'HE' ARTHUR H. CLARK r. i_l--t_ J Rr.r-'-"- \ \\ From the collection of the z n z _ m o PreTinger i a JJibrary San Francisco, California 2006 " / ==~^-S/f #-/?&, T / SYSTEM OK AS TRONOM Y, ON TH PRINCIPLES OF COPERNICUS : CONTAINING, BESIDES THE USUAL ASTRONOMICAL CALCULATIONS, A CATALOGUE OF ECLIPSES VISIBLE IN THE UNITED STATES DURING THB PRESENT CENTURY, AND THE TABLES NECESSARY FOR CALCULATING ECLIPSES AND OTHER COMPUTATIONS ON THE MOTION OE THE CELESTIAL BODIES j ACCOMPANIED WITH PLATES, EXPLAINING THE PRINCIPLES OF THE SCIENCE, AND ILLUSTRATING THE ASPECTS OF THE HEAVENS. BY JOHN VOSE, A. M. Principal of the Pembroke Academy, New-Hampshire. Deus unus potest esse Architectus et Rector tanti operi Who maketh Arcturus, Orion, and Pleiades. Job. ..*<* (fconcortr : PUBLISHED BY JACOB B. MOORE. 1827. DISTRICT OF NEW-HAMPSHIRE, tt. District Clerk's Office. . DK IT REMEMBERED, that on the 15th day of May, A. D. 1827, and in the $L S.J-*-* fifty-second year of the Independence oi the United States of America, JOHN \**v-w/ VOS, of said .iistrict, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit: * A sytttm of Astronomy , on the principles of Copernicus : containing, besides the usual astronomical calculations, a. catalogue of eclipses visible in the U- ited States during the present century, and the tables necessary for calculating eclipses and other computations on the motion of the celestial bodies ; accompanied -with plates, explaining the principles of the science, and illustrating the as- pects of the heavens. By John Vose, A. M. Principal of the Pembroke Academy , New- Hampshire. Deus unus pftest esse Architectus et Rector tanti operis. Cicero. Wu9 maketh Arcturus, Orion, and Pleiades. Job." In conformity to the act of the Congress of tht United States, entitled " An act for the encouragenu nt of learning, by securing the copies of maps, caarts, and books, to the authors and proprietors of such copies, during the times therein mentioned ;" and also to aii act, entitled < an act supplementary to an act entitle** an act for the encouragement of lea m- jng, by securing the copies of maps, eharts and books, to the authors and proprietors of such copies, during the times therein .-tntioned, and extending the benefits thereof to the arts of designing, engraving, and etching historical ad other prints." CHARl.KS W CUTTER, Clerk of the District of tfeiv-Hampshire. A true copy of Record ; Attest, CHARLES W. CUTTER, Clerk. PREFACE. THE following treatise was undertaken at the suggestion of some friends, and in a persuasion, that a classic of the kind was necessary in our institutions of learning. The larger works on astronomy seemed too unwieldly for common use. Much of Mr. Ferguson's original work had become obsolete ; and it may now be considered as defective, for want of the great improvements of Herschel and his cotemporaries. Though Dr.Brewster may have supplied the deficiency, he has retained much of the obsolete part, and his work is too expen- sive for admission into most of our seminaries. The latter objection applies with equal force to Enfield, and some others. Most of the smaller works on astronomy had not been pub- lished, or were not known to the author of this, when it was commenced. Though the public are now favored with sev- eral compends on astronomy, none of them seem calculated for that class of students, for which this was intended. A system is evidently wanted, which may occupy the middle ground between the larger and smaller works. Such a sys- tem it is hoped will here be presented. Though the work was intended to be compressed, nothing considered essential was omitted. The elements for the calculation and projec- tion of eclipses and the requisite tables, seemed indispensi- ble to the student, who would enjoy any degree of satisfac- tion or arrive at what may be termed knowledge in this sub- lime study. The author has endeavoured to avail himself of the most modern improvements in astronomy, to glean in every field that lay open on his way. *&*{ M 2843 IV PREFACE. The motions and periodical times of the planets were 'm general calculated from tables considered the most accurate. Should they differ a little from the statements in other books, it is hoped and believed, they will not be found less near the truth. The tables were calculated for the meridian of Washing- ton City, longitude, as found by Mr. Lambert, 76 55' 30. 54', west from Greenwich. This seemed most useful to the American student, and consonant with the dignity and impor- tance of the nation. For while we cheerfully pay our trib- ute of gratitude to the " old world" for its vast discoveries jm the celestial regions, and to those noble individuals of Eu- rope, who have dared to tread the milky way, u where the soul grows conscious of her birth celestial, and feels herself at home among the stars ;" we remember not only that we are far removed from the eastern world, but are an independent nation. It illy becomes the United States to move as the satellite of any foreign power. The sentiments of every true American must accord with those of the present Chief Magistrate : " While scarcely a year passes over our heads without bringing some new astronomical discovery to light, which we must receive at second hand from Europe, are we not cutting ourselves off from the means of returning light for light, while we have neither observatory nor observ- er upon our half of the globe, and the earth revolves in per- petual darkness to our unsearching eyes ?" Calculations made for the City of Washington will answer with little variation for the great body of the United States ; and, where an allowance must occasionally be made for dif- ference of longitude, with equal ease may it be calculated from the meridian of our own capital, as from that of Green- wich or Paris. No pains has been spared to render the ta- bles not only extensive, but complete and accurate. Being carried through the 19th century, they will save much of the time usually spent in bringing the numbers of the old tables to use at the present time. In the problems worked by the PREFACE. r terrestrial globe, calculations are made from the Meridian of Greenwich, longitude on the globe being reckoned front that meridian. For a full understanding of some subjects, it seemed neces- sary to introduce some trigonometrical calculations, and in a few instances, geometrical demonstrations. For the chap- ters on eclipses and parallax, the student of leisure and in- genuity would not be satisfied to pass superficially over the principles on which the calculations are founded. Yet there may be many whose time and inclination will not permit them to examine minutely by mathematical computation, and much less by demonstration. The latter class of students may pass over the very small part of the work, which may be thought by a judicious instructor, too abstruse for their investigation. For the convenience of such, the demonstrations in general are printed in a closer type. It is however, highly desira- ble, that the astronomical student should be well versed in trigonometry. Much of the knowledge of astronomy is founded on this science. Without it the scholar must not only lose much of the satisfaction to be derived from his studies ; but can scarcely believe the statements of authors, or that the mathematical results are founded in truth. Questions in our classical books are become fashionable. The author of this would not deny the merits of every book, in which they are found at large ; nor would he detract from the very respectable character of some authors, by whom they have been inserted in our books, or teachers by whom they have been used in our schools. But from his own ob- servation as a teacher, from the natural tendency of inserted questions, and from the information he has received of their use in many of our common schools, he considers their utility as very problematical. Where the questions inserted in the book only, are to be asked, the merest novice may be a teach- er ; and the answers maybe promptly given by the most su- perficial scholar, with little or no knowledge of the subject. VI PREFACE. Their principal use undoubtedly is in reviews. But even for these it was not thought they would deserve a place in a work of this nature. In stating the motions of the heavenly bodies, a minute in- sertion, at least including seconds, was thought necessary, as frequently on these, calculations must be dependant. It is not in all cases, however, requisite, that the student should commit the minutiae. The well informed instructor will ea- sily judge, when the sexigesimals ought to be committed. In many parts of the work, by carrying the calculations forward, and making them for the western hemisphere, the author was forced to explore new regions, " terra incognita." This was particularly the case in the catalogue of eclipses visible in the century. Though he has taken great pains, he cannot hope his work will be free from error. Communica- tions on this subject will be received with gratitude. CONTENTS. -**- PAGt INTRODUCTION. xiii Explanation of the term, astronomy; advantages of the study; different systems of astronomy, Ptolemaic, Brahean.and Copernican. GLOSSARY. 17 An explanation of Astronomical terms. CHAPTER I. 25 The Solar System, SECTION I. 25 The sun ; his place in the System ; turns on his axis , physical construc- tion of the sun; why cold is intense in elevated regions ; Dr. Herschel's hy- pothesis of the sun; Dr. Brewster's confirmation; spots on the sun, when and by whom discovered ; the sun's light progressive. SECTION II. 31 The Planets ; the term, planet, explained ; number of planets primary and secondary ; all subject to the great laws of Kepler. SECTION HI. 32 Jllercury ; must have intense heat according to Sir Isaac Newton ; differ- ent accounts of Dr. Herschel and Mr. Schroeter respecting spots on Mercury ; why important discoveries have not been made in Mercury ; elements of Mercury. SECTION IV. 33 Venus ; next to the sun ?.nd moon, Venus is the most brilliant of the heavenly bodies; she forms our morning and evening star; motion of Venus ; must appear more brilliant to the inhabitants of Mercury than to us ; the light of Venus remarkably pleasant and bright; Dr. Herschel observed spots on Venus, and concluded she must have an atmosphere ; Mr. Schroeter's at- count of her mountains ; Dr. Herschel's measurement makes her larger than the earth ; elements of Venus. SECTION V. 36 Mercury nnd Venus ; why these are called inferior planets; their apparent motions explained ; Mercury and Venus appear with the phases of the moon ; how the planets are illuminated. SECTION VI. 38 The Earth; its globular form ; circles of the earth ; latitude and longitude on the earth, how reckoned ; zones of the earth ; rotation of the earth on its Viii CONTENTS. I axis; the celestial sphere appears right, oblique, or parallel; form of thy earth's orbit ; how the different seasons are produced ; the year how reckoned ; summer in the northern hemisphere longer than in the southern ; motion of the aphelion in the earth's orbit ; why the earth's motions are not percepti- ble ; why we have the warmest weather when the sun is farthest from the earth ; precession of the equinoxes. SECTION VII. 48 The Moon ; her distance from the earth and revolutions ; why she always exhibit?, the same ffce to the earth ; how the earth appears at the moon ; corn- pattftive magnitude of the earth and moon ; phases o f the moon ; different parts of the moon have different portions of light; the dark parts of the moon are cavities; Dr. Brewster's account of the lunar irregularities; quantity of the moon's light at *he earth; form of the moon's orbit ; Dr. Herschel thought iie saw volcanoes in the moon ; singular appearance of the moon ; why the sun and moon appear large near the horizon; how the concavity cf the heav- ens appears ; libratious of the moon. SECTION VIII. 56 Mars ; the atmosphere of this planet causes the remarkable redness of his appearance; Miraldi's view of Mars; brightness at his polar regions ; Mars sometimes appears gibbous; appearance of the earth and moon at Mars; Dr. Herschel'd account of telescopic appearances at this planet; elements of Mars. SECTION IX. 58 Asteroids; Vesta- its light is superior to that of the other Asteroids; Juno; remarkable for the eccentricity of its orbit ; Ceres; exhibits a disk surrounded by a dense atmosphere ; Pallas; remarkable for the great obliquity of its orbit to the ecliptic; the orbits of the asteroids intersect each other ; ar- gument in favour of their being originally one planet not conclusive. SECTION X. 61 Jupiter; the largest of the planets ; surrounded with belts ; large spots have been seen in the belts ; neither spots nor belts are permanent ; some spots seem to be periodical ; elements of Jupiter; satellites of Jupiter ; eclipses of the satellites ; these eclipses of great utility ; Galileo discovered the satel- lites in 1610. SECTION XL 64 Saturn ; shines with a dim feeble light ; the most remarkable phenomenon of Saturn is his ring; the ring appears double; is inclined to the plane of the ecliptic in an angle of 31; the ring illumines one half of the planet ; one side shines on the planet for about 15 years, then the other half for the same term in succession ; Saturn has dark spots and belts; the heat of the sun at Saturn 90 times less than to us ; the spheroidical appearance of this planet is remarka- ble ; elements of Saturn ; satellites of Saturn ; remarkable change in the ap- pearance of one satellite ; Dr. Herschel considered his ring and satellites as presenting a most brilliant appearance. SECTION XII. 67 Herschel, the planet ; discovered by Dr. Herschel while viewing the small stars near the feet of Gemini in 1781 ; this planet appears like a star of CONTENTS. IX the sixth magnitude ; element! of Herschel ; six satellites attend this planet ; thej- are remarkable for retrograde motion, and revolving in orbits nearly per- pendicular to the ecliptic; general planetary table. CHAPTER II. Phenomena of the heavens as seen from different parts of the solar system. SECTION I. 73 To a spectator at the sun the planets would appear to move in harmonious order from west to east; be would probably take the period of Mercury as a standard for comparing the periods of planets ; the paths of the planets would seem to cross each other. SECTION II. 73 Prospect at Mercury ; all the planets would appear to have conjunctions and oppositions ; their motions would seem sometimes direct, sometimes retrograde. SECTION III 74 Prospect at the Earth; the inferior planets exhibit conjunctions, but no op- positions ; the superior conjunctions and oppositions in succession ; appear- ance of looped curves not compatible with our organs of vision. SECTION IV. 75' At Jupiter it can scarcely be known that there are inferior planets. SECTION V. 75 Prospect at Herschel ; Saturn the only planet visible to its inhabitants; there may be other planets, unknown to us, but well known to the inhabitants of the Georgium bidus. CHAPTER III. 75 Causes of planetary motion. Projectile, centrifugal and centripetal forcesdefined ; matter is in itself inac- tive ; a body impelled by one force always moves in a right line; circular and elliptical motion how caused; the planets move in ellipses; the larger the or- bits of the planets are, the greater must the projectile force be in proportion to the centripetal. CHAPTER IV. 73 Equation of time. Time measured by the sun differs from that of a good clock or watch; the sun and clock are together four times in a year ; the inequality in the meas- urement of time owing to the elliptical figure of the earth's orbit, and the obli- quity of the equator to the plane of the ecliptic ; the obilquity causes the greater difference ; concise equation table. CHAPTER V. 4 Harvest Moon. Shows the benevolence of the Deity ; the harvest moon caused by the posi- tion of the horizon and the moon's orbit; illustrated by patches on an artificial globe; may be belter represented by a globe taken from its frame; when the moon rises with the least angle it sets with the greatest ; the moon passes- X CONTENTS through the same signs in each revolution, but the equal rising is not perceived except in autumn ; the moon runs low when in that part of her orbit which is seuth of the ecliptic; the winter full moons are high when she is north of the ecliptic; at the poles the full moons are not visible for nearly half the year. CHAPTER VI. 89 Tides. Kepler first discovered the cause of the tides; simply the attraction of the heavenly bodies does not cause the tides, but the unequal attraction ; the tide on the side of the earth opposite to the moon how caused ; the po es can have but two tides in a revolution of the moon round the earth ; single tides in some places ; the tide not on the meridian till after the moon has passed; the sun attracts the earth more than the moon, but raises a U ss tide on account of his great distance; spring and neap tides ; when the highest tides of ail hap- pen; lakes and small seas have no tides; Mr. Ferguson's judicious remark on the tides ; vast utility of the tides. CHAPTER VII. 95 SECTION I. Planets shining by the sun's light cast shadows on the side opposite to the sun ; eclipses can happen but between a primary planet and its own secondaries ; how the extent of the earth's shadow may be found ; the obliquity of the moon's orbit to the ecliptic prevents eclipses, except when the syzygies are near the nodes ; eclipses of the moon partial, total, and central ; why the moon is visi- ble, when totally eclipsed; the dark shadow of the moon how extensive; eclipses of the sun sometimes annular ; the penumbra, the line of the moon's nodes, moves backwaids ; eclipses return at the same node after 223 mean lu- nations, in a period of a little more than 18 years ; when a series of eclipses has closed at the earth, how long before a new series will begin ; notice of the memorable eclipse in June 16, 1806 ; extent of the moon's dark shadow on the earth; how this extent may be found ; extent of the penumbra on the earth, and how found ; duration of total darkness in a solar eclipse, and how such duration maybe found ; greatest duration of a general eclipse on the earth, and mean duration of the same ; when the general eclipse begins and ends ; position of the earth's axis affects solar eclipses; catalogue of visible eclipses. SECTION n. 108 Explanation of the tables used in calculating eclipses. SECTION in. 11? To calculate new or full moon for any time in the 19th century ; to calcu- late the time of new or full moon in any year of the Christian era before the 19th century ; to calculate the time of new or full moon in any year before the Christian era; to calculate the time of new or full moon in any year after the 19th century. SECTION IV. 121 To calculate the true place of the sun at any time in the 19th century ; in the Christian era, before the 19th century ; before the Christian era ; after the 19th century ; to calculate the tine distance of the sun. from the moon's ascending node. CONTENTS. SECTION V- 125 To project an eelipse of the sun ; elements necessary; projection of the solar eclipse in July., 1860. SECTION VI. 131 Projection of lunar eclipses ; elements ; projection of the lunar eclipse in November, 1808. CHAPTER VIII. 134 Divisions of time. Periods, cycles, epact, Roman Indication ; jear Julian and Gregorian ; al- teration of style; months; days; when beguu by different nations; nautical and astronomical day; parts of a day ; domiuical letter; table of dominical letters ; how t J find on what day of the week any month begins. CHAPTER IX. 144 Obliquity of the Ecliptic. Is diminishing; diminution caused by the attraction of the moon. CHAPTER X. 147 Parallax* SECTION I. 147 Difference between diurnal and annual parallax. SECTION II. 148 Diurnal parallax of the moon; how it may he taken by one bservation ; astronomers recommend two; process. SECTION III. 150 Parallax of the sun ; method proposed by Aristarchus for finding this par- allax; method proposed by Hipparchus; the transit of Venus; Dr. Halley first suggested the method of finding the magnitude and distance of the planets by this transit ; Horrox the first who observed a transit ; Dr. Halley gave direc- tions for observing th^transits of 1761 and 1669; data given in all transits; when the distance of the earth from the sun is known, the distance of the other planets may he easily found ; how the transit of Venus may be taken by one observer ; how it maybe taken by two observers ; great interest was tak- en in the transit of 1761 ; was observed in different parts of the world; Pro- fessor Vince's method of ascertaining when the transits of Mercury and Ve- nus will happen ; table of transits. CHAPTER XI. 15& Cornel. How they were formerly considered ; their appearance ; opinions of dif- ferent authors respecting tails of comets ; some of the laws of cometary mo- tion. CHAPTER XII. 161 The fixed stars. Astronomers consider them suns to other systems ; their stationary appear- ance owing to their immense distance ; what number of stars are visible to XU CONTENTS. the naked eye ; binary stars ; stars are classed according to their magnitude ; constellations ; new stars ; advance of the solar system in absolute space ; ga- laxy ; groups, clusters of stars, and uebulse. CHAPTER XIII. 161? Refraction. Atmospheric refraction ; increases the length of the day ; causes the disk of the sun or moon to appear elliptical near the horizon ; table of refraction. CHAPTER XIV. 172 Twilight. Its limit when the sun is 18 below the hoiizon ; immense benefit of the at- mosphere. CHAPTER XV. m Zodiacal light. It resembles a triangular beam of light rounded at the vertex ; how some Account for this phenomenon. CHAPTER XVI. 174 Latitude and Longitude on the Earth. SECTION I. 175 The latitude of a place maybe determined by the distance of its zenith from the celestial equator ; it may be determined by the altitude of its elevated pole. SECTION II. 177 Longitude ; premiums offered by different nations for the best method of de- termining longitude; attention of the Unitfd States to the subject. CHAPTER XVII. 186 Depression or dip of the horizon. CHAPTER XVIII. 187 Artificial globes described ; Problems solved fay the terrestrial and celestial lobes. Xntromtctfou. ASTRONOMY is the science, which treats of the heavenly bodies. The term is compounded of two Greek words, signifying the law of the stars, or constellations. It is a science of great antiquity, and one of the most useful and sublime, that can employ the contemplation of man. By it are known the figure and magnitude of the earth, and the situation and distance of places the most re- mote. By it is investigated the cause of inequality in the seasons, the changes of day and night, with all the pleasing variety, afforded by those phe- nomena. The mariner is dependant on this science for his only sure guide on the trackless ocean. But, above all, Astronomy affords the most enlarg- ed view of the Creator's works. The astronomer seems to open his eyes in a vast and unknown ex- panse. He beholds the stars, which bespangle and beautify our canopy, magnified into so many suns ; surrounded with worlds of unknown extent, con- stituting systems, multiplied beyond the utmost bound of human imagination, and measured only by the omnipresence of Jehovah ;, all moving in perfect harmony, in subjection to his omnipotent controul. DIFFERENT SYSTEMS OF ASTRONOMY^ The learned have formed different hypotheses respecting the position and movement of the great heavenly luminaries. 2 XIV INTRODUCTION. Ptolemy, who flourished at Alexandria, or Pelu- sium, in Egypt, in the reign of Adrian and Anto- ninus, the Roman emperors, supposed the earth at rest in the centre of the universe, and that the sun, the planets, the comets, and stars, revolved round it once in twenty-four hours. Above the planets this hypothesis placed the firmament of stars and the two crystalline spheres ; all included in the primum mobile, from which they received their motion. The different phases of Mercury and Venus, the apparent retrograde motion of the planets, and the whole process of calculating eclipses, show the absurdity of this system. Tycho Brahe formed a different theory. This nobleman flourished sometime after the true sys- tem was published, being born at Knudstorp, in Sweden, 1546 ;* but, anxious to reconcile the ap- pearances of nature with the literal sense of some passages of Scripture, he adopted some of the greatest absurdities of Ptolemy ; while, in other respects, he made his system conformable to the principles of modern astronomy. In this system the earth is supposed at rest, the sun and moon revolving around it, as the centre of their motion, while the other planets revolve round the sun, and are carried with it about the earth. The phases of Mercury and Venus may be ex- plained by this hypothesis. But the opposition of the superior planets can receive no satisfactory explanation. The absurdity of this system, also, must be obvious in the calculation of eclipses. The Copernican system is now universally receiv- ed by astronomers. The revolution of Mercury and Venus round the sun, was discovered by some of the ancient Egyptians. Afterwards, Pythagoras, * Ha spent a coasiderable portion of his time in Denmark hence considered a E>ane. INTRODUCTION. XV 500 years before the Christian era, privately taught his disciples the true solar system. But it was rejected and nearly lost, till revived by Copernicus, a native of Thon, in Polish Prussia, and by him published in 1530. " Here the sun is placed in the centre of the system, about which the planets re- volve from west to east. Beyond these, at an im- mense distance, are placed the fixed stars. The moon revolves round the earth ; and the earth turns about its axis. The other secondary planets move round their primaries from west to east, at differ- ent distances, and in different periodical times." It will be seen, that the satellites of Herschel form an exception to the regular motion of secon- daries. Some authors inform us, that Copernicus finish- ed his great work in 1530 ; but that it did not ap- pear in print, till about the time of his death, which happened on the 22d of May, 1543. He died sud- denly by the rupture of a blood vessel, a little after entering his seventy-first year, and a few days after revising the first proof of his work. Copernicus was favoured in the formation of his system, not only by his own powerful contempla- tions, but by aids derived from history. " Shocked at the extreme complication of the system of Ptole- my, he tried to find among the ancient philosophers a more simple arrangement of the universe. He found that many of them had supposed Venus and Mercury to move round the Sun : that Nicetas, according to Cicero, made the Earth revolve on its axis, and by this means freed the celestial sphere from that inconceivable velocity which must have been attributed to it to accomplish its diurnal revo- lution. He learnt from Aristotle and Plutarch that the Pythagoreans had made the Earth and planets move round the Sun, which they placed in the cen- tre of the universe. These luminous ideas struck Xvi INTRODUCTION. him ; he applied them to the astronomical obser- vations, which time had multiplied, and had the satisfaction to see them yield, without difficulty, to the theory of the motion of the Earth. The diur- nal revolution of the heavens was only an illusion due to the rotation of the Earth, and the preces- sion of the equinoxes is reduced to a slight motion of the terrestrial axis. The circles, imagined by Ptolemy, to explain the alternate direct and retro- grade motions of the planets, disappeared. Coper- nicus only saw in these singular phenomena, the appearances produced by the motion of the Earth round the Sun, with that of the planets : and he determined, hence, the respective dimensions of their orbits, which, till then, were unknown. Filially, every/thing in this system announced that beautiful simplicity in the operations of nature, which delights so much when we are fortunate enough to discover it. Copernicus published it in his work, On the Celestial Revolutions ; not to shock received prejudices, he presented it under the form of an hypothesis. " Astronomers," said he, " in his dedication to Paul III., being permitted to imagine circles, to explain the motion of the stars, I thought myself equally entitled to examine if the supposition of the motion of the Earth, would render the theory of these appearances more exact and simple." * H OF TERMS USED IN THIS AND OTHER ASTRONOMICAL WORKS. Altitude of a heavenly body above tbe horizon, is an arch of a vertical circle, intercepted between the centre of the body and the horizon. Amplitude of a heavenly body, is its distance from the east or west point of the horizon, measured on an arch of Jjiat circle, when the body is in it, or referred to it by a vertical. Antipodes are inhabitants who live under opposite me- ridians, and in opposite parallels. Antceci are inhabitants who live under the same meridian, but in opposite parallels, north and south. Aphelion is the point in a planet's orbit most distant from the sun. Apogee is the point in the moon's orbit, farthest distant from the earth. It is sometimes applied to the sun, when farthest from the earth. Apsis is the aphelion or perihelion point. The line, con- necting these points, is called the line of the apsides. Argument is a quantity, by which another quantity requir- es^ may be found. Asteriods, a name given by Dr. Herschel to the four small planets, discovered in the present century. Axis of the sun or a planet is the imaginary line, on which it revolves. Azimouth of a heavenly body is an arch of the horizon be- tween the meridian and a vertical circle, passing through the body ; or it is the distance of the body from the north or south point of the horizon* * 20 GLOSSARY. Latitude of a heavenly body is its distance north or south from the ecliptic. Degrees of latitude are reckoned on *econdaries to the ecliptic, passing through the body. Latitude on the earth is the distance north or south from the equator, reckoned in degrees and minutes. Libralian of the moon is a periodical irregularity in her motion, by which exactly the same face is not always pre- sented to the earth. Limits in a planet's orbit are the two points farthest dis- tant from the nodes. Longitude on the earth is the distance east or west from some fixed meridian, assumed as first. Longitude of a heavenly body is the distance on the ecliptic from the first of Aries to the intersection of a secondary passing through the body. This longitude is reckoned east- ward, 360. Meridian is a great circle of the sphere, drawn from north to south through the poles. Nebulae, are telescopic stars, having a cloudy appearance. Nodes are two points, at which a planet's orbit crosses the plane of the ecliptic. That intersection, where a planet passes to the north, is called the ascending node ; the oppo- site, the descending node. Nonagesimal is the ninetieth degree of the ecliptic above the horizon. JVotanda, things to be noted, or observed. Oblate spheroid, a spherical body flatted at the poles. Obliquity of a circle to tkv ecliptic, the angular distance be- tween that circle and the ecliptic. Oblique sphere is a position of the sphere, in which the equator and its parallels cut the horizon in an oblique direc- tion. Opposition, opposite part of the heavens. Two bodies are said to be in opposition, when they are 180 distant, though they may not be m the same degree of celestial latitude. GLOSSARY. 21 Orbit is the figure, which a planet describes in its revolu- tion round the sun, or round its primary. Parallax is the difference between the true and apparent place of a heavenly body. When the body is in the horizon, it is called horizontal parallax. A planet would appear in its true place, if seen from the centre of the earth. It ap- pears in the apparent, when seen from the earth's surface, Parallel sphere is a position of the sphere, in which tlj equator and circles of latitude are parallel to the horizon* Penumbra is the moon's partial shadow. ^ Perigee is the point in the moon's orbit nearest the earth. The term is sometimes applied to the sun, when nearest to the earth. ' , Peri&ci are inhabitants living in the game parallel, but opposite meridians. Perihelion is the point in a planet's orbit nearest the sun. Phases are the different appearances of the moon, Mercu- ry and Venus, as the illuminated side is differently pre- sented. Phenomenon, appearance. Phenomena, the plural of phenomenon, appearances, gen- erally, unusual appearances. Planet, a revolving heavenly body. Plane of a planet's orbit is the imaginary surface in which it lies ; passing through the centre of the planet, it extends indefinitely into the heavens. Polar circles are two circles drawn round the earth from east to west, parallel to the equator, about 23, 28'* from the poles ; the northern called the Arctic, the southern the Antarctic, circles. Poles of a planet's orbit are the extremities of its axis. Precession of the equinoxes, the retrograde motion of the equinoxes from a fixed point in the heavens. Primary planets are those ^hich revolve immediately round the SUB. * Sec Obliquity, 3 2 GLOSSARY. Prime vertical is that vertical circle which crosses the meridian at right angles, cutting the horizon in the cardinal points, east and west. Projectile force, is that which impels a body in a right line. Quadrature is the point in the celestial sphere, ninety de- grees from the sun. Quadrant, the fourth part of a circle. Radius, the extent from the centre of a circle to the cir- cumference. Refraction, the incurvation of a ray of light from its rec- tilinear course. Retrograde motion of a planet, apparent motion from east to west. Right ascension of a heavenly body is its distance from the first of Aries, reckoned on the equator. .If the body be not in the celestial equator, right ascension is reckoned from the point, where the secondary, passing through the body, cuts the equator. Secant, a line drawn from the centre of a circle through one end of an arch till it meets the tangent. Secondary planets, or satellites, are those which revolve round some of the primary planets. Secondary to a great circle, is a great circle crossing it at right angles. Segment of a circle is any part, greater or less than a semi- circle, cut off by a chord. Sidereal revolution is the time in which a planet moves from a star to the same star again. Sine is a right line drawn from one end of an arch per- pendicular to the radius. Solstices are two points of the ecliptic, ninety degrees from the equinoxes. Star, a luminous heavenly body appearing always in the same, or very nearly the ssflhe situation ; hence called fixed star. Supplement of an arch, what it wants of 180. GLOSSARY. 23 I -,, " *S Synodical revolution is the time intervening between a conjunction of a planet with the sun, and the next conjunc- tion of tne same bodies. Syzygy is the conjunction or opposition of a planet with the sun. Tangent is a line touching the circumference of a circle, perpendicular to the radius. Tide, the alternate ebb and flow of the sea. Transverse is the longest axis of an ellipse. Tropical revolution is the time intervening between a planet's passing a node, and coming again to the same node. Tropics are two circles drawn round the earth parallel to the equator, at the distance of about 23 28' ; the northern called the tropic of Cancer, the southern the tropic of Ca- pricorn. Twilight, the partial light observed before sunrise in the morning, and after sunset in the evening. Vector radius is an imaginary line from a planet in any part of its orbit to the sun. Versed sine, that part of a diameter or radius which is between the sine of an arch and the circumference ; or it is what the co-sine wants of being equal to radius. Vertical circles are circles drawn through the zenith and nadir of a place, cutting the horizon at right angles. Zenith is the point in the heavens directly over the head of the observer. The opposite point is called the Nadir. These are the poles of the horizon. Zodiacal light, a pyramid of light, appearing before the twilight of the morning, and after the twilight of the evening. Zodiac is a broad circle included between two lines drawn parallel to the ecliptic, at eight degrees distance on each side. This zone includes the orbits of all the planets for- merly known. Zone, a large division of the^earth's surface ; literally, a girdle. ^r /, - &V*4&. - ' < I jtf\ CHARACTERS . I Mercury. Venus. Earth. I Mars. Vesta. 2 Juno. ? Ceres. $ u Pallas Jupiter. Saturn. ^[ Herschel. PLANETS. SP Aries. 8 Taurus, n Gemini. 5 Cancer. Leo. fln Virgo. b Libra. Hi Scorpio. t Sagittarius. V5* Capricornus. m Aquarius. H Pisces. SIGNS. S. Sign. ^i .: Degree. Minute. Seconds. "' Thirds. =-: Equality. t Plus, or Addition. Minus, or Subtraction, fi ASTRONOMY. CHAPTER Z. THE SOLAR SYSTEM. THE sun, his attendant planets, and cornels, constitute the solar system* SECTION /.-OF THE SU5T. The sun is an object pre-eminent in the solar system, The great source of light and heat, it diffuses its rays to every part of an immense sphere, giving life and motion to innumerable objects. Like its divine Author, while it con- trouls the greatest, it does not overlook the most minute. According to the Copernican system, it is the centre of all the planetary and cometary motions, all the planets and comets revolving round it in different periods, and at different distances. The sun is considered in the tower focus of the planetary orbits. Strictly, if the focus of Mercury's orbit be considered in the centre of the sun, the focus of Venus' orbit will be in the common centre of gravity between Mercury and the sun : the focus of the earth's orbit, in the common centre of gravity of Mercury, Venus and the sun ; and thus of the other planets. The foci of all the orbits, however, except those of Saturn and Herschel, will not be sensibly removed from the centre of the sun. Not will the foci of Saturn and Herschel be sensibly different from the common centre of gravity between Jupiter and the sun. The sun, though stationary m respect to surrounding ob- jects, is not destitute f motion. It turns in its axis from 26 THE SOLAR SYSTEM. west to east, making a revolution in 25d. 15h. 16m., or, according to some, in 25d. lOh. The sun is globular, its diameter being 883,246 miles. The sun's rotation is demon- strated from the revolution of its spots ; and its globular form, from its always appearing a flat, bright circle, what- ever side is presented to an observer. The physical construction of the sun has been an object of much inquiry. Considering the sun a globe of fire, some say, " The sun shines, and his rays collected by concave mirrors, or convex lenses, burn, consume, and melt the most solid bodies, or else convert them into ashes or gas ; where- fore, as the force of the solar rays is diminished by their divergency, in a duplicate ratio of the distances reciprocally taken, it is evident their force and effect are the same, when collected by a burning lens or mirror, as if we were at such distance from the sun, where they were equally dense. The sun's rays, therefore, in the neighbourhood of the sun produce the same effects, as might be expected from the most vehement fire : consequently, the sun is of a fiery substance." There seems force in this reasoning. It would lead us to conclude, that however antiquated the opinion may be, that the sun is a globe of fire, its surface must resemble a vast combustion. But, if heat come from the sun, why is it always cold in the upper regions of the air, though nearer the sun, than the surface of the earth ? and why are the tops of lofty mountains covered with per- petual snow, even under the equator ? It may be answer- ed, that animal heat is generated in the lungs from the oxygen of the atmosphere ; that air is a bad conductor of heat, and of course a good defence against cold, or rather preservative of heat, preventing its escape from the body. TJie more dense the air, therefore, the warmer in any situ- ation. The density is considered as decreasing in a geometrical proportion, upwards from the surface of the earth. If the decrease be not always thus proportioned, yet it is certain, that the air becomes very rare in high regions, as fully tested OF THE SUN, 27 by experiment on the tops of lofty mountains. Hence, the supply of heat from the oxygen of the atmosphere, and the security against cold, or the preservation of heat from the non-conducting power of the air, are greatly diminished. This must affect sensation, and in some degree the ther- mometer. But this is not the only cause, perhaps not the principal cause, why high regions of the air are cold. Chem- ists assert, that all bodies, even those to us the most frigid, radiate heat. Hence, on the common surface of the earth, not the great mass of the globe only, but thousands of other bodies, with which we are surrounded, supply us with heat. But the elevated observer on the top of Chimborazo or Him- maleh, is retired, at least in some measure, from the influ- ence of the earth, and of the bodies on its surface. He must exhaust his own treasure of heat, while, except immediately from the sun, he receives next to nothing in return. The most elevated height, to which human beings can ascend, though very considerable in regard to the height of the atmosphere, is not worthy of consideration, when com- pared with the distance of the sun. What ar'e four or five miles to ninety-five millions ? It must, however, be conceded, that besides the power- ful attraction of the sun, incompatible with its being a mass of flame only, the spots on its surface are conclusive, that, at least in part, it must be composed of other matter. The hypothesis of Dr. Herschel, respecting the sun, de- serves some detail, on account of its ingenuity,* and the eminence of its author. Rejecting the names, spots, nuclei, penumbras, faculce, and luculi, he adopts the terms, openings, shallows, ridges, nodules, corrugations, indentations, and pores. Openings, he says, are those places, where by the ac- cidental remeval of the luminous clouds of the sun, its own solid body may be seen ; and this not being lucid, the open- ings, through which we see it, may, by a common telescope, be mistaken for mere black spots. Shallows are extensive and level depressions of the lumin- f hydrostatics, the openings, shallows, indentations, and OP THE SUN. 29 pores would Instantly be filled up ; and that ridges and nodules could not preserve their elevation for a single moment. Whereas many openings have been known to last for a whole revolution of the sun ; and extensive elevations have remained supported for several days. Much less can it be an elastic fluid of an atmospheric nature ; because this would be still more ready to fill up the low places, and expand itself to a level at the top. It remains, therefore, to allow this shin- ing matter to exist in the manner of empyreal, luminous, or phosphoric clouds, residing in the higher regions of the solar atmosphere. " It appears highly probable," says Dr. Brewster, " and consistent with other discoveries, that the dark solid nucleus of the sun is the magazine, from which its heat is discharged, while the luminous, or phosphorescent mantle, which that heat freely pervades, is the region whence its light is generated." These hypotheses, like others respecting the sun, are not free from objection. If the spots are only openings in the solar clouds, why are they stationary, except their rotation, for so long a time ? and why should heat come from the dark body of the sun, rather than from its luminous surface, when that surface has so much the appearance of flame, from which heat is generally diffused on the earth ? But so much uncertainty must ever rest on the matter of the sun, perhaps no theory respecting it, can be free from objection. The improvements of modern chemistry have thrown much light upon heat or caloric. But we are not able to draw satis- factory conclusions respecting its nature. Lord Bacon con- sidered heat " the effect of an intestine motion, or mutual collision of the particles of the body heated, an expansive un- dulatory motion in the minute parts of the body." Count Rum- ford's experiments seemed to show, that caloric was " im- ponderable and capable of being produced ad infinitum from a finite quantity of matter." He concluded, that it must be " an effect arising from some species of corpuscular action amongst 4 30 THE SOLAR SYSTEM. the constituent particles of the body." Other chemists con- sider it " an elastic fluid, sui generis." In following either of these, we meet with obstacles. Perhaps the scientific world must be content, as in attraction, with knowing the operations of caloric, without attempting to investigate its nature. Any uncertainty respecting caloric, must rest on the physical construction of the sun, the prime agent of heat, in whatever way produced. The spots on the sun were first discovered by Harriot, an Englishman, or Fabricius, a German, about the year 1610. Some accounts say, they were first seen by Gallileo or Scheiner. Fabricius published an account of his observa- tions on them in 1611. The magnitude and shape of the spots are various. To most of them there is a very dark nucleus, surrounded by an umbra or fainter shade. ^The boundary between the umbra and nucleus is distinct and well defined ; and the part of the umbra nearest the dark nucleus is generally brighter, than the more distant portion. A spot revolves round the sun, so as to appear at the earth in the same position, in a little more than 21 days. The time is longer than one complete revolution of the sun on its axis, on account of the earth's motion in its orbit. No spots appear near the poles of the sun. They are generally con- fined to a zone, extending about 35 on each side of the equa- tor ; though sometimes they have been seen in the latitude 39 5'. Not a single spot was seen on the sun from the year 1676 to the year 1684. The motion of the sun's light is progressive, being a little more than eight minutes coming from the^ sun to the earth. On this account, the sun, or other heavenly body, does not appear in its true place. Let S be the sun, (Plate V. Fig. 4,) A) B) C, the equator or a parallel of latitude on the earth. If light were instantaneous, it would be noon at #, when the sun is on the meridian, as at S. But as light is pro- gressive, a meridian must pass eastward from Jl to B> more OF THE PLANETS. 31 than two degrees, after the ray starts from the sun, before it arrives at the earth. The sun must appear at R when it is over the meridian at A. It is therefore always to the west of its apparent place. Perhaps the student may think it more conformable to the Copernican system to be told, that the light, which on leaving the sun is directed towards him, does not come to him ; but presents the image of that luminary to inhabitants, living more than two degrees to the westward of his meridian. SECTION II. OF THE PLANETS. The word Planet^ is derived from the Latin Planeta. This is of Greek origin, being derived from PLANAO, / wan* der, or cause to wander. The root, or original word, seems to be a Greek primitive, PLANEE, error or wandering. Eleven primary planets have been discovered ; Mercury, Venus, the Earth, Mars, Vesta, Juno, Ceres, Pallas, Jupiter, Saturn, and Herschel. These all revolve round the sun from west to east in elliptical orbits. (Plate L Fig. 1.) There are eighteen f ecv n'larj' planets. The earth has one ; Jupiter, four ; Saturn, seven ; and Herschel, six. The discoveries of the last half century warrant the expect- ation, that the number of planets, both primary and second- ary, may yet be greatly increased. All the primary planets are subject to two great funda- mental laws, discovered by Kepler, and from him called the great laws of Kepler. 1st. If a line be conceived, drawn from the planet to the sun, called a vector radius, such line will pass over equal areas, in equal times. 2nd. The squares of the periodical times are as the cubes of their mean distances from the sun. 32 THE SOLAR SYSTEM. These laws exist " between the rate of motion in any re- volving body, whether primary or secondary, and its distance from the central body, about which it revolves." They must therefore apply to the satellites. ^ SECTION ///.OF MERCURY. This planet is nearer the sun, than any other yet discover- ed. The mean apparent diameter of the sun, as seen from Mercury, is 1 20'. The distance of Mercury from the sun is to that of our earth, as 4 to 10. Hence the intensity of light and heat, being as the squares of the distances inverse- ly, must be at Mercury as 6J to 1 at the earth. (Plate II.) The intense heat of Mercury was found by Sir Isaac New- ton sufficient to make water boil. This planet, therefore, cannot be peopled by beings constituted like the inhabitants of this earth. No revolution of Mercury on his axis has yet been discovered ; unless dependance may be placed on Mr. Schroeter 's account of discoveries. Mercury, according to Dr. Herschel, is equally luminous in every part of his body, having his disk equally well defined, without any dark spots or uneven edge. On the contrary, Mr. Schroeter pretends to have discovered, not dark spots only, but mountains in this planet.* The brilliancy of light emitted by Mercury ; the short period in which discoveries can be made upon his disk, and the position of his body, when seen through the mists of the horizon, have prevented important discoveries in this planet. * Full credence seems not to be given to Mr. Schroeter respecting his dis- coveries in the planets ; yet, they have received notice in astronomical works ; and some account of them, as they occasionally occur, may be gratifying to the student. OF VENUS. 33 ELEMENTS OF MERCURY. Character in astronomical works, 8 Inclination of Mercury's orbit to the ecliptic,, - - " / '* * ' 0' *" Diameter, - - . - - - - .. - ', "-, ;?*ftf :% 3180 miles. Mean diameter as seen from the sun, ..... 16" Periodical revolution, - - - 87d. 23h. 14' 33" Sidereal revolution, : -' "> : - - - - 87d. 23h. 15' 44" Place of ascending node, '- v; <-'': 16 * 4 ' 50" Taurus. Place of descending node, - .- - 16 14' 50" Scorpio. Motion of the nodes in longitude for 100 years, - - '"; '- 1 12' 10" Retrograde motion of the nodes in 100 years, ' - c - - - - 11' 22" Place of aphelion, 8 14 44' 17" Motion of the aphelion in longitude for 100 years, . . 1 33' 45" Diurnal rotation, according to Schroeter, ... 24h. 5' 28" Mean distance from the sun, 37,000,000 miles. Eccentricity, 7,557,630 miles. SECTION IV. OF VENUS. Next to the sun and moon, Venus is to us the most brilliant of the heavenly bodies. From her inferior to her superior conjunction, she appears west of the sun, and, rising before him, is called Phospher, Lucifer, or the morning star. From her superior to her inferior conjunction, appearing east of the sun, she sets after him, and is called Hesperus, Vesper, or the evening star. She is east or west of the sun in rotation about 92 days ; though not visible quite so long on account of her nearness to the sun. The motion of the earth in its orbit, in the same direction with Venus, retards her apparent motion round the sun. Her real revolution is performed in 224d. 16Ji. 49' 15", her apparent, in 585 days nearly. Thus, she appears longer east or west of the sun, than the whole time of a revolution in her orbit. If there be inhabitants in Mercury, they must, at times, have a much more brilliant view of Venus, than can be en- joyed by us. To them her whole illuminated side is apparent, 34 THE SOLAR SYSTEM. when at the least distance. But the illuminated side is turned from us, when she is in that part of her orbit, which is nearest to the earth. At her superior conjunction, her bright side is turned nearly or quite towards us ; but she is then, either hidden behind the sun, or so near him, as to be invisible to us. When she first appears in the part of her orbit, opposite to the earth, her disk, though nearly round, is rendered small by distance. The silver light of Venus is extremely pleasant. She is sometimes so brilliant, as to be visible in the day time to the naked eye. In her morning and evening light, shadows have been observed, defined like those of a new moon. Dr. Herschel observed spots on the surface of Venus, and that she was much brighter round her limb, than at the sepa- ration between the enlightened and dark part of her disk. From this he concluded, that Venus had an atmosphere probably replete with matter, like that of the Earth. He considered the surface of Venus less luminous than her at- mosphere. This accounts for the small number of spots ap- parent on her disk, the surface of the planet being enveloped in her atmosphere. Plate HI. Fig. I and 2, represent the spots in Venus, observed by Bianchini. On the 19th of June, 1780, Dr. Herschel observed the spots 7 as represent- ed in Fig. 3, where a, d, c, is a spot of darkish blue colour, and 6, e, 6, a brighter spot. They met in an angle at a point c, about one third of the diameter of Venus from the cusp a. Fig. 4 and 5, represent the appearance of Venus with her rugged edge and blunt horn. " Mr. Schroeter," says Dr. Brewster, " seems to have been rery successful in his observations upon Venus ; but the results, which he has obtained, are more different than could have been wished from the observations of Dr. Herschel. He discovered several mountains in this planet, and found, that like those of the moon, they were always highest in the southern hemisphere, *heir perpendicular heights being nearly, as the diameters of their respective planets. From OP VENUS. 30 the llth of December, 1789, to the llth of January, 1790, the southern hemisphere of Venus appeared much blunted with an enlightened mountain, m, (Fig. 6) in the dark hemis- phere, nearly 22 miles high." He states the following re- sult of four mountains measured by him : miles. 1st, 22,05. 2nd, 18,97. , 3rd, 11,44. 4th, 10,84. He supposes, the bluntness and sharpness, alternately ob- servable in the horns of Venus, arise from the shadow of a high mountain. From the changes, which take place in her dark spots, and, as Schroeter inferred, from the illumination of her cusps, when she is near her inferior conjunction, the atmosphere of Venus is considered very dense. Venus has been considered about 220 miles less in diame- ter, than the earth ; but from the measurements of Dr. Herschel, it appears, that her apparent mean diameter, re- duced to the distance of the earth, is 18",79, when that of the earth is 17",2. This result," says Dr. Brewster, " is rather surprising, but the observations have the appearance of accuracy." ELEMENTS OF VENUS. Character, ? Inclination of her orbit to the eclipJc, ' - 2 23' 32" Diameter, ' '"^ 7687* miles. Mean diameter as seen from the sun, 23' 3' f Tropical revolution, 224d. l'6h. 46' 15" Sidereal rerolution, 224d. 16h. 49' 15" Place of ascending node, Gemini, - - - 15 5' 3" Place of descending noJe, Sagittarius, 15 5' 3" Motion of the nodes in longitude for 100 years, 51' 40" Retrograde motion of the nodes in 100 years, 31' .'2" Place of aphelion, 10* 3 56' 27" * Aocording to Dr. Herschel, 8648, 36 THE SOLAR SYSTEM. Motion of the aphelion in longitude for 100 years, >;,->, 1 21' 0" Diurnal rotation, fc T' ... 23h. 20' 59'' Mean distance from the sun, ... 68,000,000 miles. Eccentricity, >^ 473,100 miles. "*>' SECTION F.OF MERCURY AND VENUS. Mercury and Venus are called inferior planets, because their orbits are within that of the earth, or they are nearer the sun than the earth.* These planets are often in con- junction with the sun ; never in opposition. The inferior conjunction of Mercury or Venus is, when, in the part of its orbit next to the earth, it falls into the same secondary with the sun ; the superior, when, on the opposite side of its orb it, it falls into the same longitude with the sun. In the former case, the planet comes between the earth and the sun, or as near a line with them, as the obliquity of its Orbit will admit ; in the latter, it passes beyond the sun. When an inferior planet is at its greatest elongation, a line drawn from the earth through the planet, is a tangent to the planet's orbit. Mercury's greatest elongation is 28 20' ; Venus' 47 48'. The position of these planets at the great- est elongation may be seen in Fig. 1, of Plate V, where they appear stationary. The orbits of these and of the other planets, as before stated, are elliptical, having the sun in the lower focus. Mercury and Venus, in moving from the superior conjunction to the inferior, set after the sun ; from the inferior to the superior, they rise before him. The greatest elongation of these planets on one side of the sun may not be equal to that on the other. This is manifest, their orbits being elliptical. *Some have objected to the terms superior and inferior, as applied to the plan- ets. But these terms are sanctioned by long usage ; and occur in the works of the first European astronomers. P MERCURY AND VENUS. 37 The apparent velocity of the inferior planets is greatest at the conjunctions. Their geocentric motion from the greatest elongation on one side, to the greatest elongation on the other, through the superior conjunction, is direct ; through the inferior conjunction this motion is retrograde. At their greatest elongation they appear stationary. The eye of the spectator being in the tangent line, and a small part of the orbit nearly coinciding with that line, the motion of the planet must be either towards the spectator or from* him, and of course must be imperceptible. Let 5 be the sun, E the earth, M Mercury, and V Venus. (Plate V. Fig. 1.) When the earth is at t, Mercury at b in his orbit appears stationary at e. While Mercury is moving; from b through his superior conjunction at c to cZ, his motion appears direct among the fixed stars from e to /. At d his motion is imperceptible for a little time, when he appears stationary at /. But his motion from d through his inferior conjunction to b appears to be retrograde among the fixed stars from / back to e, where he again appears stationary. It must be remembered, that the earth is moving at the same time with Mercury, and around the same focal point. It is the relative velocity of Mercury only, which gives it the appearance of retrograde motion. Venus is subject to the same appearance of direct and retrograde motion. When Mercury appears at the earth to move from d to &, the earth appears at Mercury to retrograde among the stars from h to g, the retrograde appearance being reciprocal. Hence, the superior planets, when in opposition to the sun, appear at the earth in retrograde motion. As seen from the sun, the motion of all the planets is direct ; their stationary or retrograde appearance being caused by the situation and motion of the earth. Mercury and Venus, while revolving round the sun, ap- pear with all the phases of the moon. (Plate III. Fig. 3, 4, 5, 6.) 38 THE SOLAR SYSTE3*. The sun illuminates one half of each of the planets.* The bright side of Mercury and Venus, at their inferior conjunc tion, is turned from the earth. These planets are then in- visible, except at or near the nodes, when they appear as dark spots passing over the sun's disk. At their superior conjunction, they appear nearly full, but never entirely so, as their illuminated sides are never exactly turned towards the earth, except at the nodes, when the planets are hid be- hind the sun. SECTION VI. OP THE E\RTH. The planet, next to Venus in the solar system, is the earth. The form of the earth is globular. This is evident from its shadow in eclipses of the moon appearing circular ; from the masts of a ship at sea being often seen, when the hull is hid behind the convexity of the water ; from clouds rising above the horizon, and again sinking below it. But its globu- lar figure is placed beyond doubt, by its having been circum- navigated many times. The true figure of the earth is an oblate spheroid. The equatorial diameter is reckoned by Dr. Rees at 7977, and the polar at 7940 English miles. These, however, he as- sumes, not as being perfectly correct, but " an approxima- tion to the best estimation." Dr. Bowditch makes the diameter 7964. This is taken as the mean diameter in the following work. The earth (Plate F*. Fig. 5.) is considered as encom- passed by six great circles, the equator, meridian, ecliptic, horizon, and two co/itm.f * This has been uniformly said by astronomers. Strictly, the sun illumines a fraction more than half, not only by the refraction of its rays in the atmosphere ol the planets, but, being a larger body, it shines over something more-than one half of each planet. f Great circles are those, the planes of which divide the earth into equal hemis- pheres. The planes of less circles divide the earth into unequal parts. OP THE EARTH. 39 The equator is an imaginary circle drawn round the centre of the earth from east to west. A meridian is a circle passing round the earth from north to south through the poles, and crossing the equator at right angles.* Places lying east and west of each other have dif- ferent meridians. The ecliptic is a great circle, in which the earth performs its annual revolution ; or in which the sun appears to revolve round the earth. The equator is inclined to the ecliptic in an angle of about 23 28'. (See Obliquity.) The ecliptic Is divided into 1 2 equal parts called signs, each including thirty degrees ; Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra,. Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. The horizon is a circle ninety degrees distant from the ze*- nith of any place, the plane of which divides the earth into upper and lower hemispheres. This is called the rational horizon. The sensible horizon is the circle, which bounds our sight, separating the visible part of the heavens from the invisible. The solstitial colure is a meridian, drawn through the sol- stitial points, Cancer and Capricorn. The equinoctial colure. is also a meridian, drawn through the equinoctial points, Aries and Libra. To these six may be added the zodiac, a broiyl circle, in- cluded between two lines drawn parallel to the ecliptic, at eight degrees distance on each side. This zone includes the orbits of all the planets, formerly known. Four less circles are conceived drawn round the earth, parallel to the equator ; two tropics and two polar circles. The tropics are at about 23 28' from the equator ; the northern called the tropic of Cancer, the southern, the tropic of Capricorn. The polar circles are at about 23 28' from the poles ; the northern called the Jlrctic, the southern, the Atarctic circle. * Half of this is. usually called a meridian. 40 THE SOLAR SYSTEM. Latitude i& the distance either north or south from the equa- tor, reckoned in degrees and minutes. The highest latitude is at the poles, 90 distant from the equator. Parallels of latitude are circles drawn parallel to the equa- tor. The measure of a degree in any parallel of latitude is to that of a degree on the equator, as the co-sine of the lati- tude is to radius. Longitude is th distance east or west from some meridian assumed as first. It is reckoned each way ; 180 east or west being the greatest longitude. Sometimes navigators reckon longitude one way round the globe. Particular meridians have been taken as first by different nations. The English reckon from the meridian of Greenwich ; the French from that of Paris. The meridians of Cadiz, of Teneriffe, of Ferro, and of Philadelphia have all been reckoned as first. The meridian of Washington will probably, hereafter, be assumed as the principal in the United ^States,* A fixed meridian, from which all the nations might reckon longitude, would be of great convenience. But this, though an object much to be desired, is hardly to be expected. The inhabitants, x oa different meridians, have different rel- ative time, each degpee making a difference of four minutes, 15, an hour. (See Longitude.) The surface of the earth is considered as divided into five zones. The torrid zone extends from the equator each way to the tropics ; the two temperate zones, from the tropics to the polar circles ; the two frigid zones, from the polar circles to the poles. The ingenious student will perceive the foundation for this division. So far as the torrid zone extends, the sun is verti- cal, at some time of the year. The temperate zones spread over the whole space from the tropics towards the poles, as far as the regular succession of day and night continues throughout the year. The frigid zones are alternately en- * See article Longitude. 6P THE EARTH. 41 veloped in light and darkness. When the sun is in his great- est declination north, he shines over the north pole of the earth, so that the whole northern frigid zone is illuminated. (Plate VI. Fig. 1.) The southern is then entirely dark. An effect directly contrary is produced, when the sun. is in his greatest southern decimation. The earth has three motions ; its rotation on its axis ; its annual motion round the sun ; and the motion of its axis round the poles of the ecliptic. " The rotation of the earth on its axis, called its diurnal motion, is the most uniform, with which we are acquainted. It is performed in 23h. 56m. 41s. of mean solar time, or one sidereal day." This motion must have been given to the earth at its creation ; among the first blessings of an all kind Benefactor, to his creatures in this world. It produces the succession of day and night. This motion is from west to east, causing an apparent motion of the heavenly bodies from east to west. By this motion the inhabitants on the equator are carried about 1042 miles in an hour. The velocity decreases to- wards the poles, in a direct proportion as the co-sines of the latitudes. Thus, to find the velocity, per hour, in any lati- tude, say, as radius is to the co-sine of such latitude ; so are 1042 miles, to the distance passed in one hour by any place in that parallel. A place in latitude 43 is carried about 762 miles an hour. St. Petersburg!!, in latitude 59 56', is car- ried 522 ; an inhabitant of Greenland in latitude 80, only 181 miles an hour. This motion, when on the side of the earth opposite the sun, unites with the immense velocity occasioned by the earth's motion in its orbit round the sun. The apparent circles of the heavenly bodies, occasioned by the rotation of the earth on its axis, are very different in different places. The celestial sphere is called right, oblique, or parallel, as the celestial equator is at right angles, oblique angles, or parallel to the horizon. The inhabitants at the 42 THE SOLAR SYSTEM. equator are in a right sphere, all the celestial bodies appear- ing to rise and set in circles perpendicular to the horizon. The equinoctial passes through the zenith and nadir, and the poles are in the horizon. Those, who inhabit the intermedi- ate space between the equator and the poles are in an oblique sphere. All their circles, formed by the apparent motion of the heavenly bodies, are oblique, but varying in different latitudes, and becoming more inclined to the horizon, as they are farther distant from the equator, till at the poles they Either coincide with the horizon, or become parallel to that circle. To a person at a distance from the equator, the stars, the same number of degrees from the elevated pole, do not set, but appear to revolve round, in circles, greater, as they are farther distant from the pole. Could a spectator be transported to either pole, he would be in a parallel sphere, and would have a prospect singular and sublime. All the visible stars, the polar star excepted,* would appear to revolve in circles parallel to the horizon. The sun and planets would appear to rise very gradually in spiral circles, more and more elevated, till they arrive at their greatest altitude, which to the sun would be about 23 28'. Some of the planets would rise higher ; particularly the asteroids. The moon would, at times, rise higher than any of the primaries, formerly known, except Mercury ; being sometimes 28 36' 41", above the visible horizon. The earth's annual motion round the sun forms its orbit. This is an ellipse, with the sun in its lower focus. The apparent motion of the sun in the ecliptic is caused by this revolution of the earth in its orbit, the sun and earth always appearing in opposite signs. The irregularity of the earth's motion in its orbit, was first discovered by Hipparchus, about 140 years before the Chris- tian era. It long perplexed succeeding astronomers. Various * The pole star would appear to describe a very small circle. See Longitude in the article Latitude and Longitude. Of THE EARTH. 43 cycles and epicycles were invented to explain the observed inequality ; but the true cause was not understood, till the great discovery of Kepler. He explained it, by assigning to the orbit its true elliptical figure, and establishing the curious law, before named, common to other planetary orbits, that a line, called a vector radius, connecting the revolving body to its principal, always passes over equal areas in equal times. The axis of the earth in its motion round the sun, though continually changing its place, is nearly parallel to itself. For if straight lines be drawn, representing the position of the earth's axis in different points of its orbit, these lines would be parallel to each other,except the variation by the preces- sion of the equinoxes. By this and the axis being inclined to the plane of its orbit, (Plate VI. Fig. 1,) the annual revolu- tion of the earth produces the different seasons, spring, summer, autumn, and winter ; and also causes the climates, and 'the inequality of day and night, in different parts of the earth. These may be represented by a common terrestrial globe. While an attendant holds a candle in the middle of a room, or hall, let a person place the globe, taken from the frame, east of the candle, on a level with it ; the north pole of the globe so elevated, that the axis may form an angle with the floor of about 23 28', but at right angles with a line drawn from the candle to the centre of the sphere. Nearly one half of the globe will be illuminated ; though, as the candle is less than the globe, the illuminated part is something less in proportion, than that of the earth, illuminated by the sun. While in this position, let the globe be turned gently round, from west to east. Every part of the surface will pass through a proportion of light and darkness, nearly equal. This will represent the earth, at the vernal equinox. With the north pole similarly elevated, and the axis parallel to its former position, let the globe be holden directly under the candle, and turned round as before. From the north pole of t.be globe to the arctic circle, the space representing the 44 ' THE SOLAR SYSTEM. northern frigid zone, on the earth, will turn wholly in the light. The southern frigid zone will be entirely dark. Every part north of the equator, as it turns, will enjoy more light than darkness, and proportionally more, as farther distant from the equator, towards the circle of entire light. The reverse will be seen in the southern hemisphere. Here will be a near resemblance of the earth at the summer solstice. A western position of the globe, will represent the autumnal equinox, while that directly over the candle will show the winter solstice. Let the view be enlarged. Instead of the candle and globe, or a figure, let the sun and earth be contemplated, and an idea may be formed of the cause of inequality in days and nights, and of the change of seasons. Considering the great luminaries themselves, their motions, and circles, affords a more correct idea, than the examination of any diagram. Figures, though often useful, generally give a distorted view. To those, who are not favoured with a globe, a figure may be some assistance. Plate VI. Fig. 1, represents the earth at different seasons. Let E, JV, Q, $, be the earth, JV the north and , : ,- OF THE EARTH. 47 That such a velocity, should be imperceptible, may shock the credulity of those who are unaccustomed to the contem- plation of such objects. But we are to consider, that every object around, even the atmosphere, is carried with us ; so that there is nothing, by which we can compare our motion, except the heavenly bodies. By observations on these, such motion is now rendered past doubt. Its being imperceptible is not wonderful to those who have sailed in a ship or boat on still water. There a person, having obtained the motion of the vessel, feels no inconvenience from its swiftness, and is nearly insensible of movement, but from surrounding ob- jects, till he strikes a shore, or other obstruction. The motion of the earth in its orbit is far more uniform and even, than any movement on the stillest water. The motion of the earth's axis round the poles of the eclip- tic causes the difference between the sidereal and tropical year. For by this motion the equinoxes are annually car- ried backward 50.118" of a degree from east to west, con- trary to the order of the signs. Thus in every year they meet the sun 20 minutes, 20.4 seconds, the difference be- tween the tropical and sidereal year, before the earth ar- rives at the point of the heavens, whence it started at the* commencement of the year. From this precession of the equinoxes, " and with them all the signs of the ecliptic, it follows, that those stars, which in the infancy of astronomy were in Aries, are now in Tau- rus ; those of Taurus, in Gemini. Hence likewise it is, that the stars, which rose or set at any particular season of the year, in the times of Hesiod, Eudoxus, Virgil, or Pliny, by no means answer at this time to their descriptions." The constellations on our celestial globes, placed 30 from the signs, to which they originally belonged, show the mo- tion of the equinoxes for 2164 years. The signs make a complete revolution in 25,858 years. Hence, in something- more than 12,000 years, the star, which is called the north pole, will be about 47 from the pole of the earth, and THE SOLAR STSTEM. when on the meridian will be in the zenith of some parts of New-England. How should the contemplation of these celestial motions, and long periods, lead us to improve the short fleeting mo- ments of time assigned to us ; and bring us to admire and adore the wisdom and power of Him, who formed and still governs all with infinite ease ; with whom a " thousand years are as oe day !" SECTION VIL OF THE MOON. The earth has one satellite, the moon. This constant attendant is distant from the earth 240,000 miles,* and re- volves round it from a point in the ecliptic to the same again, in 27 days, 7 hours, 43 minutes, and 5 seconds : from a star to the same again, in 27 days, 7 hours, 43 minutes, 12 sec- onds.f It performs a mean lunation from the sun to the sun again, in 29 days, 12 hours, 44 minutes, 3 seconds. This is called her synodical revolution. The moon always exhibits the same surface to the earth. Hence, it must revolve round its axis in the same time, that it performs a revolu- tion ; or we must suppose, what is very improbable, that the different sides of the moon present the same prospect. Astronomers seem agreed in the former opinion. If it be correct, it is highly probable, that the side of the moon nearest to the earth is composed of matter more dense than the opposite, and that its rotation on its axis is caused by the powerful attraction of the earth. Let E, (Plate F. Fig. 2.) be the earth, w?, B, C, J} 9 the moon in different parts of her orbit ; a a mountain on the side of the moon next to the earth. As the moon passes in her orbit from A to jB, 90, it is manifest, * This is taken for the mean distance. f De la Lande makes the sidereal revolution 27d. 7h. 43' 11.525Q". OP THE MOON. 49 that she must turn on her axis 90, in order that the same side may be towards the earth ; the mountain will then be at b. When the moon is at C, having passed half her revolution, the mountain must be at c. The moon at D presents the mountain at d. When the moon comes to Jl, the mountain must have come round to a again. So that in one com- plete revolution, 27 days, 7 hours, 43 minutes, 12 seconds, the moon must have revolved once on its axis, in order that the samp side may be towards the earth. It is surprising, that Dr. Brewster's name must be enume- rated among several authors, who state, in substance, " that the moon performs a revolution in 29J days," and in imme- diate connexion, " that it turns round on its axis in the same time that it performs a revolution." The latter is in itself trae, but not when connected with the former. It is man- ifest, from a view of the figure, that, when the moon has revolved more than once round, as it does in passing from the sun to the sun again, it must have turned more than once round ou its axis, or the same side cannot be presented to the earth. The diameter of the moon is 2180 miles. But if its ap- parent diameter be 31' 8", as stated by De la Lande, its diameter must be but 2173 miles. To the lunarians the earth appears like a moon ; but thirteen times as large as the moon does to us. It exhibits all the phases of the moon, but at opposite times, the full being at the change of the moon ; the change at her full. The magnitude of the earth is to that of the moon about as 49 to 1. " The moon is an opaque globe like the earth, and shinei only by reflecting the light of the sun ; therefore, while that half of her which is towards the sun is enlightened, the other half must he dark and invisible. Hence, she disappears when she comes between us and the sun ; because her dark side is then towards us. When she is gone a little way for- ward, we see a little of her enlightened side, (Plate IV. 50 THE SOLAR SYSTEM. Fig. 1.) which still increases to our view as she advances forward, until she comes to be opposite to the -sun ; and then her whole enlightened side is towards the earth, and she appears with a round illuminated orb, which we call the full moon, her dark side being then turned away from the earth. From the full she seems to decrease gradually, as she goes through the other half of her course, showing us less and less of her enlightened side every day, till her next change, or conjunction with the sun, and then she disappears as before." Ferguson. Without doubt, "Mr. Ferguson knew, that we never see the moon completely bright and round, her side illuminated by the sun never being turned exactly towards us. She is not directly opposite to the sun, except when in one of her nodes, and then she falls into the earth's shadow. To illustrate the different views of the moon, let 5 be the sun, (Plate V. Fig. 3.) T the earth, A, B, C, D, E, F, Gj H, the moon indifferent parts of a lunation. The varied appearances at the earth are represented in the external circle at a, 6, c, ; - , ^. S2 ELEMENTS OF SATURN. Character, ..... fa Inclination of the orbit to the ecliptic, . . 2 29' 34". Diameter, . . . 79,042 miles. Mean diameter as seen from the sun, .U' . 18" Tropical revolution, . 29y. 162d. llh. 30' 0" Sidereal revolution, . . . ^. 29y. 167d. Oh. 27' Place of the ascending node, Cancer, . 22 9/ 48" Place of descending node, Capricorn, . . . - ; 22 9' 48" Motion of the nodes in longitude for 100 years, . ..- 52' 35" Retrograde motion of the nodes in 100 years, . * fc >v > SO/ 57'" Place of aphelion, . . . , . 8 29 31' 42" Motion of the aphelion in longitude for 100 years, i? g ; . v { j 1 50' 7" Diurnal rotation, . . . . . 10h. 16^ Mean distance from the suu, . 900,000,000 miles. Eccentricity, . . , . . . 50,958,399 miles 66 THE SOLAR SYSTEM. Saturn has seven satellites, which revolve about their primary, and accompany him round the sun. Satellites. Periodical times. Distances from primary in miles. 1 22h. 3T 22" 107,000 2 Id. 8 53 8 135,000 3 1 21 18 27 170,000 4 2 17 41 22 217,000 5 4 12 25 12 303,000 6 15 22 41 13 704,000 7 79 7 48 2050,000 The seventh satellite of this planet, reckoned by some the fifth, surpasses all the others but one in brightness, when at its greatest western elongation, but is very small at other times, entirely disappearing at its greatest eastern elongation. This phenomenon, first observed by Cassini, appears to arise from one part of the satellite being more luminous than the rest. " Dr. Herschel observed this satel- lite through all its variations of light, and concluded, that, like our moon and the satellites of Jupiter, it turned round its axis at the same time it performed a revolution round the primary planet." Dr. Brewster. " There is not, perhaps," says Dr. Herschel, " another object in the heavens, that presents us with such a variety of extraordinary phenomena, as the planet Saturn ; a magnifi- cent globe, encompassed by a stupendous double ring ; at- tended by seven satellites ; ornamented with equatorial belts ; compressed at the poles ; turning upon its axis ; mu- tually eclipsing its ring and satellites, and eclipsed by them ; the most distant of the rings also turning upon its axis, and the same taking place with the farthest of the satellites ; all the parts of the system of Saturn occasionally reflecting light to each other ; the rings and the moons illuminating the HERSCHEL. nights of the Saturnian ; the globe and the satellites en- lightening the dark parts of the rings ; and the planet and rings throwing back the sun's beams upon the moons, when they are deprived of them, at the time of their conjunc- tions." SECTION XIL-OF HERSCHEL. Herschel, Uranus, or Gcorgium Sidus, was discovered by Dr. Herschel, on the 13th of March, 1781. It had, proba- bly, before been seen by astronomers, but was considered a fixed star. Dr. Herschel, when observing the small stars near the feet of Gemini, was struck with the appearance of one larger than the rest, but not so brilliant. Supposing it to be a comet, he observed it with telescopes of different magnifying powers, from 227, with which it was discovered, to 2010. Its apparent magnitude increased in proportion to the magnifying power, contrary to the fixed stars. By meas- uring its distance from some of the stars, and comparing its situation for several nights, he found, that it moved about 2| seconds in an hour. He wrote immediately to the royal society, that it might be observed by other astronomers. It was found and observed by Dr. Maskelyne, who almost im- mediately declared, he suspected it to be a planet. On the first of April, Dr. H. wrote to the astronomers of Paris an account of his discovery. It was soon observed by all the astronomers of Europe. So distant is this planet, it can scarcely be discovered by the naked eye. In a serene sky, however, it appears like a star of the sixth magnitude, with a bluish white light, and a brilliancy between Venus and the moon. THE SOLAR SYSTEM. ELEMENTS OF HERSCHEL. Character, ,< . ,. Inclination of his orbit, .... Mean diameter, ... Mean diameter as seen from the sun, Tropical revolution, .... 83y. Sidereal revolution, . . . 84y. Place of ascending node, Gemini, Place of the descending node, Sagittarius, Motion of the nodes in longitude for 100 years. Retrograde motion of the nodes in 100 years, Place of the aphelion, Motion of the aphelion in longitude for 100 years, Mean distance of the planet from the sun, . Eccentiicity, ..... 46' 26" 35,112 miles. 4" 305d. 7h. 21' 8d. 9k 33' 12 57' 30" 12 57' 30" 26' 10" 57' 2i" ll s 17=> 42' 49" 10 23' 0" 1800,000,000 miles. 86,263,800 miles Six satellites, accompanying Herschel, have been dis- covered. u The most remarkable circumstance, " says Rees' Cy- clopaedia, u attending these satellites, is, that they move in a retrograde direction, and revolve in orbits nearly perpen- dicular to the ecliptic, contrary to the analogy of other satel- lites ; which phenomenon is extremely discouraging, when we attempt to form any hypotheses, relative to the original cause of the planetary motions." Satellites. Pex-iodical times. Distances from primary in miles. d. h. m. sec. 1 5 21 25 20 230,335 2 8 16 57 47 298,838 3 10 23 2 47 348,388 4 13 10 56 29 399,r,93 5 38 1 48 746,240 6 107 16 39 56 1597,708 * " The planet is denoted by this character as the initial of the name, the hori- zontal bar being crossed by a perpendicular line, forming a kind of cross, the emblem of Christianity ; denoting, perhaps, that its discovery was made in the Christian era." GENERAL JPLAWETABY TABX.TS. NAMES. Mean diam- eters in En- glish miles Mean distance from the sun ia round numbers. Mean di- ameter as seen from the SUH. Diuritii 1 rotation on axis. Milea. Miles. it d. h- m. s. The Sun, 883,246 25 15 16 Mercury, 3,180 37,000,000 16. 24 5 28 Venus, 7,687 68,000,000 23.3 23 20 59 Earth, 7,964 95,000,000 17.3 23 56 4 Moon, 2,180 95,000,000 4.7 Mars, 4,189 144,000,000 6. 24 40 m i " Vesta, 238 225,000,000 Juno, 1,425 252,000,000 Ceres, Pallas, 163) 1,024 \ 80) 2,099 J 263,000,000 265,000,000 Jupiter, 89,170 490,000,000 37.7 9 55 37 Saturn, 79,042 900,000,000 18. 10 16 Herschel, 35,112 1800,000,000 4. TABLE .Continued, NAMES. Inclination of orbits to ecliptic. Proportion al quantity of matter. Tropical revolution. O 1 -If y. d. h. ra. s. The Sun, 333928 Mercury, 7 1 0.1654 87 23 14 33 Venus, 2 23 32 0.8899 224 16 46 15 Earth, 1. 365 5 48 52 Moon, 593 0025 Mars, ' ' 1 51 4 0.0875 686 22 57 58 Festa, in 1801 7 8 46 3 60 4 Juno, 13 3 28 4 128 Ceres, 10 37 34 4 220 12 53 34 Pallas, 34 39 Jupiter, 1 18 51 312 1 11 314 8 41 3 Saturn, 2 29 35 97.76 29 162 11 30 Jerschel, 46 26 16.84 S3 305 7 21 ( 71 ) TABLE. Continued. NAMES. Sidereal revolution. Place of aphelion. Motion in on. of aphe. in lOOy; y. d. h. m, s. S. ' " o / // The Sun, Mercury, 87 23 15 44 8 14 44 17 1 33 45 Venus, 224 16 49 15 10 8 56 21 1 21 Earth, 365 6 9 12 9 9 48 52 1 43 20 Moon, 21 7 43 12 Mars, 686 23 30 35 5 2 51 12 1 51 40 in 1809 Vesta, 2 9 42 53 Juno, 7 29 49 33 in 1802 Ceres, 4 2 57 15 in 1802 Pallas, 4 224= 17 32 34 10 1 7 Jupiter, 11 314 22 19 6 11 32 1 34 33 Saturn, 29 167 21 8 29 31 42 1 50 7 Herschel, 84 8 9 33 11 17 42 49 1 28 TAB 1:35 Concluded. NAMES. Longitude of as- cending node. Motion of nodes in Ion. in lOOy. Retrogr. notion of nodes in lOOy. Eccentricity in English miles. S. o , o / // / // Miles. The Sun, Mercury, . j^j 1 16 14 50 1 12 10 11 22 7,557,630 Venus, 2 15 5 3 '51 40 31 52 473,100 Earth, 1,597,325 Moon, Mars, 1 18 12 24 45 S3 37 59 13,474,515 re-,, L ;;'*;.' 3 13 1 20,974,725 Juno, 5 21 G 37 63,241,920 1 Ceres, 2 21 6 f 21,410,830 I*.*, : V : 5 22 28 57 ' ' 65,269,500 JifpVer, 3 8 38 59 59 30 24 2 23,762,635 Safurrc, 3 22 9 48 52 35 30 57 50,958,399 Herschel, \ \2 12 57 30 26 10 57 22 86,263,800 ftL , - ^ . . _ . ' -. .^ - -.-- . ( 73 ) CHAPTER ZZ. PHENOMENA OF THE HEAVENS, AS SEEN FROM DIFFERENT PARTS OF THE SOLAR SYSTEM, SECTION /.-PROSPECT AT THE SUN. To a spectator at the centre of the system, the planets would appear to move in harmonious order from west to east. He would probably have no means of determining their several distances, but might suppose those farthest dis- tant, which are longest in performing a revolution. Unac- quainted with our method .of computing time, he would prob- ably take the period of Mercury, with which to compare the periods of the other plafiets. He would form a conjec- ture of the magnitude of different bodies, from their apparent diameters compared with the time of their revolutions. All would not appear to move in the same orbits ; but their paths would seem to cross each other at very small angles. If he should make the path of one of the planets a standard, the paths of all the rest would be inclined to it, one half being on one side, and the other half on the other side of the standard. As in equal times they describe equal areas, the spaces passed in a given time, in different parts of the orbits would be unequal, because the orbits are ellipti- cal. The apparent diameters would also vary a little at different times. All the stars would appear at rest, and equally distant. SECTION //.PROSPECT AT MERCURY. To a spectator at Mercury a different view would be pre- sented. Being by the whole of Mercury's orbit nearer to the other planets, at some times than at others, their appa- rent diameters would to him vary in proportion to their dis- 74 PHENOMENA OF THE HEAVENS, tances. They would all have conjunctions and oppositions. Their motions would appear sometimes direct ; sometimes retrograde. At intervals they would seem stationary. Such a spectator would probably have no idea of a succession of day and night ; unless Mercury revolve on its axis. SECTION ///.-PROSPECT AT THE EARTH. A still different view is presented at the earth. The in- ferior planets exhibit conjunctions, but no oppositions ; the superior, conjunctions and oppositions in succession. Here also'the planets seem to enlarge or diminish, as they are nearer or more remote ; the superior always appearing largest in the part of their orbits nearest the earth ; the in* ferior, by the position of their illuminated side assuming the phases of the moon. The appearance at the earth of looped curves in the mo- tion of the inferior planets round the sun, however ingenious- ly described and delineated by several astronomers, seems but the product of a fruitful imagination. If the motion of the sun round the earth were real, such would be the ap- pearance at the poles of the ecliptic and other distant sta- tions on lines, perpendicular to the plane of that circle. But at the earth, though the sun seems to go round-, such a phe- nomenon is incompatible with the powers of vision. Motion directly towards an observer or from him, is imperceptible, except by the apparent enlargement or diminution of the moving object. A planet, in such motion, seems stationary. When a planet crosses the line between the earth and sun in its inferior conjunction, or the same line produced in its superior, nothing but retrograde or direct motion appears. That motion of a planet, which is oblique to the earth, may be resolved into two constituent motions. That in a line with the earth %nd planet cannot be apparent at the former. The other will appear direct or retrograde among the fixed stars. OF THE PLANETARY MOTION. 75 SECTION /r.-PROSPECT AT JUPITER. At Jupiter it can scarcely be known, that there are in- ferior planets ; the greatest elongation of the earth not being more than 11 11' ; that of Mars not exceeding 17 IS'. SECTION F.-PROSPECT AT HERSCHEL. Could an inhabitant of this earth be transported to Her- schel, he would almost lose sight of the solar system. To eyes like ours, even assisted by glasses, probably Saturn is the only planet that can be seen at Herschel. The earth can never be more than 3 2' from the sun ; Mars 4 38' ; Jupiter 15 48'. But Saturn, having his greatest elongation 30, may often be seen, exhibiting, exclusive of his ring, the different phases of the moon. Next to the far distant and diminished sun, the satellites of Herschel must be the most luminous bodies in view. For aught we know, however, there may be planets in the system, still farther from the sun, and well known to the inhabitants of the Georgium Sidus. For Omnipotence is not bounded by our limited view. CHAPTER III. CAUSES OF THE PLANETARY MOTION. Projectile force is that, which impels a body in a right line, as the tangent of a circle. Centrifugal force is that, by which a body, revolving in an orbit, endeavours to recede from the centre. 76 CAUSfcS OF THE Centripetal force is that, which attracts a revolving body to the centre. NOTE. Centrifugal force differs from projectile, as a part from the whole ; being so much of projectile force, in circular motion, as carries the body directly from the centre. Matter is in itself inactive, and moves only as it is impel- led by external 'force. When an impulse is given & a body, it always moves in a right line, till a different impulse, not in direct opposition or coincidence, turns it out of its course, and gives it anew direction. This new direction will be in a diagonal, formed by the composition of the former motion, and that produced by the last impelling force. Suppose the body #, (Plate VI. Fig. 2.) at rest, impelled by a momen- tum, sufficient to carry the body from to J3, in a given time ; it would, uninterrupted, move from B to C, and from C to jD, equal distances in equal times. But, if at B it re- ceive an impulse in the direction B E, sufficient to carry it to .E, in the same time, that the former motion would carry it to C, it would move in the diagonal B F, and be found at F at the same time, that it would have arrived at C, un- affected by the latter impulse. [See Enfield's Philosophy, Book //, Ciiap. Ill, Prop. XIF.] Circular or elliptical motion must be produced, not only by an impulse in one direction, but by a continued action, forcing a body from a right line towards a centre. The planets all move in ellipses, differing, the orbits of the asteroids excepted, but little from circles. From the pro- jectile force, given by the Creator at their formation, and the constant force of gravity, they are kept in their orbits. Let the body w3, a planet, be projected along the line .#, jB, C, (Plate V. Fig. 6,) meeting with no resistance, it would forever retain the same velocity, and the same direction. For the force, which would carry it from Jl to 5, in a given time, would, in an equal time, carry it an equal distance from B to C, as in Plate VL Fig. 2. But, if at B it fall in- to the attraction of S, the sun, which should so balance the projectile force, as to carry it to E at the same time, that it PLANETARY MOTION. T Would, by its former motion, have arrived at C, the planet would now revolve in the circle B E F. But should the attraction of be more powerful in proportion to the projec- tile force, it might bring the planet to G instead of E, or be- ing still stronger, might carry it nearer the line B 8 in any given proportion. Suppose it carried to G, it would revolve in the ellipse, B G H. Before it arrives at G, and for some distance after, the lines of motion caused by the pro- jectile and centripetal forces form an acute angle. The two powers then conspire to augment each other's motion, and, attraction increasing as the squares of the distances de- crease, the motion of the planet would be accelerated all the way in going from B to H. At // it would be nearer the centre of attraction, than at B, by twice the eccentrici- ty of its orbit, and, being much more powerfully attracted, would be drawn to S, t were not the projectile force also in* creased. This would be now so augmented, that it would carry the planet from H to /, in the same time, that attrac- tion would bring it to K. It would, therefore, be found at L, and proceed to B, completing the revolution. In going from the perihelion to the aphelion, the planet is as much retarded in its motion by gravity, as it was accelerated in passing from the aphelion to the perihelion. At B, the projectile force is so far diminished, that the planet revolves again in the same orbit Thus it appears, " tnat bodies will move in all kinds of ellipses, whether long or short, if the spaces, they move in, be void of resistance. Only those, which move in the/ longer ellipses, have so much the less projectile force im- pressed upon them, in the higher parts of their orbits." Gravity in one part of an orbit operates as projectile force in another. Thus gravity at B becomes projectile force at Jlf. Though it produces but little by direct operation, yet it is immensely increased by oblique action all the way from. jBto M. A double projectile force will always balance a quadruple power of gravity. * 10 78 EQUATION OP TIME* If an angle be taken very small, the arch, the sine, and the tangent very nearly coincide ; the less the angle the nearer the coincidence. In such a case the versed sine may repre- sent the centripetal force, and the tangent, or the arch, to ex- treme nearness, the projectile. The larger the orbit is in which a planet moves, the great- er must the projectile force be in proportion to the centripe- tal In the motion of the earth round the sun, the former is to the latter about as 103 to 1. In the superior planets, and particularly in Hershel, the disproportion is still greater. To us it is inconceivable, that the attraction of the sun can have the least perceptible effect at Herschel,being 3,240, 000,000,000,000,000 times less than it is at one mile from the sun. We are, however, to remember, that the planets move in the expansum, where there is no resistance. That a small power would move an immensely large body, balanced in empty space, cannot be doubted. Take away attraction, and we know not but Archimedes might make good his asser- tion* by the force of his hand. However, that such immense bodies, and so immensely distant from each other, should all move in perfect harmony, may well excite the admira- tion of man ; but must be infinitely easy to Almighty Power, that at creation u spake and it was done." CHAPTER XV. EQUATION OF TIME. Time as measured by the sun differs from that of a well regulated clock or watch. At four times only in a year do the sun and such clock or watch coincide, viz. on the 14th day of April, the 15th of June, 31st of August, and the 23rd " Give me where I may stand, and I will move the earth " T .is was applied by the celebrated byracusan to the mechanical force of the lever, but may be true in tne case above contemplated, I EQUATION OP TIME, * 79 of December. The days of coincidence on account of longitude are not all the same in the United States as in Europe, The greatest difference happens about the first of November, when the sun is fast of clock 16 min. 14 sec. The inequality is owing to the elliptical figure of the earth's orbit, and the obliquity of the equator to the plane of the ecliptic. fVv^4- if^A The orbits of the planets being ellipses with the sun in the lower focus, the earth in its annual revolution moves more slow- ly in the aphelion than in the perihelion of its orbit, as has been shown. The motion on its axis being perfectly uniform, any gi' r en meridian will come round to the sun sooner at the aphelion than at the perihelion. Hence the solar day, at the former, will be shorter, and at the latter, longer, than that measured by the clock. Let Sbe. the sun, T the earth. AMP the earth's or- bit, (Plate VI, Fig. 4) ; A the aphelion, Pthe perihelion, the line M S the mean proportional between the semi-axes of the orbit ; the circle E m the equator, m the point where a meridian cuts the equator. Let A S a, M S n, P S p, be equal areas of the orbit. The arches of these, there- fore, by the great law of Kepler, represent the earth's mo- tion in equal times, as a solar day. It is evident, that the point m, wnenthe earth is at a, at n, or at p, must pass from m to the line T S, to complete a solar day. It is also evident, that it must pass farther when the earth is at p, than at a, the distance at n being a mean between the extremes A day therefore, as measured by the sun, will agree with a good time-keeper when the earth is at M. At P it will be longer, and at A shorter than the true day of the clock. This equation would cause the sun to be faster than the clock while the earth is passing from the aphelion to the pe- rihelion ; the difference increasing to the mean distance, when it would be at a maximum, and decreasing to the peri- helion, where the sun and clock would coincide. The sun would be slower than the clock while the earth passed the BO EQUATION OF TIME. other half of its orbit, the difference increasing to the mear* distance, and decreasing to the aphelion, where again the sun and clock would coincide. The maximum of this equation is 7' 43". The earth being in the" aphelion on the first day of July, and the perihelion on the last day of December, in the former part of the present century, the equation is nothing on those days. The obliquity of the equator to the ecliptic, produces a still greater inequality in the measurement of time. From either equinox to the succeeding solstice, the sun, on account of this obliquity, would be faster than the clock. From the solsfices to the equinoxes it would be slower. The vernal equinox happens about the 21st of March, the autumnal, the 23i\ of September ; the summer solstice, about the 21st of June, the winter, the 22d of December. This equation, when greatest, is about 9' 54". If a line were drawn from the sun to the earth, at the vernal or autumnal equinox, and the earth's axis were per- pendicular to such line, forming a tangent to the earth's orbit, the solar and sidereal days, this cause only considered, would be equal, except twice in a year. For any meridian would revolve from the sun to the sun again, in the time of perform- ing a complete revolution. On passing from the equinox, the axis, remaining parallel to itself, would cease to be perpen- dicular to the vector radius, or line drawn from the sun. - The declination would fast increase to the solstice, where the pole would pass the sun, which woula be on the opposite side of the earth till the next solstice. A day at the solstice would be equal to one day and a half of sidereal time. Let S< be the sun, (Plate VI. Fig. 5.) A B C D the earth in different parts of its orbit, a s the axis, lying in the plane of the ecliptic, and perpendicular to the vector radius, e q the equator, the circle 7 10 8 11 7 11 59 12 58 14 14 33 13 55 icy tfi 19 24 30 May 14 29 June 5 10 1 5 2 6 3 4 4 2 59 1 55 58 31 Sept. 3 6 9 12 15 18 01 5 1 2 2 3 1 4 3 6 5 6 8 7 11 29 Dec. 2 6 7 9 11 13 1C 11 8 9 59 8 45 7 53 6 59 6 3 5 6 4 8 March 4 8 12 15 19 22 25 28 11 53 10 55 9 50 8 59 7 48 6 53 5 57 5 1 15 20 24 29 July 4 11 26 4+ 1 9 2 3 1 3 57^ 5 3 ,, 24 27 30 Oct. 3 6 10 14 19 8 13 9 14 10 13 11 9 12 1 13 5 14 2 15 ! 17 19 21 1 96 28 30 3 9 2 10 1 10 10 1 {9+ 2 in 3 17 In the columns marked + the sun is slow of clock ; in those marked it is fast of clock. Therefore when the sig-< is -}-., the equation added brings the sun to. the clock; vv eu it is ,the equation subtracted brings the sun to the cl( k. * 1 .'.iost coucist tables of this kind, minutes only are inserted; but as it is ea- sj :n re .^tof our clocks and watches to make allowance for them, it was thought the seconds ought to have olace. CHAPTER V. PHENOMENA OF THE HARVEST MOON. The moon's mean motion in her orbit in each solar day of 4 hours, is 13 10' 35". But as the earth moves in the ecliptic at the same time 59' 8", the apparent motion of the sun, the moon^s motion from the sun is 12 11' 21". Any me- ridian of the earth in its diurnal rotation, moves this distance in 48' 38" of time. But as the moon is also moving, the meri- dian will not overtake her till 50' 28". At the equator, therefore, the moon rises about 50' 28" later, each succeeding day, at all seasons of the year. But in high latitudes it is very different. In those latitudes, farmers have long ob- served the early rising of the autumnal full moon. " In this instance," says Mr. Ferguson, u as in many others, discover- able by astronomy, the wisdom and beneficence of the Deity are conspicuous, who ordered the moon so as to bestow more or less light on all parts of the earth, as their several circum- stances and seasons render it more or less serviceable. About the equator, where there is no variety of seasons, and the weather changes seldom, and at stated times, moon light is not necessary for gathering in the produce of the ground ; and there the moon rises about 50 minutes later, every day or night, than on the former. In considerable distances from the equator, where the weather and seasons are mare uncertain, the autumnal full moons rise very soon after sunset, for sev- eral evenings together". At the polar circles, where the mild season is of short duration, the autumnal full moon rises at sunset, from the first to the third quarter." These phenomena are caused by the varied positions of the horizon and the moon's orbit. To avoid embarrassment in the explanation, the moon may be considered as moving in the ecliptic, and the obliquity of her orbit, as affecting the har- vest moon, afterwards considered. PHENOMENA F THE HARVEST MOON. 55 The plane of the ecliptic forms unequal angles with the horizon of any place on the earth at different parts of the day, and at different seasons of the year. When the sun enters Libra, about the 23d of September, the earth enters Aries. Then at any place irf north latitude, the angle between the horizon and the ecliptic is less about sun setting, than at any other time of day. The full moon, which happens about the autumnal equinox, being in that part of the ecliptic opposite the sun, must rise at this angle, in latitudes below the Arctic circle* There the angle, decreasing with the increase of latitude from the equator, vanishes. The diurnal motion of the moon in its orbit 13 10' 35" will make but little variation in the time of its rising on each succeeding evening, while it remains in this part of its orbit in all places, when the angle is small. Because the less the angle, the sooner the horizon will overtake the moon. For illustration, put small patches on the ecliptic of a terrestrial globe, each side of the first degree of Aries at 12 a 11' 21" from each other, that they may represent the moon's diurnal motion from the sun ; rectify the globe for the latitude of the place, suppose 45, and with the number of patches corresponding to the days of a week, bring the westernmost to^the eastern horizon, set the index of the hour circle, at the time of the moon's rising, found by calculation or a diary, on the evening nearest to three and a half days before her arrival at Aries, turn the globe westward, which will repre- sent the rotation of the horizon eastward, in relation to th$ moon, till the second patch comes to the horizon, and the in- dex will point at the time of the moon's rising on the succeeding evening. Bring the patches in succession to the horizon, and the index will show the time when the moon will rise oa each day for a week. The moon arrives at Aries, at the equinox, when the full happens at that time. But when the equinoctial full falls any number of days before or after the 23d of September, 11 - ' &* . : & . p * CV> 4 * L-$ - i *r 8t> PHENOMENA OP THE > multiply 59' 8" by the intervening days, the product reduced to degrees gives the moon's distance from the first of Aries at the full. Compute the time by the moon's diurnal motion. The arrival is later than the full preceding the equinox ; earlier, when the equinox precedes the full. These calcula- tions may be much more easily made, by taking a degree for each day, and rejecting odd minutes, both of time and motion. The arrival at the equinox may thus be ascertained with suf- ficient exactness. The number of patches may be increased or diminished at pleasure, and the rising exhibited for a longer or a shorter time. If the index be set at 12, when the first patch is brought to the horizrri, and the other patches be brought to that cir- cle in succession, the difference of time between the moon's rising on the several nights may be seen on the hour circlet The harvest moon may be more naturally represented by an artificial globe taken from the frame. Let a candle be placed on a stand to represent the sun, and the globe holden at a little distance west of the candle and on a level with it ; but the north pole so elevated, as to form an angle of 23 28' with the horizon. A small taper placed under the globe may represent the moon at the first quarter. The taper carried to the west of the globe, may represent her at the full in Aries. Placed over the globe it may show her situation in the last quarter. By turning the globe round, and observing when any place, as Washington, comes into the light of the taper in its different positions, you may see the appearance of the moon rising at that place. If the taper in its western position be moved slowly and circularly up, so as to make 12 at the globe, while the globe turns once round, and thus continued for several revolutions, nearly the exact ap- pearance of the harvest moon may be represented. When the moon rises with the least angle, it sets with the greatest ; and, when it rises with the greatest, it sets with the least. The time of rising at the full differs the most about the vernal equinox. w^m -^' ', '>- ''*.'' ^ & HARVEST MOON. ft ' .- The moon passes the same signs in every revolution ; but her rising with the least difference, always about the first of Aries, is seldom observed, except in autumn. In winter she enters Aries about the first quarter, and rising in the day time, is scarcely noticed ; about the change in spring, and be- ing with the sun, is not seen ; in summer, about the last quar- ter and rising near midnight, is not often observed. In the quotation from Mr. Ferguson, at the commence- ment of this article, it was stated, that u at the polar circles, the autumnal full moon rises at sunset from the first to the third quarter." This is not strictly true. At those circles, the moon rises about sunset at the first quarter, and after- wards at the end of each sidereal day nearly to the third. So that during that time it rises 3' 56" earlier on each succeeding '. Mr. Thomas, in his almanack for 1806, inserted *' Duration of total obscurity, 2%' " But in 1807, he corrected himself by a note at the end of his account of eclipses for that year. " The total obscurity of the sun, in the great eclipse of June 16, 1806, was observed to be much longer than given in this almanack, ivhich was on account of there being no allowance, made for the earth's diurnal or easterly motion at the time of the ob- scurity* The duration of obscurity was observed to be at Sterling, Mass. 4' 45"." In ascertaining the duration of total darkness, allowance must be made for the motion of the place of observation by the turning of the earth on its axis. Hence the duration is longest in an eclipse nearly or quite central, the sun and moon on or near the meridian, the motion of the observer and of the moon's shadow in the same or nearly the same direc- tion. The duration may be found by comparing the moon's hori- zontal parallax with her horary motion from the sun ; for, as the moon's horizontal parallax is to the semi-diameter of the earth ; so is the moon's horary motion from the sun, to the miles passed by the shadow at the earth. The sixtieth part of this is the distance passed on the earth's surface m 104 a minute. For though strictly it is the sine of the angle at ihe centre of the earth, in so short a distance the sine and arch may be taken as equal. A meridian on the earth, and, of course, an observer, passes from the sun one fourth part of a degree in a minute. Subtract this from the distance passed in the same time by the shadow, the difference is the motion of the shadow from the observer, allowance being made for obliquity in the motions. Hence, by knowing the miles passed in a minute and the breadth of the shadow, we may compute how long it will be in passing by a particular place. How the duration of total darkness, may be found geomet- rically in projecting solar eclipses, may be seen in the direc- tions for projecting the eclipse of July 18, 1860. May 11 3 20 A M 1828 1829 ) Sept. 13 1 36 A M 1830 >,' March 9 8 32 A M Visible in Missouri Territory. DjSept. 2 5 37 P M Total Mccn rises eclipsed. [Union. 1831 IG'j Feb. 12 35 P M Annular over a large southern section ef tile 1 > lAug. 23 4 67 AM! 100 ECLIPSES. xYear '| Month D. H. M. A.P. M. NOTA3STDA. 1832 1833 1 Feb. )uly Jan. 1 5 101 P M 27 7 34 A M 6 2 48 A M Visible in the western parts of the Union. D July 1 7 32 P M About total, D Dec. 26 4 30 P M Total. 1834 June 21 3 13 A M Total. v o v. 30 2 38 P M Dec* 15 11 50 P M 183.5 1836 ) May 1 3 6 A M e May Oct. is a 14 24 8 22 A M A M Visible in Missouri Territory. 1837 n oct: I* 6 29 P M Total. 1838 j) April 990 P M 1^5 Sept. 18 4 32 P M Annular in Virginia. 1839 18401 D 'Aug. 13 2 9 A M 1841 j Feb. 5 8 49 P M Total. D Aug. 2 4 49 A M Total. 1842 1843 > July Dec. 14 5 43 677 A M P M Visible at Astoria and other western regions. Very small. 1844 > j Nov. 24 6 51! P M Total. ?t)ec 9 4 19 P M Small. 1845 May 6 A M Sun rises a little eclip&ed 1 . Nov. 13 8 7 P M 1846 O April 26 6 PM 1847 1848 D ^ept. 13 1 23 A M Total. 1849 D March 8 7 48 P M 1850 1851 ) July 13 2 8 A M ^ July 28 8 11 A M 1852 D Jan. 713 A M Total. ) Dec. 26 A M Begins 6h. 28m. 185:5 D 'an. 21 1 3 A M Small. 1854 D Nov. 4 4 22 P M Very small. Visible in N. E. 1855 b May 1 11 6 P M Total. 1 J) Oct. 25 2 42 A M Total. 1856 ]> April 20 4 10 A M D Oct. 13 6 12 P M 1857 1858 1859 D Feb March J F.-b. J27 4 55 15 6 16 17 5 36 P M A M A M Moon rises partially eclipsed. Total. f"~tJT 1 29 5 44 P M Small. I860 4 Feb. 'uly 6 9 17 18 7 55 P M A M 1861 D Dec. 17 3 9 A M i ';ec. 31 7 45 A M 1862 D June 12 1 18 A M Total. )) Dec. 6 2 43 A M Total. 1863 D June 1 6 30| p M Total. Moon rises eclipsed, D Nov. 25 4 21 A M 1864 1865 D April DOct. OlOct. 10 11 29 4 5 50 19 10 27 P M P M A M Very small. Veiy small. 186C 3867 P (March > March 30 11 30 20 3 45 P M A M Total< ECLIPSES* 107 Tear 1 en Month D H. M. A.P.M NOTANDA. y [Sept. 13 7 30' P M 18fi8 1869 ) Jan. 27 8 ?1 P M 01 Aw, 765 P M Total over a southern section of the Union. 1870 1871 D Jan. 649 P M Moon rises partially eclipsed. 1872 D l\ov. 15 29 A M Very small. 187:3 ) May 12 6 23 A M Commences 4h. 34*. Total in the western states. 1874 y Oct. 125 2 37 A M Nearly total. 1875 5iSept. 29 6 12 A M 1876 1877 5| March 10 1 5 (&|Marcii25 4 45 YUug, 23 6 2 A M P M P M Small. Total. Moon rises eclipsed. 1878 n Feb. ;17 5 58 A M e July 29 5 35 P M \t/ D Aug. 12 7 3 P M 1879 188- Dec 31 7 42 A M 1881 5 June 12 1 56 A M Total. 188J D Oct. 16 2 8 A M 1884 D April 10 6 47 A M Total in the western parts of the Union. D Oct. 4 5 14 P M Visible and total after the sun sets. 1885 6 March 16 1 28 P M D Sept. '24 2 56 A M 1886 March 5 P M Commences about sun set. Visible in the wes- Aug. 29 6 23 A M Very small. [tern states. 1887 Feb. 854 A M 1888 J) Jan. 28 6 6 P M Total. D Julv 23 35 A M Total. 1889 @Jan. 1 P M Penumbra touches Washington about sun set, Visible in the western states. D Jan. 17 18 A M 1890 D Nov. 15 7 36 P M 1892 vlay 1 ! 6 P M Visible after the son sets, 1 Oct. 20 1 40 P M .189? 1894 D Sept. 14 11 24 P M 1895 D March 10 10 28 P M Total. D Sept. 4 49 A M Total. 189H 23 1 55 A M 1897 (^l-July 29 9 45 A VI 1898 D Jan. 7 7 16l P M Small. I Dec. 27 6 37 P M Total, 1899 D Dec. 16 8 34 P M 190ul0;May |28 8 40 A M It will be seen, that some eclipses are included in the pre- ceding catalogue, which are not visible at the Capitol. A few, however, visible, in distant parts, only are not inserted. f 108 ) SECTION II. SOME EXPLANATION OP THE TABLES USED IN CALCULATING ECLIPSES. The mean place and motion of a planet at any time, are what the place and motion of that planet would be, if its movement were uniform in a circle. A mean lunation is the time intervening between one change of the moon and another, calculated in mean motion The mean anomalies of the sun and moon, are their mean dis- tance from their respective apogees reckoned in degrees, minutes and seconds.* These anomalies must have been obtained at first by accu- rate observation at long intervals, and dividing between them. The sun's distance from the moon's ascending node must have been first found in the same manner. In these and other astronomical calculations, when the signs become 12 or more, 12 or a multiple of 12, are rejected, ^ and the remainder, if any, used as the true number ; because 12 signs complete a circle. The distance passed from the apogee and the moon's node, are always taken, and not the remaining distance, however small. TABLE I, contains the mean time of new moon, in March, the anomalies of the sun and moon, and the sun's distance r from the moon's ascending node for the present century. The year is begun in March, to avoid the inconvenience otherwise arising from bissextile. A year in this table includes two months of the succeeding year. The numbers for 1800 were taken from other tables, originally formed from observation.! * No inconvenience arises from some of these calculations being made on the supposition, that the sun moves round the earth, as he always appears in the ecliptic directly opposite to the earth. f These tables were calculated for the \merulian of the capital in Washington- city, Ion. 76 55' 30" 54'". W. of Greenwich; but may be used for any oth^r place, by applying the numbers in table 16 ; the table for changing longitude into time. EXPLANATION OP TABLES. 109 The numbers for succeeding years were formed by adding 12 lunations from table second and rejecting 365 days for a common year, and 366 for a leap year. But when the new moon in March happens before the 1 1th day of the month, 13 mean lunations were added. On the Gregorian princi- ple, the year 1900 was not considered bissextile. This table may be used for old stile, by deducting 12 days from the given time. If the days of the table in March be less than 12, a lunation with its annexed numbers must be added before the subtraction is made. TABLE II, contains 13 mean lunations. The exact time of one mean lunalion, the mean anomalies of the sun and moon, and the sun's mean distance from the moon's ascending node, are placed in the first line. These are doubled for two lu- nations. The succeeding numbers are formed by adding a lunation with its anomalies and distance from the node to the preceding numbers in each case. The half lunation is sub- joined for the purpose of calculating fulls. TABLE III, was formed by deducting the time of new moon in March, 1800, with its anomalies and distance from the node from the last new moon in March, 1900, with its annexed numbers. But one day was deducted from the new moon in March, 1900, from table second, as here it must be reckon- ed bissextile. By this deduction is obtained the difference for a complete century of Julian years. By adding, the ta- ble was carried to 5,000 years, and doubled for 10:000, a hi* nation being deducted, when the days exceed 29. Its application is in calculating eclipses for any time be* fore' or after the 19th century. It may be used for any number of thousand years. Suppose 6000 required ; add the numbers in the line against 1000 to those of 5000. By additions and multiplications, this table may be carried toany number of centuries at pleasure. T^BLE IV, contains the number of days passed from the first of March, at any time of the year. These four first tables would be sufficient for calculating eclipses at any time, if the motion of the planets were equa.- 14 llU ble. But this is not the case, as before shown. At thd apogee and perigee, the place of a heavenly body is the same, as if it moved in a circle ; the anomaly being nothing, or six signs, From the apogee to the perigee, the mean place is before the true ; it is after it, from the perigee to the apogee. When the sun's anomaly is less than six signs, the moon will come round to him sooner, than if the motion of the earth and moon were uniform ; later, when the anomaly exceeds si* signs. The greatest inequality, arising from this cause is 3h. 48m 28s. The sun is in apogee on the 1st day of July ; in perigee, on the 31st of December, at the present time, 1825. When the eartb is in its aphelion, the sun is in apo- gee The aphelion moves in the signs 1' 2" in a year ; of course the apogee moves the same. See motions of the earth ; see also the anomaly in Table 10. The moon's orbit is affected by her distance from the sun, being dilated in winter and contracted in summer. The lunations of winter are therefore longer than those of sum- mer. The extreme difference is 22tn> 29s. the lunations in- creasing in length, while the sun is passing from the apogee to the perigee ; and decreasing while he is returning to the apogee. These equations, arising from the same cause, are united in TABLE V, with the titles, add or subtract, TABLE VI, was formed to correct the moon's anomaly. The table of her anomaly is calculated for mean time, and as the time of change or full is altered by the sun's anomaly, it is necessary that her anomaly should be brought to the real time of change or full. If these phenomena happen earlier on account of the sun's anomaly, the moon will not have pass 1 - ed so far from her apogee, as at the mean time. If they happen later, she will have passed farther than at the mean time. The moon's orbit is more elliptical than that of the eartb. Her motion is so unequal, that she is sometimes in conjunc- tion with the sun, or in opposition, 9h. 47m. 54s. sooner or la.- terthan she would be by equable motion in a circle. The dif- ferences are placed ia TABLE VI!, with the directions, add or subtract. . - EXPLANATION OP TABLES. Ill TABLE VIII, is founded on the different attractions of the sun and earth, upon the moon at different distances. TABLE IX., is founded on the obliquity of the moon's orbit to the ecliptic. The principle is explained under equation of time. TABLE X, was formed for ascertaining the longitude and anomaly of the sun at any given time. These were calcula- ted for the meridian of the capitol in Washington, at the noon of the last day of December, 1799 ; which are set as the longitude and anomaly for the year 1800. By adding the longitude 11^ 29 45' 40" 4% and the anomaly, 11 29 44' 38" 24'" for each succeeding year of 365 days, and the same increased by a day, the longitude 59' 8" 19'" 47'% and the anomaly 59' 8' 9'" 36"", for bissextile, the table was carried to 1900 ; and afterwards copied to the nearest seconds. The noon of the first day of January might seem more proper than that of the last day of December. This table was so constructed at first ; but on trial, in taking for the days of the months, it was found inconvenient. For complete Julian years, the motion and anomaly in one year were taken, and carried by additions to complete the table. The use of this part of the table is in calculating the sun's longitude and anomaly for years before or after the nineteenth century. When the longitude and anomaly of the sun for years less than a century are taken, a requisite number of bissextile years must be included, or the motion for the days deficient, must be added. Without such addition they may not make the complete numbers, as may be seen by adding the num- bers for ten years to those of fifty. These will not com- plete the numbers for sixty without those of an additional day. The longitude and anomaly of the sun at the noon of the last day of a month are set at the beginning of each succeed- ing month ; eo that on the first day of a month the numbers for a day are to be taken. And for any time in a month, the 113 ECLIPSES. (II .^&3~ : longitude and anomaly are to be sought against the corres- ponding numbers in the table. But in using the table for months in bissextile years, a day less than the tabular time sought in January and February must be taken. Accordingly for the first day of January, the numbers for the last day of December preceding, must be used. The sun's mean motion from the moon's node for hours, minutes and seconds is annexed to this table, being frequently useful in the calculation of eclipses.* TABLE XI, is founded on the elliptical form of the earth's orbit, showing the difference between the mean and true place of the sun. It must be sufficiently obvious to those ac- quainted with the planetary motions. TABLE XII, shows the declination of the sun, or how far he is north or south of the equator at every degree of his lon- gitude. The principle may be easily understood by inspect- ing the ecliptic and equator, as represented on an artificial globe. TABLE Xllf, like table XI, is founded on the elliptical form t)f the earth's orbit. The rem iining tables will scarcely need explanation to those acquainted with the preceding, and the general princi- ples of astronomy ; except the table of proportional loga- rithms. TABLE XIX. Proportional Logarithms are artificial num- bers. They are deduced from common logarithms and ap- plied either to time or motion. The table may be of any extent according to the pleasure of the former. Dr. Bow- ditch's table of proportional logarithms is made for three hours. In this case the logarithm of the seconds in three * A table for finding the moon's longitude is found ir some astronomical works. But ?s this table is long, and its conections many and rather embarrassing to the student, its inseition here was thought incompatible with the design of this work The tables for the four equations used by Ferguson, tl give," as stated by Presi- dent Webber in his appendix to Enfield, " the times of new and full moon with liKlp trouble, and sufficient'y true for common use ; being rarely above one or (wo minutes wide of the truth " The tables for the 4 equations in this work are ex- tracted from Ferguson, or formed on his principle. EXPLANATION OF TABLES. hours, viz. 10800, is made the foundation of the table. The logarithm of this number is 4.03342 The logarithms of all the intermediate numbers from this number to nothing, being subtracted from this, leave the proportional logarithms set to the numbers. Thus to form the logarithm of 40 minutes, the common logarithm of 2400, the seconds in 40 minutes, viz. 3.38021 is deducted from 4.03342 ; the remainder 6532 is the logarithm of 40 minutes, the right hand figure being rejected. In Table XIX, 1 is made the foundation of the table. The seconds in one degree are 3600, of which the logarithm is 3.55630. From this logarithm the logarithm of each sec- ond from 1 to nothing is deducted. The remainders form the table. EXAMPLE. Required the proportional logarithm of 20 minutes, equal to 1200 seconds. From log. 1 3.55630 Take log. 20' 3.07918 Remainder is 47712 Rejecting the right hand figure, it is 4771. The numbers at the top of the table are minutes, those in the left hand column are seconds. To take the propor- tional logarithm for any number of minutes and seconds, find the minutes at the head of the table and the seconds in the column on the left hand ; against the seconds and under the minutes is the logarithm required. EXAMPLES. Numbers. Logarithms. 0' 25" 21584 1' 20' 16532 5' 10" 10649 40' 8" . 1746 55' 4" 373 To find the minutes and seconds answering to any given log- arithm ; look for the minutes at the head of the column, and 114 ECLIPSES. the seconds at the left hand. But if the logarithm he not ex- actly found in the table, take the minutes and seconds answer- ing to the next greater logarithm. EXAMPLES. Logarithms. Values. 7674 10' 15" 1233 45' 10" 5382 IT 22" 343 55' 26" Proportional logarithms are of great use in finding a fourth proportional. As in common logarithms, addition and subtrac- tion answer the purpose of multiplication and division in common numbers. Suppose it required to find how far a meridian of the earth passes from the sun in 35 seconds. As 4m. To 1 So 35s. To 8m. 45s. =8361 An important use of this table is the application of it i. astronomical calculations to other tables made for signs and degrees only. To take for minutes and seconds from a table thus made, find the difference between the numbers against the degree given and those against the degree next higher. Then by proportional logarithms, as one degree is to the dif- ference, so are the minutes, or minutes and seconds given, to the answer required, to be added or subtracted, as may be requisite. EXAMPLES. In calculating the solar eclipse of July, 1860, the sun's anomaly is s 15 55' 24'' for taking the first equation from Table V. Against 0* 15 are Ih. 3m. 36s. Subtract this from Ih. 7m. 45s. the numbers against s 16, the remainder is 4m. 9s. EXPLANATION OF TABLES, 115 As 60> To 4m. 9s. 11601 So 55' 24" 346 To 3m. 50s. =r:11947 This added to Ih. 3m. 36s. gives Ih. 7m. 26s. the true first equation. In the same solar eclipse, the moon's equated anomaly is 4 s 6 46', 14 ', the argument for the second equation in Table VII. Against 4< 6, the numbers are 7h. 33m. 36s. From this deduct 7h. 27m. 22s. the numbers against 4 s 7, the differ* nce is 6m. 14s. As ,60' To 6m. 14s. 9834 So 46' 14" To 4m. 48s. 10966 As the numbers are here lessening with the increase of de- grees, this 4m. 48s. must be subtracted from 7h. 33m. 36s. The remainder is 7h. 28m. 48s. the true equation. In questions where the fourth proportional would exceed 60 minutes, the limit of the table, divide the third number by 2, 3, 4, 10, or any convenient number, and multiply the fourth, when found, by such number, the product is the an- swer required. EXAMPLE. If the hourly motion of the moon in longitude be 32' 56", and the moon be 50' SO" from the first degree of Aries, in what time will it arrive at that point ? Taking one half the third term, the proportion will be, As 32 56" 2605 To 60m. So 25' 15' 3750 2605 To 46m, rr:1154 This doubled is Ih, 32m. the answer, 116 ECLIPSES. When two or all the terms exceed the limits of the table, divide all the terms by some convenient number, and multi- ply the fourth proportional by such number. EXAMPLE. If Mercury move 20' 28" in two hours, how far will it jnove in 3h. 20m. ? Dividing each of the terms by 4, the proportion is, As 30m. 3010 To 5' 7'' 10692 So 50ra. 792 11484 3010 To 8'31v =8474 This multiplied by 4, gives 34' 4//, the answer. The numbers at the head of the table may be used for degrees or hours and then those in the left hand column will be minutes. EXAMPLE. If 13 hours give 2 13', what will 22h. 23m. give ? As 13h. 6642 To 2 13' 14325 So 22h. 23m. 4282 18607 6642 To 3 49' 11965 This table may be applied to any numbers proceeding in sexagesimal order. STEW AND FULL MOdN* SECTION III. TO CALCULATE THE TRUE TIME OP NEW OR FULL MOON FOR ANY TIME IN THE 19TH CENTURY. For new moon, take the mean time of new moon in March, of the year proposed, the anomalies of the sun and moon, and the sun's mean distance from the moon's ascending node from table I. For any succeeding month, take as many lu- nations as the number of months, reckoning from March, with the anomalies and distance from the node, from table II. Add these together, the sum will be the mean time of new moon, the mean anomalies of the sun and moon and the sun's mean distance from the ascending node for the month requir- ed. Except, rarely, the number of lunations must exceed by one the number of months, a lunation being a little short of a month of 30 or 31 days. For the full moon in any month, half a lunation, the anoma- lies and distance, from table II, must be added to the num- bers of the change in that month. But if the change hap- pen after the 15th of the month, the half lunation must be subtracted. Rarely two changes or two fulls happen in a month. The number of days thus found must be sought in table IV, under the month. In the same line at the left hand will be the day of the mean change or full. But if the days added fall short of the intended month, another lunation with its attendant numbers must be taken. The day of the month thus found must be set before the hours, minutes, and sec- onds, the anomalies and distance from the node, before found. With the sun's anomaly enter table V, and take the first equation for reducing the mean syzygy to the true, making proportions for the odd minutes and seconds as directed in table XIX. Observe in this and other astronomical calcula- tions, if the signs be at the top, the degrees are at the left hand ; if at the bottom, the degrees are at the right. The 15 118 NEW AND FULL MOON. titles add and subtract must also be carefully observed in all the tables. With the sun's anomaly enter table VI, and take the equa- tion of the moon's mean anomaly, applying it according to the directions, add or subtract. Find the moon's equated anomaly in table VII, and take the second equation of the mean to the true syzygy. This will bring the time sufficiently near, when peculiar accura- cy is not required. But for calculating eclipses, subtract the moon's equated anomaly from the sun's mean anomaly. With the difference, as an argument, in table VIII, find the third equation of the time. With the sun's mean distance from the node, take the fourth equation from table IX. This will give the time very nearly as shewn by a well regulated clock. To make it agree with the sun, apply the equation for reducing true to apparent time, found in table XVIII. The use of the tables may be made familiar by a few ex- amples. EXAMPLE. Required the true time of new moon at Boston, in July, 1860. New moon ^'s anom. 4)'s anom. 1 {% from node D. 11 M. s S. ' /x l S. ' " ]S o , Time in March, 1860 Add four lunations 21 118 12 2 56 11! 12 8 19 30 7 3 26 25 17 23 55 501 1 21 30 46 3 13 16 21 4 2 40 56 Mean new nOon July First equation I 7 14 1 5o 7 90 26 15 55 24 -4 6 46 14 4 7 1 1 521 5 24 1 1 42 25 SBlSun from node Timo o-ice equ ttP(i Second equ^ti m +' l.'i 7 4 ! J 28 4j 8 9 9 101 4 6 46 14 48lAr[.3d equa.IArg2d.equ3 Argument for the 4th equi. Time twice equated Third eqaation I' 21 17 4 ii | 28 Hence the true astronomical apparent time, is July 17th day, at 21h. 39m. 46s ; in common teckomng, July 18th, at 9h. 39m. 46s. A. M). Time thrice rquated Fourth equation 17 -21 True new moon Fir difference of longitude 17 + 21 22 23 9 ? Tim* at Boston Equation uf time 17 -2! 45 5 35 49 Time at B. by sun 17 21 39 4GJ NEW AND PULL MOON. 119 TO CALCULATE THE TIME OF NEW OR PULL MOON IN ANY YEAR OF THE CHRISTIAN ERA BEFORE THE 19TH CENTURY. From table I, take the mean time of new moon in March, with the anomalies and distance from the node of a year of the same number in the century with that proposed. Then from table III, take as many centuries of years, with the annexed numbers, as will reduce the year in the 19th centu- ry to the year required. Subtract these from the preceding numbers, the remainder will be the mean time of new moon in March, the anomalies and distance from the node for the proposed year. If the time set to March, of the year in the 19th century be less than the time in the centuries of years taken, a lunation from table II, with the annexed numbers must be added to the time in March. Then subtract as be- fore directed. The remaining process is the same, as in cal- culating the true time of change or full in the 19th century. In most calculations for years before or after the 19th cen- tury, the old stile is to be preferred, on account of its uni- formity. It may be reduced to the new by the subsequent rules in this work. EXAMPLE. Required the true time of full moon at Plymouth, Mass. in December, 1620, old stile. New moon M. S. 35 8 21 44 Sun's anom. 0's duoma ^Jfrom node D, H. S. / // S. / //_ fj t o . / // Time in March at W. 1820. Deduct two centuries 13 8 20 16 8 12 ! 6 21 12 38 12 6 24 5 37 21 43 27 11 9 19 35 8 54 46 46 Time in March, 1620 Add ten lunations 5 295 4 7 13 20 24 30 8 5 9 21 43 3 13 1 23 8 18 53 54 10 4 2 10 T>~ 10 41 6 42 77~2T 15 20 19 Ti 7 Time in Dec. 12d. deducted Add <| lunation [lor stile 13 14 11 18 33" 54i 5 26 22- 21 14 46 13 33 10 10 12 6 12 3 58 54 30 Mean full moon i 28 j First equation | -f- 5 55 60 561 6 11 171-4 25 19 231 4 24 17 281+ 58 28 19 1 2 43 26 Time once equated Second equation 28 b 5 46 13 13 43 1 16 1 55| 4 25 17 28| Hence the true time at Plymouth, by 21s.; in civil calendar, 29th day Oh.23m. 21s. in the morning. Time twice equated Third equation 28 11 59 56 26| Time thrice equated Fourth equation 28 11 i'B 1 3d 25 Time 4 times equated Add for difference ol Ion. 1 11 57 25 55 26 Time of full moon at Plynv) i8 12 93 21 120 NEW AND FULL MOON. TO CALCULATE THE TRUE TIME OF NEW OR FULL IN ANY TEAR BEFORE THE CHRISTIAN ERA. Find the time of new moon in March, of the year in the 19th century, which added to the year before Christ, dimin- ished by one, will make complete centuries. Subtract the 1 numbers for those centuries, taken from table III, and pro- ceed as in the other precepts. EXAMPLE. Required the true time, in Julian calendar, of new moon in September of the year, that Cadmus brought the letters into Greece, allowing that event to have been in the year before Christ, 1493. Now SViOon (2)' a anoma. 's anomaly {)fomnod D, H. M S S. ' " S. ' " Mean time in March, O. Add one lunation [1800 14 7 55 37 8 24 45 42 29 12 44 3| 23 619 11 13 44 J8 25 49 4 10 21 23 1 40 14 Deduct for 3300 years 43 20 39 40 25 3 2 29 9 23 52 1 11 23 & 1 O 9 33 18 1 13 40 59 5 11 1 37 5 9 22 46 Mean time in March, H. C Ald 6 lunations [1493 }H 17 37 11 177 4 24 18 10 47 5 24 37 56 JO 25 52 19)0 1 38 51 5 4 54 316 4 1 24 Mean time in September First equation 11 22 I 29 3 48 41 3 25 24 561 4 46 22 -3 29 19 42! 1 26 40 6 5 40 15 Time once equated Second equation 11 10 12 48111 26 5 14 -f 8 12 431 3 29 19 42 Tiaie twice equated T'lird equation 12 2 25 31 4- 020 Hence the true time of new moon in September, of that year, at the meri- an of Washington, was 12th day, 2h. 26ra. 10s. P. M. Time three times equated Fomth equation 12 2 25 51 -f 19 Tnif time by clock 12 2 26 10 I TO CALCULATE THE TRUE TIME OF NEW OR FULL MOON 1JJ ANY YEAR AFTER THE 19TH CENTURY. To the mean new moon in March, of the correspondent year in the 1 9th century, add the requisite numbers for the centuries intervening, from Table III, and proceed as before ; observing to subtract a lunation, should the addition carry the new moon beyond the 31st of March. Except, when the time sought is after March, one lunation less may be added, instead of the subtraction. JfEW AND FULL MOON. 121 EXAMPLE. Required the true time of full moon at New Orleans, in July, 1876. New moon \%'s anom. ($'s ar. nn.i. po^j D. H. fo. S.,S. ' " S. ' ft Mean new O ' n March, 1876 Add r or one century 24 13 4 8 22 21 18 10 52|0 *~l 21 401 3 19 6 8 y 15 39 ; I 14 44 1 4 " irt 2 27 23 Xefti tiivc in March, 1976-f- Adfl 4 -unations \ 1 day for stile 29 21 118 2 33 13 8 56 1213 25 2;". 40 46 25 17 11 3 21 13 584 2|4 44 9 40 56 Mean Mine in .luly Deduct % lunation" 26 14 18 29 25JO 22 210 H 6 31 3 23 10! 6 4 i? $4 soio :;'. 15 25 5 20 7 'Wan lull moon First equation 11 6 7 23 31 48 8 7 21 32 531 8 21 10 171 22 i-J 30 I 8 11 4 68J ! Time once equated Second equation 11 5 9 35 3513 34 401 16 22 36 8 21 10 Irl Time twice equated T ; iid equation 10 20 55 4 45 Time three times equated Fourth equation 10 19 56 10 1 Timr four times equated Deduct far difference of Ion. 10 19 5710 52 50 True time at New Orleans 10 19 4 201 SECTION IV. TO CALCULATE THE TRUE PLACE OF THE SUN AT ANY TIME IN THE 1$TH CENTURY. From Table X, take the mean longitude and anomaly for the year, month, day, hour, minute, and second, required ; then equate the longitude by the numbers found in Table XI, having the anomaly as an argument, and it will be the true place of the sun for the time. For any time in the Christian era before the Wth century, find the longitude and anomaly for the corresponding time in the 19th century, and deduct the longitude and anomaly set against the intervening centuries. But for time long past the old stile is to be preferred. Add the longitude And anom- aly for 12 days to those of the year sought in the 19th centu- ry, the sum will be the longitude and anomaly at the com- NEW AND FULL MOON, mencement of the year, old stile. Then proceed as before directed. For any time before the Christian era, find the longitude and anomaly of the year in the 19th century, which added to the year before Christ, minus 1, will make complete centuries. Deduct the longitude and anomaly for the centuries ; and proceed as before. For any time after the 19th century ; find the longitude and anomaly for the corresponding time in the 19th century, al- lowing for stile, and add for the intervening centuries, proceed as before. EXAMPLES. Required the sun's longitude and anomaly, July 17, 1860, at 21h. 22m. 9s. 1860 July Days 17 Hours 21 Minutes 22 Seconds 9 Mean longitude of sun Equation of sun's centre True longitude of sun Longitude. Anomaly, s o ////// //// 8 / // /// W/j 9 10 34 42 5 28 24 8 16 43 22 51 44 47 54 12 38 22 11 6 9 39 5 28 23 37 16 45 19 51 44 47 54 12 38 22 11 3 26 36 51 21 49 - 31 36 16 11 14 21 49 Anomaly. 3 28 5 15 21 49 Allowing that Alfred's reign closed Oct. 28, old stile, A. D. 900, what was the sun's longitude and anomaly ? 1800 Add for 12 days 1800, O. S. Deduct for nine centuries Longitude and anomaly in 900 October Days 28 Mean longitude and anomaly Equation of the sun's centre True longitude Longitude. Anomaly. S I " s ' " 9 10 7 13 11 49 40 6 44 12 11 49 38 9 21 56 53 6 52 14 6 12 33 50 11 21 21 36 9 15 4 39 8 29 4 54 27 35 53 6 21 12 14 8 29 4 8 27 35 48 7 11 45 26 - 1 18 48 7 10 26 38 4 17 52 10 Anomaly i NEW AND FULL MOON. 12S What was the longitude and anomaly of the sun, March 0, 0. S. in the year, that the Children of Israel removed from Egypt, before Christ, 1491 ? 1510 Add for 12 days 1810, O. S. Deduct for 3300 Commencement of they earB. C.I 491, March Days 20 Mean longitude and anomaly Equation of the sun's centre True longitude Longitude. 9 9 42 14 11 49 40 Anomaly. 6 8 53 11 49 38 9 21 31 54! 6~lT~58 31 25 11 32' 10 28 19 12 8 26 20 221 7 13 39 T9 1 28 9 11 1 28 9 1 19 42 471 19 42 43 11 14 12 20110 1 31 + 1 37 30| Anomaly 11 15 49 50l Required the true longitude and anomaly of the sun, April , 1924, at 9h. 42m. 17s. A. M. 1824 Deduct 1 day for stile Add for 1 century Commencement of 1024 April Days 11 Hours 21 Minutes 42 Seconds 17 ' Mean long, and anomaly Equation True longitude Longitude. Anomaly. g O / // /// //// s o / // /// //// 9 10 18 13 59 8 19 47 6 30 23 59 8 9 36 9 9 19 4 40 13 45 48 5 29 31 14 50 24 11 29 2 24 9 10 4 52 40 13 2 28 42 30 10 50 32 51 44 47 1 43 29 34 4i 53 5 28 33 38 50 24 2 28 42 14 10 50 30 51 44 47 1 43 29 34 41 53 20 31 23 38 40 -f 1 53 50 9 8 59 51 48 51 Anomaly. 22 25 13 38 40 This and other examples of the 20th century, may be worked by taking the longitude and anomaly for 1900 with the additional time. Table X, ought to be made familiar, mistakes being like- ly to happen without peculiar care. 124 NEW AND FULL MOON. * If the sun's longitude be required for any time at a place east or west of the meridian of Washington, the sun's motion in longitude for the difference in time must be applied. For east, subtract ; for west, add. Supqose the sun's longitude be sought at any time for a place 15 east of Washington, find for the time at Washington, and" deduct 2 f '2T 51", the motion of the sun for one hour. For a place 15 west, add the hour's motion. Proceed in the same manner for a longer or a shorter time. TO CALCULATE THE TRUE DISTANCE OF THE SUN FROM THE MOON'S ASCENDING NODE. This being the argument for the 4th equation in the syzy- gies. is taken into the examples for ascertaining the true time of new and full moon. The descending node is six signs from the ascending. If the distance at the change or full be less than the ecliptic limit, (see page 96,) an eclipse may be expected. But if the true time of conjunction or opposition be different from the mean, the sun's motion from the node for the difference found in Table X, must be applied. When the true time is later than the mean time, the mo- tion for the difference must be added ; when the true time is earlier than the mean ; the motion for the difference must be subtracted. The distance must then be equated by Table XIII. The true time of new moon, in July I860, will be 6h. 25m. 39s. later than the mean time. The sun's mean distance from the node in the example is 5 s 24 11' 42" Add for 6 hours 15' 35" 25m. - 1' 4" 55'" . . - :*;-'.;*'' ^' - - 1" 41"' 16//// Mean distance from the node at true new moon, -/ 5 s 24 2S' 23" 36"' 16' Equation, Oo 34/ True distance of the sun from the / ascending node, - - ' 5 s 2$ 54' 23" 36'" 16 PROJECTION OP ECLIPSES, ~\ '..7*^ SECTION V. TO PROJECT AN ECLIPSE OP THE SUJT. ELEMENTS NECESSARY. t. True apparent time of conjunction of the sun and moon. 2. The semi-diameter of the earth's disk, as seen from the moon, equal to the moon's horizontal parallax. 3. Sun's distance from the nearest solstice. 4. Declination of the sun. 5. Angle of the moon's path with the ecliptic. 6. Latitude of the moon. 7. Horary motion of the moon from the sun. 8. Semi-diameter of the sun. 9. Semi-diameter of the moon. 10. Serai-diameter of the penumbra. To find these elements for an eclipse ; and as an example, for the eclipse in July, 1860, at Boston. 1. The true apparent time of conjunction of the sun and moon for Boston at that time, is found by the example in page 118, to be 17d. 21h. 39m. 46s. viz. in civil time, 18d. 9h. 39m. 46s. A. M. ^ 2. To find the moon's horizontal parallax^ With the moon's anomaly as an argument efcter table XV, and making proportions, the table being foripied to every sixth degree only, find the horizontal parallax of the moon. This at the time of the eclipse in July, 1860, will be 59' 24,/. 3. To find the sun's distance from the nearest solstice. The summer solstice is 3. signs ; the winter 9 signs from the 1 of Aries. To find the sun's distance from either, at any time, find his longitude in table X, and by that, his dis- tance from the solstice to which he is ,nearest. When the longitude is less than 3 signs, or more than 6 and less than 9 ? subtract the longitude from the solstice. When the longi- tude is more than three signs, and less than 6, or more than 9, subtract the solstice from the longitude. The sun's truo longitude at the time of the eclipse in July, 1860, is found to be 3 s 26 5' 15". From this if 3 s be subtracted, the re- IB / / . ff // 126 PROJECTION OP ECLIPSES. mainder is 26 5' 15", which is the sun's distance from the summer solstice. 4 To find the declination of the sun. With his true longitude, found in table X, as an argument, find his declination in table XII. This at the time of the eclipse to be calculated will be 20 57' 20''. 5. To find the angle of the moon's path with the ecliptic. With the anomalies of the sun and moon, find their respec- tive horary motions in table XV. Subtract the horary- motion of the sun from that of the moon. Seek and note the difference in table XVII. Take the signs and degrees of the sun's true distance from the node as an argument. Against the degrees and under the difference of horary motion will be the angle of the moon's path with the ecliptic. This at the time of the eclipse to be projected will be 5 39'.* 6. To find the latitude of the moon. With the argument, the moon's equated distance from the node, equal to the sun's, find this in table XIV. This at the ecltpse will be 3V 55". 7. To find the horary motion of the moon from the sun. With the anomalies of each separately, find their horary motions in table XV, as before directed. Subtract the sun's from that of the moon. The difference is the horary motion of the moon from the sun. This at the eclipse will be 33' 25". 8. To find the semi-diameter of the sun. With the argument, the anomaly of the sun, find his semi- diameter in table XV. At the eclipse this will be* 15' 51". 9. To find the semi-diameter of the moon. With her anomaly, her semi-diameter is found in table XV, For the eclirse this will be 16' 15". 10. To find the semi-diameter of the penumbra. Add together the semi-diameters of the sun and moon, the * Mr. Ferguson says that. 5 35' may be always rated as the angle of the mooa's path with the ecliptic, without any sensible error. PROJECTION OF ECLIPSES. 127 sum is the semi-diameter of the penumbra. For the eclipse 15 51"-fl6 15/, = 32'6',. These elements collected, as they always should be for convenient use, are ; 1. Apparent time of new moon in July, I860, - 18d. 9h. 39m. 46s. A. M. 2. The moon's horizontal parallax, - , - * - - - 59' 24" 3. Distance of the sun from the summer solstice, , - 26 5' 15" 4. Declination of the sun, - - - - - - - 20 57/ 20" 6. Angle of the moon's path with the ecliptic, 5 39' 6. Latitude of the moon, north descending, - 7. Horary motion of the moon from the sun, - 8. Semi-diameter of the sun, - - - < .. 9. Semi-diameter of the moon, - } '$-...,^ :*>._ \ t ~< 10. Semi-diameter of the penumbra, ' " , " TO PROJECT THI'S ECLIPSE GEOMETRICALLY. From an accurate diagonal scale, or a scale made for the purpose of any convenient length, take as many parts, as the moon's horizontal parallax contains minutes of a degree. With this distance as a radius describe the semi-circle A M JB, (Plate IX. Fig. 1.*) Upon the centre, C, raise the per- pendicular C D. Then will A C B represent a part of the ecliptic ; C D its axis ; and D will bisect the semi-circle into two equal parts, each a quadrant f Divide one of these, as B D, into 9 equal parts, and subdivide into degrees, ma- king the quadrant 90. Take the chord of 23} of these in your dividers, and set from D each way to E and F, and draw the line E H F. With H E or H F, as a radius, and one foot of the dividers in /f, describe the semi-circle E G F, extend the line C D to G. Divide the quadrant E G into 9 equal parts, the earth's axis being on the left hand, and sub- divide it into degrees. When the sun is in Aries, Taurus, * The. plane scale on the opposite side of Gunter, when very accurate, maybe used, in taking the parts for this sweep, or the semi circle may be first drawn, and the radius divided into a number of parts equal to the moon's horizontal parallax. Great accuracy in the scale is of first importance. f A sector is convenient for projecting eclipses. This however being, in the hands of but few, it was thought proper to show the operation by the much more common instruments, 'the scale and divider*. Those acquainted with the sector will easily apply its use. 12$ PROJECTION OP ECLIPSES. Gemini, of Capricornus, Aquarius, Pisces, the northern half of the earth's axis is on the right hand of the axis of the ecliptic ; when the sun is in the other six signs, it is on the left ; or, from the winter to the summer solstice, it is on the right hand ; from the summer to the winter solstice it is on the left. Take the sine of the sun's distance from the solstice, 26 5' 15", guessing at the minutes and seconds, as the line g /i, and set it from HtoPon the line E H. P will repre- sent the north pole of the earth, on the 18th of July, 1860. Draw the line C P for the semi-axis of the earth. Subtract the sun's declination from the latitude of the place, the sine of the remainder taken from the graduated quadrant B D, and set upon the axis C P, will be the distance of the place from the ecliptic on the noon of the day., when the eclipse happens; thus 42 23' 20 57' 20" = 21 25' 40". The sine of this is the line a 6, which on the line C P will extend from C to i. Add the decimation to the latitude, the sum taken as a sine, c d, from the same graduated quad- rant, B Z), and set on the axis C P, or on the same produced if necessary beyond P, will extend from C to the position of the place at midnight of the same day, 42 23' -f 20 57' 20"= 63 20' 20" will extend from C to j on the axis : j is the point passed by Boston at midnight of July 18th, 1860. Bisect i j at k. Take the co-sine of the latitude of the place from the quadrant J5 D ; 90 42 23' = 47 37', = e f and set each way from k to VI and F/, connecting these with a straight line perpendicular to C P. F/and F/will be in the margin of the disk at the equinoxes, but at no other time. With the distance k VI draw the semi-circle VI 12 VL Di- vide each quadrant into six equal parts, and mark it 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, as in the diagram. From the points of division draw lines parallel to the axis C P to the line VI k F/for hour lines. The semi-circle should be sub-divided into quarters or minutes, and lines drawn parallel to the hour lines. These are best done with the foot of the dividers, and may, or may not, be dotted as in the example. With the exent k i draw the quadrant i I. Lay a ruler fronT A; to the PROJECTION OF ECLIPSES. several divisions on the external quadrant, 12 F/, and where it cuts the quadrant i I mark, and thus divide it into six equal parts. Or it may be divided by stepping the dividers. Through the points of division in the small quadrant, draw lines parallel to the line VI k VI, till they intersect the^ hour lines on each side of the axis. Through the points, where these lines meet the hour lines, 6, 7, &e. from F/, on one side to FT, on the other, draw with a pen or pen- cil an elliptic curve. This will represent the path of the place over the earth's disk, as seen from the moon on the day of the eclipse. When the sun is in south declination, the elliptic curve, representing the path of the place, must be drawn on the upper side of the line VI k VI. The order must be reversed in drawing for places in the south latitude. The ellipse representing the path of the place on the earth's disk may be more easily, and perhaps more elegantly delineated by considering VI k VI as the transverse, and i j as the conjugate. The mean proportional between the sum and difference of these is the distance of the foci. At the place of the hours, however, unless drawn with great attention, it might not be so accurate, as the method used in the diagram. Set the degrees and minutes in the angle of the moon's path with the ecliptic, 5 39', from D to M, her latitude being north descending. Draw the line C M for the axis of the moon's orbit. When the moon's latitude is north or south ascending, the axis of her orbit must be represented on the left hand of the axis of the ecliptic ; but when her lat- itude is north or south descending, the axis of her orbit must be on the right hand of the axis of the ecliptic. Bisect the angle D CM by the line Cm. Take the moon's latitude SI' 55" from your scale, and set it from the line A C Bio n on the bisecting line C w, as the line n o parallel to C D. Through n at right angles to the axis C M draw JV O for the path of the moon's shadow over the earth at the time of the eclipse. Take from your scale the moon's horary motion from the sun 33' 25", and making it equal to Q #, (Plate IX. Fig. 2.) 130 PROJECTION OF ECLIPSES-. divide it into 60 equal parts for minutes ; or it may be divided^ into larger parts of two, three, five, or ten minutes each, at pleasure. Set the true time of new moon on the line JV at rc, where it intersect the line C m. Then from Q /, the ]ine of horary motion, take the minutes and seconds passed after the hour preceding the conjunction, and set them from w, backwards on the path of the shadow towards JV. Thus 39m. 46s. will extend from n to IX. on that path. Take the whole extent of Q 72, and set it each way from /.Y, to the different hour marks as on the line JV O. The marks will show the centre of the moon's shadow at the times specified. The spaces may be subdivided into quarters, five minutes,' or minutes, as may be convenient. Apply the side of a square to the path of the moon's shadow, and, as you move it along;, observe, when the other side cuts the same time in that path and in the path of the place over the earth's disk. This time is the instant of greatest obscu- ration. From the scale take the sun's semi-diameter, and setting one foot of the dividers in the path of the place at the point of greatest obscuration, draw a circle to represent the sun, as seen at the centre of the eclipse. With the moon's semi-diameter, taken from the scale, as a radius, make a circle on the path of her shadow, the centre at the point, where the centre of her shadow is at the greatest obscuration, representing her disk at the same time. The circle of the moon being shaded with ink or paint, the appearance of the sun at the centre of the eclipse will be represented. The part only of the sun covered by the moon may be shaded, if preferred. ^ From the scale take the semi-diameter of the penumbra, and setting one foot of the dividers backwards, on the path of the shadow, JV O, the other on the path of the place, observe when each is at the same instant. Note this is as the beginning of the eclipse. With the dividers at the same e xtent, and one foot in each path, after the greatest obscura- tion, note the point, where each is at the same instant by the marks, as the end of the eclipse. Thus we find that the PROJECTION OF ECLIPSES. 131 eclipse of July 18th, 1860, at Boston, beginning at 7bu 22m. middle Sh. 28m. end 9h. 37m. A. M. With a ruler laid over the centres of the sun and moon, as represented, draw the diameter of the sun's disk, and divide it into 12 equal parts. The number of these within the moon's disk, are the digits eclipsed. IViost of this operation supposes the projector ,to stand at the moon, or in the ecliptic opposite, looking down upon the earth. To find the duration of complete darkness in a total eclipse of the sun, subtract the apparent semi-diameter of the sun trom that of the moon, take in the dividers the minutes of the difference from the scale, making allowance for seconds ; place one foot of the dividers in the path of the moon's shadow, the other in the path of the place, and pro- ceed in the same manner in finding the beginning and enjl of total darkness, as in finding the beginning and end of the eclipse by the semi-diameter of the penumbra. - , SECTION VI. PROJECTION OP LUNAR ECLIPSES. By page 96, we find, that when the moon is within about 11 of either of her nodes, she may be eclipsed. The elements for projecting a lunar eclipse are 8. 1. The true time of full moon. 2. The moon's horizontal parallax. 3. The sun's semi-diameter. 4. The moon's semi-diameter. 5. The semi diameter of the earth's shadow at the moon. 6. The moon's latitude. 7. The angle of the moon's visible path with the ecliptic. 8. The moon's horary motion from the sun. , 1. -To find the true time of full moon, see preceding di- rections, page 117. All the other elements for projecting a lunar eclipse, may be found by the directions for the same in solar eclipses, except the fifth. tn 13& PROJECTION OP ECLIPSES* To find the semi-diameter of the earth's shadow at the moon, add the horizontal parallax of the moon to that of the sun ; from the sum subtract the apparent semi-diameter of the sun. The eclipse of the moon in November, 1808, as seen at the Capitol, is represented in the following delineation, for an example of lunar projection. (Plate VII I. Fig. I.) The student, who acquaints himself with the course of the moon, and with the tables, will be able to vary the position of the axis, so as to project other eclipses of the moon from this example. The axis of the moon's orbit is usually placed as in solar eclipses, and when the moon is in south latitude, her course is marked from the right to the left, considering the upper part of the plate north. The representation, however, would correspond better to the real appearance, if, when the moon is south descending, the axis of her orbit be laid on the left hand, when she is south ascending, on the right ; and her path marked from the left to the right. At the time of full moon, in November, 1808, the sun's anomaly was 4 s 3 3' 6" ; the moon's, 11 s 27 21' 51" ; the sun's equated distance from the moon's ascending node 11 s 28 25' 53". To this, if 6 signs be added, it gives the moon's place 5 s 28 25' 53", bringing her within 1 34' 7// of her de- scending node. ELEMENTS. 1. True apparent time of full moon, - 'V . . - 3d. 3h. 22m, 5s. 2. The moon's horizontal parallax, ... - 54' 30" 3. The sun's semi-diameter, 16/ 15" 4. The moon's semi-diameter, ..... 14/ 54" 5. The semi-diameter of the earth's shadow at the moon, 38' 24 // 6. The moon's latitude, 8' 14" north des> 7. The angle of the moon's Hsible path, - - 5 45' 8. The moon's horary motion from the sun, - - - 27/ 40" Draw the line A C B at random, (Plate Fill. Fig. I.) From a diagonal scale, or a scale made for the purpose, take as many parts, as the moon's semi-diameter added to the semi-diameter of the earth's shadow, at the moon, contain? PROJECTION OP ECLIPSES. 133 minutes of a degree, 14' 54" + SS' 24" = 53' 18". With this extent draw the semi-circle, A D B, above the line A C #, the moon's latitude being north. For south latitude, the semi-circle must be drawn on the other side. When it may be necessary for representing the whole eclipse, a seg- ment greater than a semi-circle may be drawn, and the figure extended, as in the diagram to I K and i k. Divide one quadrant of this into degrees. Take D M, 5 45', the angle of the moon's visible path, and draw the line C M for the axis of the moon's orbit, on the right hand, the latitude of the moon being north descending. With the semi-diameter of the earth's shadow at the moon, 38' 24", from the centre C draw the semi-circle c d e, for the northern half of that shadow. Bisect D M in a, and draw the occult line, C a. Set the moon's latitude, 8' 14", perpendicularly from the line A C B to b on the line C a. Through b and perpendic- ular to the axis C JMT, dra*v the line E F for the* path of the moon through the earth's shadow. Make the line G H 9 Fig. 2j equal to the horary motion of the moon from the sun, and divide it into 60 equal parts for minutes. Or it may be divided into larger parts of 3, 5, or 10 minutes each. Place the true time of full moon at b where the .line E F intersects the line C a ; and set 22 minutes, taken from the line, G backward on the line E F from b to in. With the whole line, G //, mark the line, E F, each way from in. The dots at i, n, in, iv, v, show the moon's place at those hours. The spaces between the hour marks may be divided into minutes, or five minutes, as may be thought requisite. With the semi-diafdfcler of the moon as a radius, draw circles at/,^, and /i. -f will represent the moon's place at the beginning, g at the middle, and h at the end of the eclipse. The disk of the moon, like 'that of the sun, may be divided into 12 equal parts for dig'y^ and the amount of the eclipse ascertained. Where gre*|f accuracy is required, each digit may be divided into 6(^gual parts for minutes. Plate IX, Fig. 3 ano4, are projections of the lunar eclipse, as seen at the Capitol, January 16, 1824. It will appear, 17 134 DIVISIONS OP TIME. that the result is the same, in the different positions, in which the axis of the moon's orbit is placed. Figure 3 is deline- ated in the* manner common in such projection. But, without doubt, figure 4 best represents the true appearance. CHAPTER VIII. DIVISIONS OF TIME. Time, as measured by the heavenly bodies, is divided inta periods, cycles, years, months, weeks, days, hours, minutes, and seconds. Thirds, fourths, fifths, or any sexagesimal may be taken. Periods, astronomically considered, are large divisions of time. The Chaldean period, is a circle of 25,858 years, at the termination of which the poles of the earth will be direc- ted to the same stars, as at the beginning. The Julian period is a round of 7980 years, found by multi- plying together the cycles, 28, 19, and 15. Its commence- ment depended on the commencement of the cycles of which it is composed. The creation of the world was on the 706th year of the Julian period. The Dionysian era of Christ's birth was near the end of the 4713th year of this period. The Julian period, though imaginary, is very useful in com- paring the dates of ancient events. The Dionysian period, or circle of Easter, is formed by multiplying the solar cycle 28, into the lunar 19. CYCLES ARE REVOLUTIONS OF TIME. The Cycle of the sun is a period of 28 years. This cycle brings the days of the week to the same days of the month ; the sun to the same signs and degrees of the ecliptic with DIVISIONS OP TIME. 135 little variation in each succeeding period. The leap years also have a regular rotation in this cycle* Each of these events has separately a much shorter period. But the cycle brings them to coincide. The Cycle of the moon, or Golden number , is a circle of 1 9 years, at the expiration of which, the changes, fulls, and other aspects of the moon, return to the same month and day of the month, or within a day of the same time, as at the be- ginning. The Epact is the excess of the solar above the lunar year of 12 mean lunations, or 354 days. It is the age of the moon on the first day of January. The Roman Indiction is a period of 15 years. It was es- tablished by Constantine in the year 312, for indicating the times of certain payments made by the subjects to the gov- ernment. To find the Cycle of the sun, Golden number, and Indic- tion, add to the year of the Christian era 4713, arid divide the sum by 28, 19, and 15, respectively ; the remainders are the numbers for the year. Suppose these numbers required for the year 1825. 1825 28)6538(233 19)6538(344 15)6538(435 +471S 56 57 60 6538 93 S3 53 84 76 45 98 78 88 84 76 75 14 Cycle of the Sum 2 Golden number. 13 Indiction. To find the Julian Epact, multiply the Golden number of the year by 11, the product, if less than thirty, is the Epact. If the product exceed thirty, divide it by 30, the remainder is the Epact. To find the Gregorian Epact, find the Julian Epact, and subtract the difference between the old and new style, 12 mvisioNs or TIME. days for the present century, the remainder is the Gregorian Epact.* If nothing remain, 29 is the Epact. If the subtract tion cannot be made, add 30 to the Julian Epact, and sub- tract as before. Neither the Golden number nor the Epact can be of much use, where accuracy is required. The Roman Indiction is still less important. A year is a complete revolution of the seasons. The dif- ference between the tropical, sidereal, and anomalistic year, has been before considered. Different nations have had different methods of computing their year. The civil solar year, as used by the United States and European nations, consists of 365 days, and in bis- sextile, 366. The lunar year consists of 354 days, or 12 lunar months. In this calendar every third year is intercalary or Embolimic, a month being added to make the lunar coincide with the so- lar year. The Jews kept their accounts by lunar years. " But by intercalating no more than a month of thirty days, which they called Ve-Adar, every third year, they fell 3J days short of the solar year in that time." The year of the Greeks was composed of 12 months of 29 and 30 days alternately, comprising very nearly 12 luna- tions, or 354 days. It was difficult to connect this lunar year, with the revolutions of the sun, so as to make the several months fall in the same seasons in successive years. " The Olympic games were celebrated every fourth year during the full moon next after the summer solstice ; and the year of the Greeks was so regulated as to make this the full moon of the first month. This purpose was effected by intercala- tions ; but these were managed so injudiciously, that in the time of Meton the calendar and the celebration of the festi- vals had fallen into great confusion." * The ingenious student will perceive, that the rule of Mr. Pike and some oth- ers, to deduct 11 for the difference of the Epacts, applies to the last century only. DIVISIONS OP TIME. 137 The ancient Romans reckoned by the Lustrum, a period of 4 years. They also computed by lunar years, as established by Romulus,till Julius Caesar reformed the calendar and intro- duced the system of computation, which has borne his name to the present time. In this computation, three years w ere com- mon,consisting of 365 days, as in the present calendar. Every fourth year had 366 days, the 24th of February being twice reckoned. This being the 6th of the calends of March was called bis sextus dies, bissextile. The additional day is now placed at the last of February, and from it the year is call- ed bissextile. # jt& The Julian calendar continued for a long time in Europe. But, it having been found by observations on the time of Eas- ter, that the civil year was too long for the tropical, another attempt was made to reform the calendar. At the time of the council of Nice, 325 of the Christian- era, the vernal equinox fell on the 21st of March. In 1582, Pope Gregory XIII, observing that the same equinox happen- ed 10 days earlier in the year than it had done at the time of the Nicene council, altered the calendar 10 days, ordering, that the 5th of October should be called the 1 5th, The style thus altered was called the Gregorian, or new style. Though adopted and used in several countries of Europe, it was not received into England till the year 1752. The old style or Julian calendar still prevails in Russia. The difference be- tween the old style and the new in the present century is 12 days. Pope Gregory not only altered the style ; but endeavoured to establish a principle, by which the civil, or political year, would coincide with the tropical. By this principle bissex- tile is to be omitted three times in 400 years. When the centuries of the Christian era are divided'by 4, if nothing re- main the leap year is to be retained. But if there be a re- mainder, the year is to be reckoned common. Thus at the end of the 19th century, the leap year is to be omitted, there a being remainder, when 19 is divided by 4. 138 DIVISIONS OF TIME. The omission of three bissextiles in 400 years, still leaves the civil year 20 seconds, 24 thirds longer than the tropical year, as computed by La Place. This excess will amount to a day in 4235 years. The omission of one bissextile in 129 years would bring the different computations to great nearness. The principal division of the year is into months. These are lunar, solar and civil. The sidereal lunar month is the time the moon is passing from the star to the same again ; as before explained. But the principal lunar months consist of a lunation, or the time of the moon's passing from change to change. This seems to have been the foundation of months, and to have given the name to this division of time. The so- lar month is the time the sun is passing one of the signs, or the 12th part of a year. The civil month is of two kinds. That called the weekly month consists of 4 weeks, and is always equally long. This is the true legal month. " A month in law" says Blackstone, " is a lunar month, or twenty-eight days, unless otherwise expressed ; not only because it is one uniform period, but because it falls naturally into a quarterly division by weeks. Therefore a lease for " twelve months" is only for forty- eight weeks ; but if it be for " a twelvemonth" in the singu- lar number, it is good for the whole year." The months in our calendar are of Roman origin. The Latin names are retained, seme of them assuming an English termination. Till the time of Augustus Ca3sar, the sixth month was called Sextilis. In honour of that emperor it was changed to Augustus. To heighten the compliment, a day was taken from the last of February and added to August. Before that time August consisted of but 30 days ; February in a common year of 29.* *The number of days in each month is conveniently remembered by the follow- ing lines: " Thirty days hath September, Apiil. June and November, All the rest have thirty one, Saving February alone." DIVISIONS OP TIME. 139 A week, a well known portion of time, consists of 7 days. This division, old as creation, undoubtedly had its origin in the resting of Jehovah from his work, and the establishment of the sabbath. Days are artificial or natural. Aa artificial day is the time the sun is above the horizon. A natural day is the space of 24 hours ; or the time, in which any meridian on the earth moves from the sun to the sun again. The ancient Egyptians began their day at midnight. Most European na- tions, and the United States, begin at the same time. This is our civil day, divided into two twelves. The ancient Jews began their day at sun setting. They divided the night and the day, each into 12 equal parts, at all seasons of the year. These must therefore, have been of unequal length ; though not so unequal, as in such a division with us, Palestine being nearer the equator than the United States. The ancient Greeks also, began their day at sunsetting, a practice fol- lowed by the Bohemians, Silesians, Italians and Chinese. The Babylonians, Persians, and Syrians, commenced their day at sunrising. This is the practice of the modern Greeks. The nautical, or sea day, commences at noon, 12 hours before the civil day. The first 12 hours are marked P. M. the last A. M. The astronomical day begins at noon, 12 hours after the civil day, and is reckoned numerically from 1 to 24. An hour is the 24th part of a natural day, as measured by a good clock or watch. The division of the day into hours is very ancient. " Herodotus observes, that the Greeks learn- ed from the Egyptians, among other things, the method of dividing the day into 12 parts. The division of the day into 24 hours was not known to the Romans before the Punic war. Till that time they only regulated their days by the rising and setting of the sun." They divided the day into four watches commencing at 6, 9, 12, and 3 o'clock. The night also, they divided into four watches of three hours each. 140 DIVISIONS OF TIME. An hour is divided into 60 minutes ; a minute into 60 seconds ; a second into 60 thirds. Farther subdivisions are sometimes made, as fourths and fifths, in sexagesimal order. The first seven letters of the alphabet were formerly set in almanacks for the days of the week. They were introdu- ced by the primitive Christians, instead of the nundinal letters in the Roman calendar. As one of these must stand for the sabbath, it was written in capitals, and called the dominical letter, from Dominus, the Latin word for Lord. The dominical letter is still retained in almanacks ; but figures are substituted for the other letters. If a common Julian year, 365 days, be divided by 7, the number of days in a week, 1 will remain. Where there is no remainder, and no bissextile, each succeeding year would begin on the same day of the week. But, one remaining, the year will begin and end on the same day of the week. When January begins on Sunday, # is the dominical letter for that year. But the next year commencing on Monday, a, or the substituted figure, is set to that day, as it is always placed at the first day of January. G will, therefore, be the domini- cal letter for that year, the Lord's day being the seventh of the month. As the following year must commence on Tuesday, F is the dominical letter for that year. Thus the letters would follow in retrograde order throughout the seven, G, F, E, D, C, J5, *#; and at the end of seven years, the days of the week would return to the same days of the month, as before. But there being 366 days in bissextile, if this be divided by 7, 2 will remain, thus interrupting the regular returns. The order of placing the letters was to put A at the first day of January, B at the second, C at the third, and so on through the seven ; and then repeat the same successively through the year. The same letters, therefore, stood at the same days of each month, in every succeeding year. That this order might not be interrupted by leap year, C, always at the 28th of February, was placed at the 29th also, or ? DIVISIONS OP TIME. 141 according to some tables, D was repeated. Thus the suc- ceeding months began with the same letters in bissextile, as in common years. But two letters became dominical. Suppose D the dominical letter for a year, C, at the 28th of February, must represent Saturday, C also, must be at the 29th, if the year be bissextile, and of course become dominical ; or, if D be doubled, C at the 7th of March, be- comes dominical, and so remains through the year. The next year begins two days later in the week. On this account the seven letters, in their retrograde revolution, occupy 5 years, when leap year is twice included ; 6, when it is once included. Hence the days of the week return to the same days of the month in 5 or 6 years, according as bis- sextile is twice, or but once included. The letters will al- ways have 5 revolutions in 28 years ; except, when leap year is omitted, at the end of a century. The following table shows the dominical letter for 6006 years of the Christian era, according to the Gregorian calendar. ( 143 ) A TABLE OF DOMINICAL LETTERS FOR 6000 YEARS OF THE CHRISTIAN ERA, N. S. 1 200 300 4 500 600 700 800 The dominical 900 1000 1100 1200 ietter for any of 1300 1 4 t) 1500 1600 the years less than 1700 1800 1900 2000 100 is found in 21002200 2300 2400 the column of let- 25002600 2700 2800 ters next to those 29003000 3100 3200 years, opposite to 3 3 013 4 3500 3 6 O tn e year for 3700 3800 3900 4000 which it is sought. 4100 4200 4300 4400 For any year a- 4 5 014 6 4700 4800 bove luO, find the 4 9 00 5000 5100 5200 century at the top; 5300 15 4 5500 5600 in the column be- ;':..,.;".# :~ 5700 5800 5900 6000 neath, opposite to Yw less than 100 C E G B A the year of the century, in the column less than 100, is the dominical letter sought. 1 2 3 4 29 30 31 32 57 58 59 60 85 86 87 88 B A G F E D C B A G F E D C B G F E D C 5 "33" 61 89 I) F A B 6 34 62 90 C E G A 7 35 63 91 B F G EXAMPLE. 8 36 64 92 A G C B E D F E 9 37 65 93; F A C D Under 1800, 1038 66 94i E G B C opposite to 25 in 1139 12(40 68|96 D C B F E D A G F B A G the left hand col- umn, is B, the 13 41 69 97 _____ Q E F dominical letter 14 42 70 98 G B D E for 1826. 15 13 71 99 F A G D 16 44 72 E D G F B A C B 17 45 73 C E G A 18 46 74 B D F G 19 47 75 A C E F 20 48 76 . G F B A D C E D 21 49 77 E G B C 22 50 78 D F A B 23 51 79 C E G A 24|o2|80 B A D C F E G F 25 53 di G B D E 20 5-1 32 F A C D 27 55 a 3 E G B C 2Ji 06 04 D C F E A G B A m DIVISIONS OF TIME. 143 Knowing the dominical letter, it will be easy to find the day of the week, on which any month begins, by the subjoined table. A B C D E F G Jan . May Aug. Feb. June Sept. April Oct. March Dec. July. Nov. A TABLE showing '.he duys of the m nthf b> doimiiiea' ktt;-rs. To assist the memory, the D. Letters, A B C B E F G following couplet is inserted. January 31 1 8 2 3 10 4 11 5 12 6 13 14 somewhat appropriate, substi- October 31 15 16 17 18 19 21 21 tuted for the hacknied,unmean- 22 23 21 25 26 27 9i 29 30 ol mg one, in common use. 1 o 3 Feb. 28-29 5 6 7 8 9 10 11 All clays uecnne ; great oiessings end; Good Christians find a during friend. March 31 Nov. 30 12 19 13 20 14 21 15 22 16 23 17 24 18 25 The first letters of these 26 9,7 28 29 30 31 twelve words are the same as i 2 3 4 5 6 7 8 those at the beginning of each April 30 July 31 9 1C 10 17 ii 18 1213 1920 14 21 15 22 month. 23 24 25 2627 28 29 As much as the letter set 30 31 1 2 3 4 5 at the first day of a month is c; 7 8 9 10 1 12 Aug. 31 13 14 15 16 17 18 19 before, or after the dominical 90 9\ 22 23 24 25 as 27 28 29 30 31 letter in the year, sought, so 4 5 6 7 8 2 9 much is the day, on which the 3 Sept. 30 Dec. 31 10 17 11 18 12 19 13 20 14 21 5 22 16 23 month begins, before or after 24 S 1 25 26 27 28 29 30 the Lord's day. Thus, if Jl 1 2 3 4 5 6 >e the dominical letter, Jan- - 8 9 10 11 2 13 May 31 14 15 16 17 18 9 20 uary begins on Sunday, Febru- 21 W 9.3 94 95 >H 28 29 30 31 ! ary and March on Wednesday. _ 4 5 6 7 1 8 2 9 3 10 If B be the dominical letter, June 30 11 18 12 19 13 20 14 21 15 99 6 1 7 7 4 January begins on Saturday, 25 26 27 28 29 30 February and March on Tuesday. { 144 > CHAPTER XX. OBLIQUITY OF THE ECLIPTIC. "The obliquity of the ecliptic to the equator," says Dr. Brewster, u was long considered as a constant quantity. Even so late as the end of the 17th century, the difference be- tween the obliquity, as determined by ancient and modern as- tronomers, was generally attributed to inaccuracy of obser- vation, and a want of knowledge of the parallaxes and refrac- tion of the heavenly bodies. It appears, however, from the most accurate modern observations, at great intervals, that the obliquity of the ecliptic is diminishing. By comparing about 160 observations of the ecliptic, made by ancient and modern observers, with the obliquity of 23 28' 16", as observed by Tobias Mayer, in 1756, we have found, that the diminution of the obliquity of the ecliptic, during a century, is 51" ; a result which accords wonderfully with the best observations." This would bring the obliquity at the present time, 1825, to 23 21' 41". Professor Vince, after stating the observations of many authors, ancient and modern, concludes, " It is manifest, from these observations, that the obliquity of the ecliptic, continually decreases ; and the irregularity which here ap- pears in the diminution we may ascribe to the inaccuracy of the observations, as we know that they are subject to great- er errors, than the irregularity of this variation." The following table, extracted from Rees' Cyclopaedia, will give an idea of the diminution of the obliquity. OBLIQUITY OF THE ECLIPTIC. 145 Obliquity of the ecliptic from observations || Mean obliquity tor iorty at different times. || ' -Mimes. A, C. o / a B. C.I o / n Pytheas, 324 23 49 23 900 23 50 26 Eratosthenes, 230 '23 51 20 ' 400 23 46 30 Hipparchus, 140 23 51 20 23 43 15 A. D. A. D. Ptolemy, 140 23 48 45 100 23 42 26 Arzachel, 1104 23 33 30 500 23 .39 6 Propatius, 1300 23 32 1000 23 34 51 Waltherus, 1476 23 30 1500 23 30 33 Tycho Brahe, 1584 23 31 30 1700 23 28 4<> Kepler, 1627 23 30 30 1800 23 27 57 Flamstead, 1690 23 29 2000 23. 26 12 Mayer, 1756 23 28 16 2500 23 21 51 Maskelyne, 1800 23 27 56,6 3000 23 17 31 The part of the table on the left, taken from actual obser- vations, ancient and modern, will be found nearly to coincide with that on the right, formed, by calculation from the most accurate modern observations. The attraction of the moon, on the spheroidical figure of the earth, affords so natural an explanation of the cause of diminution, in the obliquity of the ecliptic, that it is wonderful any other should have been sought. Let T, (Plate VHL Fig. 5.) be the earth, M the moon, JV S the earth's axis, E Q the equator ; the line T M a radius of the moon's orbif at a node, or where it coincides with, the plane of the ecliptic; A B the diameter of the earth, as cut by the plane of the ecliptic. In the triangle A M Q, the line, M Q may represent the force of the moon's attraction on the accumulated matter of the earth, at the equator, on the side next to the moon. This force by the principles of motion, may be resolved into two other forces,* represented by the lines A JJfand A Q the former of which being in the plane of the ecliptic, cannot affect the inclina- tion ; but the latter operates to diminish the obliquity. This force must act in every part of the moon's orbit, except at the beginning of Aries and Libra. Enficld, Mechanics, Rook II, Chapter HI, Prop. XVI. 146 OBLIQUITY OF THE ECLIPTIC. The action of the moon on the opposite side of the earth> must be counter to that we have considered. But, from the well known principle, that the force of gravity diminishes as the squares of the distances increase, the effect on dif- ferent sides of the earth must be unequal, and least on that side, which is opposite to the moon. But if the force of the moon's attraction on the different sides of the earth were equal, the counter action on the opposite side must be less than the diminishing action on the side of the earth next to the moon ; for the line B E is equal to Jl Q ; but the line BMis longer than A M. If therefore B E and B M represent a force equal to A Q and A JJif, as in the hy- pothesis, B E must be less in proportion to the whole than A Q ; B E being less in proportion to B M than Jl Q is to A M. Unequals being taken from equals, the remainders are une- qual. The inclination of the moon's orbit to the plane of the ecliptic must cause her action to be greater at some times than at others ; but cannot prevent her operating in every revolution to diminish the obliquity. The attraction of the sun on the matter accumulated at the earth's equator must produce an effect similar in kind to that of the moon. But the distance of the sun from the * earth is so great, that the line JL Q bears a very small propor- tion to the line Q M or A M. The attraction of the sun also, in different parts of the earth, becomes almost equal, as in the case of the tides. The effect of the other planets on the obliquity must be extremely small. If the explanation here given of the cause of the diminu- tion in the obliquity be just, it can neither become station- ary nor increase without power extrinsic to the solar system ; but must continually decrease, and in time become extinct. Should the earth continue to such an event, the variety of seasons must cease. But to produce such an event, at the present ratio of decrease, would require about 165,000 years from the present time ; a period too immense for our compre- hension. He, who formed the earth by a word, can destroy j-ARALLAX. 147 it at pleasure, or renovate it, so as to produce " seed time and harvest, and summer and winter." CHAPTER 2C. SECTION /.PARALLAX. Parallax, as before defined, is the difference between the true and apparent place of a heavenly body. The true place of a body is where it would appear if seen from the centre of the earth ; apparent, where seen from its surface. Paral- lax is largest at the horizon and decreases to the zenith, where it is nothing. Let A B D (Plate VII. Fig. 10.) be the earth, C its centre ; M JV O P 9 the moon in different altitudes. When the moon is at M, she would be seen from the earth's centre among the stars at E ; but as seen from *#, the surface, she appears at F. When at JV, she would be seen from the centre at G ; but from A she seems at H. At O, her parallax is les- sened, as from the different stations, she would be seen at / and K. At P, having no parallax, she appears at the same place, being seen at Z, both from C and A. This parallax decreases with the distance (Plate VII. Fig. 10,) of the body from the earth, beiug inversely as the dis- tance.* It is often called diurnal parallax. Annual parallax is the difference in the apparent place of a heavenly body, as seen from opposite points in the earth's orbit. This orbit is about 190 millions of miles in diameter. * This is manifest from a view of the figure. It is however capable of demon- stration ; for the angle A M C is equal to the angle M C F-j-JH V C, as in Plate VII, Fig. 6. But the sum of these angles is greater than the angle M V C, the whole being greater than a part ; the angle A M C is therefore greater than the an- gle M V C, PARALLAX OF THE MOON. Hence an object, unless immensely distant, as seen from one part, must appear in a very different place in the heav- ens, from the same object as seen from the opposite part. SECTION II. PARALLAX OF THE MOON. The diurnal parallax of the moon has been long known. It may be obtained from one, observation, when she passes the meridian of a place, if the latitude of the place and the moon's declination be accurately ascertained. The latitude of many places is well known ; of any. may be known. The declination of the moon may be calculated for any time. It may be obtained with accuracy in an eclipse, central, or nearly central, at the meridian over which the moon passes at the middle of such eclipse. Let A be a meridian of the earth (Plate VII, Fig. II.) C, its centre ; Jfcf, the moon. The angle at C may be found by adding the declination of the moon to the latitude of the place, or subtracting it from that latitude, as the case may require ; the angle C A M is obtained by subtracting the ze- nith distance of the moon, found by observation, from 180. Then these two angles CA M-\-A CM taken from 180 leave the angle A M C, the moon's parallax. To find the side C JJf, the distance of the moon, the side A C is given, being the semi-diameter of the earth, and all the angles. By trigonometry, as the sine of the angle AMC is to the side A C ; so is the sine of the angle C A M^ to the side C M. In taking the altitude or zenith distance of a heavenly body, allowance must be made for refraction. Parallax depress- es ; refraction elevates the body. See Refraction. For oth- er allowances, see Latitude. Astronomers recommend, as the best method to find this parallax, two observations taken on the same meridian, one PARALLAX OP THE MOO&. 14S iior-th, tlie other south of the naoon, at^souie distance apart ; Mr. Ferguson says, fct at such a distance fro.ii each other* that the arch of the celestial meridian included between their two zeniths, may be at lea.st 80 or 90 degrees." Let A 13 D be a meridian of the earth ; (Plate Vll, Fig. 12.) C, its centre ; A, a place in north latitude ; B, H place in south latitude. Z. the zenith at A, z, the zenith at B, M the moon, t-et an observer at each of these stations with a good instrument, take the exact zenith distance of the moon's centre, when she p isses the meridian From the sum of these two zenith distances subtract the sum of the two latitudes, the remainder is the sum of the two parallaxes. In triangle A B C the sides A C and B C are known, being each equal to a semi-diameter of the earth ; the angle Jl C B is the sum of the two latitudes ; the angle C J2 Bis equal to the angle C B A, (Euclid, B. /, Prop V.) ; therefore subtract the angle Jl C B from 180o, and half the remainder is the angle B Jl C, or the angle Jl B C. All the angles therefore, and two sides being given, the side Jl B may be easily found. The angle C A ,!/ is the supplement of ZA Jkf, and the angle C B M is the supplement of z B M. Subtract the angle C Jl B from the angle C Jl M, the re- mainder is the angle B A M. ; and subtract the angle C B Ji from the angle C B M> the remainder is the angle A B M. The sum of these angles taken from 180 leaves the angle AM B. In the triangle A M B all the angles and the side Jl B may be considered as given to find the side A M, or JB M Suppose the side A M found. Then in the triamrle A C ,A/, the sides A Cand #/V/andthe angle between them, C A M, being known, the side C M* the distance of the moon from the earth, may be easily fouad by oblique trigo- nometry. 150 THE TRANSIT OF VENUS. I ! . * PARALLAX OP THE S UN. .'^, y j. Aristarchus, an astronomer of Samos, who flourished about the middle of the third century 'before Christ, proposed to find the sun's parallax, by observing the instant the moon is dichotomized, or when exactly one half of her disk appears illuminated This is a little before her first, and a little af- ter her last quarter. The moon, as seen from the sun, is then at her greatest elongation, and the angle at the moon is a right angle. The angle, which the distance of the moon from the sun subtends at the earth, is taken by observation. If then the distance of the moon from the earth be known, the parallax is easily ascertained, and the distance of the sun from the earth may be found by a common problem in rec- tangular trigonometry. But it is impossible to be very ac- curate in determining the time, when the moon is dichotomiz- ed ; and a small error in ascertaining this time will make so great a difference in the sun's parallax, that depen- dence cannot be placed on this method. Hipparchus proposed, by observing the exact time the moon is in passing the earth's shadow in a lunar eclipse, to obtain a triangle for finding the sun's parallax. But this method, like the former, is subject to great and unavoidable errors. Indeed all attempts to ascertain the parallax of the sun, prior to the seventeenth century, can scarcely be called approximations to the truth. The method then suggested, will be the subject of the following article. THE TRANSIT OF VENUS. No improvement in modern astronomy can be compared to that of determining the magnitude and distance of the plan- ets by the transit of Venus, The manner in which this may be effected was first suggested by Dr.Halley. When, in the . THE TRANSIT OP VENUS. 151 *%^ tt*' *"* ' ' V ' earHer part of his life, this great astronomer was at the Isl- and of St. Helena, for the purpose of viewing the star 8 around the south pole, he had an accurate observation of Mercu;y passing over the disk of the sun. He immediate- ly formed an idea, that such transits might be used for hud- ing the, sun's parallax. But Mercury is too near the sun to be conveniently used for the intended purpose. It is necessary, therefore, to have recourse to Penus. The transit of Venus happens but seldom. Horrox, a young English astronomer and his friend, Mr. Crabtree, as far as we know, were the first who had a view of the singular and pleasing phenomenon/ Venus passing over the sun's disk. This was on the 24th of November, 0. S 1639. But their observations were imperfect, the sun going down, in England^ during the transit. The next transit was on the 6th of June, 1761. Doctor Halley, in a paper communicated to the royal society, in the year 1691, gave particular directions for observing this, and the following transit, in 1769, though he knew they must happen some time after his death. The exact periodical times and relative distances of the planets ; the heliocentrick or angular motion of the earth and Venus in their orbits, and, of course, the excess of Venus's angular motion over that of the earth ; the latitude of Ve- nus ; the direction and extent of her path over the sun's disk ; and the duration of the transit, as viewed from the centre of the earth, were deduced from observation on her motion, or were calculated before the transit of 1761 ; and may be considered as data in any transit. If the distance of the earth from the sun be assumed at 100,000, the distances of the other principal planets would be. Mercury Venus Mars Jupiter Saturn Herschel 38,947, 71,578, 151,579, 515,789, 947,368, 1,894,736. ffiE TRANSIT OF VF.NfJS*. When the true distance of the earth from the SUIT i* known, the true distanc of the other planets may be easily found; for the great la. . r df Kepler applies, and as the square of the periodical time of the earth is to the cube of its distance ; so is the square of the periodical time of an- other primary planet to the cube of its distance, ft ore con- cisely ; as the relative distance of the earth from the sun is to the true distance, so is the relative distance of any other primary planet from the sun to its true distance. The apparent motion of a planet in a transit is always ret- rograde. The transit of Venus may be taken by one observer. The method given in Enfield's philosophy, seems one of the best for this purpose. The principle is ; (Plate VIII. Fig3<) let S be the sun, V A B L M JV, a part of Venus's orbit, 1), a part of the earth's orbit ; let the observer's station on the earth at. C be such, that the sun may be on the meridi- an about the middle of the transit, as calculated for the earth's centre This would be at a, had the earth no diur- nal rotation. But, on account of such rotation, let it be at 6, where Venus at Fis seen at the commencement of the tran- sit at /, just entering on the sun's disk. Tosuch an obser- ver, unaffected by diurnal rotation, the egress of Venus Would appear at K, when she has passed to B. But as the- observer is carried, during the transit, by such rotation east- ward ; suppose to c^ Venus would seem to leave the sun whert she arrives at A, making the apparent transit shorter than that by calculation in the proportion of V A to V B. Hence the difference between the observed and computed transit, is the time, in which Venus, by the excess of her fieliocentrick motion, would pass from A to B in her orbit, measuring the angle A KB or c Kb. The difference of time must be reduced to Venus's helro- centrick motion from the earth. This may be done by propor- tion ; for as one hour is to Venus's heliocentrick horary motion from the earth ; so is the difference between the observed TfiE TRANSIT 6P VENUS. and computed duration of the transit, to her motion from the earth during that time, viz. the arch, A B. By knowing the latitude of the place of observation, and the duration of the transit, the length of the line b c may be easily obtained, and may be compared with the serni-diame ter of the earth By thb comparison, with proper allow- ances for the direction of the observer's motion and that of Venus, the angle, whic' a semi-diameter of the earth sub- tends at the sun, equal to the sun's horizontal parallax, may be obtained. But, lest the computed duration of the transit should not be perfectly coriect, an observer ought to be stationed at or near the meridian opposite the former, and so near the en- lightened pole, that the beginning of the transit may be ob- served before sunset, and the end after sunrise. Such an observer, as seen from the sun or Venus, would appear to move, during the transit, in a direction contrary to the for- mer observer. Let D be the place of the earth in its orbit, (H. Fill, fig. 3,) and d the place of the observer at the commencement of the transit, when Venus, at L, appears first to touch the sun at /. If the observer were station- ary at d, the transit would end. when Venus arrives at Jlf. But during the transit the observer must be carried, by the diurnal motion of the earth, some distance, as to e ; Venus must, therefore, pass in her orbit to JV, 'before her apparent egress from the sun's disk, making the observed transit long- er than that by computation. From the difference between the duration of the observed and computed transit, the par- allax is obtained as before. If there be an error in the com- puted duration of the transit, the result of the two opera- tions will be unequal. The error, that increases the one, must diminish the other, so that the mean between the two results may be taken for the exact transit. The mean be- tween many results has been taken, and from them the par- allax ascertained to a degree of accuracy, equal, it may seem, to the most sanguine expectation of the scientific Halley. >i 154 THE TRANSIT OP TENCS. An accurate method of obtaining the parallax of the sun, by the transit of Venus, may be by two observers 90 from each other, observing the ingress of the planet upon the sun's disk, or egress from the s me.* (Plate VIII, Fig 4.) Sup- pose the ingress. Let , when he first observes Venus indenting the disk of the sun. Venus will then appear to touch the sun at / when she has passed to A. In the difference of absolute time between the beginning of the transit, as observed at C and that of the observer arrived at D, Venus by the excess of her heliocen- trick motion will pass from Fto J, measuring the angle VI A. The number of degrees in the arch E D may be easily known by computation, a degree being allowed for each four minutes of time. The co-sine of the arch E D is the line D F = G H. The length of the line D For G H is found by comparing it with the semi-diameter of the earth, as the co-sine of the angle measured by the arch E D is to radius. Then as D F, or its equal G H, is to the time Venus is pass- * For a suggestion of this method, the author is indebted to a very ingenious Fiiend. THE TRANSIT OP VENUS. 155 ing from Fto A by the excess of her motion ; so would G E be to the time Venus is passing by that excess from V to B The arch V E measures the angle V I B, subtended by G ?, equal to the semi diameter of the earth. Allowance must here be made for obliquity of motion in the planet and ob- server ; unless the observer should be so situated, that his motion and that of Venus must be diiectly opposite. The angle, which a semi-diameter of the earth subtends at the sun being known, the distance of the earth from the su may be easily found by rectangular trigonometry ; for the angle at E is a right angle, the line E I being a tangent to the earth's surface, and the semi-diameter of the earth is known. Making the distance radius, say, as the tangent of the angle G I E, is to the line G E ; so is radius to the line G /, the distance of the earth from the sun. In case of two observers, great care must be taken that the time keepers be accurate and regulated on the same principle. This principle of finding the parallax may be applied to other distances in the places of observation beside 90 ; and equally, if both observers be not on the same parallel. Mr. Short, of London, took great pains in deducing the quantity of the sun's parallax from the best observations made both in Britain and abroad, and found it to have been 8.52//, on the day of the transit, when the snn was near its greatest distance from the earth ; and consequently 8 65", when the sun is at its mean distance from the earth. From this Mr. Ferguson makes 23,882.84 the number of semi-diameters of the earth, which it is distant from the sun. As he reckoned the semi-diameter of the earth 3985 miles, multiply ing these together he made the mean distance of the earth from the sun 95,173,127 miles. If we take the semi-diameter of the earth 3982 miles, which it would be, according to Dr. Bow- ditch, and multiply it by the same number 23,882.84, the result is 95,101,469, for the earth's mean distance* from the sun. It is amusing and gratifying, to know what vast interest 156 Tin: TRANSIT OP was felt in the transit of 1761, and what great pains were taken to observe it with accuracy. " Early in the morning," June 6th, u when every astrono- mer was prepared for observing the transit, it unluckily happened, that both at London and the royal observatory at Greenwich, the sky was so overcast with clouds, as to render It doubtful whether any part of the transit should he seen ; and it was 38 minutes 21 seconds past 7 oVlick, apparent time, at Greenwich, when the Rev. Mr. Bliss, astronomer royal, first saw Venus on the sun " Mr. Short made his observations at Saville house, London, in the presence of several of the royal family. The transit u as observed at several other places in England ; at Paris by Bl. De la Lande. At Stockholm observatory, latitude 59 20V N. longitude 18' east from Greenwich, the whole transit being visible, was observed by Wargentin. It was observed also at Hernosand in Sweden, at Torneo in Lapland, at To- bolsk in Siberia, at Madrass, at Calcutta, and ut the Cape of Good Hope. Dr Maskelyne's observations at St. Helena _" were not completely successful on account of the cloudy state of the weather." The parallax deduced from observations on the transit of 1761, was con firmed by the transit of 1769 Without material alteration. Professor Vince has given the following convenient method of ascertaining when the transits of Mercury and Venus will happen. u The mean time from conjunction to conjunction of Venus or Mercury being known, and the time of one mean conjunction, we s'jall know the time of all the future mean conjunctions Observe, therefore, those which happen near to the node, and compute the geocentrick latitude of the planet at the time of conjunction, and, if it be less than the apparent semi-diameter of the sun, there w r ill be a transit of the planet over the sun's disk ; and we may determine the periods when such conjunctions happen in the following man- ner Let P = the periodic time of the earth, p that of Venus or Mercury. Now that a transit may happea again at THE TRANSIT OP VENUS. I57> Ihe same node, the earth must perform a certain number of complete revolutions, in the same time that the planet per- forms a certain number, for then they must come into conjunc- tion again at the same point of the earth's orbit, or nearly in the same position in respect to the node. Let the earth perform x revolutions whilst the planet performs y revolutions ; then will Px = p y, therefore, * = p p . Now P = ^65.256, and for Mercury, = 87.968 ; therefore - = = : ." From this he ascertained, " that 1, 6, 7, 13, 33, 46, &c. revolutions of the earth are nearly equal to 4, 25, 29, 54, 137, &c. revolutions of Mercury, approaching nearer to a state of equality the Anther you go. The first period ojr that of one year is not sufficiently exact ; the period of six years will sometimes bring on a return of a transit at the same node ; that of seven years more frequently ; that of 13 years still more frequently, and so on." For Venus p = hence ^ ' ." From this he makes the periods y r 3bo,:i:ob 8,235, 713, c. years. " The transits at the same node will, therefore, sometimes return in 8 years, but oftener in 235, and still oftener in 713." Those, who wish to be more particular, and calculate or project the transits of these planets, can have recourse to those larger works in astronomy, where the motions of the planets, their aphelia and nodes with secular variations, may be fout d at length in tables. Their insertion here would exceed the limits designed for this work. The following table, showing the times of transits, was formed by abridging Dr. Brewster's account of them in his supplement to Ferguson. COMETS. TRANSITS. II TRANSITS. MERCURY. II VENUS. Times of Times of 'f Times of Times of happening happening j happening happening |1707|M.iy u|1802|November 8(1 1631 1 December 612490 17 lOi November 61 18 151 November 11 1(1 6391 December 4 12498 June 12 June 9 17-23 November 9 1822 November 4 1761 June 5* 26u.J December 15 1736 November 101832 May 4 1769 June 3 2611 December 13 17*0 May 2 1835 November 7 1874JD cember 8 27.'3|.l'.uie 15 174.* November 411845 Way 81 1882 December 6 2741 June 12 1753 May 5(1848 November 9 2004 June 7 >8 46' December 16 1756 November 61861 November 11 2er 10 i ' * Astronomical time. CHAPTER XI. COMETS. Comets are large opaque bodies, moving round the sun in various directions, and in very eccentric orbits It is not wonderful, if, as we are told, comets were considered por- tentous in the days of barbarism and superstition ; if thejfc were regarded as the harbingers of war, famine, and pesti- lence ; if they presented to the frighted imaginations of mefc the convulsions of states, the dethronement of kings, and the fall of nations. Astronomers of the present day view them in a light entirely different. By the allwise Creator they are without doubt designed for benevolent and important pur- poses ; though most of those purposes must be to us unknown, or deduced only by reasoning from analogy. A comet, when viewed through a good telescope, resembles a mass of aque- ous vapour surrounding a dark nucleus, of different shades in different comets ; though sometimes nonudeusMs observed. ' Of the last kind were some seen by Dr. Herschel, and some by his. sister. As the comet approaches the sun, its nebu- lous light becomes more brilliant, its luminous train increas- COMETS. Ing gradually in length. At the perihelion its heat is great- est, and the length of its tail is at its maximum. Here the comet sometimes shines with all the splendor of Venus Retreating from the perihelion, its splendor decreases, and it re assumes its nebulous appearance. u History," says Dr. Rees, tk records, that some comets have appeared as large as the sun." Mr. Wilkins mentions one, " said to be visible at Rome, in the reign of the emperor Nero, which was not inferior in apparent magnitude to the sun. The astronomer Hevelius also observed a comet in 1652, which did not ap- pear to be less than the moon, though it was deficient in splen- dor ; having a pale, dim light, and exhibiting a dismal aspect." The number of comets which have been seen within the lim- its of the solar system is differently stated, from 350 to 500. It is indeed unknown. The orbits or paths of 98* of these up to the year 1808 have been calculated. The time of their passage through the perihelion ; longitude of the per- ihelion and the inclination of the orbits, are inserted in tables. 24 comets have passed between the sun and the orbit of Mercury ; 33 between the orbits of Mercury and Venus ; 21 between the orbits of Venus and the earth ; 16 between the orbits of the earth and Mars ; 3 between the orbits of Mars and Ceres; and 1 between the orbits of Ceres and Jupiter. Various have been the opinions of astronomers respecting the tails of comets. These tails sometimes occupy an im- mense space in the heavens. The comet of 1681 stretched its tail across 104 , and the comet of 1769 subtended an an- gle of 60 at Paris, 70 at Boulogne, 97 at the isle of Bour- bon. , These long trains of light were supposed by Appian, Cord^, and Tycho Brahe to be the light of the sun, trans- mitted through the nucleus of the comet, which they believ- ed trarfl^^ent like a lens. Kepler thought, that the impulse of the SG \lBfet drove away the denser parts of the comet's atmosphere, and thus formed the tail. Des,cartes ascribes the tail to the refraction of light by the nucleus. Newton maintained, that it is a thin vapour raised by the heat of the * u ln 1811 the number of these, wliose elements bad been calculated, was 103." Dr. Morse. OOMKT6. sun. E'ller thinks there is a great affinity between these tails, the zodiacal light and the aurora boiealis, and that Uie cause of them all is the action of the sun's light on the atmos- phere of the comets, of the sun, and of the earth. Doctor Hamilton of Duhlin supposes the tiains of comets tc be streams of electrical light. The Dr supports his opinion by these arguments : u A spectator at a distance from the earth Would see the aurora boreal is in the form of a tail opposite the sun, as the tail of a comet lies. The aurora borealis bas no effect upon the stars seen through it ; nor has the tail of a comet. The atmosphere is known to abound with elec- tric matter, and the appeara ce of the electric matter in vacuo resembles exactly that of the aurora borealis, which, from its great altitude, may be considered in as perfect a vacuum, as we can make. The electric matter in vacuo suffers the rays of light to pass through, without being affect- ed by them. The tail of a comet does not expand itself side- ways, nor does the electric matter. Hence he supposes the tails of cornets, the aurora borealis, and the electric fluid, to be the same kind of matter " In confirmation of this hy- pothesis, it may be added, that many astronomers have ob- served an undulatory motion in the trains of comets, similar to what is sometimes seen in the aurora borealis The most extensive aurora borealis, which has appeared for many years in the northern section of the United States, was about the close of the revolutionary war. This with vast undula- tions covered the whole northern half of the hemisphere, collecting into a beautiful centre in the zenith. To a spec- tator on a distant planet this might give the earth an appear- ance, resembling, in some measure, that of a comet. The following are some of the laws of cometary motion and aspect, observed by astronomers. " The elliptical orbits of comets have one of their foci in the centre of the sun, and, by radii drawn from the nu- cleus to the sun, describe areas proportioned to the times " u Their tails appear largest and most brilliant immediate- ly after their transit through the region of the sun." THE PIXFD STARS. 161 / " The tails always decline from a just opposition to the sun towards those parts, which the bodies or nuclei pass over, in their progress through their orbits. 71 " The tails are somewhat brighter, and more distinctly de- fined in their convex than in their concave parts." " The tails always appear broader at their upper extreme, than near the centre of tKe comet." " The tails are always transparent, and the smallest stars appear through them." CHAPTER XIX. THE FIXED STARS. Astronomers seem now agreed, that the fixed stars arc suns to other systems. Their immense distance is demon- strable from their always preserving the same unchangeable position in regard to each other, when viewed from different extremes of the earth's orbit. Though the earth is at one season of the year about 190 millions of miles distant from its place at the opposite season, yet the apparent position of the fixed stars is not altered, or, if they have a parallax, it is undetermined by all the observations yet made, and can scarcely exceed a single second. u From what we know," says Mr. Ferguson, u of the immense distance of the stars, the nearest may be computed at 32,000,000,000,000 of miles from us ; which is farther than a cannon ball would fly in 7,- 000,000 of years-" From the distance of the stars it may be concluded, that they shine by their own native light, aud not by the reflected rays of the sun. For those rays, de- creasing in number in any given space, as the squares of the distances increase, cannot by reflected light make objects visible at such an inconceivable distance. The fixed stars are easily distinguished from the planets fey the twmkling of their light. Viewed through a good tel- THE FIXED 8TAU5. escope, the diameter of a star appears much less than when seen by the naked eye. By increasing the power of the tel- escope, the diameter seems to increase ; but not according to any regular proportion. The number of str.rs visible to the naked eye in either hem- phere is not more than 1000. They seem indeed to be with- out number, when in a clear evening we turn our eyes to- wards the heavens. But by looking attentively we shall find, that most of those bright spots, which appeared to be stars y vanish. The British catalogue, including many stars not visible to the naked eye, contains not more than about 3000 in both hemispheres. By improved reflecting telescopes the number is found to be great beyond all conception. " Dr. Herschel says, that in the most crowded part of the milky way, he has had fields of views that contained no less than 588 stars, and these were continued for many minutes, so that in a quarter of an hour, he has seen 116,000 stars pass through the field of view of a telescope, of only 15 aperture,* and at anoth- er time, in 41 minutes, he saw 258,000 stars pass through the field of his telescope. Every improvement in his teles- copes has discovered stars not seen before, so that thei e appear no bounds to their number, or to the extent of the universe." Many stars, which to an observer unaided by instruments appear single, are found, on being examined by a good teles- cope, to consist of two, and some times of three or more stars. Those, which are in a great degree removed from the attractive force of other stars, are denominated by Dr. Herschel " insulated stars," such are our sun, Arcturus, Ca- pella, Sirius, and many others. " A binary sidereal system or double star, properly so called, is formed by two stars situated so near each other, as to be kept together by their mutual gravitation."' It is manifest, that stars, one being nearly behind the other, may appear binary, though immensely distant. The double star Epsilon, Bootes, is beautiful, composed of two stars, one a light red, the other a fine blue. * So state the books. We are not told his manner of counting. THE FIXED STARS. 163 Plate XT, Fig. 5, represents this beautiful double star as seen by telescopes of different magnifying powers. The double star Zeta Herculis is composed of a greater and a less, the former of a beautiful blueish white, the lat- ter of a fine ash colour. The star Delta of the Swan is composed of two stars very unequal, the larger, white, the less, reddish. The Alpha Hercules consists of two stars very unequal, the larger, red, the less, blueish green. Viewed by three different telescopes these stars appear as in Plate XI, Fig. 4. The pole star, the Alpha of the little Bear, is binary, con- sisting of two stars extremely unequal in magnitude, the lar- ger whi e, the less red. In Plate X/, fig. 6, is represented one of the most beau- tiful objects of this kind in the heavens, the treble star in the left fore foot of the constellation Monoceros. Viewed with attention it appears a double star ; with still more at- tention, c;ie of the component stars appears also double. All are white. Beta Lyr&is quadruple, unequal white ; but three of them a lit'le inclined to red. Lambda Orionis is quadruple, or rather a double star, having two more at a small distance, the doublestar unequal, the largest white ; the smallest a pale rose colour. A catalogue of the principal double stars may be seen in Dr. Brewster's Supplement to Ferguson. Its insertion here would exceed the limits designed for this work. The stars have been arranged into six classes, or orders, according to their magnitude. The largest are called stars of the first magnitude ; those next to them, stars of second magnitude, and so on to the sixth. Considerable difference, however, may be perceived in the stars of each magnitude, some being much larger and more brilliant than others 'I be arrangement of the stars into magnitudes was made long before the invention ejf telescopes. Stars not seen without 164 THE FIXED STARS. these are called telescopic stars. In books of modern as* tronomy we sometimes find stars mentioned of the seveath or eighth magnitude. Besides the arrangement of the stars into magnitudes, the ancients divided the starry sphere into constellations, or sys- tems, each including stars of different magnitudes. By a powerful imagination, they conceived companies of stars as having the form of certain animals or things, and applied names accordingly to such companies. Thus one constella- tion is called Aries ; another, Cassiopeia ; and another, Ori- on. In Plate X, Figures 1, 2, 3, and 4, may be seen Ursa Ma- jor, Leo, Cygnus, and Lyra, four of the constellations as they are represented on a 12 inch celestial globe. From the'se, as a specimen, the student may form some idea of that im- agination, by which they were arranged. Probably in Ursa Major or any other constellation viewed in the heavens, he tvill see but little similarity between the figure presented by the stars and the animal by which they are represented. F'gures 7, 8, and 9, of Plate X/, represent the stars of Ori- on, Bootes, and Canis Major, as they are arranged on a celes- tial globe. Stars not included in any constellation, are called unformed stars. The classing of the stars is of great antiquity. It is also, however chimerical, of vast importance, as it enables the astronomer to describe the place of a star, a planet, or comet at any time, as easily as a geographer can that of a hamlet or a town. The number of ancient constellations is 48. Of these, 12 were within the zodiac, 21 to the north, and 15 to the south of it. The animal or object of each constellation is represented on the celestial globe ; and the proportion of I he stars belonging to each denoted by the let- ters of the Greek alphabet, according to the plan adopted by M. Bayer, a German, in his u Uranometria," a large celes- tial atlas. Thus, alpha is placed to the largest star of the constellation, beta to the second, gamrw to the third, and thus on in alphabetical order. THE FIXED STARS. 166 Tables containing the constellations, with the number of stars in each, observed by the different astronomers, Piolemy, Tycho, Hevelius ; and Fiamstead. CONSTELLATIONS IN THE ZODIAC. N AMES OF CONSTEIiItATIOWS. No. of Stars. -o H 32 "3 o *< s- Chief stars. Mag^ii- tuues. ? o < ? Aries, the Ram 18 21 27 66 Taurus th> Boll Gemini the Twins C incer, the Crab 44 43 51 141 Alde-baran 25 25 38 85 Castor & Pollux 13 15 29 83 1 1 2 Leo, the Lion with corona Berenices 35 30 49 95 Regulus 1 Virgo, the Virgin 32 33 50 llOjSpica Virginia I Libra, the Scales 17 10 20 51 Zubenich Meli 2 Scorpio, the Scorpion 24 10 20 44 ! Antares 1 Sagittarius, the Archer 31 14 22 69 CH [iricornus. the Goat 28 28 29 51 Aquarius, the Water bearer 45 41 47 lOBiScheat J Pisces, the Fishes 133 36 39 1)3| NORTHERN CONSTELLATIONS. 1 No. of stars. NAiMES OF CON'STEI.IiATION'S.U) ^ ffi ^ 1? f; Sr F Chief stars. Magni- tude. Ursa Minor the lit le Bnar 8 7 12 24 Pole-?tar 2 Jrsa Major, the greauBear 35 9 73 87 Dubiie 1 )raoo, the Dragon 31 ?2 40 80 Rastaber 3 >)>heus 13 4 51 35 Alderarain 3 Jootes 23 18 52 54iArcturus 1 Jorona borealis, the northern Crown 8 8 8 21) -lercules engonasia 29 28 45 113Ras Algiatha 3 jyra, the Harp 10 11 17 21 Vega 1 ^yi/nus, the Swan 19 18 47 81 DenebAdige 1 Cassiopeia, the Lady in her chair 13 26 37 55 3 erspus 29 29 46 59 Algenib 2 AMriea, the Waggoner 14 9 40 66Capella 1 S^rpentarius 29 15 40 74Ras Alhasus 3 Serp^ns, the Serpent 13 13 22 64 Saa-ita, the Arrow 5 5 5 18 Aquila. the Eagle ) 15 12 23 71 Altair 1 Anrinous \ 3 I* "Mphinus, the Dolphin 10 10 14 18 iqnulus, Equisortio, the Horse's head 4 4 6 10 Pegasus, the flying Horse 20 19 18 89Markab li Andromeda 23 23 47 6K,Almaac 2 TriangHlum,the Triangle 4 4 12 16 3anes Vanatici, the Grey hounds 23 25 Cor Caroli, the heart of Charles 3 Triangulum minus, the little Triangle 10 Vlusca, the Fly 6 Lvnx, the Lynx 19 44 f.eo Minor, the little Lion 53 Damelopardalis 32 58 Vfous Menelaus 11 scutum Sohieski, Sobieski's Shield 7 8 H ! rcules cum Ramo and Cevbero Taurus Poniatowski 7 Vulpeoulus et Anser, the Fox and Goose 27 37 Lacerta, the Lizard 16 166 THE FIXED STARS, SOUTHERN CONSTELLATION. A JAMES OF CONSTELLATIONS. S.M of Stars. -3 _j jj -f 5^3 5* Chief Stars. tude Cetu*. t:ie Wuale 22 21 4? y? Meukar 2 Ori'>n 38 4-2 42 78 Betelj/i'use Kri laous 34 JO 27 84,Arcnenar L 'i)us. the Hare 1* 13 ^ 19 Canis VI ij >r, the gieat Dog 29 1-^ H 31 ^irius Ciuis Min'ir, the little Dog 2 2 13 14 Pi. -icy on Ar-jo, the Ship Hydra, the water Serpent Crater, the Cup 45 3 4 64iCunopus 2? 19 31 fio Cor Hydraf 7 3 10 3ll\!kes 3 ^orvus. tne Raven 7409 Algorab 3 !>ntaurus, the Centaur 37 35 Lupus, the Wolf 19 24 Ara, the Altar 7 9 Corona Australis, the soutliern Crown 13 12 ^isoes Australia, the southern Fish 18 24 Fomalhaut 1 >:,r B nix 13 ~)Ticina scnlptoria 12 Tydrus, the Watersnake in "ornax chonnica. the chemical Furnace 14 -loriln^'inm, the T'mekeeper 14 ^>tirulus Rhomboidalis 10 Xiohla* Dorado, the Swordfish 7 jela Praxi'ellis 16 Jo'umha Noachi. \oali' D^ve 10 'quiile-is pictorius. the painted Colt 8 Vl-mor.*ro*. the Unicorn 19 31 ^hi nele r >n 10 *VXH Nautica.the Mariner'* Compass 4 'JH^.U volans, the flying Fish 8 Sextan*, the ^extant 11 41 Inhur Carolinum th^ royal oak 12 IvYim Pnpurnitica, the wind Instrument 3 Cr e or Flv 4 A ip ">r Aries Indira, the Bird of Paradise 11 Circinus. the Compass 4 Q.iadn Kuc'i lis, Euclid's Square 12 T'ianulum Australis, the southern Triangle 5 >lesc f >n'ui'ii, the Telescope 9 'avo, the Peacock 14 n Uis, the Indian 12 Wcroscopium. the Microscooe 10 Ortans Hadleianus, Hadley's Octant 43 lOrus. the Crane 14 Toucan, the American Goose 9 The whole number of constellations is now 92, of which 12 are in the Zodiac ; 35 are northern, 45 southern. Prob- ablv the number may yet be increased. The ancient con- stellations are placed first in each table. Several stars have appeared in the heavens for a time, and then disappeared. Several are enumerated in ancient cata- THE FIXED STARS. 161 logues, which are no longer to be seen, even by the powerful instruments of modern astronomy. Others are now visible, winch do not appear to have been seen by the ancients. In 1572, a new stai was discovered oy Cornelius Gemma, in the chair of Cassiopeia. In brightness and magnitude, it surpassed Sirius. To some eyes it appeared larger than Ju- piter, being seen at mid day. It afterwards gradually- decay- ed, and, after sixteen months, disappeared. In 1596, Fabncius observed the Stella JMira, or wonderful star, in the neck oi the whale. It seemed to appear, and disappear seven times in six years ; though it is said never to have been wholly extinct. Lithe year 1600, Jansenius observed a changeable star in the neck of the swan. It was observed by Kepler, who de- termined its place, and wrote upon it. The same was seen by liicciolus, in 1616, 1621, and 1624 ; but was invisible from 1640 to 1650. It was seen again in 1655, by Cassini. It increased till 1660; then decreased till the end of 1661, when it disappeared. In November, 1665, it again became visible, but disappeared in 1681. It again appeared, in 1715, as a star of the sixth magnitude. This is its present appear- ance, in 1604, Kepler and some of his friends discovered a new star, near the head of Serpentarius, bright and sparkling, be- yond any they had before seen. It appeared every moment changing, assuming the different colours of the rainbow, ex- cept, when near the horizon, it was generally white. In Oc- tober of that jear it was near Jupiter, surpassing that planet in magnitude, but before the following February it disappear- ed. Many other stars have appeared, vanished, and re-appear- ed ; some of them in regular returns. ^uch changeable stars may be suns with extensive spots. By a rotation on their axes, stars of this kind may alternate- ly present their dark and luminous sides. " Maupertius is of opinion, that some stars, by their prodigious quick rotation on their axes, may not only assume the figure of oblate THE fcALAXf. spheroids, but by their great centrifugal force, arising frorU such rotation, they may become of the figures of millstones, or reduced to flat circular planes, so thin as to be quite invis- ible ; when their edges are turned towards us ; as Saturn's ring is in such positions. But, wht n any excentric planets or comets go round any flat star, in orbits much inclined to its equator, the attraction of the planets or comets in their perihelions, must alter the inclinations of that star; on which account it will appear more or less large and luminous, as its broad side is more or less turned toward us." Ferguson. The observations of modern astronomers would render doubtful the term fixed, as applied to the stars. An ad- vancement of the solar system in absolute space is now con- sidered certain. It was observed by Halley and Cassini. The first explanation of it was given by Mayer. But to Dr. Herschel it was reserved to point out the region in the heav- ens, to which the solar system is advancing. u Dr. Herschel has examined this subject with his usual success, and he has certainly discovered the direction, in which our system is gradually advancing. He found, that the apparent proper motion of about 44 stars out of 56 is very nearly in the direc- tion, which would result from a motion of the sun towards the constellation Hercules, or, more accurately to a place in the heavens, whose right ascension is 250o 52' 30', and whose north polar distance is 40 22'." THE GALAXY. The Galaxy, or M'lky way, is a luminous zone in the heavens. Its beautiful, cloudy whiteness is found by modern ^astronomers to be caused by the collected rays of innumer- able stars, not discernible by the naked eye. "That the jnilky way," says Dr. Herschel, u is a most extensive stra- tum of stars of various sizes, admits iio longer of the least doubt." Jl group of stars is a collection of stars, closely compressed, and of any figure. REFRACTION, 169 Clusters of stars, (Plate X. Fig. 6 ) differ from groups, in their beautiful and artificial arrangement ; regarded by Dr* Herschel among the most magnificent objects in the heavens. JVem/ce, v or cloudy stars, are bright spots in the heavens, (Plate XL Fig. 1, 2, and 3.) Some of them are found to be clusters of telescopic stars. The most noted nebula is be- tween the two stars in the sword of Orion, discovered by Huygens in 1656. It contains seven stars, and in another part, a bright spot upon a dark ground, seeming to be an opening into a brighter and more distant region, (Plate XL Fig. 1.) Nebulae were discovered by Dr. Halley and others. A catalogue of 103 nebulae, discovered by Messier and Mei- hain, is inserted in the Connoisance de terns, for 1783 and 1784. u But to Dr. Herschel," says Enfield, " are we indebted for catalogues of 2000 nebulae and clusters of stars, which he himself has discovered." Dr. Brewster says 2500. We cannot contemplate the fixed stars wjthout repeating the sentiment expressed in the introduction ; without admi- ration and astonishment ! How inconceivably Great and Wise and Good must be the AUTHOR and GOVERNOR of all these ! We behold, not one world only, but a system of worlds, regulated and kept in motion by the sun ; not one sun and one system only, but millions of suns and of systems, mul- tiplied without end, never conflicting, always revolving in harmonious order ! CHAPTER XIII. REFRACTION. Refraction of light is the incurvation of a ray from its rec- tilinear course, in passing from a medium into one of differ- ent density. On entering a denser medium, a ray coming obliquely is turned towards the perpendicular drawn te its 170 REFRACTION. surface. But it is turned from the perpendicular, to the surface of a rarer medium, when passing from one more dense. An object always appears in the direction, in which a ray of light from it meets the eye of the observer ; though before it may have passed in different directions. Let A II C D, (Plate VLll, Fig. 7.) be a vessel filled with water up to the line E F, and the remainder filled with spirit, or other trans- parent fluid, less dense than water. Let a ray of light be reflected from an object a at the bottom in the direction a /. This ray in passing from the water into the fluid less dense would be refracted from the perpendicular to the water's surface in a new direction, as to //, where the object at the bottom, without further refraction, would appear at b. But on leaving the rarer medium at the surface, A B, it is again reiracted, and again passes in a new direction, as to G. So that an eye at G must see the object a at c. A straight rod appears crooked, when partially immersed in water, viewed obliquely to its surface. Put a piece of money into a cowl, (Plate Vlll, Fig. 5.) and retire till the money is just hidden by the edge of the bowl ; let an attendant pour water into the bowl, the money will rise into view. When the eye is perpendicular to the surface of the medium, there is no refraction. In wading a river, the water, where you are, appears of its proper depth ; but at a little distance forward it seems more shallow, than on trial it will be found. It has been said, no doubt with truth, that this circumstance has often been the cause of drowning. The light of heavenly bodies is refracted by the atmosphere of the earth. (Plate F,F/g.5.) This refraction, greatest at the horizon, decreases towards the zenith, where it becomes noth- ing. When a medium is throughout equally dense, the refrac- tion is at the surface. But the atmosphere increases in density from its utmost height to the surface of the earth. A ray of light must therefore be more and more bent, and pass in a curvilinear course through the atmosphere. The refraction brings up a heavenly body, before it arrives at the horizon. Let A B C (Plate VIII, Fig. 9.) be a part of the earth's REFRACTION. 171 atmosphere, B F, the sensible horizon to a spectator at B, D a place of the sun below the horizon. Suppose a ray of light, passing in the direction D F, should strike the atmosphere at F. This would be refracted by the increased density of the air all the way from Fto the surface of the earth, as to B ; and would present the sun in the line of its last direction, B E. The sun would, therefore, appear in the horizon, before it arrived at that circle. Cold increases the density of the air, and of course the re- fracting power. In general, the higher the latitude the greater the refraction. Mr. Ferguson tells us, that the sun arose to some Hollanders, who wintered in Nova Zembla, in 1596, seventeen days sooner, than by calculation it would have been above the horizon. As the horizontal refraction in latitude 43, is about 33', the sun's mean diameter about 32,' the sun must be visible, when more than his whole breadth below the horizon. The horizon in such latitude passing these 33' obliquely, and re- quiring about three minutes of time, the sun is about three minutes in the morning and three at night, longer above the horizon on account of the refraction, increasing the length of the day about six minutes. The refraction of the atmosphere is sometimes the cause of a curious phenomenon, the sun and moon both visible, when the moon is eclipsed by the earth's shadow. Mr. Phillips mentions an instance of this kind, observed at Paris in 1750. The progressive motion of light has been shown to be another cause, why a heaven'y body does not appear in its true place. But this does not alter the length of the day ; for as the sun appears below its true place in the morning, it appears above it at night, leaving the length of the day unaf- fected. The disk of the sun or moon appears elliptical, when in or near the horizon. The lower limb being more refracted than the upper, not only by the atmosphere itself, but often by the floating vapour, the outline of the disk must be changed from a circle to an elliptical form. 178 TWILIGHT, The table of refraction, here inserted, is that of Dr. Bradley, extracted from Eafield. It agrees very nearly with Mr. Bowditch's table of refraction as set to degrees. MEAN ASTRONOMICAL REFRACTIONS IN ALTITUDE. A aVt P ' Refrac- tion 33 alt O iT Ki-frac-liapj*. tion. lali. ' "\\- 44723 ; lefrac-| tion. 2 14ll alt. O 35 : teftac-!iapp. ffll K frac-j tion. I 0~ 78 tin i / H ~TT O 1 24 29 12 4 23 24 2 7 36 is 1 50 48180 10 2 18 35,13 4 3';25 2 2 l! 37 16,52 44! 88 8 3 14 36' 14 3 45 28 5611*8 13 55 40185 5 4 11 51 'l5 1 1 51!|39 10 58 35 18* 2 5 9 54 16 3 17:28 47 1) ,8H60 33 89 1 6 8 28117 3 4|J29 42 11 562 30^90 7 7 20 18 2 54i,30 38. ; 42 3 ! 65 26 8 6 29 19 2 45131 35'43 1 GS 23 9 5 48 20 2 35 ! 32 31 44 59 70 21 i 10 5 15 21 2 27,33; 28 45 j57i>72 22 2 20034 24 175 1| OHAFTZ3R XXV. T'VILIGHT. The twilight is the result of refraction. The atmosphere of f he earth extends about 45 miles above the surface ; or at that height is sufficiently dense to refract the rays of the sun. Hence it is found, that when the sun is about 18 below the horizon, the morning twilight will begin, and the evening twilight end. It is said however, that the evening twilight is longer than that of the morning. This may be owing to the elevation of the atmosphere by the heat of the day, and also to the vapour exhaled by rarefaction. The continuance of twilight, increasing with the distance from the equator, must be very long in high latitudes. At ZODIACAL LIGHT. 173 the poles the sun is never more than about 23 2S' below the horizon. To a polar inhabitant, if any, it must be more than 50 days after the sun sets, before it will be 18 below the horizon ; and the same time, on its return, after it approaches within 18, before it will be above the horizon. Here we must be led to contemplate with admiration the immense benefit of the atmosphere. Not only by the chem- ical operations of air, does it cause our blood to flow, and diffuse warmth through our bodies ; but, by its reflecting and refracting powers, it gives beauty to our day, and enlarges its borders, even into the regions' of night. Astronomers generally concur with Dr. Keill ; u That it is entirely owing to the atmosphere, that the heavens appear bright in the day time. For without it, only that part of the heavens would be luminous in which the sun is placed, and, if we could live without air, and should turn our backs to the sun, the whole heavens would appear as dark as in the night. In this case also, we should have no twilight, but a sudden transition from the brightest sunshine to dark night, immediately upon the setting of the sun, which would be extremely inconvenient, if not fatal to the eyes of mortals." CHAPTER XV. ZODIACAL LIGHT. Zodiacal light seems to have been seen by Descartes in 1659, yet it attracted no general notice, till observed by Cassini in the year 1693, when it received its present name. This light, less brilliant than the milky way, appears at cer- tain seasons of the year, in the morning before the rising of 2.2 174 LATITUDE AND LONGITUDE OP THE EARTH. the sun, and at evening, after the setting of that luminary. " It resembles a triangular beam of light, rounded a little at the vertix." It lies in the direction of the zodiac, its base turned towards the sun, and resting on the horizon. About the first of March at 7 o'clock in the evening is the best time for observing this light. This luminous cone is of vast extent, stretching to 45 ; according to some, at times even beyond the meridian. This light, according to Foulquier, is always seen at Gaudaloupe, when the weather admits. Some have accounted for this phenomenon by the action of the sun's light on his own, atmosphere ; others by the refrac- tion of his rays in the atmosphere of the earth. If the former opinion be correct, the bright cone must stretch to an immense distance, when not exceeding 45 it must, if perpen- dicular to the view of the observer, be equal to the whole distance of the sun from the earth. But its being seen in one part of the earth rather than in another, equally in view, seems to indicate that it must originate in the atmosphere of the earth, and not in that of the sun. CHAPTER XVI. LATITUDE AND LONGITUDE ON THE EARTH. The great circles of the globe are considered as extended into the visible heavens, the celestial circles always lying in the same plane with those on the earth. Hence the position of the heavenly bodies, in regard to these circles, may be used in determining the latitude and longitude of places on the earth. SECTION /.-LATITUDE. LATITUDE, as before stated, is the distance north or south from the equator. It is reckoned in degrees and minutes on a meridian. The centre of this circle, as that of the equator and other great circles, is considered at the centre of the earth. The latitude of a place may be determined by ascertaining the distance of its zenith from the celestial equator. If, therefore, the declination and zenith distance of a heavenly body be known, the latitude of the place of observation may be determined. The declination of a heavenly body, as before defined, is its distance from the celestial equator, either north or south. At sea, the meridian zenith distance of a body in the heavens may be obtained by observing its altitude when on the meri- dian, or by two altitudes. When the altitude of the sun or moon are taken, four corrections are required, semi-diameter , parallax, depression of the horizon, and refraction. In a planet, the semi-diameter and parallax can be but a few seconds. In a star, they are imperceptible. For the semi-diameter of the sun or moon, see Table 1 5th. For parallax, depression of the horizon, and refraction, see those articles. On land, the irregularity of the sensible horizon renders it necessary to have recourse to an artificial horizon. TJhis may be made of mercury, molasses, or other fluid not easily affected by the wind. Such horizon does not necessarily re- quire allowance for depression of the horizon, as it may have the same elevation as the eye of the observer. Suppose, that on the 4th of July, 1825, the sun's declination by tables 10th, llth, and 12th, was found to be 22 53' 40", when it passed the meridian of New-York, and at that time the sun's true zenith distance, after proper allowances, was found to be 17 48' 20", what was the latitude of the place of observation ? 176 LATITUDE, Zenith distance 17 48' 20' Declination * 22 53' 40/> Answer 40 42' 0" Suppose Sirius, or the Dog star, at 16 30' south declina^ tion, observed to pass the meridian of a place with a zenith distance of 66 27', what is the latitude of the place ? Zenith distance 56 27' Declination 16 30' Answer 39 57' The latitude of a place may be determined by observing the altitude of its elevated pole. This altitude is always equal to the latitude of the place. The north pole of the earth at present points nearly to a particular star, called from this circumstance, the pole star. Dr. Flint, in his " Survey," makes the declination of this star, on the first of January, 1810, 88 17' 28", increasing 19. 5 annually. Hence its declination, January 1 st, 1825, was 88 22' 20", and its distance from the pole 1 37' 40". Take the altitude of this star above and below the pole. Add these altitudes, and half their sura is the altitude of the pole, and, of course, the lati- tude of the place. The pole star is of the same altitude of the pole, when at its greatest elongation from the pole, east or west. To obtain the greatest elongation, observe that the star Alioth of the constellation Ursa Major, or the Great Bear, the pole star, and the star Gamma of Cassiopeia, are nearly in a Jine.-r- When this line is in a horizontal direction, or perpendicular to the plane of the meridian, the pole star is at its greatest elongation, east or west, being on the side of the pole next to the Gamma of Cassiopeia and opposite to Alioth. Hence it is east, when Alioth is west, and it is west when Alioth is east. *The student's judgment, with a little attention, will easily determine, whether in the zenith distance and declination he ought to add or subtract. LONGITUDE. 177 For practical methods of obtaining the latitude of places, see Dr. Bowditch's standard work, " The new American Practical Navigator." SECTION II. LONGITUDE. The best method of determining longitude has long been a desideratum with the public. It has excited the attention not only of the mariner, but of the geographer, the mechanic, the statesman and the philosopher. We are informed, that Philip III, king of Spain, was the first who offered a reward* for the discovery of longitude. The States of Holland, then the rival of Spain, as a maritime power, soon after followed the example. The regent of France, during the minority of Lewis XV. offered a great reward for the discovery of longitude at sea. In the time of Charles II. of England, about they ear 1675, a royal observa- tory was built at Greenwich, and, by the intercession of Sir Jonas Moore, Mr. Flamstead was appointed astronomer royal. Instructions were given to him, and his successors, " That they should apply themselves with the utmost care and dili- gence to rectify the tables of the motions of the heavens, and the places of the fixed stars, in order to find out the so much desired longitude at sea, for the perfecting of the art of navigation." The British parliament, in the year 1714, offered a reward for the discovery of longitude, " the sum of 10,OOOZ. if the method determined the longitude tolof a great circle, or 60 geographical miles ; of 15,000/. if it determined it to 40 miles; and of 20,000/, if it determined it to 30 miles, with this proviso, that if any such method extend no further than * A hundred thousand crowns. LONGITUDE. SO miles adjoining to the coast, the proposer shall have no more than half such reward. The act also appoints the first lord of the admiralty, the speaker of the house of commons, the first commissioner of trade, the admirals of the red, white, and blue squadrons, the master of Trinity house, the president of the royal society, the royal astronomer at Green- wich," and several others, u as commissioners for the longi- tude at sea." On this act, Mr. John Harrison received the premium of 20,OOOJ. for his "time-keeper." Several other acts were passed in the reigns of George II. and George III. for the encouragement of finding longitude. In the year 1774, an act passed repealing all the former acts respecting the finding of longitude, "and offering separate rewards to any person, who shall discover the longitude, either by the lunar method, or by a watch keeping true time, within certain limits, or by any other method. The act proposes, as a reward for a time-keeper, the sum of 5,000/. if it determine the longitude to 1, or 60 geographical miles ; the sum of 7,500Z. if it determine the same to 40 miles ; and the sum of 10,OOOZ. if it determine the same to 30 miles, after proper trials specified in this act." This, we are informed, is the last act of the British parliament on the subject. The United States have not been inattentive to the subject of longitude ; so far, at least, as respects establishing a first meridian for themselves. As early as the year 1809, Mr. William Lambert of Virginia presented a memorial to Con- gress on the subject. He commences his memorial by stat- ing, " That the establishment of a first meridian for the United States cf America, at the permanent seat of Gov- ernment, hy which a farther dependence on Great-Britain, or any other foreign nation, for such a meridian, may be en- tirely removed, is deemed to be worthy the consideration and patronage of the national legislature." In March, 1810, a select committee of the House of Representatives, of which Mr. Pitkin of Connecticut was chairman, made an interest- ing report on Mr. Lambert's memorial. An extract from it is deemed pertinent to the subject. XONGITUDE. 179 ** The committee have deemed the subject worthy the at- tention of Congress, and would, therefore beg leave to ob- serve, that the necessity of the establishment of a first me- ridian, or a meridian, which should pass through some partic- ular place on the globe, from which geographers aud naviga- tors could compute their longitude, is too obvious to need elucidation. The ancient Greek geographers placed their first meridi- an to pass through one of the islands, which by them were called the Fortunate Islands, since called the Canaries. Those islands were situated as far west as any lands that had then been discovered, or were known by ancient navigators in that part of the world. They reckoned their longitude east from Hera, or Junonia, supposed to be the present island of Teneriffe. The Arabians, it is said, fixed their first meridian at the most westerly part of the continent of Africa. In the fif- teenth and sixteenth centuries, when Europe was emerging from the dark ages, and a spirit of enterprise and discovery had arisen in the south of Europe, and various plans were formed, and attempts made, to find a new route to the East Indies, geographers and navigators continued to calculate longitude from Ferro, one of the same islands, though some of them extended their first meridian as far west as the Azores, or Western Islands. In more modern times, however, most of the European nations, and particularly England and France, have establish- ed a first meridian to pass through the capital, or some place in their respective countries, and to which they have lately adapted their maps, charts, and astronomical tables. It would, perhaps, have been fortunate for the science of geography and navigation, that all nations had agreed upon a first meridian, from which all geographers and navigators might have calculated longitude ; but as this has not been, done, and, in all probability, never will take place, the com- mittee are of opinion, that, situated as we are in this west- ern hemisphere, more than three thousand miles from any 180 LONGITUDE. fixed or known meridian, it would be proper, in a national point of view to establish a first meridian for ourselves ; and that measures should be taken for the eventual establishment of such a meridian in the United States. In examining the maps and charts of the United States, and the particular states, or their sea coasts, which have been published in this country, the committee find, that the pub- lishers have assumed different places in the United States as first meridian. This creates confusion, and renders it difficult, without considerable calculation, to ascertain the relative situation of places in this country. This difficulty is increas- ed by the circumstance, that in Louisiana, our newly acquir- ed territory, longitude has heretofore been reckoned from Paris, the capital of the French empire. k The exact longitude of any place in the United States be- ing ascertained from the meridian of the observatory at Green- wich, in England, a meridian with which we have been con- versant, it would not be difficult to adapt all our maps, charts, and astronomical tables, to the meridian of such place. And no place, perhaps, is more proper than the seat of govern- ment." The memorial, the report of the committee, and papers accompanying were afterwards referred to Mr. Monroe, the late President of the United States, then Secretary of State. In his report he says : " The Secretary of State has no hes- itation to declare his accord with the committee, in their opinion in favour of the establishment of a first meridian for the United States, and that it should be at the city of Wash- ington, the seat of government." " The United States have considered the regulation of their coin and their weights and measures attributes of sove- reignty. The first has been regulated by law, and the sec- ond has occasionally engaged their attention. The estab- lishment of a first meridian appears in a like view, to be not less deserving of it ; at least, until by common consent, some particular meridian should be made a standard." LONGITUDE. 181 In accordance with this sentiment was that of a committee of the House of Representatives, of which Dr. Samuel L. Mitchell, of New-York, was chairman, and to which the subject was again referred. To these high authorities may be added that of the illus- trious Washington, as stated by Mr Lambert in his address to the President of the United States on the subject, in 1821. " The illustrious personage, by whose name the metropolis of the American Union has been designated, unquestionably intended that the Capitol, situated at, or near, the centre of the District of Columbia, should be a first meridian for the United States, by causing, during the first term of his Presi- dency, the geographical position of that point, in longitude , and its latitude 38 53' north, as found by Mr Andrew Ellicott to the nearest minute of a degree, to be recorded in the original plan of the city of Washington- 77 The apparent, or relative time, differs one hour for every 15 of longitude, or four minutes for a degree. To the east it is later, to the west, earlier. When it is noon with us, it is one P. M 15 east ; eleven AM 15 west Washington is 76 55' 30" west of Greenwich. When it is noon at Green- wich it is 6h 52m, 18s. A. M. at Washi?igton. Calcutta is 163 32' east of Philadelphia. When it is noon at Philadel- phia, it is lOh. 54m. 8s. P. M. at Calcutta If, therefore, by observation on the heavenly bodies, or other methods, the time of day at the meridian, from which the longitude is reckoned, can be known, and also the time at the place of observation, the difference turned into motion, by Table 16, will show the longitude. One method of determining longitude is by a good time- keeper, clock or watch. Such timekeeper, set for any meridian, will not correspond with the apparent time, when carried east or west. But its difference from the apparent time, at the place of observation, would show the difference 23 182 LONGITUDE. of longitude, if perfect dependence could be placed on suck time-keeper. None, however, has yet been invented, on which perfect reliance can be placed, at all times and in all places. Even the time-keeper of William Harrison, which had made a voyage from England to Barbadoes, and back, varying but 54 seconds in 156 days, CMP, as was thought with proper allowance, only 15 seconds in that time, was found subject to considerable error, when tried at the royal observ- atory, by Dr. Maskelyne. Eclipses of the moon early attracted attention, as a means of finding longitude. The moon be ing deprived of her borrow- ed light by immersion in the earth's shadow, all to whom she is visible must see the beginning and end of a lunar eclipse, at the same absolute, time. The difference, therefore, of apparent time, as before shown, converted into motion, w!ll give the longitude. " But it is not easy to determine the exact moment, either of the beginning or ending of a lunar eclipse, because the earth's shadow, through which the moon . passes, is faint and ill defined about the edges." It is con- sidered, that the rays of light, refracted in the atmosphere of the earth, render the moon visible in the midst of a central eclipse. These rays being more dense near the edges of the shadow, must render the extremes very uncertain. Eclipses of the sun may be used for determining longitude. Th*se with proper allowances may form an accurate method. But they happen seldom, and require a nicety of calculation. They nre considered of but little practical utility. Eclipses of Jupiter's satellites have been before mentioned, as forming another method of determining longitude. These like those of the moon are seen at the same absolute time at all places, where they are visible. From the difference of apparent time, therefore, the longitude may be deduced. Happening: very often, they form an excellent method of determining longitude on land But it is said the difficulty of observation renders them of but little practical utility at sea. LONGITUDE. 163 Another method of determining longitude, of great practi- cal importance, is by Lunar observations. "This method of finding the longitude is the greatest modern improvement in navigation. The idea, however, is not modern, but it has not been applied with any success until within the last fifty years. M. de la Lande mentions certain astronomers, who, above two hundred years ago, proposed this method, and contended for the honour of the discovery ; but its present state of im- provement and universal practice, he very justly ascribes to Dr. Maskelyne. The discovery, indeed, seems to claim less honor than its subsequent improvements. It is one of those things which are obvious in theory but difficult in practice." When John Morin, professor of mathematics, at Paris, proposed to Cardinal Richelieu, in the year 1635, a method of solving the problem respecting the longitude, very similar to the lunar method now in use, it was rejected as of no practical utility. Dr. Maskelyne first proposed and superintended the con- struction of the Nautical almanack, lathis is inserted the angular distance of the moon from the sun and certain fixed stars for the beginning of every third hour in the day, calcu- lated for the meridian of Greenwich. We are not to under- stand, however, that these distances are such as they would appear to an observer at Greenwich, but at the centre of the earth. They are calculated for Greenwich time. " If therefore, under any meridian, a lunar distance be observed, tke difference between the time o' observation and the time in the al- manack, when the same distance was to take place at Greenwich, will show the longitude " When the distance would be the same at Greenwich, can be easily found by calculation. For the distance being computed, and set down in the almanack for every three hours, any particular distance can easily be found by proportion, the irregularity of the moon's motion, affecting but little for a short intervening time between the times specified in the tlmanack. In these observations great care must be taken to apply the corrections for parallax, refraction, and depression. 184 LONGITUDE. The Nautical almanack is annually published hy the com- missioners of longitude in England. The stars selected for this almanack are nine, viz. Stars. Constellations. Alpha* Aries AUebaran Taurus Pollux Gemini Regulus Leo Spica Virgo Antares Scorpio Altair Aquila Foraalhaut Pisces Australis Markab Pegasus Except near the time of new moon the angular distance of the moon from these, and from the sun, may be taken at any season, when the weather is clear, and the objects more than 8 or 10 degrees above the horizon. For practice in finding longitude with the necessary tables, the student is again referred to Dr. Bowditch's useful work, the " Practical Navigator." While degrees of latitude remain of equal length, in every part of the earth, except a small variation on account of the earth's spheroidical figure, those of longitude decrease from the equator to the poles, where they become extinct. To find the extent of a degree of longitude at any degree of lati- tude, the proportion is, as radius is to the co-sine of the lati- tude ; so is the number of miles in a degree of longitude, at the equator, to the number of miles in a degree of longitude, at such latitude. The following table may be of use to the student, not only as giving the number of miles in a degree of longitude, at any distance from the equator, but for a comparison between geographical and statute miles. 69J statute miles are taken as the measure of a degree at the equator. This is common reckoning, and will be found extremely near the truth. * Not a proper name, but the first star of the constellation. LONGITUDE. 185 TABLE OF GEOGRAPHICAL AND STATUTE MILES IN A DEGREE OP LONGITUDE AT EACH DEGREE OF LATITUDE. De^. Geogra' Statute Dej;. Geojyra'i Statute Deg iGoogra'l Statute l.^t -!" ; e . nii' s. !'. ,m>s. miles iat I rni'es miles. 1 59.99 69.49 31 51. 43 : 59.57 61 29.09 33.69 2 59.96 69 46 32 50.88 58.94 62 28.17 3263 3 59 93 69 40 33 50.32 58.29 63 2724 31.55 4 59.35 69,33 34 49.74,5762 64 26.30 3047 5 59 77 69.24 35 49 15 56 93 65 2536 2-J.37 6 59.67 69 12 36 48.54i56.23 66 24.40 2827 ? ; 59.55 6898 37 47 92 '55.51 67 23 44 27 16 8^5942 6K82 38 4728 54.77 68 22 48 2604 9 59 26 68.64 | 39 46 63 54 01 69 21 50 24 91 10 : 59 09 68.44 j 40 45 96 53 24 70 20.52 2377 11 58.90 68 22 41 4528 52.45 71 1953 22.63 12 5^.69 67 98 42 4459 51.65 72 1854 21.48 13 58.46 67.72 43 43 88 50.83 73 1754 20.32 14 58.22 67 43 44 43. 16! 49 99 74 1654 19.16 15 57.96 67.13 45 42.43 49 14 75 15.53 17 99 16 57.68 66.81 46 41 68 4828 76 1452 16.81 17 57.38 66.46 47 40.92 4740 77 13.50 1563 18 57.06166 10 48 40 15 46.50 78 12.47 14.45 19 56 73 65.71 49 39.36 4560 79 11.45 1326 20 56.38 65.31 50 38.57 44.67 80 1042 12.07 21 MJ.Ol 64.88 51 37.76 43.74 81 939 10.87 22 55.63 64-44 52 36.94 42.79 8> 835 967 23 55.23 63.98 53 36.11 41.83 83 7.31 847 24 54.81 63.49 54 3x27 4085 84 627 7.26 25 54.38 62.99 55 34.41 39.86 85 5.23 606 26 53 93 62.47 56 33.55 3886 86 4.19 485 27 53.46 61.92 57 3,2 68 3785 87 3 14 364 28 5298 61 36 58 31.80 36.83 88 2.09 2.43 29 52.48 60.79 59 3^.90 35.80 j 89 1.05 1.21 30(51.96 60 19 60 ; 3000 34.75 90 0.00 000 ( 186 ) CHAPTER XVII. DEPRESSION OF THE HORIZON. Connected with the finding of latitude and longitude, and thus, in some measure, with astronomy, is the depression or dip of the horizon. This is the angle of depression made by the visible horizon below the true sensible horizon at the place of observation. It arises from the elevatkm of the observer's eye. The higher the elevation of this, the more the visible horizon is depressed. Let A B D be a great circle of the earth, C its centre, E the elevation of an observer's eye, F G H a part of the moon's orbit, ./If the moon, E G a line parallel to the sen- sible horizon ; then will the angle G E H be the depression of the horizon to such an observer. The apparent altitude of the moon to an eye so elevated, would be the angle M E H ; but her true altitude is the angle M E G. The de- pression of the horizon must, therefore, be subtracted from the observed altitude, in order to obtain the true altitude. This correction applies in taking the altitude of the sun, or other heavenly body ; and is the same, whatever be the distance or height of the object observed. The depression of the horizon may be found for any eleva- tion of the eye by trigonometry. For in the triangle B C jE, the side B C is the semi-diameter of the earth, and the side C E is the sum of the height of the eye added to the semi-diameter of the earth, the angle C B E is a right an- gle. Hence, two sides and an angle are given to find the other angles. The angle C E B being found and subtracted from 90, leaves the angle G E //, the depression of the horizon. By the same figure, the depression of the horizon being know by observation or otherwise, the elevation of the ob- server's eye may be ascertained. Thus the height of a mountain may be found, when the visible horizon can be ac- ARTIFICIAL GLOBES. 187 curately taken ; for the depression of the horizon is found by observation. The following table, extracted for the purpose, shows the depression of the horizon at the specified heights. Wl tw* t tS O Oi. W) K) ca UT jO_eo N; .&. to Ojp p O o CO CO ~J 05 05 Or U CO INJ i J33J CHAPTER XVIII, ARTIFICIAL GLOBES. The problems solved by artificial globes, astronomical in their nature, form a proper appendage to astronomy. A globe is a sphere or round body, of which every part of the surface is equally distant from the centre. There are two kinds of artificial globes, terrestrial and ce- lestial. On the terrestrial is represented the surface of the earth, diversified with land and water, and the principal di- visions of each, forming a spherical map of the whole ; on the celestial, the visible heavens, as distinguished into constellations, by the picture of the animal or other object of the constellation, and the principal stars, by which it is formed. A globe of either kind is placed upon a f ame for convenient use. On each are represented the great imag- inary circles of the sphere, the tropics and the polar circles. CIRCLES ON THE TERRESTRIAL GLOBE. The equator, about one eighth of an inch broad, is gradua- ted for the longitude, 180 each way from the first meridian. 188 ARTIFICIAL GLOBES. The ecliptic, about the same breadth, is inclined to the equator in an angle of 23 23', is divided into signs, and sub- divided into degrees, beginning at the first of Aries. The meridians, drawn with dark lines perpendicular to the equator, meet at the poles. 12 of these, 24 semicircles, form hour lines. One of the same passing through the equi- noctial points, is the equinoctial colure ; another passing through the solstitial points, is the solstitial colure. Besides these, there is a meridian of brass encompassing the globe, half an inch or more broad, graduated off the eastern side. on the upper semicircle of this, the graduation begins at the equator, and ends with 90 at each pole. On the lower sem- icircle it begins at the poles, and ends with 90 at the equator. The horizon is represented by a broad circle of wood, divi- ded at the four cardinal points, north, south, east, west. On this horizon next to the globe, are the amplitudes, a grad- uation of four nineties, beginning at the enst and west points. