{"1": {"fulltext": "", "height": "3731", "width": "2199", "jp2-path": "compendiumofastr00olms_0001.jp2"}, "2": {"fulltext": "X\\ns\\nk Co\\nA C\\n\u00e2\u0080\u00a21\\nV\\n4\\n\u00e2\u0096\u00a0A r\\nC\u00c2\u00a3* y\\nP\\n-V\\n-s\\nV\\nA\\no\\ni\\n-y\\no\\nv x\\nP.", "height": "3537", "width": "2066", "jp2-path": "compendiumofastr00olms_0002.jp2"}, "3": {"fulltext": ",0 o", "height": "3537", "width": "2066", "jp2-path": "compendiumofastr00olms_0003.jp2"}, "4": {"fulltext": "", "height": "3537", "width": "2066", "jp2-path": "compendiumofastr00olms_0004.jp2"}, "5": {"fulltext": "", "height": "3537", "width": "2066", "jp2-path": "compendiumofastr00olms_0005.jp2"}, "6": {"fulltext": "", "height": "3537", "width": "2066", "jp2-path": "compendiumofastr00olms_0006.jp2"}, "7": {"fulltext": "", "height": "3537", "width": "2066", "jp2-path": "compendiumofastr00olms_0007.jp2"}, "8": {"fulltext": "Telescopic View of the Moon.\\nTelescopic View of the Moon when five days old.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0008.jp2"}, "9": {"fulltext": "COMPENDIUM OF ASTRONOMY;\\nCONTAINING THE\\nELEMENTS OF THE SCIENCE,\\nFAMILIARLY EXPLAINED AND ILLUSTRATED,\\nWITH THE LATEST DISCOVERIES.\\nADAPTED TO THE USE OP\\nSCHOOLS AND ACADEMIES,\\nAND OP THE\\nGENERAL READER.\\nSTEREOTYPE EDITION.\\nBY DENISON OLMSTED, A. M.\\nPROFBSSOB OT NATURAL PHILOSOPHY AND ASTRONOMY IN YALE GOLLESK\\nNEW YORK:\\nROBERT B. COLLINS.\\n254 PEARL STREET.\\n1850,", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0009.jp2"}, "10": {"fulltext": "Entered according to Act of Congress, in the year 1839, by\\nDENISON OLMSTED,\\nin the Clerk s office, of the District Court of Connecticut", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0010.jp2"}, "11": {"fulltext": "PREFACE.\\nThis small volume is intended to afford to the General\\nReader, and to the more advanced pupils of our Schools and\\nAcademies, a comprehensive outline of Astronomy with its\\nlatest discoveries. For its perusal, no further acquaintance\\nwith mathematics is necessary, than a knowledge of common\\narithmetic although some slight knowledge, at least, of ge-\\nometry and trigonometry will prove very useful.\\nBy omitting mathematical formulae, and employing much\\nfamiliar illustration, we have endeavored to bring the leading\\nfacts and doctrines of this noble and interesting science, within\\nthe comprehension of every attentive and intelligent reader.\\nIn no science, more than in this, are greater advantages to be\\nderived from a lucid arrangement an order winch brings out\\nevery fact and doctrine of the science, just in the place where\\nthe mind is ready to receive it. A certain maturity of mind,\\nand power of reflection, are, however, indispensable for under-\\nstanding this science. Astronomy is no study for children.\\nLet them be employed on subjects more suited to the state of\\ntheir capacities, until those faculties are more fully developed,\\nwhich will enable them to learn to conceive correctly of the\\ncelestial motions. A work on Astronomy that is very easy,\\nmust be very superficial, and will be found to enter little into\\nthe arcana of the science. The riches of this mine lie deep\\nand no one can acquire them, who is either incompetent or\\nunwilling to penetrate beneath the surface.\\nAlthough this treatise is based on the larger work of the\\nauthor, Introduction to Astronomy, prepared for the stu-\\ndents of Yale College, yet it is not merely an abridgment of\\nthat. It contains much original jnatter adapted to the pecu-\\nliar exigencies of the class of readers for whom it is intended.\\nThe few passages taken verbatim from astronomical writers,", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0011.jp2"}, "12": {"fulltext": "IV PREFACE.\\nare not, as in the larger work, always accredited to their re-\\nspective authors, as this was deemed unimportant in a work\\nof this description.\\nIt is strongly recommended to all who study this science,\\neven in its most elementary form, early to commence learning\\nthe names of the constellations, and of the largest of the in-\\ndividual stars, in the order in which they are described in the\\nlast part of the work. A celestial globe will be found a most\\nuseful auxiliary in this as in every other part of Astronomy.\\nIf it cannot supersede, it may greatly aid reflection. The\\nreader also should, if in his power, take frequent opportunities\\nof viewing the heavenly bodies through the telescope. This\\nwill add much to his intelligence, and increase his interest in\\nthe study.\\nADVERTISEMENT.\\nSince the stereotype edition of this work was first pub-\\nlished, several new and interesting discoveries have been added\\nto Astronomy, an account of which will be found in the Sup-\\nplement. They make no change in the great facts and doc-\\ntrines of the science, but these remain unaltered and immu-\\ntable while the new discoveries extend still further our\\nknowledge of the Universe. We have, therefore, no occasion\\nto alter the text, except perhaps very slightly in one or two\\nstatements, but by giving whatever is new and important in\\nthe form of a supplement, (to which we may add as every\\nsuccessive discovery is made,) we shall endeavor to secure to\\nthis treatise the freshness and accuracy of the most recent\\ncompilations, as well as furnish to the schools what has been\\nthoroughly tested and approved by the most able teachers of\\nthe Union.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0012.jp2"}, "13": {"fulltext": "CONTENTS.\\nPreliminary Observations, Page 1\\nPart I. OF THE EARTH.\\nChapter I. Of the Figure and Dimensions of the Earth,\\nand the Doctrine of the Sphere, 5\\nChapter II. Of the Diurnal Revolution Artificial\\nGlobes, *i\\nChapter III. Of Parallax, Refraction, and Twilight, 36\\nChapter IV.\u00e2\u0080\u0094 Of Time, 45\\nChapter V. Of Astronomical Instruments Figure\\nand Density of the Earth, 51\\nPart II. OF THE SOLAR SYSTEM.\\nChapter I. Of the Sun Solar Spots Zodiacal Light, 70\\nChapter II. Of the Apparent Annual Motion of the\\nSun Seasons Figure of the Earth s Orbit, 79\\nChapter III. Of Universal Gravitation Kepler s\\nLaws, Motion in an Elliptical Orbit Precession\\nof the Equinoxes, 91\\nChapter IV. Of the Moon Phases, Revolutions, 110\\nChapter V. Of Eclipses, 137\\nChapter VI.\u00e2\u0080\u0094 Of Longitude\u00e2\u0080\u0094 Tides, 150\\nChapter VII. Of the Planets the Inferior Planets,\\nMercury and Venus, 1 67\\nChapter VIII. Of the Superior Planets Mars, Jupiter,\\nSaturn and Uranus Ceres, Pallas, Juno and Vesta, 183", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0013.jp2"}, "14": {"fulltext": "vl CONTENTS.\\nVJ Pag\u00c2\u00ab\\nChapter IX.\u00e2\u0080\u0094 Of the Motions of the Planetary System\\n\u00e2\u0080\u0094Quantity of Matter in the Sun and Planets-\\nStability of the Solar System, 205\\nChapter X.\u00e2\u0080\u0094 Of Comets, 218\\nPart IIL OF THE FIXED STARS AND THE SYS-\\nTEM OF THE WORLD.\\nChapter I.\u00e2\u0080\u0094 Of the Fixed Stars Constellations, 235\\nChapter II.\u00e2\u0080\u0094 Of Clusters of Stars\u00e2\u0080\u0094 Nebula\u00e2\u0080\u0094 Variable\\nStars\u00e2\u0080\u0094 Temporary Stars\u00e2\u0080\u0094 Double Stars, 247\\nChapter IIL\u00e2\u0080\u0094 Of the Motions of the Fixed Stars\u00e2\u0080\u0094 Dis-\\n255\\ntances Nature,\\nChapter IV.\u00e2\u0080\u0094 Of the System of the World, 265", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0014.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 Name the three\\nparU into which it is divided. What does Descriptive Astron-\\nomy respect What does Physical Astronomy What does\\nPractical Astronomy 1 What is the peculiar province of each\\n1", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0015.jp2"}, "16": {"fulltext": "2 PRELIMINARY OBSERVATIONS.\\nments, 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 1 Where was his school How correct\\nwere his views 1 Were they generally adopted 1 Give an ac-\\ncount of the Alexandrian school. When was it established and\\nby whom 1 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 of\\nNewton of La Place. Specify the respective labors of each.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0016.jp2"}, "17": {"fulltext": "PRELIMINARY OBSERVATIONS.\\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 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, the 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 di*\\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 1\\n4. What is said of the industrv and accuracy of astrono-\\nmers Can this science be taught by artificial aids alone", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0017.jp2"}, "18": {"fulltext": "4 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 aiford 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": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0018.jp2"}, "19": {"fulltext": "PART I.\u00e2\u0080\u0094 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, first, 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, by\\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.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0019.jp2"}, "20": {"fulltext": "THE EARTH.\\nFig. 1.\\na 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": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0020.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 shoulc 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.*\\n51\\nNow or about one sixteen hundredth part\\n7912 1582 r\\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 that pre-occupy the mind. To divest himself\\n7. What is the exact figure of the earth 1 How much greater\\nis its diameter through the equator than through the poles 1\\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 How\\ndeep is the deepest mine? To how much would this amount\\non an artificial globe eighteen inches in diameter\\nSir John Herschel.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0021.jp2"}, "22": {"fulltext": "8 THE 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 1 How should the learner conceive of\\nthe earth Illustrate by figure 3.\\n9. Doctrine of the sphere define it.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0022.jp2"}, "23": {"fulltext": "DOCTRINE OF TtfE SPHERE.\\n9\\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. na atj\\nAny part of the circumference of a circle is called an arc, as AC,\\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\\nABis 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 ot 1H0\u00c2\u00b0.\\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": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0023.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.\\n1 1. 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 1 What is the secondary of a circle How is the angle\\nmade by 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": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0024.jp2"}, "25": {"fulltext": "DOCTRINE 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. 1 his 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 90 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 1\\n13 What are the poles of the horizon 1 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": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0025.jp2"}, "26": {"fulltext": "12 THE EARTH.\\n14. Vertical circles are those which pass through the\\nooles 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 vertical circle wluch\\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.\\n1 5. 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\\n15. Define the axis of the earth the axis of the celestial\\nsphere the poles of the earth the poles of the heavens.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0026.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\u00e2\u0080\u0094 the polar distance.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0027.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 23J degrees out of a per-\\npendicular direction, making an angle with the plane\\nitself of 66i\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 23J\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 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 1 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\\nGiants themselves.", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0028.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\\nNorthern.\\nSouthern.\\n1.\\nAries\\nop\\n7. Libra\\n-Ti.\\n2.\\nTaurus\\n8\\n8. Scorpio\\nm\\n3.\\nGemini\\nn\\n9. Sagittarius\\nt\\n4.\\nCancer\\n\u00c2\u00a3d\\n10. Capricornus\\nvs\\n5.\\nLeo\\nSI\\n11. Aquarius\\n/vw\\n6.\\nVirgo\\nn\\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 may be 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. Right\\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 1 How\\nmany degrees are there in each 1 Name the signs. What is\\nthe mode of reckoning on the ecliptic In what two wavs\\nmay 100\u00c2\u00b0 be expressed\\n23. What is the equinoctial colure the solstitial colure 1", "height": "3525", "width": "1933", "jp2-path": "compendiumofastr00olms_0029.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 celestia.\\nlongitude and latitude.\\n25. What are parallels of latitude tropics polar circles\\nTo what is the elevation of the pole always equal also that\\nof the equator", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0030.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 anyround\\nbody, as an apple, and point out the various circles on it.\\n2*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0031.jp2"}, "32": {"fulltext": "18\\nTHE 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 Jialf\\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\u00c2\u00a3 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.\\\\ fWhen this horizon is slipped\\ni\\n29. How is the horizon represented in our model How is\\nit placed to represent the horizon of the equator How for the\\nhorizon of the poles 1 How for our own horizon 1 How shall\\nwe represent the prime vertical", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0032.jp2"}, "33": {"fulltext": "DOCTRINE OF THE SPHERE. 19\\nup to the poles, it becomes the horizon of the equator j\\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 6f 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 m\\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\\n3 1 What is meant by the projection of the sphere 1 What\\nis the projection of a circle when seen directly before the face\\nwhat when seen obliquely 1 what when seen edgewise 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0033.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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0034.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.\\n(In 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 1 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 1 What\\nare circles of diurnal revolution", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0035.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,\\nrthe 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 zenjth, 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 or\\nunequal 1 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 1 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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0036.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 ci?xles 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, they describe smaller and\\nsmaller circles, until(near the pole, their motion is hardly\\nperceptible]\\n36. Vjf 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 are parallel to the horizon.\\nTo render this view of the heavens familiar, the\\nlearner should follow round in his mincl 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0037.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^xcept 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:\\n(An 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, anil 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0038.jp2"}, "39": {"fulltext": "DIURNAL REVOLUTION.\\n25\\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.\\n88. 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 elevation of the pole, and of course to the lati-\\ntude.^)\\n38. What is the circle of perpetual apparition? I.lustrate\\nby fig. 6.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0039.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,\\n(7%e 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 the\\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\\ngreat 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 6\\n41. Most of the appearances of the diurnal revolution\\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 1 When are the days longer, and when\\nshorter than the nights", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0040.jp2"}, "41": {"fulltext": "DIURNAL REVOLUTION. 27\\naxis in the opposite direction\u00e2\u0080\u0094 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 axisA\\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\\nI horizon now passes through both the poles,Vnd through\\n^the sun, which we are to conceive of as af a great dis-\\ntance from the earth, and therefore as cut, not by the\\nterrestrial but by the celestial horizon) \u00c2\u00a3As the earth\\nturns, the horizon dips more and morei)erow 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^\\n*the 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\\n41 On what suppositions can the appearances of the diurna.\\nrevolution be explained 1 Is it the earth or the heavens tha\\nreally move 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. 8 What is the position of the ho-\\nrizon at sunrise What at. six hours afterwards What a\\nthe end of twelve hours What at the end of eighteen hours", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0041.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 a 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0042.jp2"}, "43": {"fulltext": "ARTIFICIAL GLOBES.\\n29\\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. CAn 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. v 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\\namplitudes and a wide space on which are delineated\\nthe signs^ f 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 1 What does\\nthe celestial globe W T hat do both show 1\\n45. How is the meridian of the place represented? To what\\npoints is the brass meridian fastened What supports the ring 1\\nHow is it graduated How is the horizon represented 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0043.jp2"}, "44": {"fulltext": "30 THE EARTH.\\n46. Hour Circles are represented on the terrestrial\\nglobe hy 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\\nbrassy graduated into ninety equaF 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 1 What arcs does it then measure 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0044.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\\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 ot\\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 Longitudi\\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. T\\nEx. What place on the globe is in Latitude 39 JN. ana\\nLongitude 77\u00c2\u00b0 W.\\n49. How do we rectify the globe for any place I\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0045.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 69,\\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\\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 1\\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 t\\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 1\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0046.jp2"}, "47": {"fulltext": "TERRESTRIAL GLOBE.\\n33\\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 f\\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 1\\n57. Who are the antipodes of the people of London 1\\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 the\\ncorresponding sign on the ecliptic itself.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0047.jp2"}, "48": {"fulltext": "34 THE EARTH.\\n59. Tne 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 hour 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0048.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, wih be\\nits azimuth. /f u Q\\nEx What is the altitude and azimuth of Sinus (the\\nbrightest of the fixed stars) on the 25th of December at\\n10 o clock in the evening, in Lat. 41\u00c2\u00b0?\\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\\nand 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 dine\\nTlearned JaltTdard of reference in estimating by the eye, the d,s-\\ntance between any two points on the celestial vault,", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0049.jp2"}, "50": {"fulltext": "*6\\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 Iljfc.\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0050.jp2"}, "51": {"fulltext": "PARALLAX.\\n37\\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 would appear at H. The arc Wi is called\\nthe parallactic arc, and the angle HE/i, or its equal AEO,\\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\\nRh F by the arc Yp 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\u00e2\u0080\u0094 By what is it subtended?\\n(See Art. 10. Note.) What is the effect of parallax upon the\\nplace of a heavenly body 1\\n4", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0051.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 oi\\nthe earth.*\\nREFRACTION.\\n68. While parallax depresses the celestial bodies sub-\\nject to it, refraction elevates them and it affects alike\\nthe 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 we 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0052.jp2"}, "53": {"fulltext": "qq\\nREFRACTION.\\nin passing through the atmosphere. Let us conceive of\\nhe atmosphere as made up of a great number of concen-\\ntric strata! as AA, BB, CC, and DD, (Fig 8.)\\nrapidly in density (as is known to be he fact) in ap-\\nproaching near to the surface of the earth Let S be a\\nstar! froi which a ray of light Sa enters the atmosphere\\nat a, where, being much turned towards the radius of\\nt n e Convex surface* it would change its d.rec ion into\\nthe line ab, and again into be, and cO, reaching he\\neve at O Now, since an object always appears in the\\ndiction in which the Ugh/ finally strikes the eye the\\nstar would be seen in the direction of he ray Oc and\\ntherefore, the star would apparently c hange it 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\\nurned out of its course more and more, it would there-\\nfore move, not in the polygon represented ,n 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\\nbodv Bv whatis it occasioned 2 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 1 In what line\\ndoes the light move as it goes through the atmosphere\\ndium, and when it passes out of a denser into a rarer me w\\nit approaches to the earth, because the density of the air rapidly in\\ncreases.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0053.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\\nElevation.\\nRefraction.\\nElevation.\\nRefraction.\\n0\u00c2\u00b0 10\\n32 00\\n30\u00c2\u00b0\\n1 40\\n0\u00c2\u00b0 20\\n30 00\\n40\u00c2\u00b0\\nV 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 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 Why\\nnot. When is the refraction greatest What is the amount\\nof refraction at the horizon How much does it lose within\\n1 0 of the horizon 1 What is the amount of refraction at an\\nelevation of 45\u00c2\u00b0", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0054.jp2"}, "55": {"fulltext": "REFRACTION. 41\\nview both before they have actually risen and after they\\nllflVP 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 s sun\\nhas been observed to amount to 6 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 m the former. 1 he\\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 i It\\n70. What effect has refraction upon the appearances of the\\nsun and moon when near rising or setting? Explai n 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 Ye shortened I\\n4*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0055.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,\\nnet 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\\nve 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 1 Are these bodies seen\\nunder a greater angle when in the horizon than in the zenith\\nTo what general law of optics is the enlargement to be ascri-\\nbed 1 How is it when we view the sun through smoked glass\\nTo what is the extraordinary enlargement of these luminaries\\nowing, when seen through a grove of trees", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0056.jp2"}, "57": {"fulltext": "43\\npQe ABS would be illuminated. To a ^P^tatorat C\\nwhose horizon was CD, the small segment SVx would\\nbe the twilight while, at E, the twilight would d.sap-\\npear altogether.\\n73. At the equator, where the circles of daily motion\\nappendicular to the horizon, the sun descends\\nthrough 18\u00c2\u00b0 in an hour and twelve minutes (-p=lxn.),\\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 white 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 1 Explain by the figure.\\n73 What is the length of twilight at the equator How\\nIon- does it last at the poles How is the progress from con-\\ntinual day to constant night 1 To the inhabitants of an oblique\\nsphere, in what latitudes is twilight longest", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0057.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 dav\\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 1 What is the aspect of the sky in\\nthe upper regions of the atmosphere\\nFrom old Eternity s mysterious orb,\\nWas Time cut off and cast beneath the skies. Young.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0058.jp2"}, "59": {"fulltext": "TIME.\\n45\\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\\na^ain. 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 365i\\ndays, it moves eastward nearly 1\u00c2\u00b0 a day, (59 8\\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\\n24\\n359 24 1 5^=4 m nearly.\\n75. Define time What is the standard of time What i\\na sidereal day 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0059.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 m 4 S .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 usuallyregulated 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 Define apparent time.\\n78. Define mean time. What constitutes the civil day\\nWhat makes an astronomical day When does the civil day\\nbegin When does the astronomical day begin", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0060.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 to 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?\\nWhen would they come together", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0061.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 wnc 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 1 1 min-\\nutes. This small fraction would amount in 100 years\\nto J 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\u00e2\u0080\u0094 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\\nyear only 365 days. How did Julius Caesar reform the calendar", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0062.jp2"}, "63": {"fulltext": "THE CALENDAR\\n49\\nshould 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\\n{Every 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 yearsj Yet to\\nmake every fourth year consist of 366 days would in-\\ncrease it too much by about J of a day in 100 years;\\ntherefore every hundredth year has only 365 days.\\n{Thus 1800, although divisible by 4 was not a leap year,\\nTaut a common year J But we have allowed a whole day\\nin a hundred years, whereas we 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 in one hundred years 1 To how much in a thousand\\nyears 1 To how much had it amounted from the year 325 to\\n1582 1 What changes did Pope Gregory make in the year 1\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0063.jp2"}, "64": {"fulltext": "50 THE EARTH.\\nof March but it was now made to begin on the 1st of\\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\\n-century, at present the correction is 12 days and the\\nnumber of the year wP\\\\ differ by one with respect to\\ndates between the 1st of January and the 25th of March,\\nExamples. General Washington was born Feb. 1 1\\n1731, 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,\\n1836 to what date would this time correspond in old\\nstyle 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 364 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 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.\\nIn 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0064.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 115th 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 year\\nwith respect to the day of the week 1 How is this in leap\\nyear 1\\n84. How did the most ancient nations acquire their knowl-\\nedge of the heavenly bodies 1 When were astronomical in-\\nstruments first introduced 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0065.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 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0066.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\\njL 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 What space when\\nthe circle is twenty feet in diameter 1 What are the princi-\\npal instruments used in astronomical observations\\n5*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0067.jp2"}, "68": {"fulltext": "54 THE 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 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 the 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 1 How is the\\nimage magnified 1 How is it rendered brighter 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0068.jp2"}, "69": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 55\\nnd 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. N 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 would 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, which, 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 simples-t 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 when 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 when 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 For what pur-\\nposes are telescopes chiefly employed", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0069.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.\\nm\\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 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0070.jp2"}, "71": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 5?\\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 ot\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0071.jp2"}, "72": {"fulltext": "58\\nTHE EARTH.\\nsun was on the meridian, we should set our clock at llh.\\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.\\n1\\nJan.\\nAdd.\\nM. S.\\n1U3\\nFeb.\\nAdd.\\nM. S.\\nMar.\\nArR.\\nAdd.\\nM. S.\\n476\\nMay\\nSub.\\nM. S.\\n3.\\nJUN.\\nSub.\\nM. S\\n2.38\\nJul.\\nAdd.\\nM. S.\\n319\\nAug\\nAdd.\\nM. S.\\n6. 3\\nSept.\\nAdd.\\nOct.\\nSub.\\nM. S.\\n10. 9\\nNov.\\nSub.\\nD 1\\nAdd.\\nSub.\\nM. S.\\nM. S.\\na0. 1\\nM. S.\\n16.15\\nM. S.\\n10.54\\n13.53\\n12.42\\n2\\n4.11\\n14. 1\\n12.30\\n3.48\\n3. 7\\n2.29\\n3.31\\n5.59\\n50.17\\n10.28\\n16.16\\n10.32\\n3\\n4.39\\n14. 8\\n12.18\\n3.30\\n3.15\\n2.19\\n3.42\\n5.55\\n0.36\\n10.47\\n16.17\\n10. 8\\n4\\n5. 7\\n14.14\\n12. 5\\n3.12\\n3.21\\n2.10\\n3.53\\n5.50\\n0.56\\n11. 6\\n1617\\n9.45\\n5\\n5.34\\n14.19\\n11.51\\n11.38\\n2.54\\n2.37\\n3.27\\n3.32\\n2.\\n1.49\\n4. 4\\n4.15\\n5.45\\n1.15\\n11.24\\n1616\\n9.20\\n8.55\\n6\\n6. 1\\n14.24\\n5.39\\n1.35\\n11.42\\n16.14\\n7\\n6.27\\n14.27\\n11.23\\n2.19\\n3.37\\n1.39\\n4.25\\n5.33\\n1.55\\n11.59\\n1611\\n8.30\\n8\\n6.53\\n14.30\\n11. 8\\n2. 2\\n3.42\\n1.28\\n4.34\\n5.25\\n2.15\\n12.16\\n16. 7\\n8. 4\\n9\\n7.18\\n14.32\\n10.53\\n1.45\\n3.46\\n1.17\\n4.44\\n5.18\\n2.36\\n12.33\\n16. 3\\n7.37\\n10\\n11\\n743\\n14.33\\n10.38\\n10.22\\n1.28\\n1.11\\n3.49\\n3.51\\n1. 5\\n0.53\\n4.53\\n5. 9\\n2.56\\n12.49\\n13. 5\\n15.58\\n7.10\\n8. 7\\n14.34\\n5. 1\\n5. 1\\n3.17\\n15.51\\n6.43\\n12\\n8.31\\n14.33\\n10. 6\\n0.55\\n3.53\\n0.41\\n5. 9\\n4.51\\n3.38\\n13.20\\n15.44\\n6.15\\n13\\n8.54\\n14.32\\n9.49\\n0.39\\n3.55\\n0.29\\n5.17\\n4.41\\n3.59\\n13.34\\n15.37\\n5.47\\n14\\n9.16\\n14.30\\n9.32\\n0.23\\n3.56\\n0.17\\n5.24\\n4.31\\n4.20\\n13.49\\n15.28\\n518\\n15\\n9.37\\n14.28\\n9.15\\n0. 8\\n3.56\\n0. 