\nsymbol of a faithful watchman.\\nCanis Minor (The Lesser Dog). About 25\u00c2\u00b0 north of\\nSirius, is the bright star Procyon, also of the first mag-", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0280.jp2"}, "277": {"fulltext": "CONSTELLATIONS. 261\\nnitude, which marks the side of the Lesser Dog. A\\nstar of the third magnitude (/3), 4\u00c2\u00b0 northwest of this, in\\nthe head of the figure, forms with Proeyon the lower\\nside of an elongated jDarallelogram, of which Castor and\\nPollux, 25\u00c2\u00b0 north, form the upper side.\\nMonoceeos is a large constellation, occupying the\\nspace between the Greater and the Lesser Dog, but has\\nno conspicuous members.\\nHydka occupies a long space south of Leo, Yirgo,\\nand Libra. Its head, which is south of the fore paws\\nof the Lion, consists of four stars of the fourth magni-\\ntude, of nearly uniform appearance and about 15\u00c2\u00b0 S.\\nE. of these is the Heart [Cor Hydrce), 23\u00c2\u00b0 south of\\nRegulus. Resting on Hydra, and south of the hind\\nfeet of Leo, is Crater (the Cup), consisting of six stars\\nof the fourth magnitude, arranged in the form of a\\nsemicircle and a little further east, also perched on\\nthe back of Hydra, is Corvus (the Crow), the two\\nbrightest components of which are situated in one of\\nthe wings of the figure, in a line between Crater and\\nSpica irginis.\\n306. According to an intimation given in a note on\\np. 246, the constellations may be advantageously studied\\nat four different periods of the year, as near the equi-\\nnoxes and the solstices, according to the following direc-\\ntions. The latitude supposed is 41\u00c2\u00b0.\\nLesson I. For the middle of September, from 8 to\\n10 o clock. At 8 o clock Scorpio is near setting in the\\nS. W., Antares being 10\u00c2\u00b0 high. The bow of Sagittarius\\nis seen on the eastern margin of the Milky Way, the\\narrow being directed to a point a little below Antares.\\nAt 9 o clock, the horns of the Goat come upon the\\nmeridian and at 10 o clock, the western shoulder of\\n305. Describe the constellations south of the Zodiac, Cetus,\\nOrion, Lepus, Monoceros, Cards Major, Canis Minor, Hydra,\\nCrater, Corvus.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0281.jp2"}, "278": {"fulltext": "262 CONSTELLATIONS.\\nAquarius. The other shoulder, and the figure Y in the\\narm, may also be easily found from the description\\ngiven on p. 251 also, the Pentagon, in Pisces, and\\nFomalhaut (the Southern Fish), a solitary bright star far\\nin the south, only 16\u00c2\u00b0 above the horizon. The head of\\nAries appears in the east, and the Pleiades are but\\nlittle above the horizon, while Aldebaran is just rising.\\nReturning now to the west* (at 10 o clock), the Crown\\nis 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\\nand following down the Milky Way, the Eagle is seen\\non its eastern margin over against Lyra on the western\\nand the Dolphin, a little eastward of the Eagle, and\\nas far above the horns of Capricornus as the latter are\\nabove the southern horizon. Following on the east of\\nthe meridian, the great square in Pegasus may next be\\nidentified and since the northeastern corner of the\\nsquare is in the head of Andromeda, this constellation\\nmay next be learned and then Perseus and Auriga,\\nwhich appear still further east. Directly north of Per-\\nseus, is Cassiopeia s chair and next to that we may\\ntake the Pole-star, the Little Bear, and the Great Bear,\\nthe Dipper only being traced for the present. Com-\\nmencing now at the tail of the Dragon, we may trace\\nround this figure between the two Bears to the head,\\nwhich brings us back to Lyra and the feet of Her-\\ncules. The boundaries of this constellation, and of\\nOphiuchus, which lies south of it, will end the first\\nlesson.\\nLesson II. For the middle of Decetnber, from 1 to\\n10 o clock. Of the constellations of the Zodiac,\\nTaurus and Gemini are now favorably situated for ob-\\nservation in the east. At 1 o clock, the tail of Cetus\\njust reaches the meridian, its head being seen below\\nthe feet of Aries. Orion is just risen in the S. E. At\\n9 o clock, just above the western horizon, are seen in\\nsuccession from south to north, Aquarius, the Dolphin,\\nthe Eagle, the Lyre, and the Dragon s head. Between", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0282.jp2"}, "279": {"fulltext": "CONSTELLATIONS. 263\\nthe Eagle and the Lyre, at a little higher altitude, we\\nperceive the Swan, flying directly downwards. Be-\\ntween the tail of the Swan and the Pole-star, is Ce-\\npheus and from the pole, along the meridian, we trace\\nCassiopeia, the feet of Andromeda, the head of Aries,\\nand the neck of the Whale. At 10 o clock, Perseus\\nhas reached the meridian, the star Algol, in the head\\nof Medusa, being directly overhead. The Pleiades\\nare but little eastward of the zenith and following\\nalong south from the pole, at the interval of from one\\nto two hours east of the meridian, we may trace in\\nsuccession, Camelopard, Auriga, Taurus, Orion, and\\nthe Hare. Turning along the eastern horizon, we find\\nCanis Major, Monocer-os, Cam s Minor, the head of\\nHydra (just rising), Cancer, Leo, the sickle just ap-\\npearing about 3\u00c2\u00b0 north of the east point. Leo Minor\\nand Ursa Major complete the survey; and we may now\\nadvantageously trace out the various parts of the Great\\nBear, as described on p. 252 the two stars composing\\nits hindmost paw being scarcely above the horizon.\\nLessor III. For the middle of Mareh, from 8 to 10\\no clock. At 8 o clock, we see the Twins nearly over-\\nhead, and Procyon and Sirius, at different intervals,\\ntowards the south. Along the west we recognize the\\nneck and head of the Whale, the head, of Aries, and\\nthe head of Andromeda next above these, Orion,\\nTaurus, Perseus, Cassiopeia, and Cepheus and north\\nof the head of Orion, we see Auriga and Camelopard.\\nIn the S., Hydra is now fully displayed and fol-\\nlowing on north, we obtain fine views of the Greater\\nand the Lesser Lion, and the Great Bear. At 9 o clock,\\nCrater and Corvus appear in the S. E. on the back of\\nHydra Virgo extends from Leo down to the horizon,\\nSpica Virginis being about 5\u00c2\u00b0 high and north of Vir-\\ngo, we trace in -succession Coma Berenices, Cor Caroli,\\nBootes, with Arcturus and the Crown lying far in the\\nKE.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0283.jp2"}, "280": {"fulltext": "264 CONSTELLATIONS.\\nLesson IV. For the middle of June, from 9 to 10\\no clock. At 9 o clock, Bootes, Corona Borealis, the\\nhead of Libra, the Serpent, and Scorpio, lie along on\\neither side of the meridian. Castor and Pollux are just\\nsetting, and Leo is about an hour high. East of Leo,\\nYirgo is seen extending along towards the meridian,\\nSpica being about 30\u00c2\u00b0 above the southern horizon.\\nNorth of Leo and Yirgo, we recognize Leo Minor,\\nComa Berenices, Cor Caroli, and Ursa Major. At 10\\no clock, we trace along the eastern side of the meridian,\\nDraco, Hercules, and Ophiuchus and east of these,\\nthe Lyre, the Eagle, Antinous, Sagittarius, and Capri-\\ncornus. North of the Eagle, and round to the east, we\\nfind Cepheus and Cassiopeia, Andromeda rising in the\\nnortheast, Pegasus in the east, and Aquarius in the\\nsoutheast. Thus we may advantageously complete a\\nreview of the constellations.\\nCHAPTER II.\\nDOUBLE STARS\u00e2\u0080\u0094 TEMPORARY STARS VARIABLE STARS\\nCLUSTERS AND NEBULAE.\\n307. The view hitherto taken of the starry heavens\\npresents little that is new, since most of the constella-\\ntions, visible in our latitude, and the most conspicuous\\nof the individual stars, have been known from antiquity.\\nBut the objects to be described in the present chapter\\nare chiefly such as have been discovered by modern\\n306. Lesson I. Describe the appearance of the heavens for\\nthe middle of September from 8 to 10 o clock.\\nLesson II. For the middle of December from 7 to 1 o clock.\\nLesson III. For the middle of March from 8 to 10 o clock.\\nLesson IV. For the middle of June from 9 to 10 o clock.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0284.jp2"}, "281": {"fulltext": "DOUBLE STARS. 265\\nastronomy, aided by the powerful telescopes which,\\nsince the time of Sir William Herschel, have been\\ndirected to the heavens. Different orders and systems\\nof stars have been brought to light, and a new and\\nstill more wonderful class of bodies, called Nebulae,\\nhave been reached in the depths of the stellar universe.\\n308. The introduction into practical astronomy of\\nHerschel s great Forty Feet Reflector, in 1789, was a\\ngrand event in the study of the stars. This instrument,\\nin its previous humble forms, had been very little em-\\nployed upon the stars, they being supposed to be too\\nremote for its powers, which seemed only suited to\\nnearer worlds, as the sun and planets. It was not, how-\\never, an increase of magnifying power that was wanted\\nfor researches on these distant objects, but an increase\\nof light, by which a few scattered rays sent to us from\\nbodies hidden in the depths of space, might be collected\\nin such numbers, and directed into the eye, as would\\nrender visible objects otherwise invisible, not because\\nthey do not transmit to us any light, but because not\\nenough of what they transmit enters the small pupil\\nof the eye for the purposes of distinct vision. Tele-\\nscopes of great aperture, therefore, by collecting a large\\nbeam of light and conveying it to the eye, greatly en-\\nlarge the powers of this organ, and enabl,: it to pene-\\ntrate proportionally further into the most distant regions\\nof the universe. Sir W. Herschel himself made won-\\nderful progress in the knowledge of the starry heavens,\\nand by his own researches discovered a large portion of\\nthose bodies which we are now to describe and his son,\\nSir John Herschel, has cultivated, with great success,\\nthe same field, and especially by a residence of five\\nyears at the Cape of Good Hope, devoted assiduously\\nto observations with large instruments, has greatly\\n307. What new objects present themselves in this chapter\\nBy what instrument have they been revealed to us\\n23", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0285.jp2"}, "282": {"fulltext": "266 DOUBLE STARS.\\naugmented our knowledge of the stellar systems of the\\nsouthern hemisphere. Moreover, telescopes of still\\ngreater power than that of the elder Herschel, and es-\\npecially instruments capable of nicer angular measure-\\nments, have recently enriched the department of prac-\\ntical astronomy. The most remarkable of these are the\\ngrand Reflector constructed by Lord Rosse, an Irish\\nnobleman, and the great Refractors belonging respec-\\ntively to the Pulkova and Cambridge Observatories.\\nLord Rosse s telescope considerably exceeds in dimen-\\nsions and in power the forty feet reflector of Sir W.\\nHerschel, being 50 feet in focal length, and having a\\ndiameter of 6 feet, whereas that of the Herschelian\\ntelescope was only 4 feet. This unexampled magnitude\\nmakes this instrument superior to all others in light,\\nand fits it pre-eminently for observations on the most\\nremote and obscure celestial objects, such as the faintest\\nnebulae. But its unwieldy size, and its liability to loss\\nof power, by the tarnishing or temporary blurring of\\nthe great speculum, will render it far less available for\\nactual research than the great refractors which come in\\ncompetition with it. Until recently, it was thought im-\\npossible to form perfect achromatic object-glasses of\\nmore than about five inches diameter but they have\\nbeen successively enlarged, until we can no longer set\\nbounds to the dimensions which they may finally as-\\nsume. The Pulkova telescope (at St. Petersburg) has\\na clear aperture of about 15 inches, and a focal length\\nof 22 feet. The telescope recently acquired by Harvard\\nUniversity, is perhaps the finest refractor hitherto con-\\nstructed. It was made by the same artists, and upon\\nthe same scale with that, but its performances are\\nthought even to exceed those of the Pulkova instru-\\n308. What is said of Herschel s forty feet reflector? What\\nis the peculiar advantage of such large telescopes Describe the\\nLeviathan telescope of Lord Rosse, and those of Pulkova and\\nCambridge.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0286.jp2"}, "283": {"fulltext": "DOUBLE STARS. 267\\nment. We now proceed to review some of the dis-\\ncoveries among the stars, which the researches made\\nwith such instruments as the foregoing have brought to\\nlight.\\n309. Double Stars are those which appear single to\\nthe naked eye, but are resolved into two by the tele-\\nscope or if not visible to the naked eye, are seen in\\nthe telescope very close together. Sometimes three or\\nmore stars are found in this near connection, constitu-\\nting triple or multiple stars. Castor, for example, when\\nCastor. Pole-star. Triple.\\nseen by the naked eye, appears as a single star but in\\na telescope, even of moderate powers, it is resolved into\\ntwo stars, between the third and fourth magnitudes,\\nwithin 5 of each other. These two stars are of nearly\\nequal size, but frequently one is exceedingly small in\\ncomparison with the other, resembling a satellite near\\nits primary, although in distance, in light, and in other\\ncharacteristics, each has all the attributes of a star, and\\nthe combination, therefore, cannot be that of a planet\\nwith a satellite.\\nWhen Sir William Herschel began his observa-\\ntions on double stars, about the year 1780, he was\\nacquainted with only 4. By his own researches he ex-\\ntended the number to 2400. Sir John Herschel, Sir\\nJames South, and M. Struve, the great Russian astrono-\\nmer, prosecuted the same line of research and when\\nSir John Herschel left England for the Cape of Good\\nHope, in 1833, the whole number of double stars en-\\nrolled was 3346 and this number was increased, by\\nthat eminent astronomer, by adding those of the south-\\nern hemisphere, to 5542. The number of double stars\\nis more than five thousand, and therefore considerably", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0287.jp2"}, "284": {"fulltext": "268 DOUBLE STARS.\\nexceeds all the stars visible to the naked eye. In some\\ninstances, this proximity arises undoubtedly from the\\ntwo members lying nearly in the same line of vision,\\nand therefore being projected very near to each other on\\nthe face of the sky but in most cases the double stars\\nare proved to have a physical relation to each other,\\nand are therefore said to be physically double, while\\nthe former are said to be optically double. There is no\\nlonger any doubt that among the stars are separate\\nsystems, in which two, three, and even in one instance\\nat least six stars are bound together in relations of\\nmutual dependence, suns with suns, as the members of\\nthe 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\\nstar, the members of which form a small trapezium\\nand recent observations have detected in two of these,\\nseverally, companions of extreme minuteness, the whole\\ncomposing a figure like the following\\nMany of the double stars are distinguished by the\\ncomponents exhibiting different colors, often finely con-\\ntrasted with each other, as orange with blue or green,\\nyellow with blue, and white with purple. Gamma\\nAndromedse is a close double star, the components of\\nwhich are both green. Insulated stars of a red color,\\nalmost as deep as that of blood, occur in many parts of\\n309. What are Double Stars Give an example. With\\nhow many was Sir W. Herschel acquainted in 1780 State\\nthe successive additions, and the distinction between stars\\nphysically and optically double. Are there separate systems\\namong the stars What is said of the quadruple star in\\nOrion s Sword Are the double stars ever of different colors", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0288.jp2"}, "285": {"fulltext": "TEMPORARY STARS. 269\\nthe heavens, but no green or blue star of any decided\\nhne has ever been noticed nnassociated with a compan-\\nion brighter than itself.*\\n310. Temporary Stars are new stars which have sud-\\ndenly made their appearance, and, after a certain inter-\\nval, as suddenly disappeared and returned no more.\\nIt was the appearance of a new star of this kind, 125\\nyears before the Christian era, that prompted Hippar-\\nchus to form a catalogue of the stars, the first on record.\\nSuch also was the star which suddenly shone out, A. D.\\n389, in the Eagle^ as bright as Venus, and after remain-\\ning three weeks, disappeared entirely. At other peri-\\nods, at distant intervals, similar phenomena have pre-\\nsented themselves. Thus the appearance of a new star\\nin 1572 was so sudden, that Tycho Brahe, returning\\nhome one evening, was surprised to find a collection\\nof country people gazing at a star, which he was sure\\ndid not exist half an hour before. It was then as bright\\nas Sirius, and continued to increase until it surpassed\\nJupiter when brightest, and was visible at midday. In\\na month it began to diminish, and in three months after-\\nwards it had entirely disappeared. Some stars are now\\nmissing which were registered in the older catalogues.\\nIn one instance, at least (that of Neptune), the supposed\\nstar has proved to have been a planet.\\n311. Variable Stars are those which undergo a\\nperiodical change of brightness. One of the most re-\\nmarkable is the star Mira, in the neck of the Whale\\n(Omicron Ceti). It appears once in 11 months, remains\\nat its greatest brightness about a fortnight, being then,\\non some occasions, equal to a star of the second mag-\\nnitude. It then decreases about three months, until it\\nbecomes completely invisible, and remains so about\\n310. What are temporary stars? What led Hipparchus to\\nform a catalogue of the stars Star discovered by Tycho.\\nHerschel.\\n23*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0289.jp2"}, "286": {"fulltext": "270 VARIABLE STARS.\\nfive months, when it again becomes visible, and con-\\ntinues increasing during the remaining three months of\\nits period.\\nAnother very remarkable variable star is Algol\\n{Beta Persei). It is suddenly visible as a star of the\\nsecond magnitude, and continues such for 2d. 14h.,\\nwhen it begins rapidly to diminish in splendor, and in\\nabout 3^ hours is reduced to the fourth magnitude. It\\nthen begins again to increase, and in Z\\\\ hours more, is\\nrestored to its usual brightness, going through all its\\nchanges in less than three days. This remarkable law\\nof variation appears strongly to suggest the revolution\\nround it of some opake body, which, when interposed\\nbetween us and Algol, cuts off a large portion of its\\nlight. It is (says Sir J. Herschel) an indication of a\\nhigh degree of activity in regions where, but for such\\nevidence, we might conclude all to be lifeless. Our\\nsun requires almost nine times this period to perform a\\nrevolution on its axis. On the other hand, the periodic\\ntime of an opake revolving body, sufficiently large,\\nwhich would produce a similar temporary obscuration\\nof the sun, seen from a fixed star, would be less than\\nfourteen hours.\\nThe duration of these periods is extremely various.\\nWhile that of Beta Persei, above mentioned, is less\\nthan three days, others are more than a year, and others\\nmany years.\\n312. In various parts of the firmament are seen large\\ngroups, or clusters, which, either by the naked eye, or\\nby the aid of the smallest telescope, are perceived to\\nconsist of a great number of small stars. Such are the\\nPleiades, Coma Berenices, and Prsesepe, or the Bee-\\nhive, in Cancer. The Pleiades, or Seven Stars, as they\\nare called, in the neck of Taurus, is the most conspicu-\\n311. What are variable stars Give examples. What marks\\nof activity do they indicate What is the duration of thes j\\nperiodic variations", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0290.jp2"}, "287": {"fulltext": "NEBULAE. 271\\nous cluster. When we look directly at this group, we\\ncannot distinguish more than six stars, but by turning\\nthe eye sideways* upon it, we discover that there are\\nmany more. The telescope only can, however, display\\nthe real magnificence of the Pleiades. Coma Bereni-\\nces has fewer stars, but they are of a larger class than\\nthose which compose the Pleiades. The Bee-hive, or\\nNebula of Cancer, is one of the finest objects of this\\nkind for a small telescope, being, by its aid, converted\\ninto a rich congeries of shining points. A cluster in\\nthe sword-handle of Perseus, below Cassiopeia s chair,\\nthough but a dim speck to the naked eye, is a very ele-\\ngant object to a large telescope, being separated into\\nbright and beautiful stars, embracing several distinct\\nsubordinate clusters of exceedingly minute stellar points.\\nThe head of Orion affords an example of another cluster,\\nthough less remarkable than the others.\\n313. Nebulae are faint misty objects seen in various\\nparts of the firmament, always maintaining a fixed\\nposition, which resemble comets, or a speck of fog.\\nThe Galaxy, or Milky Way, presents a constant suc-\\ncession of large nebulas. Of the individual nebulae,\\nseen by the naked eye, the most conspicuous is that\\nnear the girdle of Andromeda. It is the oldest known\\nnebula, having attracted the attention of star-gazers as\\nearly as the beginning of the tenth century, although\\nit is commonly said to have been discovered by Simon\\nMarius, in 1612. No powers of the telescope have\\nbeen able to resolve this into separate stare, although\\nthe great Cambridge telescope reveals a vast number\\nof stars, more than 1500, of various degrees of bright-\\n312. What is said of clusters of stare? Give examples.\\nIndirect vision is far more delicate than direct. Tims we can see the\\nZodiacal Light or a comet s tail much more distinctly and better de-\\nfined (partly, perhaps, by the effect of contrast), if we fix one eye on\\na part of the sky at some distance, and turn the other eye obliquely\\nupon the object.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0291.jp2"}, "288": {"fulltext": "272\\nNEBULAE.\\nness, scattered over its surface but these appear not to\\nbelong to the nebula itself, which has hitherto afforded\\nno evidence of resolution. Its dimensions are astonish-\\ningly great, since it covers a space of a quarter of a\\ndegree in diameter and we must bear in mind that,\\nat such a distance as the fixed stars, a space of 15 im-\\nplies an immense extent. Its figure is oval, and ellip-\\ntical nebulae constitute a common variety among the\\nfigures which these bodies exhibit. Another very com-\\nmon figure are the globular nebulae. A grand speci-\\nmen of this variety may be easily found in the constel-\\nlation Hercules, between Zeta and Eta. Draw a line\\nfrom Lyra to Gemma of the Crown, and 3\u00c2\u00b0 above the\\ncenter of that line will be the place of this nebula.\\nWhen viewed with a small telescope, it exhibits only a\\nglobular cloud, but to a more powerful instrument it\\nreveals its real glories in a form truly exciting to the\\nbeholder.* About 4000 nebulae have been detected and\\ndescribed, of which about 1700 have recently been\\nadded by Sir John Herschel, from his Eesults of Ob-\\nservations at the Cape of Good Hope. Among the\\nlatter are two remarkable spots, well known to naviga-\\ntors, situated near the south pole, called Magellanic\\nClouds by sailors, but by astronomers, the Nubecula\\nMajor and the Nubecula Minor. They are found to\\nconsist of a wonderful collection of nebulae, the greater\\nembracing 278 nebulae, and the lesser 37. Both to-\\ngether compose a most magnificent assemblage. In\\nthe sword of Orion is a celebrated nebula, long known,\\nwhich, until recently, had resisted all attempts to re-\\nsolve it into stars but the great Reflector of Lord\\nRosse, and more recently the great Refractor of the\\nCambridge Observatory, have succeeded in a partial\\nresolution, at least, of this grand object, and have\\nauthorized the anticipation that, with a small increase\\nof telescopic power, the whole will be shown to consist\\nof an immense collection of exceedingly minute stars.\\nSee frontispiece.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0292.jp2"}, "289": {"fulltext": "NEBUL-E. 273\\nThese great telescopes, by the superior light they\\nafford, display their peculiar powers in this department\\nof astronomy, and those astronomers who, for the first\\ntime, have gazed at these sidereal pictures as seen in\\nthe Leviathan of Lord Rosse, have expressed, in glow-\\ning terms, their mingled delight and astonishment.\\nThe perfect forms, and strange but symmetrical config-\\nurations, exhibited by these instruments, of nebulse that\\nwere before seen of irregular or fantastic shapes, afford\\ngrounds for believing that such irregularities are often\\nif not always owing to the objects being but partly de-\\nveloped. Thus the Crab Nebula of Lord Rosse had\\nbeen long known as a faint, ill-defined nebula of an\\nelliptical shape but the higher powers of that instru-\\nment exhibit the before concealed appendages which\\nare essential to the completeness of the figure. The\\nWhirlpool Nebula of Rosse, when seen in separate\\nparts, exhibited no signs of order or symmetry; but\\nwhen viewed with the great Reflector, it develops the\\nwonderful structure of a perfect spiral.*\\n314. Nebulae were formerly divided into two classes,\\nresolvable and irresolvable, the former term inrplying\\nthat the body was shown by the telescope to consist of\\nstars, and the latter implying that the body is not com-\\nposed of stars, but of a shining cloudy kind of matter\\ndiffused throughout the mass. Astronomers, at present,\\ninclude all resolvable neublse under the head of clus-\\nters, appropriating the term nebulas exclusively to such\\nof these bodies as have never been resolved. The\\nquestion whether this distinction is not merely relative\\nto the powers of the telescope, and whether, on the in-\\n313. What are nebulae? What is said of the Milky Way?\\nOf the nebula of Andromeda Of globular nebulae How\\nmany nebulas have been described W T hat is said of the Magel-\\nlanic Clouds? -Of the nebula in Orion s Sword? How do the\\nnebulae appear in great telescopes like that of Rosse\\nSee frontispiece.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0293.jp2"}, "290": {"fulltext": "274 xebulyE,\\ncrease of these powers, this class of bodies would not\\nall be resolved into stars, is not easily determined,\\nsince the same increase of telescopic power which con-\\nverts existing nebulae into clusters, brings to light a\\ngreater number of those which are irresolvable.\\nThese remote objects of the universe occasionally\\nexhibit traces of that regard to beauty which every-\\nwhere, in these nether worlds, characterizes the works\\nof the Creator. In the Cross, a brilliant constellation\\nof the southern hemisphere, for example, is a cluster\\nsurrounding the star Kappa Cruris, which consists of\\nabout 110 stars from the seventh magnitude down-\\nwards, eight of the more conspicuous of which are\\ncolored with various shades of red, green, and blue, so\\nas to give to the whole the appearance of a rich piece\\nof jewelry.\\n315. Nebulous stars are such as exhibit a sharp\\nand brilliant star, surrounded by a disk or atmosphere\\nof nebulous matter. These atmospheres, in some cases,\\npresent a circular, in others an oval figure and in\\ncertain instances, the nebula consists of a long, narrow,\\nspindle-shaped ray, tapering away at both ends to\\npoints. Annular NebulcB (King-shaped) are among\\nthe rarest objects in the heavens. The most conspicu-\\nous of this class is in the Constellation Lyra, between\\nthe stars Beta and Gamma, about 6\u00c2\u00b0 S. E. of Alpha\\nLyres. This remarkable object is believed to be in fact\\na resolvable nebula or cluster, and yet the greatest\\npowers of the telescope hitherto applied have only\\neffected such changes as are regarded as giving signs\\nof resolvability, but its perfect resolution has not been\\nattained. Should it be achieved by an increased power\\nof the instrument, astronomers look for a splendid coro-\\n314. Point out the distinction between resolvable and irre-\\nsolvable nebulae. Are the figures of the nebulas ever beautiful\\n315, What is said of nebulous stars? Of annular nebula;", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0294.jp2"}, "291": {"fulltext": "NEBULA. 275\\nnet of stars, more glorious, perhaps, than any thing\\nhitherto discovered in the starry heavens.\\n316. Planetary JVebulce constitute another variety, and\\nare very remarkable objects. They have, as their name\\nimports, exactly the appearance of planets. Whatever\\nmay be their nature, they must be of enormous magni-\\ntude. One of them is to be found in the parallel of\\nv Aquarii, and about 5m. preceding that star. Its appa-\\nrent diameter is about 20 Another in the constella-\\ntion Andromeda, presents a visible disk of 12 perfectly\\ndefined and round. Granting these objects to be equally\\ndistant from us with the stars, their real dimensions\\nmust be such as, on the lowest computation, would fill\\nthe orbit of Uranus. It is no less evident that, if they\\nbe solid bodies, of a solar nature, the intrinsic splendor\\nof their surfaces must be almost infinitely inferior to\\nthat of the sun. A circular portion of the sun s disk,\\nsubtending an angle of 20 would give a light equal to\\n100 full moons; while the objects in question are hardly,\\nif at all, discernible with the naked eye.*\\n317. The Milky Way, or Galaxy, is a well-known\\nluminous zone, encircling the sphere nearly in the\\ndirection of a great circle. Near the Swan, in the\\nnorthern sky, it is seen to be divided into two bands,\\nwhich remain asunder for 150\u00c2\u00b0, and then reunite. The\\nGalaxy owes its peculiar appearance to the blended\\nlight of myriads of small stars too minute to be indi-\\nvidually recognized by the naked eye, but which are\\nseen in their true character by a telescope of only\\nmoderate powers. Sir William Herschel estimated that,\\non one occasion, in forty-one minutes, no less than\\n258,000 stars passed through the small field of his tele-\\n316. What is said of planetary nebulae?\\n317. Describe the Milky Way or Galaxy.\\nHerschel.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0295.jp2"}, "292": {"fulltext": "2*76 MOTIONS OF THE STARS.\\nscope. In approaching the border of the Milky Way,\\nthere is found a regular but rapid increase in the num-\\nber of stars, even before entering the limits of the\\nluminous zone itself. Sir J. Herschel computes the\\nwhole number of stars in the Milky Way at five and a\\nhalf millions, including such only as are visible in his\\ntwenty feet reflector. The Galaxy is itself supposed\\nto be a nebula, of which our sun with its planets\\nforms a constituent part and it is thought that it ap-\\npears so much greater than other nebulae, only in con-\\nsequence of our situation with respect to it, and its\\ngreater proximity to our svstem.\\nCHAPTER III.\\nMOTIONS OF THE FIXED STAES DISTANCES NATUEE.\\n318. In 1803, Sir William Herschel first determined\\nand announced to the world, that there exist among the\\nstars separate systems, composed of two stars, revolv-\\ning about each other in regular orbits. These he de-\\nnominated Binary Stars, to distinguish them from\\nother double stars where no such motion is detected,\\nand whose proximity to each other may possibly arise\\nfrom casual juxtaposition, or from one being in the\\nrange of the other. At present, more than a hundred\\nof the binary stars are known, and as the number of\\nsuch revolutions known among the double stars is con-\\nstantly increasing as the times of comparison increase,\\nit may be anticipated that, in after ages, so large a\\nproportion of all the double stars will be found to pos-\\nsess this character, as to authorize the belief that they\\nuniversally consist of subordinate systems, of which\\nthe members have a revolution around a common\\n318. What is said of binary stars Of their periodic times", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0296.jp2"}, "293": {"fulltext": "MOTIONS OF THE STARS. 277\\ncenter of gravity. The periodic times of the binary\\nstars are very various. While some (as Zeta Her cutis,\\nand Eta Coronce) complete their revolutions in 30 or 40\\nyears, others (as Gam?na Virginis) require more than\\n170, and others still (as 65 Piscium) take up the long\\nperiod of 3000 years.\\n319. The revolutions of the binary stars have assured\\nus of this most interesting fact, that the law of gravita-\\ntion extends to the fixed stars. Before these discoveries,\\nwe could not decide, except by a feeble analogy, that\\nthis law transcended the bounds of the solar system.\\nIndeed, our belief of the fact rested more upon our\\nidea of unity of design in all the works of the Creator,\\nthan upon any certain proof but the revolution of one\\nstar around another in obedience to forces which must\\nbe similar to those that govern the solar system, estab-\\nlishes the grand conclusion, that the law of gravitation\\nis truly the law of the material universe.\\nWe have the same evidence (says Sir John Herschel)\\nof the revolutions of the binary stars about each other,\\nthat we have of those of Saturn and Uranus about the\\nsun and the correspondence between their calculated\\nand observed places in such elongated ellipses, must\\nbe admitted to carry with it a proof of the prevalence\\nof the Newtonian law of gravity in their systems, of\\nthe very same nature and cogency as that of the calcu-\\nlated and observed places of comets round the center\\nof our own system.\\nBut (he acids) it is not with the revolutions of bodies\\nof a planetary or cometary nature round a solar center\\nthat we are now concerned it is with that of sun around\\nsun, each, perhaps, accompanied with its train of planets\\nand their satellites, closely shrouded from our view by\\nthe splendor of their respective suns, and crowded into\\n319. Of what interesting fact has the revolution of the binary\\nstars assured us\\n24", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0297.jp2"}, "294": {"fulltext": "278 MOTIONS OF THE STARS.\\na space, bearing hardly a greater proportion to the enor-\\nmous interval .which separates them, than the distances\\nof the satellites of our planets from their primaries, bear\\nto their distances from the sun itself.\\n320. Some of the fixed stars appear to have a Proper\\nMotion, or a real motion in space.\\nThe apparent change of place in the stars arising\\nfrom the precession of the equinoxes, has been already\\nmentioned and several other sources of irregularity\\nwhich give an apparent motion to the stars are well\\nknown but after all these corrections are made,\\nchanges of place still occur, which cannot result from\\nany changes in the earth, but must arise from changes\\nin the stars themselves. Such motions are called the\\nproper motions of the stars. Nearly 2000 years ago,\\nHipparchus and Ptolemy made the most accurate de-\\nterminations in their power of the relative situations of\\nthe stars, and their observations have been transmitted\\nto us in Ptolemy s Almagest from which it appears\\nthat the stars retain at least very nearly the same places\\nnow as they did at that period. Still, the more accurate\\nmethods of modern astronomers have brought to light\\nminute changes in the places of certain stars, which\\nforce upon us the conclusion, either that our solar sys-\\ntem causes an apparent displacement of certain stars,\\nby a motion of its own in space, or that they have thein-\\nselves a proper motion. Possibly, indeed, both these\\ncauses may operate.\\n321. If the sun, and of course the earth which ac-\\ncompanies him, is actually in motion, the fact may\\nbecome manifest from the apparent approach of the\\nstars in the region which he is leaving, and the re-\\ncession of those which lie in the part of the heavens\\ntowards which he is travelling. Were two groves of\\ntrees situated on a plain at some distance apart, and we\\n320. What is said of the proper motion of the stars", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0298.jp2"}, "295": {"fulltext": "MOTIONS OF THE STARS. 2l9\\nshould go from one to the other, the trees before us\\nwould gradually appear further and further asunder,\\nwhile those we left behind would appear to approach\\neach other. Some years since, Sir William Herschel\\nsupposed he had detected changes of this kind among\\ntwo sets of stars in opposite points of the heavens, and\\nannounced that the solar system was in motion towards\\na point in the constellation Hercules. As, for many\\nyears after this announcement, other astronomers failed\\nto find evidence of such a motion of the solar system,\\nthe doctrine was generally discredited, until, within a\\nfew years, new and very refined researches have been\\ninstituted by several of the most eminent astronomers,\\nwhich have fully confirmed the observations of Her-\\nschel. The great Russian astronomer, Struve, by a\\ncomparison of the best observations, finds the exact\\npoint towards which the solar system is moving is in a\\nline which joins the two stars Pi and Mu Herculis, a\\npoint which can be easily found on the celestial globe,\\nand thence transferred to the heavens. The researches\\nof the younger Struve have conducted him to the\\nvelocity with which the solar system is moving in space,\\nand he infers that the space through which the sun\\nmoves annually is 154,000,000 miles. Great as this\\nspace is, yet it may be remarked that it is only about\\none-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\\nhave been continued, the direction appears rectilinear\\nbut all analogy leads to the belief that it is in fact a\\nmotion of revolution, although, on account of the im-\\nmense size of the orbit, and, consequently, its small\\ncurvature, many years will be requisite in order to\\ndetermine the deviation from the line of the tangent.\\n322. When we reflect on the immense distance of\\n321. How is the motion of the sun in space indicated\\nTowards what constellation is it moving", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0299.jp2"}, "296": {"fulltext": "280 MOTIONS OF THE STARS.\\nthe stars, we may readily believe that they may be in\\nfact in rapid motion, and yet appear quiescent as a\\ndistant ship, under full sail, appears at rest, although\\nactually moving at the rate of ten knots an hour. Thus\\nit is found that a motion of the sun in space, so\\nseen from the nearest fixed stars, would make it de-\\nscribe an arc of only about one-third of a second\\nannually, although traversing a space of 154 millions\\nof miles. But a small change in the place of a star in\\na single year may, in a long series of years, accumulate\\nto a very sensible amount. For example, the latitudes\\nof the three bright stars, Sirius, Arcturus, and Alde-\\nbaran, were determined by Hipparchus 130 years be-\\nfore the Christian era, and their assigned places are\\ntransmitted to us in the Almagest of Ptolemy. About\\nthe year 1700, Dr. Halley found that these stars had,\\nduring the interval of nearly 2000 years, moved\\nsoutherly through the spaces respectively of 37 42\\nand 33 The immense pains that have of late years\\nbeen bestowed upon catalogues of the stars, and es-\\npecially of particular portions of the heavens, with the\\nview of furnishing, to after ages, the most accurate\\ndata for comparison, will enable future astronomers to\\nstudy the proper motions of the stars with far greater\\nadvantages than the present generation enjoys. In\\nmost cases where a proper motion in certain stars has\\nbeen suspected, its annual amount has been so small,\\nthat many years are required to assure us that the effect\\nis not owing to some other than a real progressive mo-\\ntion in the stars themselves but in a few instances the\\nfact is too obvious to admit of any doubt. A greater\\nproportion of the double stars than of any other in-\\ndicate proper motions, especially the binary stars, or\\nthose which have a revolution around each other.\\n322. How may a star be in rapid motion, and yet appear\\nnearly at rest Through what space does the sun move an-\\nnually? What class of stars Lave the greatest proper motion?", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0300.jp2"}, "297": {"fulltext": "DISTANCES OF THE STARS. 281\\nDISTANCES OF THE FIXED STAKS.\\n323. It has long been considered one of the highest\\nproblems that can be proposed to the human mind, to\\nmeasure the distance to any of the fixed stars. Noth-\\ning more, indeed, would be necessary than to determine\\nits horizontal parallax but this is so exceedingly small,\\nthat, until recently, all efforts to measure it had proved\\nunavailing. For all measurements relating to the dis-\\ntances of the sun and planets, the diameter of the earth\\nfurnishes the base line. The length of this line being-\\nknown, and likewise the horizontal parallax of the body\\nwhose distance is sought, we readily obtain the distance\\nby the solution of a right-angled triangle. But any\\nstar viewed from the opposite sides of the earth, would\\nappear from both stations to occupy precisely the same\\nsituation in the celestial sphere, and of course it would\\nexhibit no horizontal parallax. But astronomers have\\nendeavored to find a parallax in some of the fixed stars,\\nby taking the diameter of the earth s orbit as a base\\nline. Yet even a change of position amounting to 190\\nmillions of miles, has, until within a few years, proved\\ninsufficient to alter the apparent place of a single fixed\\nstar, from which it was concluded that the fixed stars\\nhave not even any annual parallax or that the angle\\nsubtended by the semidiameter of the earth s orbit, at\\nthe nearest fixed star, is insensible. The errors to which\\ninstrumental measurements are subject, are such, that\\nthe angular determinations of celestial arcs, it was\\nsupposed, could not be relied on to less than 1 and\\nthe change of place in any star that had been examined\\nfor parallax being less than one second when viewed at\\nopposite extremities of the earth s orbit, the conclusion\\nwas, that the parallax of the fixed stars, if any exist, is\\ntoo minute ever to be measured by instruments.\\nAfter many fruitless and delusory efforts to meas-\\nure the immense interval that separates us from\\nthe fixed stars, the great Prussian astronomer, Bessel,\\n24*", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0301.jp2"}, "298": {"fulltext": "282 DISTANCES OF THE STARS.\\nin the year 1838, determined this interesting and im-\\nportant element, by observations on a double star in the\\nSwan (61 Cygni). This star was selected for the fol-\\nlowing reasons first, it was known to have a great\\nproper motion, indicating a comparatively great prox-\\nimity to our system secondly, situated as it is among\\nthe circumpolar stars, observations could be made\\nupon it nearly every night in the year and, thirdly,\\nthe great number of small stars in the immediate\\nneighborhood, furnished the opportunity of select-\\ning favorable stationary points from which (inasmuch\\nas these more remote objects might be considered as\\nentirely devoid of parallax) any changes of place in\\nthe nearer, in consequence of an annual parallax, might\\nbe readily estimated. By observations of the last de-\\ngree of refinement, conducted for a period of several\\nyears, a parallax was decisively indicated, amounting\\nto about one-third of a second or, more exactly, to\\n0. 3183, implying a distance of 592,200 times the mean\\ndistance of the earth from the sun, or a space which it\\nwould take light, moving at the rate of twelve millions\\nof miles per minute, nine and a quarter years to\\ntraverse. To form some familiar notions of this dis-\\ntance, let us suppose a railway-car to travel night and\\nday, at the rate of twenty miles an hour we should\\nfind it would take it about 517 years to reach the sun\\nbut to reach 61 Cygni would require 324,000,000 of\\nyears.\\n324. The observations of Bessel enabled him to es-\\ntimate also the period of revolution of the two stars\\n323. What has been long considered one of the greatest of\\nproblems What element must be first determined before we\\ncan measure the distance of a fixed star What is used as a\\nbase line What is said of the minuteness of the annual\\nparallax, and of the discovery of that of 6 1 Cygni What is\\nthe amount of this parallax How long would it take light to\\ntraverse the distance How long a rail-car", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0302.jp2"}, "299": {"fulltext": "DISTANCES OF THE STAES. 283\\ncomposing the binary system of 61 Cygni, and the\\ndimensions of the orbit, and he found the periodic time\\nabout 540 years, and the length of the orbit about two\\nand a half times that of Uranus. Knowing also the\\ndistance of this star, we can now determine from its\\nproper motion (five seconds a year) the velocity of its\\nmotion this is found to be about forty-four miles per\\nsecond more than double that of the earth in its orbit\\namounting to about one thousand millions of miles\\nper annum.\\nOn account of the smallness of the supposed parallax\\nthus found, it would not be unreasonable still to enter-\\ntain a lingering suspicion, that it is nothing more than\\nthe unavoidable imperfection of instrumental measure-\\nments, as proved to be the case in previous attempts to\\nfind the same element but the most satisfactory evi-\\ndence which the world can have that such is not the\\nfact in the present instance, but that the parallax is\\ntruly found, is that the most celebrated astronomers of\\nthe age, after rigorous scrutiny, have acknowledged the\\nreality and soundness of the determination. Our con-\\nfidence that the parallax of 61 Cygni was truly deter-\\nmined by Bessel, is strengthened by the fact that a\\nseparate determination recently made by Peters at the\\nPulkova Observatory, gives almost precisely the same\\nresult, that of Bessel being 0. 318, and that of Peters\\n0. 349. In the case of several stars still more distant,\\nthe parallax has been found, with more or less proba-\\nbility, but with sufficient to command the general con-\\nfidence of astronomers. Thus, the parallax of Arcturus,\\nAlpha Lyrse, and Polaris, were also found bv Peters to\\nbe respectively 0/127, 0/123, 0. 067, that of the Pole-\\n324. What is the peiiodic time of the stars composing the\\nbinary system of 61 Cygni, and the length of orbit What is\\nsaid of the evidence attending these results Also of the\\nparallax of Arcturus, Alpha Lyrse, the Pole-star, and Alpha\\nCentauri", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0303.jp2"}, "300": {"fulltext": "284 NATURE OF THE STARS.\\nstar being only one-fifth as great as that of 61 Cygni\\nand, consequently, if light would require 9 years to\\ncome from that star, it would require more than 46\\nyears to come to us from the Pole-star. A star in the\\nsouthern hemisphere, (Alpha Centauri,) indicates a\\nparallax of about 1 and hence appears at present the\\nnearest of the fixed stars.\\nMATURE OF THE STARS.\\n325. The stars are bodies greater than our earth. If\\nthis were not the case they could not be visible at such\\nan immense distance. Dr. Wollaston, a distinguished\\nEnglish philosopher, attempted to estimate the magni-\\ntudes of certain of the fixed stars from the light which\\nthey afford. By means of an accurate photometer (an\\ninstrument for measuring the relative intensities of\\nlight) he compared the light of Sirius with that of the\\nsun. He next inquired how far the sun must be re-\\nmoved from us in order to appear no brighter than\\nSirius. He found the distance to be 141,400 times its\\npresent distance. But Sirius is more than 200,000 times\\nas far off as the sun. Hence he inferred that, upon the\\nlowest computation, Sirius must actually give out twice\\nas much light as the sun. Indeed, he has rendered it\\nprobable that the light of Sirius is equal to fourteen suns.\\nFrom the smallness of its parallax it is inferred to be\\nequal to sixty-three suns.\\n326. The fixed stars are suns. We have already\\nseen that they are large bodies that they are immensely\\nfurther off than the furtherest planet that they shine\\nby their own light, as is evident by the nature of the\\nlight as tested by polarization in short, that their ap-\\npearance is, in all respects, the same as the sun would\\n325. What evidence have we that the Stars are greater than\\nthe Earth Also that they are Suns How much larger is\\nSirius than the Sun", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0304.jp2"}, "301": {"fulltext": "SYSTEM OF THE WORLD. 285\\nexhibit if removed to the region of the stars. Hence\\nwe infer that they are bodies of the same kind with\\nthe sun.\\nWe are justified therefore by a sound analogy, in\\nconcluding that the stars were made for the same end\\nas the sun, namely, as the centers of attraction to other\\nplanetary worlds, to which they severally dispense light\\nand heat. Although the starry heavens present, in a\\nclear night, a spectacle of ineffable grandeur and\\nbeauty, yet it must be admitted that the chief purpose\\nof the stars could not have been to adorn the night,\\nsince by far the greatest part of them are wholly in-\\nvisible to the naked eye nor as landmarks to the\\nnavigator, for only a very small proportion of them are\\nadapted for this purpose nor, finally, to influence the\\nearth by their attractions, since their distance renders\\nsuch an effect entirely insensible. If they are suns,\\nand if they exert no important agencies upon our\\nworld, but are bodies evidently adapted to the same\\npurpose as our sun, then it is as rational to suppose\\nthat they were made to give light and heat, as that the\\neye was made for seeing and the ear for hearing. It\\nis obvious to inquire next, to what they dispense these\\ngifts if not to planetary worlds and why to planetary\\nworlds, if not for the use of percipient beings We\\nare thus led, almost inevitably, to the idea of a Plu-\\nrality of Worlds and the conclusion is forced upon\\nus, that the spot which the Creator has assigned to us\\nis but a humble province of his boundless empire.\\nSYSTEM OF THE WORLD.\\n327. The arrangement of all the bodies that compose\\nthe material universe, and their relations to each other,\\nconstitute the System of the World.\\nIn the earliest ages of the world mankind believed\\nthat the earth was an extended plane, at rest in the\\n326. For what purpose were the stars created", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0305.jp2"}, "302": {"fulltext": "286 SYSTEM OF THE WORLD.\\ncenter of the universe, and that all the heavenly bodies\\ndaily revolved around it. The ancient Greek astrono-\\nmers, however, taught that the earth is round, and one\\nof the most celebrated of them, Pythagoras, even went\\nso far as to maintain that the sun is the true center\\naround which the earth and planets resolve. But this\\nopinion found hardly any supporters, until it was re-\\nvived and matured into a system by Copernicus, a\\nPrussian astronomer, not far from the year 1500. It is\\nnow universally regarded by astronomers as the true\\nview of the mechanism of the solar system.\\nThe Copemican System, as was briefly mentioned\\nnear the beginning of this work, maintains (1), That the\\napparent diurnal revolution of the heavenly bodies,\\nfrom east to west, is owing to the real revolution of the\\nearth on its own axis from west to east, in the same\\ntime and (2), That the sun is the center around which\\nthe earth and planets all revolve from west to east, con-\\ntrary to the opinion that the earth is the center of motion\\nof the sun and planets.\\nPirst, the earth revolves on its axis.\\n1. This supposition is vastly more simple, than that\\nthe whole host of heaven, sun, planets, and stars, in-\\ncluding millions of bodies larger than the earth, is all\\ncarried daily around our little planet.\\n2. The velocity which such a daily circuit would im-\\nply, especially in the fixed stars, is wholly incredible.\\n3. Such a revolution of the earth is agreeable to\\nanalogy, since the other planets are seen, by the tele-\\nscope, to turn on their axes.\\n4. The sp heroidal figure of the earth, and the dimin-\\nished tveight of bodies at the equator, are the natural\\neffects of such a revolution.\\nSecondly, the planets, including the earth, revolve\\nabout the sun.\\n1. The phases and motions of Mercitry and Venus\\nare precisely such as would result from their revolving\\nabout the sun in orbits within that of the earth, and in-\\nconsistent with any other supposition.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0306.jp2"}, "303": {"fulltext": "SYSTEM OF THE WORLD. 287\\n2. The superior planets are found by actual measure-\\nment always to keep at nearly the same distance from\\nthe sun, and therefore they revolve around the sun as a\\ncenter.\\n3. The earth itself also is proved by the most con-\\nclusive arguments to revolve around the sun, and not\\nthe sun around the earth. For the sun being vastly\\nlarger and heavier than the earth, its centrifugal force\\nwould be greater than could be balanced by the earth s\\nattraction, and would carry it away from the earth into\\nspace, drawing the earth after it.\\nThirdly, Since it is known that the laws of the plane-\\ntary system, namely, the law of gravitation and Kep-\\nler s laws, extend to the stars, and that some of them,\\nas the Binary stars, are bound together in systems\\nsimilar to the solar system, and that many other stars\\nare seen to be in motion the most rational conclusion\\nis, that there exist multitudes of starry systems, con-\\nstructed upon the same model as the planetary system,\\nand, finally, that all these subordinate systems of worlds\\nare combined under the same mechanical laws to form\\nthe grand machine of the Universe.\\n32*7. Define the term system of the world. What opinions\\nprevailed respecting it in the earliest ages What among the\\nancient Greek astronomers What are the two leading points\\nof the Copernican system How is it proved that the earth\\nturns on its axis How that it revolves about the sun What\\nhigher systems are supposed to exist How are these combined\\nto form the Universe", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0307.jp2"}, "304": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0308.jp2"}, "305": {"fulltext": "VALUABLE WORKS\\nPUBLISHED BY\\nROBERT B. COLLINS,\\nTCo. 254 frtfl Sfireef, fob J|ori|.\\nPROFESSOR OLMSTED S SERIES.\\nOLMSTED S NATURAL PHILOSOPHY. 8vo. College\\nedition.\\nAn Introduction to Natural Philosophy designed as a text-\\nbook for students in Yale College.\\nOLMSTED S ASTRONOMY. 8vo. College edition.\\nAn Introduction to Astronomy designed as a text-book for the\\nuse of students in Yale College.\\nThe two works were originally prepared by the author (Denison\\nOlmsted, L.L.D.) for the use of the classes under his care in Yale\\nCollege, and have been adopted as text-books in most of the col-\\nleges and higher seminaries of learning in the country.\\nMASON S SUPPLEMENT.\\nAn Introduction to Practical Astronomy, designed as a Supple-\\nment to Olmsted s Astronomy containing Special Rules for the\\nAdjustment and Use of Astronomical Instruments, together with\\nthe Calculation of Eclipses and Occupations, and the method of\\nfinding the Latitude and Longitude. By Ebenezer Porter Mason.\\nOLMSTED S SCHOOL ASTRONOMY. 12mo.\\nA Compendium of Astronomy containing the Elements of the\\nScience familiarly explained and illustrated, with the Latest Dis-\\ncoveries, for the use of schools and academies and of the general\\nreader.\\nOLMSTED S RUDIMENTS. l8mo.\\nRudiments of Natural Philosophy and Astronomy designed for\\nthe younger classes in academies and for common schools. A very\\nvaluable text-book for beginners.", "height": "3568", "width": "2152", "jp2-path": "compendiumofast00olm_0309.jp2"}, "306": {"fulltext": "ROBERT B. COLLINS S PUBLICATIONS.\\nPROFESSOR COFFIN S WORKS.\\nCOFFIN S ECLIPSES.\\nSolar and Lunar Eclipses, Familiarly Illustrated and Explained,\\nwith the Method of Calculating them according to the Theory of\\nAstronomy, as taught in the New England Colleges.\\nCOFFIN S CONIC SECTIONS.\\nElements of Conic Sections and Analytical Geometry.\\nThese works, by Prof. James H. Coffin, of Lafayette College, Pa.,\\nhave received the highest recommendations from qualified author-\\nity. Of the second named, (Conic Sections, (fee.) Prof. Loomis,\\n(College of New Jersey,) Prof. Sadler, Prof. Mason, and other dis-\\ntinguished gentlemen, unite in approval.\\nBY LYMAN PRESTON.\\nPRESTON S DISTRICT SCHOOL BOOK-KEEPING,\\nAffording an interesting and profitable exercise for youth, being\\nespecially designed for Classes in our Common Schools.\\nPRESTON S BOOK-KEEPING BY SINGLE ENTRY,\\nAdapted to the use of Retailers, Farmers, Mechanics, and Common\\nSchools.\\nPRESTON S TREATISE ON BOOK-KEEPING\\nA common-sense guide to a common-sense mind. In two parts\\nthe first the Single Entry method, the second being arranged more\\nparticularly for the instruction of young men who contemplate\\nthe pursuit of mercantile business, showing the method of keeping\\naccounts by Double Entry, and embracing a variety of useful forms.\\nThis is the most popular work upon the subject, and is in very\\nextensive use throughout the country.\\nADAMS S ARITHMETICAL SERIES.\\nADAMS S PRIMARY ARITHMETIC,\\nOr Mental Operationsin Numbers, an Introduction to Adams s New\\nArithmetic, revised edition. An excellent work for young learners.\\nADAMS S NEW ARITHMETIC. Revised edition.\\nBy Daniel Adams, M.D. A new edition of this superior work,\\nwith various improvements and additions, as the wants of the\\ntimes demand. A Key is published separately.\\nADAMS S MENSURATION, MECHANICAL POWERS,\\nAND MACHINERY.\\nThis admirable work is designed as a senuel to the Arithmetic.", "height": "3616", "width": "2152", "jp2-path": "compendiumofast00olm_0310.jp2"}, "307": {"fulltext": "ROBERT B. COLLINS S PUBLICATIONS.\\nADAMS S BOOK-KEEPING.\\nA Treatise on Book-keeping by Single Entry, accompanied b\\nblanks for the use of learners.\\nABBOTT S SERIES.\\nABBOTT S HEADERS.\\nThe Mount Yernon Reader for Junior Classes. 18mo\\nThe Mount Vernon Reader for Middle Classes. 18mo.\\nThe Mount Vernon Reader for Senior Classes. 12mo.\\nABBOTT S FIRST ARITHMETIC.\\nThe Mount Vernon Arithmetic. Part First Elementary.\\nThe Mount Vernon Arithmetic. Part Second Fractions.\\nABBOTT S ABERCROMBIE S PHILOSOPHY.\\nInquiries concerning the Intellectual Powers and the Investiga-\\ntion of Truth. By John Abercrombie, M.D. F.R.S. Edited, with\\nadditions, by Jacob Abbott.\\nThe Philosophy of the Moral Feelings. By John Abercrombie.\\nEdited by Jacob Abbott.\\nABBOTT S DRAWING CARDS.\\nIn three Sets, 40 Cards to each.\\nWHELPLEY S COMPEND OF HISTORY.\\nWith Questions by Joseph Emerson. 12mo.\\nBADLAM S WRITING BOOKS.\\nThe Common School Writing Books. A New Series of Nine\\nNumbers. By Otis GL Badlam.\\nADDICK S ELEMENTS\\nOF THE FRENCH LANGUAGE\\nAn excellent elementary work.\\nGIRARD S ELEMENTS\\nOF THE SPANISH LANGUAGE.\\nA. practical work to Teach, to Speak, and Write Spanish. By\\nJ. F. Girard.\\nKIRKHAM S GRAMMAR.\\nEnglish Grammar in Familiar Lectures, for the Use of Schools.\\nBy Samuel Kirkham. The work is very extensively used.\\nDAY S MATHEMATICS.\\nA Treatise for Students, by President Day, of Yale College.", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0311.jp2"}, "308": {"fulltext": "ROBERT B. COLLINS S PUBLICATIONS.\\nTHE GOVERNMENTAL INSTRUCTOR.\\nA Brief and Comprehensive View of the Government of the\\nUnited States, and of the State Governments, in easy lessons, for\\nthe use of Schools. By J. B. Shurtleff.\\nTHE OXFORD DRAWING-BOOK.\\nContaining Progressive Lessons on Sketching, Drawing and\\nColoring Landscape Scenery, Animals and the Human Figure.\\nWith 100 Lithographic Drawings. 4to.\\nJOHN RUBENS SMITH S DRAWING-BOOK.\\nThe Rudiments of the Art explained in Easy Progressive Les-\\nsons, embracing Drawing and Shading. With numerous Copper-\\nplate Engravings.\\nSTUDIES IN FLOWER PAINTING.\\nBy Jas. Andrews. Colored plates.\\nDYMOND S ESSAYS.\\nOn the Principles of Morality, and the Private and Political\\nRights and Obligations of Mankind. By J. Dymond.\\nKEMPIS.\\nThe Imitation of Christ. By Thomas a Kempis. Translated\\nby John Payne, with Introductory Essay by Thomas Chalmers.\\njESOP S fables.\\nA New Version, by Rev. Thomas James. Illustrated by James\\nTenniel. The best edition published in the country.\\nOUR COUSINS IN OHIO.\\nBy Mary Howitt. From the Diary of an American Mother. 1 8uao\u00e2\u0080\u009e\\nGABRIEL.\\nA Story of Wichnor Wood. By Mary Howitt,\\nTHE AMERICAN SCHOOL PRIMER.\\nIllustrated. 46 pp., 12mo.\\nTHE CHILD S PRIMER.\\nIllustrated. 36 pp., 18mo.\\nJOHN WOOLMAN S JOURNAL.\\nDAVID SANDS JOURNAL.\\nTHE NEW TESTAMENT.\\n8vo. Large print.", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0312.jp2"}, "309": {"fulltext": "", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0313.jp2"}, "310": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0314.jp2"}, "311": {"fulltext": "", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0315.jp2"}, "312": {"fulltext": "", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0316.jp2"}, "313": {"fulltext": "", "height": "3580", "width": "2116", "jp2-path": "compendiumofast00olm_0317.jp2"}, "314": {"fulltext": "003 630 374", "height": "3575", "width": "2148", "jp2-path": "compendiumofast00olm_0318.jp2"}}