4\\nAdd\\n5.30\\n4.20\\n4.41\\n14. 2\\n1518\\n4.49\\nSab.\\n16\\n9.58\\n14.25\\n8.58\\n0. 7\\n3.56\\n0. 8\\n5.37\\n4. 8\\n5. 2\\n14.15\\n15. 8\\n4.20\\n17\\n10.19\\n14.20\\n8.41\\n0.22\\n3.55\\n0.21\\n5.42\\n3.56\\n5.23\\n14.28\\n14.56\\n3.50\\n18\\n10.38\\n14.16\\n8.23\\n0.36\\n3.54\\n0.34\\n5.48\\n3.44\\n5.44\\n14.39\\n14.44\\n3.21\\n19\\n10.57\\n14.10\\n8. 5\\n0.50\\n3.52\\n0.47\\n5.52\\n3.31\\n6. 5\\n14.51\\n14.31\\n2.51\\n20\\n21\\n11.15\\n11.33\\n14. 4\\n13.58\\n7.47\\n7.29\\n1. 3\\n1.16\\n3.49\\n3.46\\n1.\\n1.13\\n5.57\\n6.\\n3.17\\n3. 3\\n6.26\\n6.47\\n15. 1\\n14.17\\n2.21\\n1.51\\n15.11\\n14. 3\\n22\\n11.49\\n13.50\\n7.11\\n1.29\\n3.42\\n1.26\\n6. 3\\n2.49\\n7. 8\\n15.21\\n13.47\\n1.21\\n23\\n12. 5\\n13.42\\n6.52\\n1.41\\n3.38\\n1.39\\n6. 6\\n2.34\\n7.29\\n15.29\\n13.31\\n0.51\\n24\\n12.20\\n13.34\\n6.34\\n1.52\\n3.33\\n1.52\\n6. 8\\n2.19\\n7.49\\n15.3713.14\\n0.21\\n25\\n12.35\\n13.25\\n13.15\\n6.15\\n2. 4\\n3.28\\n3.22\\n2. 5\\n2.18\\n6. 9\\n6.10\\n2. 3\\n1.47\\n8.10\\n8.30\\n15.4412.56\\n15.5112.38\\naO. 9\\n0.39\\n26\\n12.48\\n5.57\\n2.14\\n27\\n13. 1\\n13. 4\\n5.38\\n2.24\\n3.16\\n2.30\\n6.10\\n1.30\\n8.50\\n15.57jl2.18\\n1. 9\\n28\\n13.13\\n12.54\\n5.20\\n2.34\\n3. 9\\n2.43\\n6.10\\n1.13\\n9.11\\n16. 2JU.58\\n1.39\\n29\\n13.24\\n5. 1\\n2.43\\n3. 2\\n2.55\\n6. 9\\n0.56\\n9.30\\n16. 611.38\\n2. 8\\n30 13.35\\n4.43\\n2.52\\n254\\n3. 8\\n6. 8\\n6. 5\\n0.38\\n0.20\\n9.50\\n16.1011.16\\n2.37\\n31\\n13.44\\n4.25\\n2.46\\n16.13\\n3. 6\\n91. Is the equation of time the same or different in different\\nyears In what book may it be found exactly for the cur-\\nrent year", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0072.jp2"}, "73": {"fulltext": "ASTRONOMICAL INSTRUMENTS. 59\\n90 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 dav, but simply indicates how long it is\\nsince the equinoctial point crossed the meridian tor\\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 What does\\nit measure I How many degrees does a star pass over man\\nhour When does sidereal time commence hat is de\\nnoted by the hour and minute of a sidereal clock 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 1 To what degree of\\nperfection are clocks brought! By what instrument are\\nclocks regulated?", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0073.jp2"}, "74": {"fulltext": "60 THE EARTH.\\ntinue the same from day to day and the right asce^\\nsion of \u00e2\u0080\u00a2various 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-\\nstrument from figure 13", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0074.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\\nFig. 13.\\na horizontal axis and capable of two motions, one m al-\\ntitude parallel to the circle abc, and the other in azimuth\\nparallel to EFG. Hence it can be easily brought to\\n6", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0075.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 apgulai\\ndistance between the moon and a star 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0076.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 ot\\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 OF 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0077.jp2"}, "78": {"fulltext": "64 THE EARTH.\\nimportant that it should be ascertained with the greater\\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\u00e2\u0080\u0094 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 flattened 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-\\ned 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 In how many different ways is this\\nelement ascertained 1 Specify them. What is meant by the\\ncentrifugal force Give an illustration. Describe figure 1\u00c2\u00ab5.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0078.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 1 What figure would the earthhave 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 1 How was the spheroidal\\nfigure of the earth inferred before the fact was established by\\nobservation 1\\n6*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0079.jp2"}, "80": {"fulltext": "66\\nTHE 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 What is the difference between the two diameters\\nWhat fraction expresses the ellipticity of the earth 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0080.jp2"}, "81": {"fulltext": "ASTRONOMICAL INSTRUMENTS.\\n67\\nPlaces of observation.\\nPeru,\\nPennsylvania,\\nItaly,\\nFrance,\\nEngland,\\nSweden,\\nLatitude.\\nLength of a deg ree in miles\\n00\u00c2\u00b0 00 00\\n68.732\\n30 12 00\\n68.89G\\n43 01 00\\n68.998\\n4G 12 00\\n69.054\\n51 29 541\\n69.164\\n66 20 10\\n69.29 2\\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 4 d of the greatest. This fraction 9 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\u00e2\u0080\u0094 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 1\\nTo what conclusions have pendulum observations, made in va-\\nrious parts of .he earth, led 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0081.jp2"}, "82": {"fulltext": "68\\nTHE 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-J e The density was first\\nestimated by Dr. Hutton, from observations made by Dr\\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 1 6. Why is the density of the\\nearth so important an element", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0082.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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0083.jp2"}, "84": {"fulltext": "PART II. OF THE SOLAR SYSTEM.\\n101. Having considered the Earth, in its astronomicaJ\\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 ZODIACAL LIGHT.\\n102. The figure which the sun presents to us is that\\nV a perfect circle, whereas most of the planets exhibit a\\nJisk 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 1 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 1 How is\\nit inferred that the figure of the sun is spheroidal", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0084.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.\\n104. In density, the sun is only one-fourth that of the\\nearthy 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 16 J- feet in a second\\n103. What is the distance of the sun from the earth How\\nlong would a railway car, moving at the rate of 20 miles per\\nhour, require to reach the sun 1 How many bodies equal to\\nthe earth could lie side by side across the sun How long\\nwould a ship be in sailing across it at 10 miles an hour 1 If\\nthe sun s center were made to coincide with the center of the\\nearth, how much farther would it reach than the moon 1 What\\nis the sun s apparent diameter What is its linear diameter\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0085.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. n.\\n105. Solar spots. Are they constant or variable in number\\nand appearance 1 How many are sometimes seen on the sun s\\ndisk at once Are they usually large or small How many\\nmiles in diameter are the largest Describe a spot. What\\nchanges occur in the nucleus 1 What is the umbra 1 In what\\npart of the sun do the spots mostly appear What apparent\\nmotions have they What is the period of their revolution", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0086.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. 7h. 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;\\n.Thus, 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? 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 19.\\n7", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0087.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 27-1- 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 AAB (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\\njust equal to the time of the\\nsun s revolution on his axis.\\nBut during the 21\\\\ 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 21\\\\ 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 1 How may these shades be made", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0088.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\\nwhich 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 What objections are there against it 1\\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 theory l What are facula", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0089.jp2"}, "90": {"fulltext": "76 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 of\\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 are also seen,\\nin different parts, places that are brighter than the neigh-\\nboring portions of the disk. These are called f acuta.\\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 come| 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, 1836. 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 different dis-", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0090.jp2"}, "91": {"fulltext": "ZODIACAL LIGHT. 77\\nFig. 20.\\ntances from the sun by different observers, according to\\ntheir respective powers of vision.\\n2. ilts 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 1 What is its form How far does it reach Where\\nbrightest How do its aspects vary at different seasons of\\nthe\u00c2\u00b0year What motions has it Is it equally conspicuous\\nevery year What was it formerly held to be With what\\nphenomenon has it been supposed to be connected\\n7*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0091.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 SJwwers, 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0092.jp2"}, "93": {"fulltext": "79\\nCHAPTER II.\\nOF THE APPARENT ANNUAL MOTION OF THE SUN SEASONS\\nFIGURE OF THE EARTH S ORBIT.\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0093.jp2"}, "94": {"fulltext": "80\\nTHE 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 opposite 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 When the earth is at Libra, where does the\\nsun appear to be 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0094.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 o]\\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\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0095.jp2"}, "96": {"fulltext": "82 THE SUN.\\nto be two great circles distinctly delineated on the face\\nof the sky. On comparing observations made at dinei-\\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 forever\\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 1 How do we find from\\n*hese observations, the obliquity of the ecliptic", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0096.jp2"}, "97": {"fulltext": "THE SEASONS.\\nword (iq*\u00e2\u0084\u00a2) 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 tar\\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 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0097.jp2"}, "98": {"fulltext": "34 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!}\\n;^When the earth is at one of the equinoxes, the sun is at\\nthe other, and the circle of illumination passes through\\nboth the Dolest When the earth reaches one of the\\n115. The Seasons. On what two causes doos 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, sines\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0098.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\\nligure 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 doe?-\\\\he sun enlighten at once\\nDefine the circle of illumination. How does it cut the earth at\\nthe equinoxes How at the solstices 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0099.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 5 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\\nenjoy 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 s 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0100.jp2"}, "101": {"fulltext": "THE SEASONS.\\n87\\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 1\\nWhat would have been the consequence had the equator been\\nat right angles to the ecliptic 1 How would the sun appear to\\nmove to a person on the equator 1 How to one situated at the\\npole How to an inhabitant of an oblique sphere 1 How\\nwould have been the vicissitudes of heat and cold 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0101.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 EARTH S 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 1 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 of\\nthe earth How do we construct a figure representing the\\nearth s orbit Explain figure 23.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0102.jp2"}, "103": {"fulltext": "FIGURE OF THE 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 b, c, c. successive positions of the sun\\nthe relative lengths of the lines Ea, E6, 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 sun vary\\nin different parts of the year? When is it greatest, and\\nwhen smallest Define the terms perihelion and aphelion.\\n8*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0103.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 According to what law does the\\nvelocity vary 1 How may we ascertain the sun s daily rate\\nWhat ffreat doctrine is it necessary to be acquainted with, in\\norder to understand the celestial motions 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0104.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^ 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 obedi-ence 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 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0105.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\\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\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0106.jp2"}, "107": {"fulltext": "LAWS OF GRAVITY. 93\\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.\\n(Thirdly, 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 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\\nthe surface to the center", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0107.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 ox\\nrest 16 T 2 2 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 16-^. Conse-\\nquently, in two seconds the fall will be 64J, in three se-\\nconds 144f, and in ten seconds 1608J feet, that is,\\nthrough one hundred times lG^ 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 How far in two seconds What is\\nthe weight of a body", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0108.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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0109.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\\ndenned\\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 A.\\nt Pembevton s View of Newton s Philosophy.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0110.jp2"}, "111": {"fulltext": "UNIVERSAL BRAVITATION.\\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 B6,\\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 1 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 1 Explain by figure 25. How is it proved that gravity\\nand no other force causes the moon to revolve about the earth 1\\n9", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0111.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.\\nkepler s laws.\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0112.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 G\u00c2\u00a3 or GF of the focus from the\\n128. Recite the first law. In a circle, how are all the diam-\\neters 1 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\\n2\u00c2\u00a7 How eccentric is the earth s orbit", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0113.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 m Art. 118, we find that the difference between", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0114.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.\\nft 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.\\n130. 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 byfigure 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0115.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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0116.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. As 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 fall 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 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0117.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.\\nlocity of projection is greater. Thus 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0118.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-\\nrity, 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\\nFig. 30.\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0119.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 ball describe different orbits", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0120.jp2"}, "121": {"fulltext": "PRECESSION OF THE EQUINOXES. 107\\nPRECESSION OP THE EQUINOXES.\\n136 The Precession op the equinoxes, is a slow\\nbut continual shifting of the equinoctial points from east\\nSuppose that we mark the exact place in the heavens\\nwhere, during the present year, the sun crosses the equa-\\n7or and that this point is close to a certain star next\\nye the sun will cross the equator a little .way w\\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\\nSox will occupy successively every part of the echp-\\nUc until we come round to the same star again As,\\ntherefore, the sun, revolving from west to eastin his ap-\\nnarent orbit, corns round towards the point where ,t\\nFef the equinox, it meets the equinox before it reaches\\nhat point The appearance is as though the equinox\\nZes forward to med the sun, and hence the phenome-\\nnon is called the Precession of the Equinoxes, and the\\nfact s expressed by saying that the equinoxes retrograde\\nn thl eSptic, until tne line of the e\u00e2\u0080\u0094 xes .makes a\\n\u00e2\u0080\u00a2omDlete revolution from east to west. The equatoi 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,\\nWmc .remains fixed, may be slid quite around it g.vmg\\na corresponding motion to the two points of intersec-\\ntion Itmust be observed, however, that this mode of\\nconceiving of the precession of the equinoxes is purely\\nimag^rf, and is employed merely for the convenience\\nof representation.\\n137. (The amount of precession annually is 50/ l;\\nwhence, since there are 3600 in a degree, and 360 in\\nIf the sim\\n136 Precession of the Equinoxes.\u00e2\u0080\u0094 Define it. If tlie sv\\ncrosses fhe equator {ear a certain star thi^, wW g*\\nnr^* it next vear Why is the fact called the precession 01\\nZ equinoxes? How i/tfce equator conceived as moving\\nwith regard to the ecliptic 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0121.jp2"}, "122": {"fulltext": "1 08 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, flffence 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. fin about\\n13,000 years, the bright star Lyrae, 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 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0122.jp2"}, "123": {"fulltext": "PRECESSION OF THE EQUINOXES. 109\\nwill be within 5\u00c2\u00b0 of the pole, and will constitute the\\nPole Star.) As a Lyrae now passes near our zenith, the\\nlearner might suppose that the change of position of the\\npole among the starsj 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 SO.^l 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0123.jp2"}, "124": {"fulltext": "110 THE MOON.\\n50. 1 1 year: :30\u00c2\u00b0( 108000 2155.6 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 1\\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 1 Why would water appear darker than land\\nWhat does the telescope reveal to us respecting the moon", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0124.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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0125.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 Frontispiece.)\\n1. Tycho, A. Mare Humorum,\\n2. Kepler, B. Mare Nubium,\\n3. Copernicus, C. Mare Imbrium,\\n4. Aristarchus, D. Mare Nectaris,\\n5. Helicon, E. Mare Tranquilitatis,\\n6. Eratosthenes, F. Mare Serenitatis,\\n7. Plato, G. Mare Fecunditatis,\\n8. Archimedes, H. Mare Crisium.\\n9. Eudoxus,\\n10. Aristotle,\\nIt is earnestly recommended to the student of astronomy, to exam-\\nine the moon repeatedly with the best telescope he can command, using\\nlow powers at first, for the sake of a better light", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0126.jp2"}, "127": {"fulltext": "LUNAR GEOGRAPHY. 113\\nThe frontispiece represents the appearance of the\\nmoon in the telescope when full and when five days\\nold. In 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 sun s 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 Are the mountains like or unlike ours 1 What is the\\nfirst variety What is the shape of the insulated mountains\\nHow can their heights be calculated 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0127.jp2"}, "128": {"fulltext": "114 THE MOON.\\nrangement and an aspect very different from the moun-\\ntain scenery of our globe. J 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.\\n^Secondly, Mountain Ranges, extending in length two\\noiTthree 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0128.jp2"}, "129": {"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 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0129.jp2"}, "130": {"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 1\\n147. What evidence is there of a lunar atmosphere 1\\nThe foregoing accurate description of the lunar mountains and cav\\nems is from Dick s Celestial Scenery.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0130.jp2"}, "131": {"fulltext": "LUNAR GEOGRAPHY. 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\\nthe 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 are there\\nto the contrary\\n149. Is it probable that artificial structures in the rnoon 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0131.jp2"}, "132": {"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 have the moon examined for this pur-\\npose", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0132.jp2"}, "133": {"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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0133.jp2"}, "134": {"fulltext": "120 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, hei\\nform is thlt 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 1 State\\nthe successive appearances of the moon from new to full. In\\nwhat parts of her revolution is she horned, and in what parts\\ngibbous 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0134.jp2"}, "135": {"fulltext": "PHASES.\\n121\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0135.jp2"}, "136": {"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. At\\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.\\n1 54. The moon revolves around the earth from west\\nto east, making the entire circuit of the heavens in about\\n27J 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 sv-\\nnodical month. Why so called What is the length of the\\nsynodical month Also of the sidereal month 1 What is the\\nmoon s dailj motion", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0136.jp2"}, "137": {"fulltext": "REVOLUTIONS. 123\\na degree a day, during the 27 days of the moan 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 what the de-\\nscending node\\n156. Why does the moon run high and low 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0137.jp2"}, "138": {"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 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0138.jp2"}, "139": {"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 way 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 ot\\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,\\n158. 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 always turned exactly towards us 1\\n11*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0139.jp2"}, "140": {"fulltext": "126 THE 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 latitude\\nDitto the diurnal librations.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0140.jp2"}, "141": {"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 360 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\\n1 60. How many days would an inhabitant of the moon have\\nin a lunar month What vicissitudes of temperature would\\noccur in a single day 1 Would a spectator on the side of the\\nmoon opposite to us, ever see the earth How would the earth\\nappear to a spectator on the side of the moon next to us\\nFrancoeur, Uranog. p. 91.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0141.jp2"}, "142": {"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 2\\\\ 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0142.jp2"}, "143": {"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 verv 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 1 How is the elliptical path of the moon around the earth\\nto be conceived of How is this illustrated by the motions of\\na man in a steamboat Alsc by the motions of a nail in vhe\\nrim of a coach wheel 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0143.jp2"}, "144": {"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. tWe 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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0144.jp2"}, "145": {"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 would 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 fall towards the sun, how would they fall How\\nmight we conceive them as situated in a plane 1 When is the\\nmoon more attracted than the earth 1 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\\ndestroved, at conjunction, at opposition, and at quadrature.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0145.jp2"}, "146": {"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 How\\ndoes the eccentricity of the lunar orbit compare with that of\\nthe solar", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0146.jp2"}, "147": {"fulltext": "REVOLUTIONS. 133\\njarth 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 moon s nodes constantly shift their positions\\nin the ecliptic from east to west, at the rate of 19\u00c2\u00b0 35 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 we 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 346i days. For since the node shifts its\\n1 67. How do the moon s nodes shift their position In\\nwhat time do they make a complete revolutin in the ecliptic\\nExplain what is mean* by saying that the nodes retrogade.\\n12", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0147.jp2"}, "148": {"fulltext": "134 THE MOON.\\nplace to the westward 19\u00c2\u00b0 35 per annum, the sun, m\\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\u00e2\u0080\u009419=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 29.5305887 x 223 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\\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 How many\\nconjunctions of the moon with the sun occur during this pe-\\nriod 1 What us6 did the Athenians make of this lunar cycle", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0148.jp2"}, "149": {"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,\\nalso 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0149.jp2"}, "150": {"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 t?y 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 1 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 1 Will they a ways\\ncontinue to be accelerated 1\\nAstronomer Royal of Great Britain, and cotemporary with Sir Isaac\\nNewton.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0150.jp2"}, "151": {"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\\nwill 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 1 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0151.jp2"}, "152": {"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 1 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 When only can 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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0152.jp2"}, "153": {"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 off\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0153.jp2"}, "154": {"fulltext": "140 THE MOON.\\nsun s disk if he were nearer the shadow than either oi\\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\\nfigure 34.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0154.jp2"}, "155": {"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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0155.jp2"}, "156": {"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\\nbe 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 1\\n176. Why is the disk of the moon still visible in a total\\neclipse of the moon 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0156.jp2"}, "157": {"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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0157.jp2"}, "158": {"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\\n178. 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0158.jp2"}, "159": {"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. How are theleadingparticulars of an eclipse of the sun\\nascertained 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 1\\n13", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0159.jp2"}, "160": {"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 just\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0160.jp2"}, "161": {"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\\neffect, 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\\nan 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 moon s\\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. How 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 How long\\nmay an annular eclipse last 1\\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 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0161.jp2"}, "162": {"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 mav 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 cloud-\\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 Givd\\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 oJ the Al\\nbany Institute, by the late Chancellor De Witt", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0162.jp2"}, "163": {"fulltext": "ECLIPSES\\n149\\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\\ntwilightT 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(sxXBiyig,) 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-\\n%ined 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, (lunse\\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 What ideas\\nhad certain ancient nations respecting eclipses 1 With what\\nceremonies did they observe them? How were eclipses re-\\ngarded among the Chinese\\n1 o", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0163.jp2"}, "164": {"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 Stat^l,\\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\\n1 S6. 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0164.jp2"}, "165": {"fulltext": "LONGITUDE.\\n151\\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 1 1 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=22^\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\u00a3\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 1 How do we ascertain\\nthe longitude of a place by it Would it be necessary to re-\\npair to Greenwich to regulate our chronometer What is said\\noi the accuracy of some chronometers Why is not this\\nmethod adapted to general use", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0165.jp2"}, "166": {"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\\n1 90. 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0166.jp2"}, "167": {"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 sameT 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 60\u00c2\u00b0\\nwest.\\n191. Explain the lunar method of finding the longitude.\\nWhat measurements are made 1 How do we find the corres-\\nponding time at Greenwich 1\\nThe Nautical Almanac, is a book 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 ot\\nstatistical matter. It is well deserving of a place in the library of the\\nutudent.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0167.jp2"}, "168": {"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\\nSee Bowditch s Navigator, Tenth Ed. p. 226.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0168.jp2"}, "169": {"fulltext": "LONGITUDE. 135\\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 siii-\\ncrle observation with the best sextant, may be liable io\\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 in 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. lhe\\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 much later is the tide of to-day than the same tide ot\\nyesterday What is the average height of the tide for the\\nwhole globe To what extreme height does it sometimes rise 1\\nHave inland lakes and seas any tides 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0169.jp2"}, "170": {"fulltext": "156 THE 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\\nuext 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 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0170.jp2"}, "171": {"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-\\nFig. 30.\\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 tcrthe 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-\\n1 96. Explain the tides upon the doctrine of the center of\\ngravity. Where would the tide-wave always be seen were it\\naot for impediments What are these 1\\n14", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0171.jp2"}, "172": {"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 \u00c2\u00b0f e distance of the moon, while it is\\nless than yotroo \u00c2\u00b0f e 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0172.jp2"}, "173": {"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 Also of the\\nNeap tides How long after the syzigies does the highest\\ntide occur 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0173.jp2"}, "174": {"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\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0174.jp2"}, "175": {"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.\\n,^M\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0175.jp2"}, "176": {"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\\nfar 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 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0176.jp2"}, "177": {"fulltext": "TIDES. 163\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0177.jp2"}, "178": {"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 moonC 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0178.jp2"}, "179": {"fulltext": "TIDES.\\n165\\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, H?\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0179.jp2"}, "180": {"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\\n209. What is said of the difficulty of applying the principle\\nof universal gravitation to all the circumstances of the tides", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0180.jp2"}, "181": {"fulltext": "167\\nCHAPTER VII.\\nOF THE PLANETS THE INFERIOR PLANETS, MERCURY\\nAND VENUS.\\n211. The name planet signifies a wanderer* 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, Venus, Earth, Mars, Jupiter, and Saturn. To\\nthese, in 1781, was added Uranus,f (or Herschel,as it is\\nsometimes called from the name of its discoverer,) and,\\nas late as the commencement of the present century,\\nfour more were added, namely, Ceres, Pallas, Juno, and\\nVesta. These bodies are designated by the following\\ncharacters\\n1. Mercury\\nS\\n2. Venus\\n3. Earth\\ne\\n4. Mars\\n5. Vesta\\nfi\\n6. Juno\\n7. Ceres\\n8. Pallas\\n9. Jupiter\\nU\\n10. Saturn\\n11. Uranus\\nW\\nThe foregoing are called the primary planets. Sev-\\neral of these have one or more attendants, or satellites,\\n210. Has the atmosphere any tide 1 Is it sufficient to influ-\\nence meteorological phenomena\\n211. Whence is the name planet derived 1 Which of the\\nplanets have been long known 1 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\\nbodies have satellites State the whole number of planets.\\nFrom the Greek ^avn-rrn. t From Ovpavos.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0181.jp2"}, "182": {"fulltext": "168 THE PLANETS.\\nwhich revolve around them, as they revolve around the\\nsun. The earth has one satellite, namely, the moon\\nJupiter has four Saturn, seven and Uranus, six. These\\nbodies also are planets, but in distinction from the others\\nthey are called secondary planets. Hence, the whole\\nnumber of planets are 29, viz. 11 primary, and IS sec\\nondary planets.\\n212. With the exception of the four new planets,\\nthese bodies have their orbits very nearly in the same\\nplane, and are never seen far from the ecliptic. Mer-\\ncury, whose orbit is most inclined of all, never departs\\nfarther from the ecliptic than about 7\u00c2\u00b0, while most of\\nthe other planets pursue very nearly the same path with\\nthe earth, in their annual revolutions around the sun.\\nThe new planets, however, make wider excursions from\\nthe plane of the ecliptic, amounting, in the case of Pal-\\nlas, to 34^\u00c2\u00b0.\\n213. Mercury and Venus 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 seven, while more than\\nhalf have none at all. It will aid the memory, and\\nrender our view of the planetary system more clear and\\ncomprehensive, if we classify, as far as possible, the\\nvarious particulars comprehended under the foregoing\\nheads.\\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 t\\nWhy are the other planets called superior What diversities\\ndo the planets exhibit among themselves", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0182.jp2"}, "183": {"fulltext": "DISTANCES FROM THE SUN.\\n169\\n214. DISTANCES FROM THE SUN.\\n1. Mercury,\\n2. Venus,\\n3. Earth,\\n4. Mars,\\n5. Vesta,\\n6. Juno,\\n7. Ceres,\\n8. Pallas,\\n9. Jupiter,\\n10. Saturn,\\n11. Uranus,\\n37,000,000\\n68,000,000\\n95,000,000\\n142,000,000\\n225,000,000\\n261,000,000\\n485,000,000\\n890,000,000\\n1800,000,000\\nThe dimensions of the planetary system are seen\\nfrom this table to be vast, comprehending a circular\\nspace thirty six hundred millions of miles in diameter.\\nA railway car, travelling constantly at the rate of 20\\nmiles an hour, would require more than 20,000 years to\\ncross the orbit of Uranus.\\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 Venus 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 the\\nseries but the discovery of the new planets has filled\\nthe void.\\n214. State the distancelof each of the planets from the sun.\\nWhat is said of the dimensions of the planetaty system How\\ndo the distances of those planets which are nearest the sun in-\\ncrease 1 Also those which are more distant How may the\\nmean distances of the planets from the sun be determined\\nGive an example in computing the distance of Jupiter.\\n15", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0183.jp2"}, "184": {"fulltext": "170\\nTHE PLANETS.\\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\\nby means of the sun s horizontal parallax, and the pe-\\nriod of any other planet, as Jupiter, being learned from\\nobservation, we say as 3G5.256 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,\\nEarthy\\nMars,\\nCeres,\\nJupiter,\\nSaturn,\\nUranus,\\nDiam. in Miles.\\nMean apparent Diam\\nVolume\\n3140\\n6 .9\\ntV\\n7700\\n61 .9\\nA\\n7912\\n1\\n4200\\n6 .3\\n1\\n7\\n160\\n0 .5\\n89000\\n36 .7\\n1281\\n79000\\n16 .2\\n995\\n35000\\n4 .0\\n80\\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\\nfo as large as the earth, Mars, a superior planet is only y\\nwhile Jupiter is 1281 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 exactly\\n61 .9, and that of Jupiter being when greatest only\\nabout J of a minute.\\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 1\\nThis is the number of days in one revolution of Jupiter.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0184.jp2"}, "185": {"fulltext": "PERIODIC TIMES MERCURY\\nAND V]\\nSNU8. 171\\n216.\\nPERIODIC TIMES.\\nMercury,\\nVenus,\\nRevolution in\\n3 months\\n17 1 n\\n1 2\\nits orbit.\\nor 88 days,\\n224\\nMean daily motion.\\n4\u00c2\u00b0 5 32 \\\\6\\n1\u00c2\u00b0 36 7 .8\\nEarth,\\nMars,\\nCeres,\\n1 year,\\n2 years,\\n4\\nu\\nCI\\n3G5\\n687\\n1681\\nM\\nit\\n0\u00c2\u00b0 59 8 .3\\n0\u00c2\u00b0 31 26 .7\\n0\u00c2\u00b0 12 50 .9\\nJupiter,\\nSaturn,\\n12\\n29\\nSi\\nu\\n4332\\n10759\\na\\nu\\n0\u00c2\u00b0 4 59 .3\\n0\u00c2\u00b0 2 0 .6\\nUranus,\\n84\\na\\n30686\\na\\n0\u00c2\u00b0 0 42 .4\\nFrom this view, it appears that the planets nearest the\\nsun move most rapidly. Thus Mercury performs nearly\\n350 revolutions while Uranus performs one. This is\\nevidently not owing merely to the greater dimensions of\\nthe orbit of Uranus, for the length of its orbit is not 50\\ntimes that of the orbit of Mercury, while the time em-\\nployed in describing it is 350 times that of Mercury.\\nIndeed this ought to follow from Kepler s law that the\\nsquares of the periodical times are as the cubes of the\\ndistances, from which it is manifest that the times of\\nrevolution increase faster than the dimensions of the or-\\nbit. Accordingly, the apparent progress of the most\\ndistant planets is exceedingly slow, the daily rate of\\nUranus being only 42 .4 per day so that for weeks and\\nmonths, and even years, this planet but slightly changes\\nits place among the stars.\\nTHE INFERIOR PLANETS, MERCURY AND VENUS.\\n217. The inferior planets, Mercury and Venus, hav-\\ning their orbits so far within that of the earth, appear to\\nus as attendants upon the sun. Mercury never appears\\nfarther from the sun than 29\u00c2\u00b0 (28\u00c2\u00b0 48 and seldom so\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0185.jp2"}, "186": {"fulltext": "172\\nTHE PLANETS.\\nfar; and Venus never more than about 47\u00c2\u00b0 (47 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.\\nFig. 40.\\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\\n217. What is Mercury s greatest elongation from the sun\\nWhat is Yenus s What is said respecting the difficulty of see-\\ning 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 but\\ntwice-", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0186.jp2"}, "187": {"fulltext": "MERCURY AND VENUS.\\n173\\nseen at A and B when at its greatest elongations, and\\nwill appear no further from the sun than the arc S A or\\nS B respectively.\\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 Venus have each two conjunctions, the inferior,\\nand the superior. The inferior conjunction is its posi-\\ntion when in conjunction on the same side of the sun\\nwith the earth, as at C in the figure the superior con-\\njunction is its position when on the side of the sun most\\ndistant 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 being\\nin motion, the time of the synodical revolution exceeds\\nthat of the sidereal revolution of Mercury or Venus\\nfor when the planet comes round to the place where it\\nbefore overtook the earth, it does not find the earth at\\nthat point, but far in advance of it. Thus, let Mercury\\ncome into inferior conjunction with the earth at C, (Fig.\\n40.) In about 88 days, the planet will come round to\\nthe same point again; but meanwhile the earth has\\nmoved forward through the arc EE and will continue\\nto move while the planet is moving more rapidly to over-\\ntake her, the case being analogous to that of the hour\\nand minute hand of a clock.\\nThe synodical period of Mercury is 1 16, and of Venus\\n584 days.\\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 1 Explain by figure 40.\\nWhat is the synodical period of Mercury and Venus respect-\\nively\\n15*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0187.jp2"}, "188": {"fulltext": "174 THE PLANETS.\\n220. The motion of an inferior planet is direct in\\npassing through its superior conjunction, and retrogade\\nin passing through its inferior conjunction. Thus Ve-\\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 retrogade, returning on the same\\narc from left to right. If the earth were at rest, there-\\nfore, (and the sun, of course, at rest,) the inferior planets\\nwould appear to oscillate backwards and forwards across\\nthe sun. But, it must be recollected, that the earth is\\nmoving in the same direction with the planet, as respects\\nthe signs, but with a slower motion. This modifies the\\nmotions of the planet, accelerating it in the superior and\\nretarding it in the inferior conjunctions. Thus in figure\\n40, Venus while moving through BDA would seem to\\nmove in the heavens from B to A were the earth at\\nrest but meanwhile the earth changes its position from\\nE to E by which means the planet is not seen at A\\nbut at A being accelerated by the arc A A in conse-\\nquence of the earth s motion. On the other hand, when\\nthe planet is passing through its inferior conjunction\\nACB, it appears to move backwards in the heavens from\\nA to B if the earth is at rest, but from A to B if the\\nearth has in the mean time moved from E to E being\\nretarded by the arc B B Although the motions of the\\nearth have the effect to accelerate the planet in the superi-\\nor conjunction, and to retard it in the inferior, yet, on ac-\\ncount of the greater distance, the apparent motion of the\\nplanet is much slower in the superior than in the infe-\\nrior conjunction.\\n221. When passing from the superior to the inferior\\nconjunction, or from the inferior to the superior conjunc-\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0188.jp2"}, "189": {"fulltext": "MERCURY AND VENUS.\\n175\\ntion through the greatest elongations, the inferior plan-\\nets 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 to\\ngive it a relative motion eastward, and becomes retro-\\ngrade as it. approaches the inferior conjunction. Its sta-\\ntionary point obviously lies between its place of greatest\\nelongation, and the place where its motion becomes re-\\ntrograde. Mercury is stationary at an elongation of\\nfrom 15\u00c2\u00b0 to 20\u00c2\u00b0 from the sun and Venus at about 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 last\\nquarters and when on the side of their superior con-\\njunctions thev appear gibbous. At the moment of su-\\nperior 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 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.\\n221. When are the inferior planets stationary Why are\\nthev not stationary at the points of greatest elongation 1 At what\\nelongation are Mercury and Venus stationary respectively\\n222. What phases do Mercury and Venus exhibit 1 Explain\\nby figure 40. Whence do these bodies derive their light Is\\nthe same true of the other planets 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0189.jp2"}, "190": {"fulltext": "176\\nTHE 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\\n3 semi-mainr avia while that of XT\\nMercury s orbi\\nS Mercury, v\\nferent distances from the earth, varies much in his appa-\\nrent diameter, which is only 5 in the apogee but 12\\nin the perigee. The inclination of his orbit to his equa-\\ntor being very great, the changes of his seasons must be\\nproportionally great.\\nThese different aspects of an inferior planet will be\\neasily understood from Fig. 41, where the earth is atE,\\nFig. 41.\\nand the placet 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\\nv? 3 V hat 1S SaM f the ecc entricity and inclination of the\\ncurv vLv f C H y U T d eS the W\u00e2\u0084\u00a2*\\ncurv vary How are his changes of seasons\\nThe new planets of course excepted.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0190.jp2"}, "191": {"fulltext": "MERCURY AND VENUS. 177\\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 point\\nbetween its greatest elongation and inferior conjunction.\\nIts maximum brilliancy would happen at the inferior\\nconjunction, (being then nearest to us,) if it shined by\\nits own light but in that position its dark side is turned\\ntowards us. Still, its maximum cannot be when most\\nof the illuminated side is towards us for then, being at\\nthe superior conjunction, it is at its greatest distance\\nfrom us. The maximum must therefore be somewhere\\nbetween the two. Venus gives her greatest light when\\nabout 40\u00c2\u00b0 from the sun.\\n225. Mercury and Venus oik revolve on their axes,\\nin nearly the same, time with the earth.\\nThe diurnal period of Mercury is 24h. 5m. 28s., and\\nthat of Venus 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. Venus 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 ac-\\ncordingly gave them different names, calling the morn-\\ning star Lucifer, and the evening star Hesperus. At her\\nperiod of greatest splendor, Venus casts a shadow, and is\\nsometimes visible in broad daylight. Her light is then\\nestimated as equal to that of twenty stars of the first\\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 1\\n225. In what time do Mercury and Venus, respectively, re-\\nvolve on their axes 1 How are these periods ascertained", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0191.jp2"}, "192": {"fulltext": "178 THE PLANETS.\\nmagnitude. At her period of greatest elongation, Ve-\\nnus is visible from three to four hours after the setting\\nor before the rising of the sun.\\n227. Every eight years, Venus forms her conjunctions\\nwith the sun in the same part of the heavens.\\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 Venus between the first and second conjunc-\\ntions. Deducting 720\u00c2\u00b0, or two entire circumferences\\nthe remainder, 215\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\u00b0.6x 5 1078\u00c2\u00b0, which is\\nnearly three entire circumferences, so that at the end of\\nfive synodical revolutions, occupying 2920 davs, 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 passage\\nacross the sun s disk, as the moon passes over it in a solar\\neclipse.\\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.\\n226. What erroneous notions had the ancients respecting the\\nmorning and evening star What is said of the brilliancy oi\\nVenus at her greatest splendor How long may Venus be in\\nsight after sunset\\n227. What happens to Venus every eight years", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0192.jp2"}, "193": {"fulltext": "MERCURY AND VENUS. 179\\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^\u00c2\u00b0 with the\\necliptic, ana Mercury an angle of 7\u00c2\u00b0 and moreover,\\nthe apparent diameter of each of these bodies is yery\\nsmall, both of which circumstances conspire to render a\\ntransit a comparatively rare occurrence, since it can hap-\\npen only when the sun, at the time of an inferior con-\\njunction, chances to be at or extremely near the planet s\\nnode. The nodes of Mercury lie in longitude 40 and\\n226\u00c2\u00b0, points which the sun passes through in May and\\nNovember. It is only in these months, therefore, that\\ntransits of Mercury can occur. For a similar reason,\\nthose of Venus occur only in June and December. Since,\\nhowever, the nodes of both planets have a small retro-\\ngrade motion, the months in which transits occur will\\nchange in the course of ages\\n229 Transits of Mercury occur more frequently than\\nthose of Venus. The periodic times of Mercury and\\nthe earth are so adjusted to each other, that Mercury\\nperforms nearly 29 revolutions while the earth performs\\n7 If therefore, the two bodies meet at the node in any\\ngiven year, seven years afterwards they will meet nearly\\nat the same node, and a transit may take place, accord-\\ningly, at intervals of 7 years. But 54 revolutions of\\nMercury correspond still nearer to 13 revolutions of the\\n228 What is meant by the transit of Mercury or Venus 1\\nWhen only can a transit take place 1 What angles do the or-\\nbits of Venus and Mercury respectively make with the ecliptic T\\nIn what months does the sun pass through the nodes of each\\nof these planets\\n229 Which planet has the most frequent transits W hat is\\nthe shortest interval of the transits of Mercury What are the\\nlonger intervals 1 When will the next occur 1 What are in-\\ntervals of the transits of Venus When was the last transit\\nof Venus, and when will the next occur 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0193.jp2"}, "194": {"fulltext": "180 THE PLANETS.\\nearth, and therefore a transit is still more probable after\\nintervals of 13 years. At intervals of 33 years, transits\\nof Mercury are exceedingly probable, because in that\\ntime Mercury makes almost exactly 137 revolutions.\\nIntermediate transits however may occur at the other\\nnode, these intervals having reference merely to the\\nsame node. Thus transits of Mercury happened at the\\nascending node in 1815, and 1822, at intervals of\\n7 years; and at the descending node in 1832, which\\nwill return in 1845, after an interval of 13 years. Tran-\\nsits of Venus are much more unfrequent than those of\\nMercury. Eight revolutions of the earth are completed\\nin nearly the same time as thirteen revolutions of Venus,\\nand hence two transits of Venus may occur at an in-\\nterval of 8 years, as was the case at the last return of\\nthis phenomenon, one transit having occurred in 1761,\\nand another in 1769. But if a transit does not happen\\nafter 8 years, it will not happen, at the same node, until\\nan interval of 235 years but intermediate transits may\\noccur at the other node. The next transit of Venus will\\ntake place in 1874, being 235 years after the first that was\\never observed, which occurred in the year 1639. In the\\nmean time, as already mentioned, two transits have oc-\\ncurred at the other node, at intervals of 8 years.\\n230. The great interest attached by astronomers to a\\ntransit of Venus, arises from its furnishing the most accu-\\nrate means in our power of determining the sun s hori-\\nzontal parallax an element of great importance, since it\\nleads us to a knowledge of the distance of the earth from\\nthe sun, and, consequently, by the application of Kepler s\\nlaw, (Art. 130,) of the distances of all the other planets.\\nHence, in 1769, great efforts were made throughout the\\ncivilized world, under the patronage of different govern-\\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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0194.jp2"}, "195": {"fulltext": "MERCURY AND VENUS. 181\\nments, to observe this phenomenon under circumstances\\nthe most favorable for determining the parallax of the\\nsun.\\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.\\n231. If the sun and Venus were equally distant from\\nus, they would be equally affected by parallax as viewed\\nby spectators in different parts of the earth, and hence\\ntheir relative situation would not be altered by it but\\nsince Venus, at the inferior conjunction, is only about\\none third as far off as the sun, her parallax is propor-\\ntionally greater, and therefore spectators at distant points\\nwill see Venus projected on different parts of the so-\\nlar 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 pla-\\nces are selected for observation. Thus in the transit\\nof 1769, among the places selected, two of the most\\nfavorable were Wardhuz in Lapland, and Oteheite, one\\nof the South Sea Islands.\\nThe appearance of Venus 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 exact-\\nness of the result and astronomers repose so much con-\\nfidence in the estimation of the sun s horizontal parallax\\nas derived from the observations on the transit of 1769,\\nthat this important element is thought to be ascertained\\n231. How is Venus projected on the sun to spectators m\\ndifferent parts of the earth 1 What places were selected for\\nobserving the transit of 1769\\n16", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0195.jp2"}, "196": {"fulltext": "182 THE PLANETS.\\nwithin jV of a second. The general result of all these\\nobservations gives the sun s horizontal parallax 8 .6, or\\nmore exactly, 8/ 5776.\\n232. During the transits of Venus over the sun s disk\\nin 1761 and 1769, a sort of penumbral light was ob-\\nserved around the planet by several astronomers, which\\nwas thought to indicate an atmosphere. This appear-\\nance was particularly observable while the planet was\\ncoming on and going off the solar disk. The total im-\\nmersion and emersion were not instantaneous but as\\ntwo drops of water when about to separate, form a liga-\\nment between them, so there was a dark shade stretched\\nout between Venus and the sun, and when the ligament\\nbroke, the planet seemed to have got about an eighth part\\nof her diameter from the limb of the sun. The various\\naccounts of the two transits abound with remarks like\\nthese, which indicate the existence of an atmosphere\\nabout Venus of nearly the density and extent of the\\nearth s atmosphere. Similar proofs of the existence of\\nan atmosphere around this planet, are derived from ap-\\npearances of twilight.\\nThe elder astronomers imagined they had discovered\\na satellite accompanying Venus in her transit. If Venus\\nhad in reality any satellite, the fact would be obvious at\\nher transits, as the satellite would be projected near the\\nprimary on the sun s disk but later astronomers have\\nsearched in vain for any appearances of the kind, and\\nthe inference is that former astronomers were deceived\\nby some optical illusion.\\nAstronomers have detected very high mountains on\\nVenus, sometimes reaching to the elevation of 22 miles\\nand it is remarkable that the highest mountains in Ve-\\nnus, in Mercury, in the moon, and in the earth, are al-\\nways in the southern hemisphere.\\n232. What indications have been observed of an atmos-\\nphere about Venus Has Venus any Satellite What is said\\nof the mountains of Venus", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0196.jp2"}, "197": {"fulltext": "SUPERIOR PLANETS.\\nCHAPTER VIII.\\n183\\nOP THE SUPERIOR PLANETS MARS, JUPITER, SATURN, AND\\nURANUS CERES, PALLAS, JUNO, AND VESTA.\\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 Venus, 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,\\nso distant 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 4200 miles. He also,\\nat times, comes nearer to the earth than any other planet\\nexcept Venus. His mean distance from the sun is\\n142,000,000 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\\n233. Name the Superior Planets. How are they distin-\\nguished from the Inferior 1 Which of them exhibits phases\\nWhy do not the rest 1\\n234. Mars.\u00e2\u0080\u0094 State his diameter Mean distance from the\\nsitn\u00e2\u0080\u0094 inclination of his orbit. How distinguished from the\\nother planets Why do his brightness and apparent magni-\\ntude vary so much 1 Illustrate by figure 42.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0197.jp2"}, "198": {"fulltext": "184\\nTHE PLANETS.\\nit 2\u00c2\u00b0. He is distinguished from all the planets by his\\ndeep red color, and fiery 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 splen-\\ndor but when he passes to the other side of the sun to\\nhis superior conjunction, he dwindles to the appearance\\nof a small star, being then 237,000,000 miles from us.\\nThus, let M (Fig. 42,) represent Mars in opposition,\\nand M in the superior conjunction, while E represents\\nthe earth. It is obvious that in the former situation, the\\nplanet must be nearer to the earth than in the latter\\nby the whole diameter of the earth s orbit.\\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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0198.jp2"}, "199": {"fulltext": "MARS.\\n185\\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, accord-\\ning to the position of each pole with respect to the sun.\\nIt\u00c2\u00b0has been common to ascribe the ruddy light of this\\nplanet to an extensive and dense atmosphere, which was\\nsaid to be distinctly indicated, by the gradual diminution\\nof light observed in a star as it approached very near to\\nthe planet in undergoing an occultation but more re-\\ncent observations afford no such evidence of an atmos-\\nphere.\\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 of\\nhis axis to that of his orbit is also nearly the same,\\nbeing 30\u00c2\u00b0 18 10 .8.\\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-\\ndeed the compression or ellipticity of Mars greatly ex-\\nceeds that of the earth, being no less than of the\\nequatorial diameter, while that of the earth is only 3^.\\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\\nsnow 1 To what is the ruddy hue of Mars ascribed 1\\n237. How do we learn his revolution on his axis 1 In what\\ntime does it take place 1 What is the figure of Mars How\\ndoes its ellipticity compare with that of the earth 1\\n16*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0199.jp2"}, "200": {"fulltext": "186 THE PLANETS.\\nThis remarkable flattening of the poles of Mars has been\\nsupposed to arise from a great variation of density in the\\nplanet in different parts.\\n238. Jupiter is distinguished from all the other plan-\\nets by his vast magnitude. His diameter is 89,000\\nmiles, and his volume 1280 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 equa-\\ntor of Jupiter must turn 27 times as fast as on the ter-\\nrestrial equator. The distance of Jupiter from the sun\\nis nearly 490,000,000 miles, and his revolution around\\nthe sun occupies nearly 12 years.\\n239. The view of Jupiter through a good telescope,\\n(Fig. 43,) is one of the most magnificent and interesting\\nspectacles in astronomy. The disk expands into a large\\nFig. 43.\\nand bright orb like the full moon the spheroidal figure\\nwhich theory assigns to revolving spheres, is here pal-\\n238. Jupiter. State his diameter, volume, figure, revolu-\\ntion on his axis, velocity of his equator, distance from the sun,\\nperiodic time.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0200.jp2"}, "201": {"fulltext": "JUPITER.\\n187\\npably exhibited to the eye across the disk, 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 pecu-\\nliar interest on Jupiter and his moons, as affording a\\nminiature representation of the whole solar system,\\nrepeating on a smaller scale, the same revolutions, and\\nexemplifying, in a manner more within the compass\\nof our observation, the same laws as regulate the\\nentire assemblage 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 atmo-\\nsphere of the planet, agitated by winds, as is indicated\\nby their frequent changes, and made to assume the\\nform of belts parallel to the equator by currents that\\ncirculate around the planet like the trade winds and\\nother currents that circulate around our globe. Sir\\nJohn Herschel supposes that the belts are not ranges\\nof clouds, but portions of the planet itself brought into\\nview by the removal of clouds and mists, that exist in\\nthe atmosphere of the planet through which are open-\\nings made by currents circulating 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 oi\\ntwo of them have been occasionally seen with the naked\\neye. In the largest telescopes, they severally appear as\\n239. What does the telescopic view of Jupiter exhibit?\\nWhy do astronomers regard it with so much interest\\n240. Describe Jupiter s Belts\u00e2\u0080\u0094 to what are they ascribed?", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0201.jp2"}, "202": {"fulltext": "188\\nTHE PLANETS.\\nbright as Sirius. With such an instrument, the view of\\nJupiter with his moons and belts is tru y a magnificent\\nspectacle, a world within itself. As the orbits ot the\\nsatellites do not deviate far from the plane of the eclip-\\ntic, and but little from the equator of the planet, they\\nare usually seen in nearly a straight line with each other\\nextending 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 Jupiter,\\nthe first being that which is nearest to him. 1 heir ap-\\nparent motion is oscillatory, like that of a pendulum,\\ngoing alternately from their greatest elongation on one\\nfide 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 distances are given in radii of the primary.\\nSatellite.\\n1\\n2\\n3\\n4\\nDiameter.\\n2508\\n2068\\n3377\\n2890\\nMean Distance.\\n6.04853\\n9.62347\\n15.35024\\n26.99835\\nSidereal Revolution.\\nId. 18h. 28m.\\n3 13 14\\n7 3 43\\n16 16 32\\nHence it appears, first, that Jupiter s satellites are all\\nexcept the second, somewhat larger than the moon, but\\nthat the second satellite is the smallest, and the third\\nthe largest of the whole, but the diameter of the latter\\nis only about ^t P art of that of the P rimaI T secondly,\\nthat the distance of the innermost satellite from the planet\\n241. How do the satellites appear to the telescope\\n242. Describe the motions of the satellites\u00e2\u0080\u0094 magnitudes-\\ndistances periods of revolution.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0202.jp2"}, "203": {"fulltext": "JUPITER.\\n189\\nis three times his diameter, while that of the outermost\\nsatellite is nearly fourteen times his diameter thirdly,\\nthat the first satellite completes his revolution around the\\nprimary in one day and three fourths, while the fourth\\nsatellite requires nearly sixteen and 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-\\ni ilar situation with respect to Jupiter as the moon would\\nj be with respect to the earth if her orbit nearly coincided\\nJ with 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, ow-\\ning to the greater inclination of its orbit, sometimes\\nthough rarely escapes eclipse, and sometimes merely\\ngrazes the limits of the shadow or suffers a partial\\neclipse. These eclipses, moreover, are not seen, as is\\nthe case with those of the moon, from the center of\\ntheir motion, but from a remote station, and one whose\\nsituation with respect to trie line of the shadow is vari-\\nable. This, of course, makes no difference in the times\\nof the eclipses, but a very great one in their visibility,\\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 1 Are these eclipses seen in different\\nparts of the earth at the same moment of absolute time t", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0203.jp2"}, "204": {"fulltext": "190\\nTHE PLANETS.\\nand in their apparent situations with respect to the\\nplanet at the moment of their entering or quitting the\\nshadow.\\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 b, and ad-\\nvances to its greatest elongation at c. The other satellites\\ntraverse the shadow in a similar manner. These ap-\\npearances 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 Jupiter\\nand the sun it casts its shadow on the primary as the\\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\\ndisk of the planet", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0204.jp2"}, "205": {"fulltext": "JUPITER.\\n191\\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 Venus 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, as\\nat 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 Gali-\\nleo, which was one of the first fruits of the invention of\\nthe telescope, forms one of the most memorable epochs\\nin the history of astronomy. The first astronomical so-\\nlution of the great problem of the longitude, the\\nmost important problem for the interests of mankind\\nthat has ever been brought under the dominion of strict\\nscientific principles, dates immediately from their dis-\\ncovery. The final and conclusive establishment of the\\nCopernican system of astronomy, may also be considered\\nas referable to the discovery and study of this exquisite\\nminiature system, in which the laws of the planetary\\nmotions, as ascertained by Kepler, and especially that\\nwhich connects their periods and distances, were speed-\\nily traced, and found to be satisfactorily maintained.\\n246. Why have the eclipses of Jupiter s satellites been stud-\\nied with so much attention 1 Who first discovered these eclip-\\nses 1 What bearing has the system of Jupiter and his satel-\\nlites upon the Copernican system of astronomy", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0205.jp2"}, "206": {"fulltext": "192 THE PLANETS.\\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 for\\nfinding the longitude. It must be remarked, however,\\nthat the extinction of light in the satellite at its immer-\\nsion, and the recovery of its light at its emersion, are not\\ninstantaneous but gradual; for the satellite, like the\\nmoon, occupies some time in entering into the shadow\\nor in emerging from it, which occasions a progressive\\ndimunition or increase of light. The better the light\\nafforded by the telescope with which the observation is\\nmade, the later the satellite will be seen at its immer-\\nsion, and the sooner at its emersion.* In noting the\\neclipses even of the first satellite, the time must be con-\\nsidered as uncertain to the amount of 20 or 30 seconds\\nand those of the other satellites involve still greater un-\\ncertainty. Two observers, in the same room, observing\\nwith different telescopes the same eclipse, will frequently\\ndisagree in noting its time to the amount of 15 or 20\\nseconds and the difference will be always the same\\nway.\\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\\n247. Explain how these eclipses are used in finding the lon-\\ngitude. What imperfections attend this method Is this meth-\\nod much employed at present 1 Why can it not be used at\\nsea\\nThis is the reason why observers are directed in the Nautical Al-\\nmanac to use telescopes of a certain power.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0206.jp2"}, "207": {"fulltext": "SATURN. 193\\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 Roemer, 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 the\\ndiameter of the earth s orbit, making the velocity of light\\nabout 192,000 miles per second. So great a velocity star-\\ntled astronomers at first, and produced some degree of\\ndistrust of this explanation of the phenomenon but the\\nsubsequent discovery of what is called the aberration of\\nlight, led to an independent estimation of the velocity of\\nlight with almost precisely the same result.\\n249. Saturn 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\\nseven satellites. But a still more wonderfnl appendage\\nis its Ring, a broad wheel encompassing the planet at a\\ngreat distance from it. We have already intimated that\\nSaturn s system is on a grand scale. As, however, Sat-\\n248. How was the progressive motion of light first discovered\\nExplain the mariner of the discovery. How long is light in\\ntraversing the diameter of the earth s orbit What is its ve-\\nlocity per second How does this agree with that derived\\nfrom the aberration of light\\n17", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0207.jp2"}, "208": {"fulltext": "194\\nTHE PLANETS.\\nurn is distant from us nearly 900,000,000 miles, we are\\nunable 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\\na high 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 re-\\nality an interval of not less than about 1800 miles. The\\ndimensions of the whole system are in round numbers\\nas follows\\nMiles.\\nDiameter of the planet, 79,000\\nFrom the surface of the planet to the inner ring, 20,000\\nBreadth of the inner ring, 17,000\\nInterval between the rings, 1,800\\nBreadth of the outer ring, 10,500\\nExtreme dimensions from outside to outside, 176,000\\nFig. 45.\\nThe figure represents Saturn as it appears to a power-\\nful telescope, surrounded by its rings, and having its body\\nstriped with dark belts, somewhat similar but broader\\n249. Saturn. State his diameter and volume, number oi\\nsatellites, ring, distance from the sun.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0208.jp2"}, "209": {"fulltext": "8ATURN.\\n195\\nand less strongly marked than those of Jupiter, and\\nowing doubtless to a similar cause. That the ring is a\\nsolid opake substance, is shown by its throwing its shad-\\now on the body of the planet on the side nearest the sun\\nand on the other side receiving that of the body. From\\nthe parallelism of the belts with the plane of the ring,\\nit may be conjectured that the axis of rotation of the\\nplanet is perpendicular to that plane and this conjec-\\nture is confirmed by the occasional appearance of exten-\\nsive dusky spots on its surface, which when watched\\nindicate a rotation parallel to the ring in lOh. 29m. 17s.\\nThis motion, it will be remarked, is nearly the same\\nwith the diurnal motion of Jupiter, subjecting places on\\nthe equator 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\\nstriking view of Saturn with his rings and belts and sat-\\ntellites for we must bear in mind, that in the distance\\nof Saturn one second of angular measurement corres-\\nponds to 4,000 miles, a space equal to the semi-diameter\\nof our globe. But with a telescope of moderate powers,\\nthe leading phenomena of the ring itself may be ob-\\nserved.\\n251. Saturn s ring, in its revolution around the sun f\\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\\n250. How is the ring divided by large telescopes? State the\\nseveral dimensions of Saturn and his rings. Describe the\\nfigure. How is the ring inferred to be a solid opake sub-\\nstance In what time does Saturn revolve on his axis 1 What\\nfigure does this give to the planet 1 What kind of telescope is\\nrequired to see the phenomena of Saturn to advantage", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0209.jp2"}, "210": {"fulltext": "196 THE PLANETS.\\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\\nwill 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\\nso distant a body as Saturn, very near the sun, these\\nappearances are presented to us in nearly the same man-\\nner as though we viewed them from the sun. Accord\\ndingly, we sometimes see Saturn s ring under the form\\nof a broad ellipse, which grows continually more and\\nmore acute until it passes into a line, and we either lose\\nsight of it altogether, or by the aid of the most power-\\nful telescopes, 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\\nLet A, B, C, c. represent successive positions of Sat-\\nurn and his ring in different parts of his orbit, while\\n251. How is the position of the ring with respect to itself\\nin all parts of its revolution How may the various appear-\\nances of the ring be represented", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0210.jp2"}, "211": {"fulltext": "SATURN.\\n197\\nabc represents the orbit of the earth.* Were the ring\\nwhen at C and G perpendicular to the CG, it would be\\nseen by a spectator situated at a or d a perfect circle,\\nbut being inclined to the line of vision 28\u00c2\u00b0 4 it is pro-\\njected into an ellipse. This ellipse contracts in breadth\\n46.\\nas the ring passes towards its nodes at A and E, where\\nit dwindles into a straight line. From E to G the ring\\nopens again, becomes broadest at G, and again contracts\\ntill it becomes a straight line at A, and from this point\\nexpands till it recovers its original breadth at C. These\\nsuccessive appearances are all exhibited to a telescope of\\nmoderate powers. The ring is extremely thin, since the\\nsmallest satellite, when projected on it, more than covers\\nit. The thickness is estimated at 100 miles.\\n253. Saturn 1 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 sun is\\nenlightened and it is remarkable, that the illumination\\nof the ring is greater than that of the planet itself, but\\n252. Explain the revolution of the ring by figure 46.\\n253. Whence does the ring derive its light What causes\\noccasion the disappearance of the ring At what intervals\\ndo these disappearances occur 1\\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 oibit, but merely as the projection of circles seen very obliquely.\\n17*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0211.jp2"}, "212": {"fulltext": "198 THE PLANETS.\\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\\nof the ring produced may pass between the earth and\\nthe sun, in which case also the ring becomes invisi-\\nble, the illuminated side being wholly turned from us.\\nThus when the ring is approaching its node at E, a spec-\\ntator at a would have the dark side of the ring presented\\nto him. The ring was invisible in 1833, and will be\\ninvisible again in 1847. The northern side of the ring\\nwill be seen until 1845, when the southern side will\\ncome into view.\\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 un-\\nilluminated side is towards the earth.\\n254. Saturn s ring revolves in its own plane in about\\n10^ hours, (lOh. 32m. 15s.4). La Place inferred this\\nfrom the doctrine of universal gravitation. He proved\\nthat such a rotation was necessary, otherwise the matter\\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 lOJ 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 with\\nthe planet, yet recent measurements of extreme delicacy\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0212.jp2"}, "213": {"fulltext": "SATURN.\\n199\\nhave demonstrated, that the coincidence is not mathe-\\nmatically exact, but that the center of gravity of the rings\\ndescribes around that of the body a very minute orbit.\\nThis fact, unimportant as it may seem, is of the utmost\\nconsequence to the stability of the system of rings. Sup-\\nposing them mathematically perfect in their circular form,\\nand exactly concentric with the planet, it is demonstrable\\nthat they would form (in spite of their centrifugal force)\\na system in a state of unstable equilibrium, which the\\nslightest external power would subvert not by causing\\na rupture in the substance of the rings but by precip-\\nitating them unbroken on the surface of the planet.\\nThe ring may be supposed of an unequal breadth in its\\ndifferent parts, and as consisting of irregular solids,\\nwhose common center of gravity does not coincide with\\nthe center of the figure. Were it not for this distribu-\\ntion of matter, its equilibrium would be destroyed by\\nthe slightest force, such as the attraction of a satellite,\\nand the ring would finally precipitate itself upon the\\nplanet.\\nAs the smallest difference of velocity between the\\nplanet and its rings must infallibly precipitate the rings\\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\\n255. Are the rings concentric with the planet? What ad-\\nvantage results from this arrangement 1 How must the rings\\nappear when seen from the planets", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0213.jp2"}, "214": {"fulltext": "200 THE PLANETS.\\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 seven satellites. Although\\nbodies of considerable size, their great distance prevents\\ntheir being visible to any telescopes but such as afford a\\nstrong light and high magnifying powers. The outer-\\nmost satellite is distant from the planet more than 30\\ntimes the planet s diameter, and is by far the largest of\\nthe whole. It is the only one of the series whose theory\\nhas been investigated further than suffices to verify Kep-\\nler s law of the periodic times, which is found to hold\\ngood here as well as in the system of Jupiter. It ex-\\nhibits, like the satellites of Jupiter, periodic variations of\\nlight, which prove its revolution on its axis in the time\\nof a sidereal revolution about Saturn. The next satellite\\nin order, proceeding inwards, is tolerably conspicuous\\nthe three next are very minute, and require pretty pow-\\nerful telescopes to see them while the two interior sat-\\nellites, which just skirt the edge of the ring, and move\\nexactly in its plane, have never been discovered but with\\nthe most powerful telescopes which human art has yet\\nconstructed, and then only under peculiar circumstances.\\nAt the time of the disappearance of the rings (to ordinary\\ntelescopes) they were seen by Sir William Herschel\\nwith his great telescope, projected along the edge of the\\nring, and threading like beads the thin fibre of light to\\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", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0214.jp2"}, "215": {"fulltext": "URANUS. 201\\nwhich the ring is then reduced. Owing to the obiquity\\nof the ring, and of the orbits of the satellites to that of\\ntheir primary, there are no eclipses of the satellites, the\\ntwo interior ones excepted, until near the time when the\\nring is seen edgewise.\\n257 Uranus is the remotest planet belonging to our\\nsystem, and is rarely visible except to the telescope. Al-\\nthough his diameter is more than four times that ot the\\nearth, (35,112 miles,) yet his distance from the sun is\\nlikewise 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 sta-\\ntionary. His path lies very nearly in the ecliptic, being\\ninclined to it less than one degree, (46 28 .44.)\\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\\nthere 400 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.\\n258 Uranus is attended by six satellites. So minute\\nobject s are they, that they can be seen only by powerful\\ntelescopes. Indeed, the existence of more than two is\\nstill considered as somewhat doubtful. These two,\\n257. Uranus.\u00e2\u0080\u0094 State his diameter\u00e2\u0080\u0094 distance from the sun\u00e2\u0080\u0094\\nperiodic time\u00e2\u0080\u0094 inclination of his orbit. How would the sun\\nAppear from Uranus State the history of his discovery", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0215.jp2"}, "216": {"fulltext": "202 THE PLANETS.\\nhowever, offer remarkable, and indeed quite unexpected\\nand unexampled peculiarities. Contrary to the unbro-\\nken analogy of the whole planetary system, the planes\\nof their orbits are nearly perpendicular to the ecliptic,\\nbeing inclined no less than 78\u00c2\u00b0 58 to that plane, and in\\nthese orbits their motions are retrograde that is, instead\\nof advancing from west to east around their primary, as\\nis the case with all the other planets and satellites, they\\nmove in the opposite direction. With this exception, all\\nthe motions of the planets, whether around their own\\naxes, or around the sun, are from west to east. The sun,\\nhimself, turns on his axis from west to east all the pri-\\nmary planets revolve around the sun from west to east\\ntheir revolutions on their own axes are also in the sair t;\\ndirection 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 the\\nworld.\\nTHE NEW PLANETS, CERES, PALLAS, JUNO, AND VESTA.\\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\\n258. By how many satellites is Uranus attended What is\\nsaid of their minuteness What remarkable peculiarities have\\nthey In what direction are the motions of all the bodies in\\nthe solar system What does this fact indicate with respect to\\ntheir origin", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0216.jp2"}, "217": {"fulltext": "203\\nNEW PLANETS. uo\\n\u00e2\u0080\u009ef the otherplanets. 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 i conti\\nnent of Europe of twenty-four observers who divided\\nhe sky into as many zones, one of winch was allotted\\nto each member of the association. The discovery of\\nthe first of these bodies was however made accidentally\\nbv 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 re-discov-\\nefed in Germany. Piazzi called it Ceres, in honor of\\nthe tutelary goddess of Sicily and her emblem the\\nsickle?, has been adopted as its appropriate symbol\\nThe difficulty of finding Ceres induced I ;01be s,\\nBremen, to examine with particular care all the small\\nftars that lie near her path, as seen from the earth and\\nwhile prosecuting these observations, m March, 1802, he\\ndiscovered another similar body, very nearly at the same\\nd stance from the sun, and resembling the former in\\nmanv other particulars. The discoverer gave to this se-\\ncond planet the name of Pallas, choosing for its symbol\\nthe lance i the characteristic of Minerva.\\n260 The most surprising circumstance connected\\n\u00e2\u0096\u00a0with 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 th 1S\\nsfncmlarity, Dr. Gibers 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 hypothecs\\nsuggested the probability that there might be other frag-\\n259. Name the New Planets. When were they ^covered?\\nWhat had been conjectured previous to their discovery Who\\ndiscovered the first What is its name 1 How was Pallas dis-\\ncovered", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0217.jp2"}, "218": {"fulltext": "204 THE PLANETS.\\nmerits, whose orbits, however they might differ in ec\\ncentricity and inclination, might be expected to cross the\\necliptic at a common point, or to have the same node.\\nDr. Olbers, therefore, proposed to examine carefully every\\nmonth, the two opposite parts of the heavens in which\\nthe orbits of Ceres and Pallas intersect one another, with\\na view to the discovery of other planets, which might\\nbe sought for in those parts with greater chance of suc-\\ncess than in a wider zone, embracing the entire limits\\nof these orbits. Accordingly, in 1804, near one of the\\nnodes of Ceres and Pallas, a third planet was discovered.\\nThis was called Juno, and the character was adopted\\nfor its symbol, representing the starry sceptre of the\\nqueen of Olympus. Pursuing the same researches, in\\n1807, a fourth planet was discovered, to which waa\\ngiven the name of Vesta, and for its symbol the char-\\nacter was chosen an altar surmounted with a censer\\nholding the sacred fire.\\nAfter this historical sketch, it will be sufficient to clas-\\nsify under a few heads the most interesting particulars\\nrelating to the New Planets.\\n261. The average distance of these bodies from the\\nsun is 261,000,000 miles; and it is remarkable that\\ntheir orbits are very near together. Taking the distance\\nof the 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\\n4^ years\\nIn respect to the inclination of their orbits, there is\\nconsiderable diversity. The orbit of Vesta is inclined\\n260. How do Ceres and Pallas compare in distance from tho\\nsun and the place of their nodes What hypothesis did Olbers\\nadopt State the circumstances connected with the discovery\\nof Juno and Vesta:.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0218.jp2"}, "219": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM.\\n205\\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-\\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 Vesta is estimated at only\\none fifteen thousandth part of the earth s, and her surface\\nis only about equal to that of the kingdom of Spam.\\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\u00e2\u0080\u0094 QUANTITY OF MAT-\\nTER IN THE SUN AND PLANETS\u00e2\u0080\u0094 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-\\n261. What is the average distance of the New Planets from\\nthe sun How do these orbits lie with respect to each other?\\nAre thev subject to Kepler s third law What is their average\\nperiodical time 1 What is said of the inclination of their or-\\nbits Also, of the eccentricity What is their size\\n18", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0219.jp2"}, "220": {"fulltext": "206 THE PLANETS.\\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.\\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 cohsideiing 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 pos-\\nsession 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 dif-\\nficult.\\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 of\\nevery thing material, without light or life, and without\\nbounds. Of such a space we could not predicate the\\nideas of up or down, east, west, north, or south, but all\\nreference 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-\\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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0220.jp2"}, "221": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 207\\ntention upon this object, 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\\npoints. We suppose ourselves next to be placed on the\\nsurface of the sun, and the firmament of stars to be\\nlighted up. The slow revolution of the sun on his axis,\\nwould be indicated by a corresponding movement of the\\nstars in the opposite direction and in a period equal to\\nmore than 25 of our days, the spectator would see the\\nheavens perform a complete revolution around the sun,\\nas he now sees them revolve around the earth once in\\n24 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 points\\nwould be immediately suggested.\\nThus prepared, we may now enter upon the conside-\\nration of the planetary motions.\\n264. Standing on the sun, we see all the planets mo\\nvine siowly 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 dailv 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\\n263 How can we form a correct idea of absolute space\\nWhat can we predicate of such a space If the sun were pla-\\nced in such a void, what new ideas would present themselves I\\nHow should we get a knowledge of the cardinal points", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0221.jp2"}, "222": {"fulltext": "208\\nTHE PLANETS.\\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\\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 mero 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 trace\\nout 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, w r ere made of thin\\nplates of glass, and that the paths of the respective plan-\\nets were marked out on their planes indistinct 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-\\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\\nand the orbit of Mercury to be represented on the sky 1 How\\nshall we conceive of the planes of these orbits as distinguished\\nfrom the 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": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0222.jp2"}, "223": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 209\\nface and visible lines to aid us in giving position and fig-\\nure to the planetary orbits, let us now throw aside these\\ndevices, and hereafter conceive of these planes and or-\\nbits as they are in nature, and learn to refer a body to a\\nmere mathematical plane, and to trace its path in that\\nplane through absolute space.\\n265. A clear understanding of the motions of Mercury\\nand of the relation of its orbit to the plane of the eclip-\\ntic, will render it easy to understand the same particulars\\nin regard to each of the other planets. Standing on the\\nsun we should see each of the planets pursuing a similar\\ncourse to that of Mercury, all moving from west to east,\\nwith motions differing from each other chiefly in two re-\\nspects, namely, in their velocities, and in the distances\\nto 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 specta-\\ntor on the sun, who views the motions of the planets as\\nthey actually exist in nature, would make no such dis-\\ntinction between the different orbits, but merely inquire\\nhow they were mutually related to each other. Taking,\\nhowever, the ecliptic as the plane to which all the others\\nare referred, we do not, as in the case of the other plan-\\nets, inquire how its plane is inclined, nor what are its\\nnodes, since it has neither inclination nor node.\\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\\n18*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0223.jp2"}, "224": {"fulltext": "210 THE PLANETS.\\nmeans of diagrams, or even orreries, is usually a failure\\nThe student who relies exclusively on such aids as\\nthese, will acquire ideas on this subject that are both in-\\nadequate and erroneous. They may aid reflection, but\\ncan never supply its place. The impossibility of rep-\\nresenting things in their just proportions will be evident\\nwhen we reflect, that to do this, if, in an orrery, we\\nmake Mercury as large as a cherry, we should require to\\nrepresent the sun by a globe six feet in diameter. If we\\npreserve the same proportions in regard to distance, we\\nmust place Mercury 250 feet, and Uranus 12,500 feet,\\nor more than two miles from the sun. The mind of the\\nstudent of astronomy must, therefore, raise itself from\\nsuch imperfect representations of celestial phenomena as\\nare afforded by artificial mechanism, and, transferring his\\ncontemplations to the celestial regions themselves, he\\nmust conceive of the sun and planets as bodies that bear\\nan insignificant ratio to the immense spaces in which\\nthey circulate, resembling more a few little birds flying\\nin the 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 view them out of the center of their or-\\nbits secondly, ice are ourselves in motion. From the\\nfirst cause, the apparent places of the planets are greatly\\nchanged by perspective and from the second cause,\\n266. What is said of the attempt to represent the positions\\nand motions of the solar system by diagrams and orreries\\nGive examples.\\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 geo-\\ncentric place of a planet", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0224.jp2"}, "225": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 211\\nwe attribute to the planets changes of place which arise\\nfrom our own motions of which we are unconscious.\\nThe situation of a heavenly body as seen from the\\ncenter of the sun 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 Venus 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 apparent\\nmotions of these planets are accelerated by the motion\\nof the earth but that while moving through the infe-\\nrior conjunction, at which time their motions are retro-\\ngrade, they are apparently retarded by the earth s mo-\\ntion. Let us now see what are the geocentric motions\\nof the Superior Planets.\\n269. Let A, B, C, (Fig. 47,) represent the earth in\\ndifferent positions in its orbit, and M a superior planet as\\nMars, 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\\nF are the two points of greatest elongation of the earth\\nfrom the sun as seen from the planet hence between\\n268. Describe the apparent motions of Mercury and Venus\\nfrom figure 40.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0225.jp2"}, "226": {"fulltext": "212\\nTHE PLANETS.\\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 R\\nto N, and is therefore retrograde. As the arc described\\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 R\\nin the one case, and from R to N in the other, is the\\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 1\\nWhat when in superior conjunction 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0226.jp2"}, "227": {"fulltext": "MOTIONS OF THE PLANETARY SYSTEM. 213\\nsame in both cases, the retrograde motion is much swifter\\nthan the direct, being 1 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 ret-\\nrograde 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, kfter having been once seen in opposition, does not\\ncome 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 appar-\\n270. How does the real motion of the planet modify the foro\\ngoing results How in respect to the remotest planets, as Ura\\nnus, and how in respect to a nearer planet as Mars 1 How\\noften is Mars in opposition What is his appearance then", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0227.jp2"}, "228": {"fulltext": "214 THE PLANETS.\\nent 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\\nit exerts, and this force is estimated by its effects.\\nHence worlds are weighed with as much ease as a peb-\\nble or an article of merchandise.\\n272. The sun contains about 355,000 times as much\\nmatter as the earth, and 800 times as much matter as all\\nthe planets. This however, is owing rather to its great\\nsize than to the specific gravity of its materials, for the\\ndensity of the sun is only one fourth as great as that of\\nthe earth. The earth is nearly 5\u00c2\u00a3 times as heavy as\\nwater, but the sun is only a little heavier than that fluid.\\nThe planets near the sun are in general more dense than\\n271. What is said of the apparent difficulty of weighing the\\nsun and planets What great principles lead us to this re-\\nsult 1 How do we learn the quantity of matter in the bodies\\nof the solar system\\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\\nmuch heavier is the earth than water How much heavier is\\nthe sun than water Which of the planets have the greatest\\ndensity 1 How heavy is Mercury How heavy is Saturn", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0228.jp2"}, "229": {"fulltext": "STABILITY OF THE SOLAR SYSTEM. 215\\nthose more remote Mercury being heavier than lead,\\nwhile Saturn is as light as a cork. The decrease in\\ndensity however, is not entirely regular, since Venus is\\na little lighter than the earth, while Jupiter is heavier\\nthan Mars, and Uranus than Saturn.\\nSTABILITY OF THE SOLAR SYSTEM.\\n273. The perturbations occasioned by the motions of\\nthe planets by their action on each other are very nu-\\nmerous, since every body in the system exerts an attrac-\\ntion on every other, in conformity with the law of Uni-\\nversal Gravitation. Venus and Mars, approaching as\\nthey do at times comparatively near to the earth, sen-\\nsibly disturb its motions, and the satellites of the re-\\nmoter planets greatly disturb each other s movements.\\n274. The derangement which the planets produce in\\nthe motion of one of their number will be very small in\\nthe course of one revolution but this gives us no secu-\\nrity that the derangement may not become very large\\nin the course of many revolutions. The cause acts per-\\npetually, and it has the whole extent of time to work in.\\nIs it not easily conceivable then, that in the lapse of ages,\\nthe derangements of the motions of the planets may\\naccumulate, the orbits may change their form, and their\\nmutual distances may be much increased or diminished 1\\nIs it not possible that these changes may go on without\\n273. What is said of the perturbations occasioned by the ac-\\ntion of the planets on each other 1 Which planets in particu-\\nlar, disturb the motions of the earth\\n274. How is the derangement produced by the planets upon\\nany one of them, in a single revolution 1 What may be the\\nultimate effect of these disturbing forces What would be\\nthe consequence of increasing the eccentricity of the earth s\\norbit or of bringing the moon nearer the earth or of alter-\\ning the positions of the planets with respect to that of the\\nearth 1 What changes are actually going on in the motions\\nof the heavenly bodies", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0229.jp2"}, "230": {"fulltext": "210 THE PLANETS.\\nlimit, and end in the complete subversion and ruin of the\\nsystem? If, for instance, the result of this mutual\\ngravitation should be to increase considerably the eccen-\\ntricity of the earth s orbit, or to make the moon approach\\ncontinually nearer and nearer to the earth at every revo-\\nlution, it is easy to see that in the one case, our year\\nwould change its character, producing a far greater ir-\\nregularity in the distribution of the solar heat in the\\nother, our satellite must fall to the earth, occasioning a\\ndreadful catastrophe. If the positions of the planetary\\norbits with respect to that of the earth, were to change\\nmuch, the planets might sometimes come very near us,\\nand thus increase the effect of their attraction beyond cal-\\nculable limits. Under such circumstances we might have\\nyears of unequal length, and seasons of capricious tem-\\nperature planets and moons of portentous size and as-\\npect glaring and disappearing at uncertain intervals tides\\nlike deluges sweeping over whole continents and, per-\\nhaps, the collision of two of the planets, and the conse-\\nquent destruction of all organization on both of them.\\nThe fact really is, that changes are taking place in the\\nmotions of the heavenly bodies, which have gone on\\nprogressively from the first dawn of science. The ec-\\ncentricity of the earth s orbit has been diminishing from\\nthe earliest observations to our times. The moon has\\nbeen moving quicker from the time of the first recorded\\neclipses, and is now in advance by about four times her\\nown breadth, of what her own place would have been if\\nit had not been affected by this acceleration. The ob-\\nliquity of the ecliptic also, is in a state of diminution,\\nand is now about two fifths of a degree less than it was\\nin the time of Aristotle. (Whewell, in the Bridgewater\\nTreatises, p. 128.)\\n275. But amid so many seeming causes of irregular-\\nity, and ruin, it is worthy of grateful notice, that effec-\\ntual provision is made for the stability of the solar sys-\\ntem. The full confirmation of this fact, is among the\\ngrand results of Physical Astronomy. Newton did not\\nundertake to demonstrate either the stability or insta-", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0230.jp2"}, "231": {"fulltext": "STABILITY OF THE SOLAR SYSTEM. 217\\nbility of the system. The decision of this point re-\\nquired a great number of preparatory steps and simplifi-\\ncations, and such progress in the invention and improve-\\nment of mathematical methods, as occupied the best\\nmathematicians of Europe for the greater part of the\\nast century. Towards the end of that time, it was\\nhown by La Grange and La Place, that the arrange-\\nnents of the solar system are stable that, in the\\nong run, the orbits and motions remain unchanged;\\nand that the changes in the orbits, which take place in\\nshorter periods, never transgress certain very moderate\\nlimits. Each orbit undergoes deviations on this side\\nand on that side of its average state but these devia-\\ntions are never very great, and it finally recovers from\\nthem, so that the average is preserved. The planets\\nproduce perpetual perturbations in each other s motions,\\nbut these perturbations are not indefinitely progressive,\\nbut periodica], reaching a maximum value and then di-\\nminishing. The periods which this restoration requires\\nare for the most part enormous, not less than thou-\\nsands, and in some instances millions of years. Indeed\\nsome of these apparent derangements, have been going\\non in the same direction from the creation of the world.\\nBut the restoration is in the sequel as complete as the\\nderangement; and in the mean time the disturbance\\nnever attains a sufficient amount seriously to affect the\\nstability of the system. (Whewell, in the Bridgewater\\nTreatises, p. 128.) I have, succeeded in demonstrating\\n(says La Place) that, whatever be the masses of the plan-\\nets, in consequence of the fact that they all move in the\\nsame direction, in orbits of small eccentricity, and but\\nslightly inclined to each other, their secular irregulari-\\nties are periodical and included within narrow limits\\nso that the planetary system will only oscillate about a\\n275. Is the system stable Did Newton prove this Who\\nfully established this point Have all the inequalities of the\\nplanetary motions a fixed period How long are some of these\\nperiods 1\\n19", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0231.jp2"}, "232": {"fulltext": "218 COMETS.\\nmean state, and will never deviate from it except by a\\nvery small quantity. The ellipses of the planets have\\nbeen and always will be nearly circular. The ecliptic\\nwill never coincide with the equator and the entire ex-\\ntent of the variation in its inclination, cannot exceed\\nthree degrees.\\n276. To these observations of La Place, Professor\\nWhewell adds the following on the importance, to the\\nstability of the solar system, of the fact that those plan-\\nets which have great masses have orbits of small eccen-\\ntricity. The planets Mercury and Mars, which have\\nmuch the largest eccentricity among the old planets, are\\nthose of which the masses are much the smallest. The\\nmass of Jupiter is more than two thousand times that of\\neither of these planets. If the orbit of Jupiter were as\\neccentric as that of Mercury, all the security for the sta-\\nbility of the system, which analysis has yet pointed out,\\nwould disappear. The earth and the smaller planets\\nmight, by the near approach of Jupiter at his perihelion,\\nchange their nearly circular orbits into very long ellipses,\\nand thus might fall into the sun, or fly off into remote\\nspace. It is further remarkable that in the newly discov-\\nered planets, of which the orbits are still more eccentric\\nthan that of Mercury, the masses are still smaller, so that\\nthe same provision is established in this case also.\\nCHAPTER X.\\nOF COMETS.\\n277. A Comet, when perfectly formed, consists of\\nthree parts, the Nucleus, 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\\n276. What planets have orbits of small eccentricity How\\ndoes this fact contribute to the stability of the system", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0232.jp2"}, "233": {"fulltext": "COMETS. 219\\nvery dense portion of matter. Though it is usually ex-\\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 is\\na 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.\\n277. Of what three parts does a comet consist 1 Describe\\neach.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0233.jp2"}, "234": {"fulltext": "220 COMETS.\\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 day time.\\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 130\\nhave been computed, and arranged in a table for future\\ncomparison. Of these six are particularly remarkable,\\nviz. the comets, of 1680, 1770, and 1811; and those\\nwhich bear the names of Halley, Biela, and Encke.\\nThe comet of 1680, was remarkable not only for its as-\\ntonishing size and splendor, and its near approach to the\\nsun, but is celebrated for having submitted itself to the\\nobservations of Sir Isaac Newton, and for having en-\\njoyed the signal honor of being the first comet whose\\nelements were determined on the sure basis of math-\\nematics. The comet of 1770, is memorable for the\\nchanges its orbit has undergone by the action of Jupiter,\\nas will be more particularly related in the sequel. The\\ncomet of 1811 was the most remarkable in its appear-\\nance of all that have been seen in the present century.\\nIt had scarcely any perceptible nucleus, but its train\\nFig. 49.\\nwas veiy long and broad, as is represented in figure 49.\\nHa] ley s comet (the same which re-appeared in 1835) is", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0234.jp2"}, "235": {"fulltext": "COMETS\\n221\\ndistinguished as that whose return was first successfully\\npredicted, and whose orbit is best determined; and\\nBiela s and Encke s comets are well known for their\\nshort periods of revolution, which subject them fre-\\nquently to the view of astronomers.\\n279. In magnitude and brightness comets exhibit a\\ngreat diversity. History informs us of comets so bright\\nas to be distinctly visible in the day time, even at noon\\nand in the brightest sunshine. Such was the comet\\nseen at Rome a little before the assassination of Julius\\nCaesar. The comet of 1680 covered an arc of the heav-\\nens of 97\u00c2\u00b0, and its length was estimated at 123,000,000\\nmiles. That of 1811, had a nucleus of only 428 miles\\nin diameter, but a tail 132,000,000 miles long. Had it\\nbeen coiled around the earth like a serpent, it would\\nhave reached round more than 5,000 times. Other com-\\nets are of exceedingly small dimensions, the nucleus\\nbeing estimated at only 25 miles and some which are\\ndestitute of any perceptible nucleus, appear to the largest\\ntelescopes, even when nearest to us, only as a small\\nspeck of fog, or as a tuft of down. The majority of\\ncomets can be seen only by the aid of the telescope.\\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 horrendce magnitudinis\\nin 1456 its tail reached from the horizon to the zenith,\\nand inspired such terror, that by a decree of the Pope of\\nRome, public prayers were offered up at noon-day in all\\nthe Catholic churches to deprecate the wrath of heaven,\\nwhile in 1682, its tail was only 30\u00c2\u00b0 in length, and in 1759\\n27% What is said of the number of comets 1 How many\\nhave been arranged in a table. Specify the six that are most\\nremarkable. State particulars respecting each.\\n279. What is said of the magnitude and brightness of com-\\nets 1 What was the length of the comet of 1680 Ditto of\\n1811 Has the same comet different aspects at different re-\\nturns 1 Example in Halley s comet.\\n19*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0235.jp2"}, "236": {"fulltext": "222 COMETS.\\nit was visible only to the telescope, until after it had pas-\\nsed the perihelion. At its recent return in 1835, the\\ngreatest length of the tail was about 12\u00c2\u00b0. These changes\\nin the appearances of the same comet, are partly owing\\nto the different positions of the earth with respect to\\nthem, being sometimes much nearer to them when they\\ncross its track than at others also one spectator so situ-\\nated as to see the coma at a higher angle of elevation or\\nin a purer sky than another, will see the train longer than\\nit appears to another less favorably situated but the\\nextent of the changes are such as indicate also a real\\nchange in magnitude and brightness.\\n280. The periods of comets in their revolutions\\naround the sun, are equally various. Encke s comet,\\nwhich has the shortest known period, completes its rev-\\nolution in 3^ years, or more accurately, in 1208 days\\nwhile that of 1811 is estimated to have a period of 3383\\nyears.\\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 by reflecting the light of the sun.\\nIn one or two instances they have exhibited distinct\\n\u00e2\u0080\u00a2phases, although the nebulous matter with which the\\nnucleus is surrounded, would commonly prevent such\\n280. How are the periods of comets What is that of\\nEncke s comet, and that of the comet of 1811\\n281. How are the distances of comets from the sun Com-\\npare Encke s and Halley s. Do comets always return to the sun", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0236.jp2"}, "237": {"fulltext": "COMETS.\\n223\\nphases from being distinctly visible, even when they\\nwould otherwise be apparant. 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\\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 reach\\nits maximum until after the perihelion passage. In re-\\nceding from the sun, the tail again contracts, and nearly\\nor quite disappears before the body of the comet is en-\\ntirely out of sight. The tail is frequently divided into\\ntwo portions, the central parts, in the direction of the\\naxis, 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 hne from tne\\nsun, although more or less curved, like a \u00c2\u00abng quill or\\nfeather, being convex on the side next to tne 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 irr 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, suscepti-\\nble of being penetrated through their whole substance by\\n282. Do comets shine by direct or by reflected light 1 Do\\nthey exhibit phases How is it known that their light is re-\\nflected and not direct light\\n283 How are the tails of comets affected by being near the\\nsun How many tails have some comets In what direction\\nis the tail in respect to the sun", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0237.jp2"}, "238": {"fulltext": "224\\nCOMETS.\\nthe sunbeams, and reflecting them alike from their inte-\\nrior parts and from their surfaces. It appears, perhaps,\\nincredible that so thin a substance should be visible by\\nreflected light, and some astronomers have held that the\\nmatter of comets is self-luminous but it requires but\\nvery little light to render an object visible in the night,\\nand a light vapor may be visible when illuminated\\nthroughout an immense stratum, which could not be\\nseen if spread over the face of the sky like a thin cloud.\\nFrom the extremely small quantity of matter of these\\nbodies, compared with the vast spaces they cover, New-\\nton calculated that if all the matter constituting the\\nlargest tail of a comet, were to be compressed to the\\nsame density with atmospheric air, it would occupy no\\nmore than a cubic inch. This is incredible, but still\\nthe highest clouds that float in our atmosphere, must be\\nlooked upon as dense and massive bodies, compared with\\nthe filmy and all but spiritual texture 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 did\\nnot perceptibly change their motions. The same comet\\nalso came very near the earth so near, that, had its\\nmass 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 A of that of\\nthe earth, and might have been less than this to any ex-\\n284. How is the quantity of matter in comets Of what do\\nthe tails consist Can a substance so thin shine by reflected\\nlight What opinion had Newton of the extreme tenuity of\\nthe material of comets tails", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0238.jp2"}, "239": {"fulltext": "COMETS.\\n225\\ntent. It may indeed be asked, what proof we nave that\\ncomets have any matter, and are not mere reflections of\\nlicrht. 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-\\nformity with the laws of universal gravitation. A deli-\\ncate compass may be greatly agitated by the vicinity of\\na mass of iron, while the iron is not sensibly affected by\\nthe 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 to\\nbe an ellipse, requiring for a complete revolution only\\n5| 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 within\\nthe sphere of Jupiter s attraction. Calculating the amount\\nof this attraction from the known proximity of the two\\nbodies, it was found what must have been its orbit pre-\\nvious to the time when it became subject to the disturb-\\ning action of Jupiter. The result showed that it then\\n285. How is the small quantity of matter in comets proved\\nHow was this indicated by the comet of 1770 What did Us\\nquantity of matter not exceed as compared with the earth s 1\\nMay we not infer that they have no matter", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0239.jp2"}, "240": {"fulltext": "226 COMETS.\\nmoved in an ellipse of greater extent, having a period of\\n50 years, and having its perihelion instead of its aphelion\\nnear Jupiter. It was therefore evident why, as long as\\nit continued to circulate in an orbit so far from the cen-\\nter of the system, it was never visible from the earth.\\nIn January 1767, Jupiter and the comet happened to be\\nvery near one another, and as both were moving in the\\nsame direction, and nearly in the same plane, they re-\\nmained in the neighborhood of each other for several\\nmonths, the planet being between the comet and the\\nsun. The consequence was, that the comet s orbit was\\nchanged into a smaller ellipse, in which its revolution\\nwas accomplished in 5| years. But as it was approach-\\ning the sun in 1779, it happened again to fall in with\\nJupiter. It was in the month of June, that the attrac-\\ntion of the planet began to have a sensible effect and\\nit was not until the month of October following, that\\nthey were finally separated.\\nAt the time of their nearest approach, in August, Ju-\\npiter was distant from the comet only J 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 or-\\nbit, which even at its perihelion came no nearer to the\\nsun than the planet Ceres. In this third orbit, the comet\\nrequires about 20 years to accomplish its revolution;\\nand being at so great a distance from the earth, it is in-\\nvisible, and will forever remain so, unless, in the course\\nof ages, it may undergo new perturbations, and move\\nagain in some smaller orbit as before.\\n286. How may a comet have its orbit changed How was\\nthe orbit of the comet of 1770 changed? How was this fact as-\\ncertained 1 What action did Jupiter exert upon it in 1767, and\\nagain in 1779 How far was Jupiter from the comet at the\\ntime of their nearest approach How many years does it now\\nrequire to perform its revolution", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0240.jp2"}, "241": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 227\\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 interme-\\ndiate class of bodies between planets and comets,) move\\nin orbits which are nearly circular, and all very near to\\nthe plane of the ecliptic, and all move in the same direc-\\ntion from west to east. But the orbits of comets are far\\nmore eccentric than those of the planets they are in-\\nclined to the ecliptic at various angles, being sometimes\\neven nearly perpendicular to it and the motions of\\ncomets are sometimes retrograde.\\n288. The Elements of a comet are five, viz. (1) The\\nperihelion distance (2) longitude of the perihelion (3)\\nlongitude of the node (4) inclination of the orbit (5)\\ntime of the perihelion passage. m\\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. Inis\\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 on y\\na very small portion of their course, that they are visible\\nfrom the earth, and the observations made m 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 ot\\nthe sio-ns in the zodiac, and sometimes nearly perpen-\\ndicukr to the plane of the ecliptic so that their appa-\\n297. How do the orbits of comets differ from those of planets?\\n288. What particulars are called the elements of a comet\\nWhat is said of the difficulty of determining these elements 1\\nSpecify the several reasons of this difficulty.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0241.jp2"}, "242": {"fulltext": "228 comets.\\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 ec-\\ncentric orbits, the slightest change in the position of the\\ncurve near the vertex, where alone the comet can be ob-\\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 the\\nmajor axis of the ellipse, and consequently the periodical\\nrevolution.* An error of only a few seconds may cause\\na difference of many hundred years. In this manner,\\nthough Bessel determined the revolution of the comet of\\n1769 to be 2089 years, it was found that an error of no\\nmore than 5 in observation, would alter the period either\\nto 2678 years, or to 1692. Some astronomers, in calcula-\\nting the orbit of the great comet of 1680, have found the\\nlength of its greater axis 426 times the earth s distance\\nfrom the sun, and consequently its period 8792 years\\nwhilst others estimate the greater axis 430 times the\\nearth s distance, which alters the period to 8916 years.\\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 thi\\nperiodic time by Kepler s law, which applies as well to comets as ter\\nplanets.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0242.jp2"}, "243": {"fulltext": "MOTIONS AND ORBITS OF COMETS.\\n229\\nNewton and Halley, however, judged that this comet\\naccomplished its revolution m only 570 years.\\n090 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 m its physi-\\ncal 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 Halley 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.\\nT ime of appear.\\n1456\\n1531\\n1607\\n1682\\nInclin. of the nrbit\\n17\u00c2\u00b0 56\\n17 56\\n17 02\\n17 42\\nLon. of Node.\\nLon. of Per\\nPer. Dist.\\nCourse.\\n48\u00c2\u00b0 30\\ns301\u00c2\u00b0 00\\n0.58\\nRetrograde\\n49 25\\n301 38\\n0.57\\n50 21\\n302 16\\n0.58\\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\\n290. Can we identify a comet with one that has been seen\\nbefore, by its appearance I 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 W hat\\ncauses alter the periods of its return 1\\n20", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0243.jp2"}, "244": {"fulltext": "230 COMETS.\\ndays by the action of Jupiter, and 518 days by that of\\nSaturn. This would delay its appearance until early in\\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\\nlooked for with no less interest than in 1759. Several\\nof the most accurate mathematicians of that age had cal-\\nculated its elements with inconceivable labor. Their\\nzeal was rewarded by the appearance of the expected\\nvisitant at the time and place assigned it travelled the\\nnorthern sky presenting the very appearances, in most\\nrespects, that had been anticipated and came to its pe-\\nrihelion on the 16th of November, within two days of\\nthe time predicted by Pontecoulant, a French mathe-\\nmatician who had, it appeared, made the most success-\\nful calculation.* On its previous return, it was deemed\\nan extraordinary achievement to have brought the pre-\\ndiction within a month of the actual time.\\nMany circumstances conspired to render this return of\\nHalley 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\\n3i years,) affords peculiar facilities for ascertaining the\\n291 How was the return of Halley s comet in 1835 re-\\ngarded by astronomers What circumstances conspired to\\nproduce this feeling 1\\nSee Professor Loomis s Observations on Halley s Comet. Amer.\\nJour. Science, 30, 209.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0244.jp2"}, "245": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 231\\nlaws of its revolution and it has kept the appointments\\nmade for it with great exactness. On its late return\\n(1839) it exhibited to the telescope a globular mass ot\\nnebulous matter, resembling fog, and moved towards its\\nperihelion 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 leather\\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 bad 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 maybe counteracted by the attraction\\nof one or more of the planets, near which it may pass in\\nits successive returns to the sun.\\n292. Are the elements of Encke s comet calculated with ex-\\nactness 1 What was its appearance in 1839 What has made\\nI peculiarly famous Why should it be so favorable for detec-\\nt ng a resisting medium What has been its effect on the\\nmotions of the comet What will be its ultimate effect", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0245.jp2"}, "246": {"fulltext": "2 **2 COMETS.\\n293. It is peculiarly interesting to see a portion of\\nmatter, of a tenuity exceeding the thinnest fog, pursuing\\nits path 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\\nas sure and steady a pace as the heaviest and largest\\nbodies in the system.\\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\\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 op-\\nposite effects of the extreme cold to which it would be\\n293. Does the extreme tenuity of this body prevent its mov-\\nng in obedience to the laws that regulate the motions of the\\nlargest bodies in the system\\n294. Is the physical nature of comets well understood I How\\nare the variations in the lengths of their tails accounted for I\\nHo w near did the comet of 1 680 approach to the sun What\\nbeat did it acquire Does this account for the direction of the\\ntan f How is that accounted for by some writers", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0246.jp2"}, "247": {"fulltext": "ORBITS AND MOTIONS OF COMETS. 233\\nsubject in the regions remote from the sun, would be ad-\\nequate 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,\\nas Delambre, suppose that the nebulous matter of the\\ncomet after being expanded to such a volume, that the\\nparticles 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\\neach other. They are Tike 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\\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 lay 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 ac-\\ntually approached near to the earth What would be the con-\\nsequences were a comet to strike the earth\\n20*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0247.jp2"}, "248": {"fulltext": "284 COMETS.\\nthat it will not be in the same plane, are almost infinite.\\nIt is also extremely improbable that a comet will 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 might\\nhave passed through a portion of the nebulous atmos-\\nphere of the comet. The earth was within a month of\\nreaching that point. This might at first view seem to\\ninvolve some nazard yet we must consider that a\\nmonth short, implied a distance of nearly 50,000,000\\nmiles. La Place has assigned the consequences that\\nwould ensue in case of a direct collision between the\\nearth and a comet but terrible as he has represented\\nthem on the supposition that the nucleus of the comet\\nis a solid body, yet considering a comet (as most of them\\ndoubtless are) as a mass of exceedingly light nebulous\\nmatter, it is not probable, even were the earth to make\\nits way directly through a comet, that a particle of the\\ncomet would reach the earth. The portions encountered\\nby the earth, would be arrested by the atmosphere, and\\nprobably inflamed and they would perhaps exhibit, on\\na more magnificent scale than was ever before observed,\\nthe phenomena of shooting stars, or meteoric showers.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0248.jp2"}, "249": {"fulltext": "PART III. OF THE FIXED STARS AND THE SYS-\\nTEM OF THE WORLD.\\nCHAPTER I.\\nOF THE FIXED STARS CONSTELLATIONS.\\n296. The Fixed Stars are so called, because, to\\ncommon observation, they always maintain the same\\nsituations 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. These magnitudes are not\\ndetermined by any very definite scale, but are merely\\nranked according to their relative degrees of brightness,\\nand this is left in a great measure to the decision of the\\neye alone. The brightest stars to the number of 15 or\\n20, are considered as stars of the first magnitude the 50\\nor 60 next brightest, of the second magnitude the next\\n200 of the third magnitude and thus the number of\\neach class increases rapidly as we descend the scale, so\\nthat no less than fifteen or twenty thousand are included\\nwithin the first seven magnitudes.\\n297. 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 wri-\\ntings under the same names as they bear at present.\\nThe names of the constellations are sometimes founded\\n296. Fixed Stars. Why so called How classed 1 Into\\nhow many magnitudes are they divided How many are there\\nof each magnitude 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0249.jp2"}, "250": {"fulltext": "236 FIXED STARS,\\non a supposed resemblance to the objects to which the\\nnames belong as the Swan and the Scorpion were evi-\\ndently so denominated from their likeness to those ani-\\nmals but in most cases it is impossible for us to find\\nany reason for designating a constellation by the figure\\nof the animal or the hero which is employed to repre-\\nsent it. These representations were probably once\\nblended with the fables of pagan mythology. The\\nsame figures, absurd as they appear, are still retained for\\nthe convenience of reference since it is easy to find\\nany particular star, by specifying the part of the figure\\nto which it belongs, as when we say a star is in the neck\\nof Taurus, in the knee of Hercules, or in the tail of the\\nGreat Bear. This method furnishes a general clue to\\nits position but the stars belonging to any constellation\\nare distinguished according to their apparent magnitudes\\nas follows first, by the Greek letters, Alpha, Beta,\\nGamma, c. Thus Alpha Orionis, denotes the largest\\nstar in Orion Beta Andromedce, the second star in An-\\ndromeda; and Gamma Leonis, the third brightest star\\nin the Lion. Where the number of the Greek letters is\\ninsufficient to include all the stars in a constellation,\\nrecourse is had to the letters of the Roman alphabet, a,\\nb, c, c. and, in cases where these are exhausted, the\\nfinal resort is to numbers. This is evidently necessary,\\nsince the largest constellations contain many hundrerds\\nor even thousands of stars. Catalogues of particular\\nstars have also been published by different astronomers,\\neach author numbering the individual stars embraced in\\nhis list, according to the places they respectively occupy\\nin the catalogue. These references to particular cata-\\nlogues are sometimes entered on large celestial globes.\\nThus we meet with a star marked 84 H., meaning that\\n297. Constellations. How long known 1 Which are men-\\ntioned in the most ancient writings 1 How far are the names\\nfounded on resemblance Why are the ancient figures still\\nretained How are the individual stars of a constellation dis-\\ntinguished What is said of catalogues of the stars 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0250.jp2"}, "251": {"fulltext": "FIXED STARS.\\n237\\nthis is its number in Herschel s catalogue or 140 M., de-\\nnoting the place the star occupies in the catalogue of\\nMayer.\\n298. The earliest catalogue of the stars was made by\\nHipparchus of the Alexandrian school, about 140 years\\nbefore the Christian era. A new star appearing m the\\nfirmament, he was induced to count the stars and to re-\\ncord their positions, in order that posterity might be able\\nto judge of the permanency of the constellations. His\\ncatalogue contains all that were conspicuous to the\\nnaked eye in the latitude of Alexandria, being 1022.\\nMost persons unacquainted with the actual number of\\nthe stars which compose the visible firmament, would\\nsuppose it to be much greater than this but it is found\\nthat the catalogue of Hipparchus, embraces nearly all\\nthat can now be seen in the same latitude, and that on\\nthe equator, when the spectator has the northern and\\nsouthern hemispheres both in view, the number of stars\\nthat can be counted does not exceed 3000. A careless\\nview of the firmament in a clear night, gives us the im-\\npression of an infinite multitude of stars but when we\\nbegin to count them, they appear much more sparsely\\ndistributed than we supposed, and large portions of the\\nsky appear almost destitute of stars.\\nBy the aid of the telescope, new fields of stars present\\nthemselves of boundless extent the number contin-\\nually augmenting as the powers of the telescope are in-\\ncreased. Lalande, in his Histoire Celeste, has registered\\nthe positions of no less than 50,000 and the whole\\nnumber visible in the largest telescopes amounts to many\\nmillions.\\n299. It is strongly recommended to the learner to ac-\\nquaint himself with the leading constellations at least,\\n298. Why did Hipparchus make a catalogue How many\\nstars did he number What is the greatest number that can\\nbe seen by the naked eye in both hemispheres 1 How many\\ncan be seen by the telescope 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0251.jp2"}, "252": {"fulltext": "238\\nFIXED STARS.\\nand with a few of the most remarkable individual stars.\\nThe task of learning them is comparatively easy, and\\nhardly any kind of knowledge, attained with so little\\nlabor, so amply rewards the possessor. It will generally\\nbe advisable, at the outset, to get some one already ac-\\nquainted with the stars, to point out a few of the most\\nconspicuous constellations, those of the Zodiac for ex-\\nample the learner may then resort to maps of the stars,\\nor what is much better, to a celestial globe and fill up\\nthe outline by tracing out the principal stars in each\\nconstellation as there laid down. By adding one new\\nconstellation to his list every night, and reviewing those\\nalready acquired, he will soon become familiar with the\\nstars, and will greatly augment his interest and improve\\nhis intelligence in celestial observations, and practical\\nastronomy.\\nCONSTELLATIONS.\\n300. We will point out particular marks by which the\\nleading constellations may be recognized, leaving it to\\nthe learner, after he has found a constellation, to trace\\nout additional members of it by the aid of the celestial\\nglobe, or by maps of the stars. Let us begin with the\\nConstellations of the Zodiac, which succeeding each\\nother as they do in a known order, are most easily\\nfound. J\\nAries (The Ram) is a small constellation, known by\\ntwo bright stars which form his head, Alpha and Beta\\nAmetis. These two stars are four degreesf apart, and\\ndirectly south of Beta at the distance of one degree, is\\n299. Specify the directions for learning the constellations.\\nJ,I OX tH f T^ f rectif in the S^he so as to represent the ap-\\npearance of the heavens on any particular evening, see page 34, Art.\\nnnl T w e r m T n T 0t intended t0 be stated with exactness, but\\nonly with such a degree of accuracy as may serve for a general guide.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0252.jp2"}, "253": {"fulltext": "CONSTELLATIONS.\\n239\\na smaller star, Gamma Arietis. It has been already\\nintimated (Art. 139) that the vernal equinox probably\\nwas near the head of Aries, when the signs of the Zo-\\ndiac received their present names.\\nTaurus (The Bull) will be readily found by the\\nseven stars or Pleiades, which lie in his neck. The\\nlargest star in Taurus is Aldebaran, in the Bull s eye, a\\nstar of the first magnitude, of a reddish color somewhat\\nresembling the planet Mars. Aldebaran and four other\\nstars in the face of Taurus, compose the Hyades.\\nGemini (The Twins) is known by two very bright\\nstars, Castor and Pollux, four degrees asunder. Castor\\n(the northern) is of the first, and Pollux of the second\\nmagnitude.\\nCancer (The Crab.) There are no large stars in this\\nconstellation, and it is regarded as less remarkable than\\nany other in the Zodiac. It contains however an inter-\\nesting group of small stars, called Prcesepe or the Neb-\\nula of Cancer, which resembles a comet, and is often\\nmistaken for one, by persons unacquainted with the\\nstars. With a telescope of very moderate powers this\\nnebula is converted into a beautiful assemblage of ex-\\nceedingly bright stars.\\nLeo (The Lion) is a very large constellation, and has\\nmany interesting members. Regulus {Alpha Leonis)\\nis a star of the first magnitude, which lies directly in the\\necliptic, and is much used in astronomical observations.\\n300. Constellations of the Zodiac. Aries. How known\\nHow far are the two brightest stars apart 1 Where was the\\nvernal equinox situated when the signs of the Zodiac received\\ntheir present names\\nTaurus. How found Name the largest star in Taurus.\\nWhat stars compose the Hyades\\nGemini. How known How far are Castor and Pollux\\nasunder 1 Of what magnitudes are they respectively\\nCancer. Are there any large stars in Cancer What is\\nsaid of Praesepe\\nL eo What is its size What is said of Regulus Where\\nis the sickle Where is Denebola situated 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0253.jp2"}, "254": {"fulltext": "^4C FIXED STARS.\\nNorth of Regulus lies a semi-circle of bright stars, form-\\ning a sickle of which Regulus is the handle. Denebola,\\na star of the second magnitude, is in the Lion s tail, 25\u00c2\u00b0\\nnorth east of Regulus.\\nVirgo (The Virgin) extends a considerable way\\nfrom west to east, but contains only a few bright stars.\\nSpica, however, is a star of the first magnitude, and\\nlies a little east of the place of the autumnal equinox.\\nTwenty-two degrees north of Spica, is Vindemiatrix, in\\nthe arm of Virgo, a star of the third magnitude.\\nLibra (The Balance) is distinguished by three large\\nstars, of which the two brightest constitute the beam\\nof the balance, and the smallest forms the top or handle.\\nScorpio (The Scorpion) is one of the finest of the\\nconstellations. His head is formed of five bright stars\\narranged in the arc of a circle, which is crossed in the\\ncenter by the ecliptic nearly at right angles, near the\\nbrightest of the five, Beta Scorpionis. Nine degrees\\nsoutheast of this, is a remarkable star of the first mag-\\nnitude, of a reddish color, called Cor Scorpionis, or An-\\ntares. South of this a succession of bright stars sweep\\nround towards the east, terminating in several small\\nstars, forming the tail of the Scorpion.\\nSagittarius (The Archer.) Northeast of the tail of\\nthe Scorpion, are three stars in the arc of a circle which\\nconstitute the bow of the Archer, the central star being\\nthe brightest, directly west of which is a bright star\\nwhich forms the arrow.\\nCapricornus (The Goat) lies northeast of Sagittarius,\\nand is known by two bright stars, three degrees apart,\\nwhich form the head.\\nVirgo. Extent from east to west What is said of Spica,\\nand of Vindemiatrix 1\\nLibra. How distinguished\\nScorpio. His appearance His head how formed Where\\nis Antares situated\\nSagittarius. Describe his bow.\\nCapricornus. Where situated from Sagittarius How\\nknown", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0254.jp2"}, "255": {"fulltext": "CONSTELLATIONS. 241\\nAquarius (The Water Bearer) is recognized by\\ntwo stars in a line with Alpha Capricorni, forming the\\nshoulders of the figure. These two stars are 10\u00c2\u00b0 apart,\\nand 4\u00c2\u00b0 southeast is a third star, which, together with the\\nother two, makes an acute triangle, of which the west-\\nernmost is the vertex.\\nPisces (The Fishes) lie between Aquarius and Aries.\\nThey are not distinguished by any large stars, but are\\nconnected by a series of small stars, that form a crooked\\nline between them. Piscis Australis, the Southern\\nFish, lies directly below Aquarius, and is known by a\\nsingle bright star far in the south, having a declination\\nof 30\u00c2\u00b0. The name of this star is Fomalhaut, and it is\\nmuch used in astronomical measurements.\\n301. The Constellations of the Zodiac, being first\\nwell learned, so as to be easily recognized, will facil-\\nitate the learning of others that lie north and south of\\nthem. Let us therefore next review the principal North-\\nern Constellations, beginning north of Aries and pro-\\nceeding from west to east.\\nAndromeda, is characterized by three stars of the sec-\\nond magnitude, situated in a straight line, extending\\nfrom west to east. The middle star is about 17\u00c2\u00b0 north\\nof Beta Arietis. It is in the girdle of Andromeda, and\\nis named Mirach. The other two lie at about equal\\ndistances, 14\u00c2\u00b0 west and east of Mirach. The western\\nstar, in the head of Andromeda, lies in the Equinoctial\\nColure. The eastern star, Alamak, is situated in the\\nfoot.\\nPerseus lies directly north of the Pleiades, and con-\\ntains several bright stars. About 18\u00c2\u00b0 from the Pleiades\\nAquarius. How recognized 1 How far apart are the shoul-\\nders of Aquarius 1\\nPisces. Where situated How connected Where is\\nPiscis Australis situated By what name is it commonly\\nknown\\n301 Northern Constellations. Andromeda, how character-\\nized Where are Mirach and Alamak situated 1\\n21", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0255.jp2"}, "256": {"fulltext": "242 FIXED STARS.\\nis Algol, a star of the second magnitude in the Head of\\nMedusa, which forms a part of the figure and 9\u00c2\u00b0 north-\\neast of Algol is Algenib, of the same magnitude in the\\nback of Perseus. Between Algenib and the Pleiades are\\nthree bright stars, at nearly equal intervals, which com-\\npose the right leg of Perseus.\\nAuriga (the Wagoner) lies directly east of Perseus,\\nand extends nearly parallel to that constellation from\\nnorth to south. Capella a very white and beautiful\\nstar of the first magnitude, distinguishes this constella-\\ntion. The feet of Auriga are near the Bull s Horns.\\nThe Lynx comes next, but presents nothing particu-\\nlarly interesting, containing no stars above the fourth\\nmagnitude.\\nLeo Minor consists of a collection of small stars\\nnorth of the sickle in Leo, and south of the Great Bear.\\nIts largest star is only of the third magnitude.\\nComa Berenices is a cluster of small stars, north of\\nDenebola, (a star in the tail of the Lion,) and of the head of\\nVirgo. About 12\u00c2\u00b0 north of Berenice s Hair, is a single\\nbright star called Cor Caroli, or Charles s Heart.\\nBootes, which comes next, is easily found by means\\nof Arcturus, a star of the first magnitude, of a reddish\\ncolor, which is situated near the knee of the figure.\\nArcturus is accompanied by three small stars forming a\\ntriangle a little to the southwest. Two bright stars\\nGamma and Delta Bootis, form the shoulders, and\\nBeta of the third magnitude is in the head of the\\nfigure.\\nCorona Borealis, (The Crown,) which is situated east\\nPerseus. How situated with respect to the Pleiades\\nWhere is Algol Where is Algenib What stars compose\\nthe right leg of Perseus\\nAuriga. How situated from Perseus What large star dis-\\ntinguishes this constellation Where are the feet of Auriga\\nLynx. Size of its stars 1\\nLeo Minor. Where situated Size of its largest star\\nComa Berenices. Describe it. Where is Cor Caroli 1\\nBootes. What large star is in this constellation", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0256.jp2"}, "257": {"fulltext": "CONSTELLATIONS. 243\\nof Bootes, is very easily recognized, composed as it is of\\na semi-circle of bright stars. In the center of the bright\\ncrown, is a star of the second magnitude, called Gem-\\nma the remaining stars are all much smaller.\\nHercules, lying between the Crown on the west and\\nthe Lyre on the east, is very thick set with stars, most\\nof which are quite small. The Constellation covers a\\ngreat extent of the sky, especially from N. to S., the\\nhead terminating within 15\u00c2\u00b0 of the equator, and marked\\nby a star of the third magnitude, called Ras Algethi,\\nwhich is the largest in the Constellation.\\nOphiucus is situated directly south of Hercules, ex-\\ntending some distance on both sides of the equator, the\\nfeet resting on the Scorpion. The head terminates near\\nthe head of Hercules, and like that, is marked by a\\nbright star within 5\u00c2\u00b0 of Alpha Herculis. Ophiucus is\\nrepresented as holding in his hands the Serpent, the\\nhead of which, consisting of three bright stars, is sit-\\nuated a little south of the Crown. The folds of the\\nserpent will be easily followed by a succession of bright\\nstars which extend a great way to the east.\\nAquila (The Eagle) is conspicuous for three bright\\nstars in its neck, of which the central one, Altair, is a\\nvery brilliant white star of the first magnitude. Anti-\\nnous lies directly south of the Eagle, and north of the\\nhead of Capricornus.\\nDelphinus (The Dolphin) is a small but beautiful\\nConstellation, a few degrees east of the Eagle, and is\\ncharacterized by four bright stars near to one another,\\nforming a small rhombic square. Another star of the\\nsame magnitude 5\u00c2\u00b0 south, makes the tail.\\nCorona Borealis. Describe it. Where is Gemma situated\\nHercules. Between what two constellations is it What\\nis said of its extent 1 Where is Ras Algethi\\nOphiucus. Where is it from Hercules 1 How is it repre-\\nsented 1\\nAquila. How distinguished Where is Altair 1 Where is\\nA.ntinous 1\\nThe Dolphin Describe it.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0257.jp2"}, "258": {"fulltext": "244 FIXED STARS.\\nPegasus lies between Aquarius on the southwest arid\\nAndromeda on the northeast. It contains but few large\\nstars. A very regular square of bright stars is composed\\nof Alpha Andromedce, and the three largest stars in Pe-\\ngasus, namely, Scheat, Markab, and Algenib. The\\nsides composing this square are each about 15\u00c2\u00b0. Alge-\\nnib is situated in the Equinoctial Colure.\\n302. We may now review the Constellations which\\nsurround the North Pole, within the circle of perpetual\\napparition. (Art. 38.)\\nUrsa Minor (The Little Bear) lies nearest the\\npole. The Pole-star, Polaris, is in the extremity of the\\ntail, and is of the third magnitude. Three stars in a\\nstraight line 4\u00c2\u00b0 or 5\u00c2\u00b0 apart, commencing with the Pole-\\nstar, lead to a trapezium of four stars, and the whole\\nseven form together a dipper, the trapezium being the\\nbody, and the three stars the handle.\\nUrsa Major (The Great Bear) is situated between\\nthe pole and the Lesser Lion, and is usually recognized\\nby the figure of a larger and more perfect dipper, which\\nconstitutes the hinder part of the animal. This has also\\nseven stars, four in the body of the dipper, and three in\\nthe handle. All these are stars of much celebrity The\\ntwo in the western side of the dipper, Alpha and Beta, are\\ncalled Pointers, on account of their always being in a\\nright line with the Pole-star, and therefore affording an\\neasy mode of finding that. The first star in the tail, next\\nthe body, is named Alioth, and the second Mizar. The\\nhead of the Great Bear lies far to the westward of the\\nPegasus. Between what two constellations is it situated?\\nHow may a square be formed of certain stars in this constel-\\nlation\\n302. Northern Constellations. Ursa Minor.\u00e2\u0080\u0094 How situated\\nwith respect to the pole Show how the dipper in this con-\\nstellation is formed\\nUrsa Major. Where situated How recognized What\\nare the Pointers Where is Alioth Mizar Of what is the\\nhead composed", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0258.jp2"}, "259": {"fulltext": "CONSTELLATIONS. 24f\\nPointers, and is composed of numerous small stars and\\nthe feet are severally composed of two small stars very\\nnear to each other. rv OQ t\\nDraco (The Dragon) winds round between the l*reat\\nand the Little Bear and commencing with the tail, be-\\ntween the Pointers and the Pole-star, it is easily traced\\nbv a succession of bright stars extending from west to\\neast, passing under Ursa Minor it returns westward, and\\nterimnates in a triangle which forms the head of Draco,\\nnear the feet of Hercules, northwest of Lyra.\\nCepheus lies eastward of the breast of the Dragon,\\nbut has no stars above the third magnitude.\\nCassiopeia is known by the figure of a chair, com-\\nposed of four stars which form the legs, and two which\\nform the back. This constellation lies between Perseus\\nand Cepheus, in the Milky Way.\\nCygnus (The Swan) is situated also in the Milky Way,\\nsome distance southwest of Cassiopeia, towards the Ea,\\nele Three bright stars, which he along the Milky\\nWav form the body and neck of the Swan, and two\\nothers in a line with the middle one of the three, one\\nabove and one below, constitute the wings. 1 his Con-\\nstellation is among the few, that exhibit some resem-\\nblance to the animals whose names they bear.\\nLyra (The Lyre) is directly west of the Swan, and\\nis easily distinguished by a beautiful white star of the\\nfirst magnitude, Alpha Lyras.\\n303. The Southern Constellations are comparatively\\nfew in number. We shall notice only the Whale, Orion,\\nthe Greater and Lesser Dog, Hydra, and the Crow.\\nDraco.\u00e2\u0080\u0094 liow situated with respect to the two Bears\\nTrace its course\\nCepheus.\u00e2\u0080\u0094 How situated from Draco 1\\nCassiopeia.-Kow known? Where situated?\\nCygnus.\u00e2\u0080\u0094 How situated 1 Of what stars formed Has this\\nconstellation any resemblance to a Swan\\n303. Southern Constellations. Cetus.\u00e2\u0080\u0094Ite extent Size\\nof its stars What is said of Menkar, and of Mira I\\n21*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0259.jp2"}, "260": {"fulltext": "246 FIXED STARS.\\nCetus (The Whale) is distinguished rather for its\\nextent than its brilliancy, reaching as it does through\\n40\u00c2\u00b0 of longitude, while none of its stars except one,\\nare above the third magnitude. Menkar {Alpha Ceti)\\nin the mouth, is a star of the second magnitude, and\\nseveral other bright stars directly south of Aries, make\\nthe head and neck of the Whale. Mira (Omicron\\nCeti) in the neck of the Whale is a variable star.\\nOrion is one of the largest and most beautiful of the\\nconstellations, lying southeast of Taurus. A cluster of\\nsmall stars form the head two large stars, Betalgeus of\\nthe first and Bellatrix of the second magnitude, make\\nthe shoulders three more bright stars compose the\\nbuckler, and three the sword and Rigel, another star of\\nthe first magnitude, makes one of the feet. In this\\nConstellation there are 70 stars plainly visible to the\\nnaked eye, including two of the first magnitude, four of\\nthe second, and three of the third.\\nCanis Major lies S. E. of Orion, and is distinguished\\nchiefly by its containing the largest of the fixed stars,\\nmnus.\\nCanis Minor a little north of the equator, between\\nCanis Major and Gemini, is a small Constellation, con-\\nsisting chiefly of two stars, of which Procyon is of the\\nfirst magnitude.\\nHydra has its head near Procyon, consisting of a\\nnumber of stars of ordinary brightness. About 17\u00c2\u00b0 S.\\nE. of the head, is a star of the second magnitude, form-\\ning the heart, {Cor Hy dree and eastward of this, is\\na long succession of stars of the fourth and fifth magni-\\ntudes composing the body and the tail, and reaching a\\nfew degrees south of Spica Virgmis.\\nOrion. What is said of its size and beauty Describe its\\ndifferent parts. How many stars does it contain which are\\nvisible to the naked eye\\nCanis Major. Where situated from Orion What large\\nstar is in it\\nCams Minor.\u00e2\u0080\u0094 -Where situated What large star does it\\ncontain\\nHi/dra.\u00e2\u0080\u0094TvsiQe its course.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0260.jp2"}, "261": {"fulltext": "247\\nCLUSTERS OF STARS.\\nCorvus (The Crow) is represented as standing on the\\ntail of Hydra. It consists of small stars, onlv three of\\nwhich are as large as the third magnitude.\\n304 The foregoing brief sketch is designed merely\\nto aid the student in finding the principal constellations\\nand the largest fixed stars. When we have once learned\\nto recognize a constellation by some characteristic marks,\\nwe maf afterwards fill up the outline by the aid of a\\ncelestial globe or a map of the stars. It will be of little\\navau however, merely to commit this sketch to memory\\nbut t will be very useful for the student at once to ren-\\nder himself familiar with it, from the actual specimens\\nwhich every clear evening presents to his view.\\nCHAPTER II.\\nOF CLUSTERS OP STARS\u00e2\u0080\u0094 NEBULA\u00e2\u0080\u0094 VARIABLE STARS-\\nTFMPORARY STARS DOUBLE STARS.\\n305 In various parts of the firmament are seen large\\ngroup or clusters, which, either by the naked eye or by\\nthe aid of the smallest telescope, are perceived to con-\\nsist of a -real number of small stars. Such are the\\nP eiades, 6oma Berenices, and Pr-sepe or the Bee-nrve\\nin Cancer. The Pleiades, or Seven stars, as they are\\ncalled in the neck of Taurus, is the most conspicuous\\ncluster When we look directly at this group, we can.\\nnot distinguish more than six stars, but by turning the\\neye tideways* upon it, we discover that there are many\\nCorvus.\u00e2\u0080\u0094 How represented pipiades\\n305. Cl\u00c2\u00bbsters.-~!l*me a few of the lar ges Pleiades\\nwhere situated 1 How many stars does it con am What\\nis said of Coma Berenices, a nd of the Bee-hive I\\n^^te^L^rfA^tS heavens at scne dista.ee. and\\nturn the other eye obliquely upon the object.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0261.jp2"}, "262": {"fulltext": "248 FIXED STARS.\\nmore. Telescopes show 50 or 60 stars crowded to-\\ngether and apparently insulated from the other parts of\\nthe heavens. Coma Berenices has fewer stars, but they\\nare of a larger class than those which compose the Plei-\\nades. The Bee-hive or Nebula of Cancer as it is called,\\nis one of the finest objects of this kind for a small tel-\\nescope, being by its aid converted into a rich congeries\\nof shining points. The head of Orion affords an exam-\\nple of another cluster, though less remarkable than the\\nothers.\\n306. Nebula are those faint misty appearances which\\nresemble comets, or a small speck of fog. The Galaxy\\nor Milky Way, presents a continued succession of large\\nnebulae. A very remarkable Nebula, visible to the naked\\neye, is seen in the girdle of Andromeda. No powers of\\nthe telescope have been able to resolve this into separate\\nstars. Its dimensions are astonishingly great. In diam-\\neter it is about 15 The telescope reveals to us innumer-\\nable objects of this kind. Sir William Herschel has given\\ncatalogues of 2000 Nebulae, and has shown that the neb-\\nulous matter is distributed through the immensity of\\nspace in quantities inconveivably great, and in separate\\nparcels of all shapes and sizes, and of all degrees of\\nbrightness between a mere milky appearance and the\\ncondensed light of a fixed star. Finding that the gra-\\ndations between the two extremes were tolerably regu-\\nlar, he thought it probable that the nebulae form the ma-\\nterials out of which nature elaborates suns and systems\\nand he conceived that, in virtue of a central gravitation,\\neach parcel of nebulous matter becomes more and more\\ncondensed, and assumes a rounded form. He inferred\\nfrom the eccentricity of its shape, and the effects of the\\nmutual gravitation of its particles, that it acquires gradu-\\n306. Nebula. What are they What is said of the nebula\\nin the girdle of Andromeda 1 How many nebulae has Sir W.\\nHerschel included in his catalogue What are his ideas re\\nspecting nebulae", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0262.jp2"}, "263": {"fulltext": "NEUUL.E. 249\\nally a rotary motion that the condensation gues on m\\ncreasing until the mass acquires consistency and solidity\\nand all the characters of a comet or a planet that by a\\nstill further process of condensation, the body becomes a\\nreal star, self-shining and that thus the waste of the ce-\\nlestial bodies, by the perpetual diffusion of their light, is\\ncontinually compensated and restored by new formations\\nof such bodies, to replenish forever the universe with\\nplanets and stars.\\n307. These opinions are recited here rather out of re-\\nspect to their notoriety and celebrity, than because we\\nsuppose them to be founded on any better evidence than\\nconjecture. The Philosophical Transactions for many\\nyears, both before and after the commencement of the\\npresent century, abound with both the observations and\\nspeculations of Sir William Herschel. The former are\\ndeserving of all praise the latter of much less confi-\\ndence. Changes, however, are going on m some of the\\nnebulae, which plainly show that they are not, t e plan-\\nets and stars, fixed and permanent creations. 1 nus the\\ncrreat nebula in the girdle of Andromeda, has very much\\naltered its structure since it first became an object of tele-\\nscopic observation. Many of the nebulae are of a globu-\\nlar form, (Fig. 50,) but frequently they present the ap-\\npearance of a rapid increase of numbers towards the cen-\\n(Fiff. 50.) (Fig. 51.)\\nter, (Fig. 51,) the anterior boundary being irregular,\\nand the central parts more nearly spherical.\\n307. What is said of Herschel s speculations and of his ob-\\nservations What changes occur in the nebulae? What\\nforms have they", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0263.jp2"}, "264": {"fulltext": "250 FIXED STARS.\\n308. The nebula in the sword of Orion is particularly\\ncelebrated, being very large and of a peculiarly interest-\\ning appearance. According to Sir John Herschel, its\\nnebulous character is very different from what might be\\nsupposed to arise from the assemblage of an immense\\ncollection of small stars. It is formed of little flocculent\\nmasses like wisps of clouds and such wisps seem to\\nadhere to many small stars at its outskirts, and especially\\nto one considerable star which it envelops with a neb-\\nulous atmosphere of considerable extent and singular\\nfigure.\\nDescriptions, however, can convey but a very imper-\\nfect idea of this wonderful class of astronomical objects,\\nand we would therefore urge the learner studiously to\\navail himself of the first opportunity he may have to\\nview them through a large telescope, especially the Neb-\\nula of Andromeda and of Orion.\\n309. Nebulous Stars are such as exhibit a sharp and\\nbrilliant star surrounded by a disk or atmosphere of neb-\\nulous matter. These atmospheres in some cases present\\na circular, in others an oval figure and in some in-\\nstances, the nebula consists of a long, narrow spindle-\\nshaped ray, tapering away at both ends to points.\\nPlanetary Nebulce constitute another variety, and are\\nvery 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\\nGamma Aquarii, and about 5m. preceding that star. Its\\napparent diameter is about 20 Another in the Con-\\nstellation Andromeda, presents a visible disk of 12 per-\\nfectly defined and round. Granting these objects to be\\n308. What is said of the nebula in the sword of Orion\\nCan the nebulae be fully learned from description\\n309. Nebulous stars what are they? What forms have\\ntheir atmospheres Planetary nebulae, their appearance\\nWhat apparent diameters have thev What is said of their\\nlight", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0264.jp2"}, "265": {"fulltext": "VARIABLE STARS.\\n\u00c2\u00ab,\u00e2\u0084\u00a2\u00c2\u00abv distant from us with the stars, their real dimen-\\nX mS te such as, on the lowest conjputauon, wo u d\\nfill the orbit of Uranus. It is no less evident that, it they\\nbe sohd bodies, of a solar nature, the intrinsic splendor\\no fi surfaces must be almost infinitely mfenor to\\nthat of the sun. A circu lar portion of the sun j*\u00c2\u00a3\\n\u00c2\u00abnhtendin\u00c2\u00b0- an angle of 20 wouia give i n u m\\n100 full moons while the objects in quest.on are hardly,\\nif at all, discernible with the naked eye.\\n310 The Galaxy or Milky Way is itself supposed\\nbv some to be a nebula of which the sun forms a com-\\nnonenTpart and hence it appears so much greater than\\nher neCi only in consequence of J\\nrespect to it, and its greater P\u00e2\u0084\u00a2*^*\\nSo crowded are the stars in some parts of this zone, max\\n1\u00c2\u00b0 W Uiam Herschel, by counting the J*\u00c2\u00ab g\\ntlu n f his telescope, estimated that 50,000 had passed\\nunder his review Tn a zone two degrees in breadth du-\\nrhit a s\u00c2\u00bbi tie hour s observation. Notwithstanding the\\nynlarent Sontio uity of the stars which crowd the galaxy,\\nkTs certain Aat their mutual distances must be incon-\\nceivably great.\\n311 Variable Stars are those which undergo a pe-\\nriod Lai change of brightness. One of the most remark-\\nable is the star Miral the Whale, Jg^Jh ight\\nannears once in 11 months, remains at its gieatest Drigm\\nn P eL about a fortnight, being then, on some occasion*\\nS^ATSS -dSnui: i= h sing W Lng\\nthe remaining three months of its period.\\nAnoTher very remarkable variable star is Algol (Beta\\nPetsei.) Itls uLally visible as a star of the second magm-\\n310. Galaxy or Milky Way-what is said respecting it\\nGive an example of the multitude of stars in it", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0265.jp2"}, "266": {"fulltext": "252 FIXED STARS.\\ntude, and continues such for 2d. 14h. when it suddenly\\nbegins to diminish in splendor, and in about 3| hours is\\nreduced to the fourth magnitude. It then begins again\\nto increase, and in gi hours more, is restored to its usual\\nbrightness, going through all its changes in less than\\nthree days. This remarkable law of variation appears\\nstrongly to suggest the revolution round it of some opake\\nbody, which, when interposed between us and Algol,\\ncuts off a large portion of its light. It is (says Sir J.\\nHerschel) an indication of a high degree of activity in\\nregions where, but for such evidences, we might con-\\nclude all lifeless. Our sun requires almost nine times\\nthis period to perform a revolution on its axis. On the\\nother hand, the periodic time of an opake revolving\\nbody, sufficiently large, which would produce a similar\\ntemporary obscuration of the sun, seen from a fixed star,\\nwould be less than fourteen hours.\\nThe duration of these periods is extremely various.\\nWhile that of Beta Persei above mentioned, is less than\\nthree days, others are more than a year, and others many\\nyears.\\n312. Temporary Stars are new stars which have ap-\\npeared suddenly in the firmament, and after a certain in-\\nterval, 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 Hipparchus\\nto draw up 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 periods,\\nat distant intervals, similar phenomena have presented\\nthemselves. Thus the appearance of a star in 1572,\\nwas so sudden, that Tycho Brahe returning home one\\n311. Variable stars what are they What is said of Mira t\\nAlso of Algol How are their periods of revolution\\n312. Temporary stars what are they? Give examples.\\nDo they ever return Do stars ever disappear", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0266.jp2"}, "267": {"fulltext": "DOUBLE STARS.\\n203\\nday was surprized to find a collection of country people\\ngazing at a star which he was sure did not exist half an\\nhour before. It was then as bright as Sirius, and con-\\ntinued to increase until it surpassed Jupiter when bright-\\nest, and was visible at mid-day. In a month it began\\nto diminish, and in three months afterwards it had en-\\ntirely disappeared.\\nIt has been supposed by some that in a few instances,\\nthe same star has returned, constituting one of the peri-\\nodical or variable stars of a long period.\\nMoreover, on a careful re-examination of the heavens,\\nand a comparison of catalogues, many stars are now\\nfound to be missing.\\n313. 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 the\\ntelescope so close together as to be recognized as objects\\nof this class. Sometimes three or more stars are found\\nin this near connexion, constituting triple or multiple\\nstars. Castor, for example, when seen by the naked\\neye, appears as a single star, but in a telescope even of\\nmoderate powers, it is resolved into two stars of between\\nthe third and fourth magnitudes, within 5 7/ of each other.\\nThese two stars are nearly of equal size, but frequently\\none is exceedingly small in comparison with the other,\\nresembling a satellite near its primary, although in dis-\\ntance, in light, and in other characteristics, each has all\\nthe attributes of a star, and the combination therefore\\ncannot be that of a planet with a satellite. In some in-\\nstances, also, the distance between these objects is much\\nless than 5 and in many cases it is less than V. The\\nextreme closeness, together with the exceeding minute-\\nness of most of the double stars, requires the best tele-\\n313. Double stars what are they? What are multiple\\nstars Give an example of a double star How do the two\\nstars sometimes differ What is required in order to observe\\nmost of the double stars 1\\n22", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0267.jp2"}, "268": {"fulltext": "254\\nFIXED STARS.\\nscopes united with the most acute powers of observa-\\ntion. Indeed, certain of these objects are regarded as\\nthe severest tests, both of the excellence of the instru-\\nment and of the skill of the observer. The following\\ndiagram represents four double stars, as seen with ap-\\npropriate magnifiers. No. 1. exhibits Epsilon Bootis with\\na power of 350 No. 2, Rigel with a power of 130\\nNo. 3, the Pole-star with a power of 100 and No. 4,\\nCastor with a power of 300.\\nFig. 52.\\n314. Our knowledge of the double stars almost com-\\nmenced with Sir William Herschel, about the year 1780.\\nAt the time he began his search for them, he was ac-\\nquainted with only four. Within five years, he discov-\\nered nearly 700 double stars.* In his memoirs, pub-\\nlished in the Philosophical Transactions, he gave most\\naccurate measurements of the distances between the two\\nstars, and of the angle which a line joining the two,\\nformed with the parallel of declination. These data\\nwould enable him, or at least posterity, to judge whether\\nthese minute bodies ever change their position with re-\\nspect to each other.\\n314. Who began the discovery of double stars When did\\nhe publish his account of them By whom have these re-\\nsearches been since prosecuted What two circumstances add\\na high degree of interest to the phenomena of the double stars\\nDuring his life he observed in all, 2400 double stars.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0268.jp2"}, "269": {"fulltext": "MOTIONS OF THE FIXED STARS.\\n255\\nSince 1821, these researches have been prosecuted\\nwith great zeal and industry by Sir James South and\\nSir John Herschel in England, and by Professor Struve\\nat Dorpat in Russia and the whole number of double\\nstars now known, amounts to several thousands. Two\\ncircumstances add a high degree of interest to the phe-\\nnomena of the double stars\u00e2\u0080\u0094 the first is, that a few of\\nthem at least are found to have a revolution around\\neach other, and the second, that they are supposed to\\nafford the means of obtaining the parallax of the fixed\\nstars. Of these topics we shall treat in the next chapter.\\nCHAPTER 111.\\nOF THE MOTIONS OF THE FIXED STARS DISTANCES\\nNATURE.\\n315. In 1803, Sir William Herschel first determined\\nand announced to the world, that there exist among the\\nstars, separate systems, composed of two stars revolving\\nabout each other in regular orbits. These he denomin-\\nated Binary Stars, to distinguish them from other\\ndouble stars where no such motion is detected, and\\nwhose proximity to each other may possibly arise from\\ncasual juxta-position, or from one being in the range of\\nthe other. Between fifty and sixty instances of changes\\nto a greater or less amount of the relative position of\\ndouble stars, are mentioned by Sir William Herschel\\nand a few of them had changed their places so much\\nwithin 25 years, and in such order, as to lead him to the\\nconclusion that they performed revolutions, one around\\nthe other, in regular orbits.\\n315. Binary Stars.\u00e2\u0080\u0094 Who first discovered this class of\\nbodies How are they distinguished from ordinary double\\nstars 1 What conclusions did Sir W. Herschel draw respect-\\ning them", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0269.jp2"}, "270": {"fulltext": "256\\nFIXED STARS.\\n316. These conclusions have been fully confirmed by\\nlater observers, so that it is now considered as fully es-\\ntablished, that there exist among the fixed stars, binary\\nsystems, in which two stars perform to each other the\\noffice of sun and planet, and that the periods of revolu-\\ntion of more than one such pair have been ascertained\\nwith something approaching to exactness. Immersions\\nand emersions of stars behind each other have been ob-\\nserved, and real motions among them detected rapid\\nenough to become sensible and measurable in very short\\nintervals of time. The following table exhibits the\\npresent state of our knowledge on this subject.*\\nNames.\\nPeriod in years.\\nMajor axis of the orbit.\\nEccentricity.\\n/Coronas,\\n^Cancri,\\nsUrsae Majoris,\\n70 Ophiuchi\\nCastor,\\n^Coronas,\\n61 Cygni,\\nyVirginis,\\n/Leonis,\\n43.40\\n55.00\\n58.26\\n80.34\\n252.66\\n286.00\\n452.00\\n628.90\\n1200.00\\n7 .714\\n8.784\\n16.172\\n7.358\\n30.860\\n24.000\\n0.4164\\n0.4667\\n0.7582\\n0.6112\\n0.8335\\nFrom this table it appears, first, that the periods of the\\ndouble stars are very various, ranging, in the case of\\nthose already ascertained, from forty-three years to one\\n316. Have the conclusions of Herschel been confirmed Dy\\nothers What doctrine is now considered as fully established\\nHow are the periods of the double stars What is the figure of\\ntheir orbits Which is the most remarkable of the Binary\\nstars What is its size How long since it was first observed\\nto be double 1 What changes has it undergone since When\\ndid it pass its perihelion\\nThose who do not understand the Greek letters, can pass over thii\\ntable to the inferences which follow.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0270.jp2"}, "271": {"fulltext": "MOTIONS OF THE FIXED STARS. 257\\nthousand secondly, that their orbits are very small\\nellipses, more eccentric than those of the planets, the\\ngreatest of which (that of Mercury) having an eccentri-\\ncity of only about .2 of the major axis.\\nThe most remarkable of the binary stars is Gamma\\nVirginis, on account not only of the length of its period,\\nbut also of the great diminution of apparent distance,\\nand rapid increase of angular motion about each other\\nof the individuals composing it. It is a bright star of\\nthe fourth magnitude, and its component stars are almost\\nexactly equal. It has been known to consist of two\\nstars since the beginning of the eighteenth century, their\\ndistance being then between six and seven seconds so\\nthat any tolerably good telescope would resolve it.\\nSince that time they have been constantly approaching,\\nand are at present hardly more than a single second asun-\\nder so that no telescope that is not of a very superior\\nquality, is competent to show them otherwise than as a\\nsingle star, somewhat lengthened in one direction. It\\nfortunately happens that Bradley (Astronomer Royal) in\\n1718, noticed, and recorded in the margin of one of his\\nobservation books, the apparent direction of their line of\\njunction, as being parallel to that of two remarkable\\nstars Alpha and Delta of the same constellation, as seen\\nby the naked eye, a remark which has been of signal\\nservice in the investigation of their orbit. It is found\\nthat it passed its perihelion, August 18th, 1834.\\n317. The revolutions of the binary stars have assured\\nus of that 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 this\\nlaw transcended the bounds of the solar system. In-\\n17. What great fact have the revolutions of the binary stars\\nrevealed to us How was this doctrine limited before this\\ndiscovery Are these revolutions those of a planetary or\\ncometary nature\\n22*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0271.jp2"}, "272": {"fulltext": "258 FIXED STARS.\\ndeed, our belief of the fact rested more upon our idea of\\nunity of design in all the works of the Creator, than\\nupon any certain proof; but the revolution of one star\\naround another in obedience to forces which must be\\nsimilar to those that govern the solar system, establishes\\nthe grand conclusion, that the law of gravitation is truly\\nthe 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 be\\nadmitted to carry with it a proof of the prevalence of the\\nNewtonian law of gravity in their systems, of the very\\nsame nature and cogency as that of the calculated and\\nobserved places of comets round the center of our own\\nsystem.\\nBut (he adds) it is not with the revolution of bodies\\nof a planetary or cometary nature round a solar center\\nthat we are now concerned it is with that of sun\\naround sun, each, perhaps, accompanied with its train of\\nplanets and their satellites, closely shrouded from our\\nview by the splendor of their respective suns, and crowd-\\ned into a space, bearing hardly a greater proportion to\\nthe enormous interval which separates them, than the\\ndistances of the satellites of our planets from their pri-\\nmaries, bear to their distances from the sun itself.\\n318. Some of the fixed stars appear to have a real mo-\\ntion in space.\\nThere are several apparent changes of place among\\nthe stars which arise from real changes in the earth,\\nwhich, as we are not conscious of them, we refer to the\\nstars but there are other motions among the stars which\\n318. Have any of the fixed stars a real motion in space\\nAre the places of the stars as described in^ ancient times by\\nPtolemy nearly the same as at present To what conclu-\\nsions on this subject are we now forced", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0272.jp2"}, "273": {"fulltext": "MOTIONS OP THE FIXED STARS. 259\\ncannot result from any changes in the earth, but must\\narise from changes in the stars themselves. Such mo-\\ntions are called the proper motions of the stars. Nearly\\n2000 years ago, Hipparchus and Ptolemy made the most\\naccurate determinations in their power of the relative\\nsituations of the stars, and their observations have been\\ntransmitted to us in Ptolemy s Almagest from which it\\nappears that the stars retain at least very nearly the same\\nplaces now as they did at that period. Still the more\\naccurate methods of modern Astronomers, have brought\\nto light minute changes in the places of certain stars,\\nwhich force upon us the conclusion, either that our solar\\nsystem causes an apparent displacement of certain stars,\\nby a motion of its own in space, or that they have them-\\nselves a proper motion. Possibly, indeed, both these\\ncauses may operate.\\n319. If the sun, and of course the earth which accom-\\npanies him, is actually in motion, the fact may become\\nmanifest from the apparent approach of the stars in the\\nregion which he is leaving, and the recession of those\\nwhich lie in the part of the heavens towards which he\\nis travelling. Were two groves of trees situated on a\\nplain at some distance apart, and we should go from one\\nto the other, the trees before us would gradually appear\\nfarther and farther asunder, while those we left behind\\nwould appear to approach each other. Some years since,\\nSir William Herschel supposed he had detected changes\\nof this kind among two sets of stars in opposite points\\nof the heavens, and announced that the solar system\\nwas in motion towards a point in the constellation Her-\\ncules but other astronomers have not found the changes\\nin question such as would correspond to this motion, or\\n319. If the solar system is really in motion, how may the\\nfact become manifest 1 Towards what constellation did Sir\\nWilliam Herschel suppose it movmg 1 Has the opinion been\\nconfirmed by later observers", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0273.jp2"}, "274": {"fulltext": "260 FIXED STARS.\\nto any motion of the sun and while it is a matter of\\ngeneral belief that the sun has a motion in space, the\\nfact is not considered as yet entirely proved.\\n320. In most cases where a proper motion in certain\\nstars has been suspected, its annual amount has been so\\nsmall, that many years are required to assure us, that the\\neffect is not owing to some other cause than a real pro-\\ngressive motion in the stars themselves but in a few\\ninstances the fact is too obvious to admit of any doubt.\\nThus the two stars 61 Cygni, which are nearly equal,\\nhave remained constantly at the same, or nearly at the\\nsame distance of 1 5 for at least fifty years past. Mean-\\nwhile they have shifted their local situation in the\\nheavens, 4 23 the annual proper motion of each star\\nbeing 5 .3, by which quantity this system is every year\\ncarried along in some unknown path, by a motion which\\nfor many centuries must be regarded as uniform and rec-\\ntillinear. A greater proportion of the double stars than\\nof any other indicate proper motions, especially the bi-\\nnary stars or those which have a revolution around each\\nother. Among stars not double, and no way differing\\nfrom the rest in any other obvious particular, Mu Cassi-\\nopeia has the greatest proper motion of any yet ascer-\\ntained, amounting to nearly 4 annually.\\nDISTANCES OF THE FIXED STARS.\\n321. We cannot ascertain the actual distance of any\\nof the fixed stars, but can certainly determine that the\\nnearest star is more than (20,000,000,000,000,) twenty\\nbillions of miles from the earth.\\n320. What length of time is required in order to detect\\nproper motions in the stars What changes have occurred in\\nthe two stars 61 Cygni? What sort of stars indicate proper\\nmotions Of stars not double, what star has the greatest\\nproper motion", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0274.jp2"}, "275": {"fulltext": "DISTANCES OF THE FIXED STARS. 261\\nFor all the measurements relating to the distances of\\nthe sun and planets, the radius of the earth furnishes the\\nbase line. (Art. 96.) The length of this line being\\nknown, and the horizontal parallax of the body, whose\\ndistance is sought, we readily obtain the distance by tne\\nsolution of a right angled triangle. But any star viewed\\nfrom the opposite sides of the earth, would appear from\\nboth stations, to occupy precisely the same situation in\\nthe celestial sphere, and of course it would exhibit no\\nhorizontal parallax.\\nBut astronomers have endeavored to find a parallax in\\nsome of the fixed stars, by taking the diameter of the\\nearth s orbit as a base line. Yet even a change of posi-\\ntion amounting to 190 millions of miles, proves insuffi-\\ncient to alter the place of a single star, from which it is\\nconcluded that the stars have not even any annual par-\\nallax that is, the angle subtended by the semi-diameter\\nof the earth s orbit, at the nearest fixed star is insensible.\\nThe errors to which instrumental measurements are sub-\\nject, arising from the defects of the instruments them-\\nselves, from refraction, and from various other sources of\\ninaccuracy, are such, that the angular determinations of\\narcs of the heavens cannot be relied on to less than V.\\nBut the change of place in any star when viewed at op-\\nposite extremities of the earth s orbit, is less than 1 and\\ntherefore cannot be appreciated by direct measurement.\\nIt follows, that, when viewed from the nearest star, the\\ndiameter of the earth s orbit would be insensible.\\n322. Taking, however, the annual parallax of a fixed\\nstar at 1 it can be demonstrated that the distance of\\nthe nearest fixed star must exceed 95000000 x 200000\\n190000000x100000, or one hundred thousand times\\n32 1 What do we know respecting the distances of the fixed\\nstars 1 Hare the fixed stars any parallax What is taken as\\nthe base line for measuring the parallax What angle is\\ncreater than would be subtended by the diameter of the earth s\\norbit as seen from the nearest fixed star", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0275.jp2"}, "276": {"fulltext": "262 FIXED STARS.\\none hundred and ninety millions of miles. Of a dis-\\ntance so vast we can form no adequate conceptions, and\\neven seek- to measure it only by the time that light,\\n(which moves more than 192,000 miles per second, and\\npasses from the sun to the earth in 8m. 13.3sec.,) would\\ntake to traverse it, which is found to be more than three\\nand a half years.\\nIf these conclusions are drawn with respect to the\\nlargest of the fixed stars, which we suppose to be vastly\\nnearer to us than those of the smallest magnitude, the\\nidea of distance swells upon us when we attempt to es-\\ntimate the remoteness of the latter. As it is uncertain,\\nhowever, whether the difference in the apparent magni-\\ntudes of the stars is owing to a real difference, or merely\\nto their being at various distances from the eye, more or\\nless uncertainty must attend all efforts to determine the\\nrelative distances of the stars but astronomers generally\\nbelieve, that the lower orders of stars are vastly more\\ndistant from us than the higher. Of some stars it is\\nsaid, that thousands of years would be required for their\\nlight to travel down to us.\\n323. We have said that the stars have no annual par-\\nallax yet it may be observed that astronomers are not\\nexactly agreed on this point. Dr. Brinkley, a late emi-\\nnent Irish astronomer, supposed that he had detected an\\nannual parallax in Alpha Lyrae amounting to 1 .13 and\\nin Alpha Aquilse of l .42. These results were contro-\\nverted by Mr. Pond, of the Royal Observatory of Green-\\nwich and Mr. Struve of Dorpat, has shown that in a\\nnumber of cases, the parallax is in a direction opposite\\nto that which would arise from the motion of the earth.\\nHence it is considered doubtful whether in all cases of\\n322. If we take the parallax at 1 what must the distance\\nbe 1 What time would it take light to traverse this space\\nHow much farther off than this may some of the smaller stars be?\\n323. Is it entirely settled that the fixed stars have no paral-\\nlax What did Dr. Brinkley assert Have his observations\\nbeen confirmed 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0276.jp2"}, "277": {"fulltext": "DISTANCE OF THE FIXED STARS. 263\\nan apparent parallax, the effect is not wholly due to\\nerrors of observation.\\n324. Indirect methods have been proposed for ascer-\\ntaining the parallax of the fixed stars by means of obser-\\nvations on the double stars. If the two stars composing\\na double star are at different distances from us, parallax\\nwould affect them unequally, and change their relative\\npositions with respect to each other and since the ordi-\\nnary sources of error arising from the imperfection of\\ninstruments, from precession, and refraction, would be\\navoided, (since they would affect both objects alike, and\\ntherefore would not disturb their relative positions,)\\nmeasurements taken with the micrometer of changes\\nmuch less than 1 may be relied on. Sir John Herschel\\nproposes a method by which changes may be determined\\nwhich amount to only j\\\\ of a second.*\\nThe immense distance of the fixed stars is inferred\\nalso from the fact, that the largest telescopes do not in-\\ncrease their apparent magnitude. They are still points,\\nwhen viewed with the highest magnifiers, although\\nthey sometimes present a spurious disk, which is owing\\nto irradiation.f\\n324. What indirect methods have been proposed for ascer-\\ntaining the parallax of the fixed stars State the particulars\\nof this method. How minute changes of place is it supposed\\nmay be detected. How do the largest telescopes affect their\\napparent magnitudes 1\\nVery recent intelligence informs us, that Prof. Bessel of Kbnigs-\\nberg, has obtained decisive evidence of an annua] parallax in 61 Cygni,\\namounting to 0 .3136. This makes the distance of that star, equal to\\n657700 times 95 millions of miles a distance which it would take light\\n10.3 years to traverse.\\nt Irradiation is an enlargement of objects beyond their proper bounds,\\nin consequence of the vivid impression of light on the eye. It is sup-\\nposed to increase the apparent diameters of the sun and moon from three\\nto four seconds, and to create an appearance of a disk in a fixed star,\\nwhich, when this cause is removed, is seen as a mere point.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0277.jp2"}, "278": {"fulltext": "264 FIXED STARS.\\nNATURE 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 light)\\nhe compared the light of Sirius with that of the sun.\\nHe next inquired how far the sun must be removed from\\nus in order to appear no brighter than Sirius. He found\\nthe distance to be 141,400 times its present distance.\\nBut Sirius is more than 200,000 times as far off as the\\nsun. Hence he inferred that, upon the lowest compu-\\ntation, Sirius must actually give out twice as much\\nlight as the sun or that, in point of splendor, Sinus\\nmust be at least equal to two suns. Indeed, he has ren-\\ndered it probable that the light of Sirius is equal to\\nfourteen suns.\\n326. The fixed stars are suns. We have already seen\\nthat they are large bodies that they are immensely\\nfarther off than the farthest planet that they shine by\\ntheir own light in short, that their appearance is, in all\\nrespects, the same as the sun would exhibit if removed\\nto the region of the stars. Hence we infer, that they\\nare bodies of the same kind with the sun.\\nWe are justified therefore by a sound analogy, in con-\\ncluding that the stars were made for the same end as\\nthe 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 beauty,\\n325. Nature of the stars. How large are the stars compared\\nwith the earth How did Dr. Wollaston endeavor to estimate\\nthe magnitudes of certain fixed stars 1 How distant would this\\nmethod make Sirius T how many suns is Sinus equal 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0278.jp2"}, "279": {"fulltext": "SYSTEM OF THE WORLD. 265\\nyet it must be admitted that the chief purpose of the\\nstars could not have been to adorn the night, since by\\nfar the greatest part of them are wholly invisible to the\\nnaked eye nor as landmarks to the navigator, for only a\\nvery small proportion of them are adapted to this pur-\\npose nor, finally, to influence the earth by their attrac-\\ntions, since their distance renders such an effect entirely\\ninsensible. If they are suns, and if they exert no im-\\nportant agencies upon our world, but are bodies evidently\\nadapted to the same purpose as our sun, then it is as ra-\\ntional to suppose that they were made to give light and\\nheat, as that the eye was made for seeing and the ear\\nfor hearing. It is obvious to inquire next, to what they\\ndispense these gifts if not to planetary worlds and why\\nto planetary worlds, if not for the use of percipient be-\\nings We are thus led, almost inevitably, to the idea\\nof a Plurality of Worlds and the conclusion is forced\\nupon us, that the spot which the Creator has assigned to\\nus is but a humble province of his boundless empire.*\\nCHAPTER IV.\\nOF THE SYSTEM 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.\\nIt is otherwise called the Mechanism of the Heavens\\nand indeed, in the System of the World, we figure to\\nourselves a machine, all the parts of which have a mu-\\n326. Prove that the fixed stars are suns. For what purpose\\nwere they made 1 Could they have been designed to adorn the\\nnight or as landmarks to the navigator 1 If they are suns, for\\nwhat farther purpose were they designed 1\\nSee this argument, in its full extent, in Dick s Celestial Sctuery.\\n23", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0279.jp2"}, "280": {"fulltext": "266 SYSTEM OF THE WOULD.\\ntual dependence, and conspire to one great end. The\\nmachines that are first invented (says Adam Smith) to\\nperform any particular movement, are always the most\\ncomplex and succeeding artists generally discover that\\nwith fewer wheels and with fewer principles of motion\\nthan had originally been employed, the same effects may\\nbe more easily produced. The first systems, in the\\nsame manner, are always the most complex and a par-\\nticular connecting chain or principle is generally thought\\nnecessary to unite every two seemingly disjointed ap-\\npearances but it often happens, that one great connect-\\ning principle is afterwards found to be sufficient, to bind\\ntogether all the discordant phenomena that occur in a\\nwhole species of things. This remark is strikingly\\napplicable to the origin and progress of systems of as\\ntronomy.\\n328. From the visionary notions which are generally\\nunderstood to have been entertained on this subject by\\nthe ancients, we are apt to imagine that they knew less\\nthan they actually did of the truths of astronomy. But\\nPythagoras, who lived 500 years before the Christian\\nera, was acquainted with many important facts in our\\nscience, and entertained many opinions respecting the\\nsystem of the world which are now held to be true.\\nAmong other things well known to Pythagoras were the\\nfollowing\\n1. The principal Constellations. These had begun to\\nbe formed in the earliest ages of the world. Several of\\nthem bearing the same names as at present, are men-\\ntioned in the writings of Hesiod and Homer and the\\nsweet influences of the Pleiades and the bands of\\nOrion, are beautifully alluded to in the book of Job.\\n2. Eclipses. Pythagoras knew both the causes of\\neclipses and how to predict them not indeed in the ac-\\n327. What constitutes the System of the World? Under\\nwhat image do we figure it to ourselves What properties\\ncharacterize the machines first invented", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0280.jp2"}, "281": {"fulltext": "ASTRONOMICAL KNOWLEDGE OF THE ANCIENTS. 267\\ncurate manner now employed, but by means of the Saros.\\n(Art. 168.)\\n3. Pythagoras had divined the true system of the\\nworld, holding that the sun and not the earth, (as was\\ngenerally held by the ancients, even for many ages after\\nPythagoras,) is the center around which all the planets\\nrevolve, and that the stars are so many suns, each the\\ncenter of a system like our own. Among lesser things,\\nhe knew that the earth is round that its surface is nat-\\nurally divided into five Zones and that the ecliptic is\\ninclined to the equator. He also held that the earth re-\\nvolves daily on its axis, and yearly around the sun that\\nthe galaxy is an assemblage of small stars and that it\\nis the same luminary, namely, Venus, that constitutes\\nboth the morning and the evening star, whereas, all the\\nancients before him had supposed that each was a sepa-\\nrate planet, and accordingly the morning star was called\\nLucifer, and the evening star Hesperus. He held also\\nthat the planets were inhabited, and even went so far as\\nto calculate the size of some of the animals in the moon.\\nPythagoras was so great an enthusiast in music, that he\\nnot only assigned to it a conspicuous place in his system\\nof education, but even supposed the heavenly bodies\\nthemselves to be arranged at distances corresponding to\\nthe diatonic scale, and imagined them to pursue their sub-\\nlime march to notes created by their own harmonious\\nmovements, called the music of the spheres but he\\nmaintained that this celestial concert, though loud and\\ngrand, is not audible to the feeble organs of man, but\\nonly to the gods.\\n329. With few exceptions, however, the opinions of\\nPythagoras on the System of the World, were founded\\n328. What is said of our usual estimate of the knowledge of\\nastronomy possessed by the ancients 1 What things were\\nknown to Pythagoras How early were the principal constel-\\nlations known What did Pythagoras know of eclipses Also\\nrespecting the System of the World What lesser things did\\nhe know What notions had he of the music of the spheres", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0281.jp2"}, "282": {"fulltext": "\u00e2\u0080\u00a2268 SYSTEM OF THE WORLD.\\nin truth. Yet they were rejected by Aristotle and by\\nmost succeeding astronomers down to the time of Coper-\\nnicus, and in their place was substituted the doctrine of\\nCrystalline Spheres, first taught by Eudoxus. Accord-\\ning to this system, the heavenly bodies are set like gems\\nin hollow solid orbs, composed of crystal so pellucid that\\nno anterior orb obstructs in the least the view of any of\\nthe orbs that lie behind it. The sun and the planets\\nhave each its separate orb but the fixed stars are all set\\nin the same grand orb and beyond this is another still,\\nthe Primum Mobile, which revolves daily from east to\\nwest, and carries along with it all the other orbs. Above\\nthe whole, spreads the Grand Empyrean, or third heav-\\nens, the abode of perpetual serenity.\\nTo account for the planetary motions, it was supposed\\nthat each of the planetary orbs as well as that of the sun,\\nhas a motion of its own eastward, while it partakes of\\nthe common diurnal motion of the starry sphere. Aris-\\ntotle taught that these motions are effected by a tutelary\\ngenius of each planet, residing in it, and directing its\\nmotions, as the mind of man directs his motions.\\n330. On coming down to the time of Hipparchus, who\\nflourished about 150 years before the Christian era, we\\nmeet with astronomers who acquired far more accurate\\nknowledge of the celestial motions. Previous to this\\nperiod, celestial observations were made chiefly with the\\nnaked eye, but Hipparchus was in possession of instru-\\nments for measuring angles, and knew how to resolve\\nspherical triangles. He ascertained the length of the\\nyear within 6m. of the truth. He discovered the eccen-\\ntricity of the solar orbit, (although he supposed the sun\\nactually to move uniformly in a circle, but the earth to\\nbe placed out of the center,) and the positions of the\\n329. Were the opinions of Pythagoras generally embraced\\nby the ancients? What was the doctrine of Crystalline\\nSpheres 1 How were the planetary motions accounted for\\n330. When did Hipparchus flourish How did he make\\nhis observations What great facts did he ascertain", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0282.jp2"}, "283": {"fulltext": "THE PTOLEMAIC SYSTEM. 269\\nsun s apogee and perigee. He formed very accurate es-\\ntimates of the obliquity of the ecliptic, and of the preces-\\nsion of the equinoxes. He computed the exact period\\nof the synodic revolution of the moon, and the inclina-\\ntion of the lunar orbit discovered the motion of her\\nnode and of her line of apsides and made the first at-\\ntempts to ascertain the horizontal parallaxes of the sun\\nand moon.\\nSuch was the state of astronomical knowledge when\\nPtolemy wrote the Almagest, in which he has transmit-\\nted to us an encyclopaedia of the astronomy of the an-\\ncients.\\n331. The systems of the world which have been most\\ncelebrated are three the Ptolemaic, the Tychonic, and\\nthe Copernican. We shall conclude this part of our\\nwork with a concise statement and discussion of each\\nof these systems of the Mechanism of the Heavens.\\nTHE PTOLEMAIC SYSTEM.\\n332. The doctrines of the Ptolemaic System were not\\noriginated by Ptolemy, but being digested by him out of\\nmaterials furnished by various hands, it has come down\\nto us under the sanction of his name.\\nAccording to this system, the earth is the center of\\nthe universe, and all the heavenly bodies daily revolve\\naround it from east to west. In order to explain the\\nplanetary motions, Ptolemy had recourse to deferents and\\nepicycles an explanation devised by Apollonius one of\\nthe greatest geometers of antiquity. He conceived that,\\nin the circumference of a circle, having the earth for its\\ncenter, there moves the center of another circle, in the\\ncircumference of which the planet actually revolves.\\nThe circle surrounding the earth was called the deferent,\\n331. What are the most celebrated Systems of the World?\\n332. Ptolemaic System?\u00e2\u0080\u0094 Bid Ptolemy originate this sys-\\ntem? State the outlines of it. What was the deferent?\\nWhat was the epicycle\\n23*", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0283.jp2"}, "284": {"fulltext": "270\\nSYSTEM OF THE WORLD.\\nwhile the smaller circle whose center was always in the\\nperiphery of the deferent, was called the epicycle. The\\nmotion in each was supposed to be uniform. Lastly, it\\nwas conceived that the motion of the center of the epi-\\ncycle in the circumference of the deferent, and of the\\nplanet in that of the epicycle, are in the same directions.\\n333. But these views will be better understood from a\\ndiagram. Therefore, let ABC (Fig. 53,) represent the\\ndeferent, E being the earth a little out of the center.\\nLet dbc represent the epicycle, having its center at v, on\\nthe periphery of the deferent. Conceive the circumfer-\\nence of the deferent to be carried about the earth every\\ntwenty four hours in the order of the letters and at the\\n333. Explain the Ptolemaic System by figure 53.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0284.jp2"}, "285": {"fulltext": "THE PTOLEMAIC SYSTEM. 271\\nsame time, let the center v of the epicycle abed, have a\\nslow motion in the opposite direction, and let a body re-\\nvolve in this circle in the direction abed. Then a body\\nrevolving in the circle abed, and at the same time having\\na motion eastward in common with the circle, would\\ndescribe the looped curves klmnop. At I and m, and at\\nn and o, it would appear stationary, because in these\\npoints its motion would be either directly towards or\\nfrom the spectator. The motion would be direct from\\nk to being in the order of the signs, and retrograde\\nfrom I torn; direct again from m to n, and retrograde\\nfrom n to o.\\n334. Such a deferent and epicycle may be devised\\nfor each planet as will fully explain all its ordinary mo-\\ntions but it is inconsistent with the phases of Mercury\\nand Venus, which being between us and the sun on\\nboth sides of the epicycle, would present their dark\\nsides towards us in both these positions, whereas at one\\nof the conjunctions they are seen to shine with ful\\nface It is moreover absurd to speak of a geometrical\\ncenter which has no bodily existence, moving around the\\nearth on the circumference of another circle and hence\\nsome suppose that the ancients merely assumed this hy-\\npothesis as affording a convenient geometrical represen-\\ntation of the Phenomena,\u00e2\u0080\u0094 a diagram simply, without\\nconceiving the system to have any real existence in na-\\nture.\\n335. The objections to the Ptolemaic system, in gen-\\neral, are the following First, it is a mere hypothesis,\\nhaving no evidence in its favor, except that it explains\\nthe phenomena. This evidence is insufficient of itself,\\nsince it frequently happens that each of two hypotheses,\\n334. State the objections to this mode of representing the\\nmotions of the planets. Whv is it inconsistent with the phases\\nof Mercury and Venns 1 What is said of the supposition of a\\ngeometrical center moving around the earth 1", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0285.jp2"}, "286": {"fulltext": "272 SYSTEM OF THE WOELD.\\ndirectly opposite to each other* will explain all the known\\nphenomena. But the Ptolemaic system does not even\\ndo this, as it is inconsistent with the phases of Mercury\\nand Venus, as already observed. Secondly, now that\\nwe are acquainted with the distances of the remoter\\nplanets, and especially of the fixed stars, the swiftness\\nof motion implied in a daily revolution of the starry\\nfirmament around the earth, renders such a motion\\nwholly incredible. Thirdly, the centrifugal force that\\nwould be generated in these bodies, especially in the\\nsun, renders it impossible that they can continue to re-\\nvolve around the earth as a center.\\nThese reasons are sufficient to show the absurdities\\nof the Ptolemaic System of the World.\\nTHE TYCHONIC SYSTEM.\\n336. Tycho Brahe, like Ptolemy, placed the earth in\\nthe center of the universe, and accounted for the diur-\\nnal motions in the same manner as Ptolemy had done,\\nnamely, by an actual revolution of the whole host of\\nheaven around the earth every twenty four hours. But\\nhe rejected the scheme of deferents and epicycles, and\\nheld that the moon revolves about the earth as the cen-\\nter of her motions that the sun and not the earth, is\\nthe center of the planetary motions and that the sun\\naccompanied by the planets moves around the earth\\nonce a year, somewhat in the manner that we now con-\\nceive of Jupiter and his satellites as revolving around\\nthe sun.\\n337. The system of Tycho serves to explain all the\\ncommon phenomena of the planetary motions, but it is\\nencumbered with the same objections as those that have\\n335. State the objections to the Ptolemaic System in general.\\nDoes it explain all the phenomena 1 What swiftness of motion\\ndoes it imply\\n336. Tyckonic System. State its leading points.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0286.jp2"}, "287": {"fulltext": "THE COrERNICAN SYSTEM. 273\\nbeen mentioned as resting against the Ptolemaic system,\\nnamely, that it is a mere hypothesis that it implies an\\nincredible swiftness in the diurnal motions and that it\\nis inconsistent with the known laws of universal grav-\\nitation. But if the heavens do not revolve, the earth\\nmust, and this brings us to the system of Copernicus.\\nTHE COPERNICAN SYSTEM.\\n338. Copernicus was born at Thorn in Prussia in\\n1473. The system that bears his name was the fruit of\\nforty years of intense study and meditation upon the\\ncelestial motions. As already mentioned, (Art. 6,) it\\nmaintains (1) That the apparent diurnal motions of the\\nheavenly bodies, from east to west is owing to the real\\nrevolution of the earth on its own axis from west to east\\nand (2) That the sun is the center around which the\\nearth and planets all revolve from west to east. It rests\\non the following arguments\\nFirst, the earth revolves on its own axis.\\n1. Because this supposition is vastly more simple.\\n2. It is agreeable to analogy, since all the other plan-\\nets that afford any means of determining the question,\\nare seen to revolve on their axes.\\n3. The spheriodal figure of the earth, is the figure of\\nequilibrium, that results from a revolution on its axis.\\n4. The diminished weight of bodies at the equator,\\nindicates a centrifugal force arising from such a rev-\\nolution.\\n5. Bodies let fall from a high eminence, fall eastward\\nof their base, indicating that when farther from the cen-\\nter of the earth they were subject to a greater velocity,\\nwhich in consequence of their inertia, they do not en-\\ntirely lose in descending to the lower level.\\n337. How far does the Tychonic System explain the plan-\\netary motions 1 With what objections is it encumbered 1\\n338. Copernican System. Who was Copernicus? State\\nthe principles of his System. State the five reasons why the\\nearth revolves on its axis.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0287.jp2"}, "288": {"fulltext": "274 SYSTEM OF THE WORLD.\\n339. Secondly, the planets, including the earth, revolve\\nabout the sun.\\n1. The phases of Mercury and Venus are precisely\\nsuch, as would result from their circulating around the\\nsun in orbits within that of the earth; but they are\\nnever seen in opposition, as they would be if they cir-\\nculate around the earth.\\n2. The superior planets do indeed revolve around the\\nearth but they also revolve around the sun, as is evi-\\ndent from their phases and from the known dimensions\\nof their orbits and that the sun and not the earth, is the\\ncenter of their motions, is inferred from the greater sym-\\nmetry of their motions as referred to the sun than as re-\\nferred to the earth, and especially from the laws of grav-\\nitation which forbid our supposing that bodies so much\\nlarger than the earth, as some of these bodies are, can\\ncirculate permanently around the earth, the latter re-\\nmaining all the while at rest.\\n3. The annual motion of the earth itself is indicated\\nalso by the most conclusive arguments. For, first, since\\nall the planets with their satellites, and the comets, re-\\nvolve about the sun, analogy leads us to infer the same\\nrespecting the earth and its satellites. Secondly, The\\nmotions of the satellites, as those of Jupiter and Saturn,\\nindicate that it is a law of the solar system that the\\nsmaller bodies revolve about the larger. Thirdly, on\\nthe supposition that the earth performs an annual revolu\\ntion around the sun, it is embraced along with the plan-\\nets, in Kepler s law, that the squares of the times are as\\nthe cubes of the distances otherwise, it forms an ex-\\nception, and the only known exception to this law.\\n340. It only remains to inquire, whether there sub-\\nsist higher orders of relations between the stars them-\\nselves.\\n339. State the three reasons why the planets revolve about\\nthe sun how argued from the phases of Mercury and Venus 1\\nfrom the aspects and positions of the superior planets from\\nthe annual motion of the earth", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0288.jp2"}, "289": {"fulltext": "THE COPEENICAN SYSTEM. 2 5\\nThe revolutions of the binary stars afford conclusive\\nevidence of at least subordinate systems of suns, .gov-\\nerned by the same laws as those which regulate the mo-\\nt ons of the solar system. The nebula, also compose\\npeculiar systems, in which the members are evidently\\nbound together by some common relation. _\\nIn theie marks of organization.-of stars associated\\ntogether in clusters,\u00e2\u0080\u0094 of sun revolving around sun,\u00e2\u0080\u0094\\nand of nebula, disposed in regular figures, we recognize\\ndifferent members of some grand V^^J^.\\ngreat chain that binds together all parts of the universe\\nas we see Jupiter and his satellites combined in one sub-\\nordinate system, and Saturn and his satellites in another,\\n^ach avast kingdom, and both uniting With a num-\\nber of other indivfdual parts to compose an empire still\\nmore vast.\\n341 This fact being now established, that the stars\\nare immense bodies lik! the sun, and that they are sub-\\nfeet toXs laws of gravitation, we cannot conceive how\\n{hey can be preserved from falling into final disorder and\\nruin unless they move in harmonious concert like the\\nmembers of the solar system. Otherwise, those that\\nare situated on the confines of creation, being retained\\nW no forces from without, while they are subject to the\\nattraction of all the bodies within, must leave their sta-\\nins and move inward with accelerated velocity and\\nthus all the bodies in the universe would at length tall\\ntogether in the common center of gravity, the im-\\nmfnse distance at which the stars are placed from each\\nSher would indeed delay such a catastrophe but such\\nmust blthe ultimate tendency of the material world, un-\\n340. Proofs of higher orders of relations among ^the stars\\nthemselves-from the binary stars-from the nebute. What\\ndo we recognize in these marks of organization\\n341. How are these systems preserved from falling into dis\\norder and ruin How should we be justified in inferring that\\nother worlds are not subject to forces which operate to hasten\\ntheir decay 1 To what final conclusions are we led", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0289.jp2"}, "290": {"fulltext": "276 SYSTEM OF THE WORLD.\\nless sustained in one harmonious system by nicely ad-\\njusted motions. To leave entirely out of view our con-\\nfidence in the wisdom and preserving goodness of the\\nCreator, and reasoning merely from what we know of\\nthe stability of the solar system, we should be justified\\nin inferring, that other worlds are not subject to forces\\nwhich operate only to hasten their decay, and to involve\\nthem in final ruin.\\nWe conclude, therefore, that the material universe is\\none great system that the combination of planets with\\ntheir satellites constitutes the first or lowest order of\\nworlds that next to these planets are linked to suns\\nthat these are bound to other suns, composing a still\\nhigher order in the scale of being and, finally, that all\\nthe different systems of worlds, move around their com-\\nmon center of gravity.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0290.jp2"}, "291": {"fulltext": "277\\nSUPPLEMENT,\\nCONf AINING AN ACCOUNT OF THE LATEST DISCOV-\\nERIES IN ASTRONOMY.\\nArt. I. Great Comet of 1843.\u00e2\u0080\u0094 On the 28th of Feb-\\nruary, 1843, the attention of numerous observers, in\\nvarious parts of the world, was arrested by a comet\\nseen at noonday a little eastward of the sun. It re-\\nsembled a white cloud of great density, being nearly\\nequally brilliant through its whole length, which at\\nthis time was estimated by different observers to be\\nabout three degrees. During the first week in March,\\nthe appearance of the comet in the southern hemi-\\nsphere was splendid and magnificent, enhanced, in\\nboth respects, by the transparency of a tropical sky,\\nand the higher angle of elevation above that at which\\nit was seen by northern observers. At Pernambuco,\\nin South America, on the 4th of March, it presented a\\ngolden hue and it was, as described by the com-\\nmander of a ship, so brilliant as to throw a strong\\nlight on the sea.\\nAt New Haven, the comet was first seen after sun-\\nset on the 5th of March, and by the writer on the 6th.\\nIt then lay far in the southwest. On account of the\\npresence of the moon, it was not seen under the most\\nfavorable circumstances until the evening of the 17th.\\nIt then stretched along the southern sky from the point\\nof sunset to the bright star Sirius, covering a space\\n40 deg. in length, but unusually limited in breadth,\\nthe whole figure resembling that of a long goose-quill,\\nbeing similarly curved. It was, at first, of a delicate\\nrose-red color, but afterwards nearly a pure white.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0291.jp2"}, "292": {"fulltext": "278 DISTANCES OF THE STARS.\\nAll the astronomers of the age have concurred in\\nthe opinion, that this is one of the most remarkable\\nexhibitions of a comet ever witnessed, although they\\nare not fully agreed respecting the elements of its\\norbit, or its periodic time. Some maintain that its\\ntime of revolution is 175 years, and consequently that\\nthe present is its first return since 1668; but others\\nthink that its true period is 21 J years, and that it will\\nvisit our sphere again in 1865. It passed its perihelion\\non the 27th of February, at which time it almost\\ngrazed the surface of the sun, approaching nearer to\\nthat luminary than any comet hitherto observed. Its\\nmotions at this time were astonishingly swift, and its\\nbrilliancy such as to induce the belief that it was at a\\nwhite heat through its whole extent.\\nArt II. Distances of the Stars. After many fruit-\\nless and delusory efforts to measure the immense in-\\nterval that separates us from the fixed stars, the great\\nPrussian astronomer, Bessel, in the year 1838, deter-\\nmined this interesting and important element by ob-\\nservations on a double star in the Swan, (61 Cygni.)\\nBy observations of the last degree of refinement,\\nconducted for a period of several years, a parallax\\n(see page 36) was decisively indicated amounting to\\nabout one third of a second; or, more exactly, to\\n0 .3483, implying a distance of 592,200 times the\\nmean distance of the earth from the sun or a space\\nwhich it would take light, moving at the rate of\\ntwelve millions of miles per minute, 9} years to tra-\\nverse. To form some familiar notions of this distance,\\nlet us suppose a railway-car to travel night and day\\nat the rate of twenty miles an hour, we should find it\\nwould take it about 547 years to reach the sun but\\nto reach 61 Cygni would require 324,000,000 of years.\\nThe observations of Bessel enabled him to estimate\\nalso the period of revolution of the two stars compo-\\nsing the Binary System (see p. 255) of 61 Cygni, and\\nthe dimensions of the orbit and he found the period", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0292.jp2"}, "293": {"fulltext": "NEW PLANETS.\\n279\\nabout 540 years, and the length of the orbit about 21\\ntimes that of Uranus. Knowing also the distance of\\nthis star, we can now determine, from its proper mo-\\ntion (five seconds a year) the velocity with which it\\nmoves this is found to be forty-four miles per second,\\n\u00e2\u0080\u0094more 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 paral-\\nlax thus found, it would not be unreasonable still to\\nentertain a lingering suspicion, that it is nothing more\\nthan the unavoidable imperfection of instrumental\\nmeasurements; but the most satisfactory evidence\\nwhich the world can have that such is not the fact\\nin the present instance, but that the parallax is truly\\nfound, is that the most celebrated astronomers of the\\nage, after rigorous scrutiny, have acknowledged the\\nreality and soundness of the determination.\\nSeveral other stars have of late been supposed to\\nindicate a parallax and one of them, (Alpha Centauri,)\\nthe brightest star of the Centaur, a constellation of the\\nsouthern hemisphere, is thought by some to be nearer\\nto us than 61 Cygni, having a parallax of nine-tenths\\nof a second. The evidence, however, upon which this\\ncase and several similar cases of supposed parallax\\nrest, is not such as to have inspired so high a degree\\nof confidence as the determination by Bessel, and it is\\nstill claimed only that the distance of one star, namely,\\n61 Cygni, is accurately measured.\\nArt. III. New Planets.\u00e2\u0080\u0094 The discovery of the planet\\nNeptune by a distinguished French astronomer, Le\\nVerrier, is one of the most remarkable events in as-\\ntronomy both its existence and its place in the heav-\\nens having been determined by mathematical calcula-\\ntion, founded on the doctrine of universal gravitation,\\nbefore it was seen by the telescope. The method of\\ninvestigation, although laborious and intricate, is not\\ndifficult to be understood, and may be explained in", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0293.jp2"}, "294": {"fulltext": "280 NEW PLANETS.\\nvery simple terms. The planet Uranus has long been\\nknown to be subject to certain irregularities in its\\nrevolution around the sun, not accounted for by all\\nthe known causes of perturbation. In some cases,\\nthe deviation from the true place, as given by the\\nlatter, differs from actual observation two minutes of\\na degree, a quantity, indeed, which seems small, but\\nwhich is still far greater than occurs in the case of the\\nother planets, Jupiter and Saturn for example, and far\\ntoo great to satisfy the extreme accuracy required by\\nmodern astronomy. This long since suggested to as-\\ntronomers the possibility of one or more additional\\nplanets, hitherto undiscovered, which, by their attrac-\\ntions, exerted on Uranus a great disturbing influence.\\nLe Verrier, assuming the existence of such a planet,\\napplied himself, by the aid of the most profound math-\\nematical calculations guided by the law of gravitation,\\nto the inquiry Where is it situated at what distance\\nfrom the sun and in what point of the starry heavens\\nAs Saturn is nearly twice as far from the sun as Ju-\\npiter, and Uranus just twice as far as Saturn, he in-\\nferred that, if a planet exists beyond Uranus, its dis-\\ntance is probably twice that of Uranus, or about thirty-\\nsix millions of miles from the sun. After reasoning\\nfrom analogy, and the doctrine of universal gravita-\\ntion, respecting the position and quantity of matter\\nwhich a body must have in order to occasion the per-\\nturbations of Uranus to be accounted for, and sub-\\nmitting the whole to mathematical calculation, he was\\nenabled to say that the planet was just then passing\\nits opposition, and was consequently most favorably\\nsituated for observation, and, on account of the slow-\\nness of its motion, would remain in a very favorable\\nposition for three months afterwards. Le Verrier\\nwrote to M. Galle, a practical astronomer of Berlin,\\ncommunicating his latest results, and requesting him\\nto reconnoitre for the stranger, directing his telescope\\nto a point about five degrees eastward of the well-\\nknown star Delta Capricorni. That astronomer no", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0294.jp2"}, "295": {"fulltext": "NEW PLANETS. 281\\nsooner pointed his telescope to the region assigned,\\nthan he at once recognised the body, its place being\\nonly 52 minutes of a degree distant from the position\\nmarked out for it by Le Verrier, and its apparent di-\\nameter being almost the same that he had assigned.\\nBy a singular coincidence, a young mathematician\\nof the University of Cambridge, (Eng.,) Mr. Adams,\\nhad, without the least knowledge of what M. Le Ver-\\nrier was doing, arrived at the same great result. But\\nhaving failed to publish his paper until the world was\\nmade acquainted with the facts through the other\\nmedium, he has lost much of the honor which the\\npriority of the discovery would have gained for him.\\nThus two distinguished mathematicians, unknown to\\neach other, and by entirely independent processes, ar-\\nrived at the same results, as regarded both the exist-\\nence of the supposed planet, and the region of the\\nstarry heavens where at that time it lay concealed\\nand, to crown all, astronomers, in obedience to the\\ndirections of one of them, pointed their telescopes to\\nthe spot, and found it there. The conviction on the\\nmind of every one was, that nothing but absolute truth\\ncould abide a test so unequivocal.\\nThis is justly regarded as one of the greatest results\\never reached by pure mathematical reasoning and\\nnothing could better convince us of the power of the\\nCalculus, (the highest branch of mathematical science,)\\nas an instrument for guiding human thought in the\\ninvestigation of truth, than its pointing out the place\\nof a body, which had lain concealed in the starry fir-\\nmament from the creation of the world to the present\\ntime, and which is so small as to be visible only to a\\nlarge telescope. It is like finding a single pearl buried\\nin the depths of the ocean, or a grain of gold hidden\\namong the sands of the seashore. Nor has any dis-\\ncovery ever more fully illustrated the immutability of\\ntruth, and its fertility, or that property by which the\\ndiscovery of one great truth conducts the human mind\\nto others which before lay entirely beyond its reach.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0295.jp2"}, "296": {"fulltext": "282 CENTER OF THE UNIVERSE.\\nThis, as well as many other great truths hidden in the\\nabysses of the universe, is among the legitimate fruits\\nof Newton s grand discovery the law of Universal\\nGravitation.\\nOne satellite accompanying Neptune has already\\nbeen discovered, and the existence of another satellite,\\nand of a ring resembling that of Saturn, is strongly\\nsuspected, but is not fully confirmed.\\nAsteroids. In addition to the four small planets,\\nCeres, Pallas, Juno, and Vesta, discovered near the\\nbeginning of the present century, and having their\\norbits in the long space between Mars and Jupiter,\\nfive more similar bodies have recently been revealed\\nto us, lying in the same region of the heavens, namely\\nAstrcea, Iris, Hebe, Flora, and Metis. Like the former,\\nthey are very small bodies, as faint stars visible only\\nto the telescope, and are characterized by orbits of\\ngreater eccentricity than those of the old planets.\\nThis multiplication of asteroids faintly countenances\\nthe hypothesis of Dr. Olbers, one of the original dis-\\ncoverers of this class of bodies, that they are frag-\\nments of a single large planet that once occupied the\\nsame region between Mars and Jupiter.\\nArt. IV. Center of the Universe. At the end of the\\npreceding work, we have suggested reasons for be-\\nlieving that the whole host of heaven revolve around\\na common center. Dr. Msedler, of the Imperial Ob-\\nservatory at Dorpat, has recently not only asserted\\nthis doctrine, but has endeavored to show the exact\\nposition of that center. He fixes it in the Pleiades,\\nand asserts that Alcyone, the brightest star of this\\ngroup, is the true central sun, around which all the\\nstars of our visible firmament revolve, in obedience to\\nthe law of universal gravitation. The proofs of this\\nremarkable hypothesis are deemed too incomplete, at\\npresent, to command entire assent but the method of\\ninvestigation pursued by this distinguished astrono-\\nmer, opens a new field of observation and of specula-", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0296.jp2"}, "297": {"fulltext": "TELESCOPES.\\n283\\ntion, and promises to lend a new interest to inquirers\\ninto the mechanism of the heavens.\\nArt, V. Telescopes.\u00e2\u0080\u0094 Practical Astronomy has of\\nlate been enriched with a number of great telescopes,\\nwhich have discovered new wonders in the starry\\nheavens. The most remarkable of these are the grand\\nReflector constructed by Lord Rosse, an Irish noble-\\nman, and the great Refractors belonging respectively\\nto the Pulkova, the Cincinnati, and the Cambridge\\nobservatories.\\nLord Rosse s telescope considerably exceeds in di-\\nmensions the great 40 feet reflector of Sir William\\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 magni-\\ntude makes this instrument superior to all others in\\nlight, and fits it pre-eminently for observations on the\\nmost remote and obscure celestial objects, as the faint-\\nest nebulse, for example. But its unwieldy size, and\\nits liability to loss of power by the tarnishing or tem-\\nporary blurring of the great speculum, will render it\\nfar less available for actual research than the great\\nrefractors which come in competition with it.\\nUntil recently, it was thought impossible to form\\nachromatic object-glasses for telescopes of more than\\nabout five inches diameter but they have been suc-\\ncessively enlarged, until we can no longer set bounds\\nto the dimensions which they may finally assume.\\nThe Pulkova telescope (at St. Petersburg) has a clear\\naperture of about 15 inches and a focal length of 22\\nfeet. That of Cincinnati is somewhat smaller, its ob-\\nject-glass being 12 inches in diameter, and its length\\n17 feet. The telescope recently acquired by Harvard\\nUniversity, is perhaps the finest refractor hitherto\\nconstructed. Its dimensions are nearly the same with\\nthose of the Pulkova instrument, but its performances\\nare thought to be superior even to that. It has recently\\nadded to the system of Saturn an eighth satellite.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0297.jp2"}, "298": {"fulltext": "284 TELESCOPES.\\nThese magnificent telescopes have afforded views\\nof celestial objects, more splendid and exciting than\\nany previously enjoyed by man. In a scientific point\\nof view, the most interesting of these revelations con-\\nsist in the resolution of Nebulas before deemed irre-\\nsolvable, and thus countenancing the idea that this\\nterm is applicable only to the comparative powers of\\nour instruments that, if any objects of this class re-\\nmain unresolved, it will only be because the telescope\\nhas not yet acquired the requisite power to separate\\nthem into stars. Under these mighty instruments,\\nwhat was before a faint wisp of fog on the confines\\nof creation, expands suddenly into innumerable suns,\\ncomposing a glorious firmament of stars. The Cam-\\nbridge telescope has succeeded in the resolution of the\\ngreat Nebula of Orion, more complete than had been\\neffected even by Lord Rosse s Leviathan Reflector,\\nand is thus proved to be one of the finest instruments\\n(probably the finest refractor) in the world.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0298.jp2"}, "299": {"fulltext": "VALUABLE WORKS\\nPUBLISHED AND FOR SALE BY\\nROBERT B.COLLINS,\\n254 PEARL STREET, NEW YORK.\\nOLMSTED S NATURAL PHILOSOPHY. 8vo.\\nOLMSTED S ASTRONOMY. 8vo.\\nThese two works, originally prepared by Professor Olmsted, for the\\nuse of the students of Yale College, and adopted as text-books in a ma-\\njority of the American Colleges and higher seminaries of learning, are\\nso well known to the public, and so highly appreciated, that it is deemed\\nunnecessary to adduce individual testimonials to their merit, although it\\nwould be easy to multiply those of the highest authority. The latest\\neditions of the Astronomy are enriched with several new articles, em-\\nbracing the recent discoveries in the science.\\nMASON S SUPPLEMENT TO OLMSTED S\\nASTRONOMY. 8vo.\\nContaining a concise Treatise on Practical Astronomy, and\\nspecial rules for the Use and Adjustment of Astronomi-\\ncal Instruments, and the Calculation of Eclipses and\\nother Astronomical Phenomena.\\nO This Supplement may be had either separately, or bound up with\\nthe Astronomy.\\nOLMSTED S SCHOOL ASTRONOMY. 12mo.\\nContaining the Elements of the Science, familiarly ex\\nplained and illustrated; with the latest Discoveries.\\nAdapted to the use of Schools and Academies, and of\\nthe general reader.\\nThe introduction of this work into many of the best Schools of the\\ncountry, as a text-book, and the extensive and increasing demand for it,\\nattest the high estimation in which it is held as a class-book. It is\\ndeemed superfluous to present recommendations of a work so generally\\nknown and approve!", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0299.jp2"}, "300": {"fulltext": "ROBERT B. COLLINS PUBLICATIONS.\\nOLMSTED S RUDIMENTS OF NATURAL PHILOSOPHY\\nAND ASTRONOMY. 1 vol. 18mo.\\nFor Common Schools and Younger Classes in Academies.\\ntd^ Each part is also bound by itself, and sold separately.\\nThis attractive little volume is the latest of the series of Text-books in\\nNatural Philosophy and Astronomy prepared by Professor Olmsted. Its\\nleading object is to afford an easy explanation of those truths of these\\nsciences, which are most important to be known by mankind in general,\\nbeing truths of the greatest practical utility. No similar work, it is be-\\nlieved, ever contained, in the same compass, a greater amount of useful\\nand interesting matter. It is rendered easy and intelligible by familiar\\nillustrations and expressive diagrams, and is adapted to the comprehen-\\nsion of young learners, to a degree which can be attained by those only,\\nwho, like the author, have had great experience in teaching.\\nOn account of its simplicity of style and happy way of illustrating\\nprofound truths, it has been published in the form of raised letters for\\nthe use of the blind in the Massachusetts Asylum, at Boston, and has\\nbeen widely circulated by the American Board among the Missionary\\nSchools in distant parts of the earth.\\nM CURDY S FIRST LESSONS IN GEOMETRY:\\nAdapted, in connection with the Charts of Geometry, to the\\nuse of Public Schools and Academies. By D. M Curdy\\nof Washington, D. C. 12mo.\\nM CURDY S TWO CHARTS OF GEOMETRY\\nOn Rollers. Size 34 by 48 inches.\\nM CURDY S EUCLID S ELEMENTS, OR SECOND\\nLESSONS IN GEOMETRY. 12mo.\\nCOFFIN S SOLAR AND LUNAR ECLIPSES.\\nFamiliarly Illustrated and Explained, with the Method of\\nCalculating them, as taught in the New England Col-\\nleges. By Jas. H. Coffin. 8vo.\\nMURRAY S SEQUEL TO THE ENGLISH READER.\\n12mo.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0300.jp2"}, "301": {"fulltext": "ROBERT B. COLLINS PUBLICATIONS.\\nCOFFIN S CONIC SECTIONS AND ANALYTICAL\\nGEOMETRY. 8vo.\\nBy Jas. H. Coffin, of Lafayette College, Pa.\\nThe Demonstrations in this work are considered more sim-\\nple and concise than in other treatises.\\nFrom Prof. Loomis, College of New Jersey, Princeton, N. J.\\nu Your treatise on Analytical Geometry, appears to me to possess ad-\\nvantages over any other treatise which I have examined. One of these\\nadvantages I consider to be the division into Propositions distinctly enun-\\nciated, so as to keep constantly before the mind of the student the object\\nof his investigation. Another advantage consists in the introduction of\\nnumerical examples, which afford a useful exercise to the student, and\\npresent the best test of the clearness of his conceptions.\\nABERCROMBIE S INTELLECTUAL PHILOSOPHY:\\nWith Additions, Explanations and Questions, to adapt the\\nwork to the use of Schools and Academies, by Jacob\\nAbbott. Revised edition. 12mo.\\nABERCROMBIE S MORAL PHILOSOPHY:\\nWith Additions and Explanations, and also Questions for\\nthe Examination of Classes, by Jacob Abbott. Revised\\nand enlarged. 12mo.\\nPRESTON S TREATISE ON BOOK-KEEPING:\\nComprising both Single and Double Entry. Enlarged and\\nimproved edition. 8vo.\\nPRESTON S SINGLE ENTRY BOOK-KEEPING:\\nVdapted to the use of Retailers, Farmers, Mechanics, and\\nCommon Schools. 8vo.\\nPRESTON S DISTRICT SCHOOL BOOK-KEEPING:\\nPrinted on thick demy writing paper, for practice. An\\nexcellent work for beginners. Quarto.\\nWHELPLEY S COMPEND OF HISTORY.\\nWith Questions, by Joseph Emerson. 12mo.", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0301.jp2"}, "302": {"fulltext": "PUBLICATIONS.\\nABBOTT S MOUNT VERNON JUNIOR READER.\\n18mo.\\nAJBBOTT S MOUNT VERNON MIDDLE CLASS\\nREADER. 18mo.\\nABBOTT S MOUNT VERNON SENIOR READER.\\n12mo.\\nTHE COMMON SCHOOL WRITING BOOK.\\nBy Otis G. Badlam. A progressive series of five numbers\\neach page containing fac simile copies of the author s\\nhandwriting.\\nABBOTT S COMMON SCHOOL DRAWING CARDS.\\nForty Cards of Landscapes and Flowers, with Directions,\\nfor drawing the subject, on the back of each Card. In a\\nneat case.\\nADDICK S ELEMENTS OF THE FRENCH LANGUAGE.\\nAn elementary practical work for learning to speak the\\nFrench Language, expressly adapted to the capacity of\\nChildren containing a table of the French Sounds and\\nArticulation, with corresponding lessons in Pronouncing\\nand Reading. 12mo.\\nGIRARD S ELEMENTS OF THE SPANISH LANGUAGE.\\nAn elementary practical work for learning to Speak and\\nWrite the Spanish Language, from the method of Dr.\\nJ. H. P. Seidenstuecker. By J. F. Girard. 12mo.\\nKIRKHAM S ENGLISH GRAMMAR.\\nIn Familiar Lectures containing a new systematic order\\nof Parsing, exercises in False Syntax, and a system of\\nPhilosophical Grammar, in notes; to which are added\\nan Appendix, and a Key to the Erf rain**- V?w\\n3 5ir", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0302.jp2"}, "303": {"fulltext": "", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0303.jp2"}, "304": {"fulltext": "", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0304.jp2"}, "305": {"fulltext": "", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0305.jp2"}, "306": {"fulltext": "", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0306.jp2"}, "307": {"fulltext": "~v\\nv--\\n_ i\\n\u00e2\u0080\u00a2Kt,\\nv.\\nf\\n,V\\no X\\n\u00e2\u0080\u00a2JO\\n0c\\nA-\\no*\\n,x\\\\\\n\u00c2\u00abv\\nj\\nv\\nx\u00c2\u00b0\\nA -P\\nV\\n,0o\\n-o N\\nX", "height": "3525", "width": "1969", "jp2-path": "compendiumofastr00olms_0307.jp2"}, "308": {"fulltext": "", "height": "3719", "width": "2029", "jp2-path": "compendiumofastr00olms_0308.jp2"}}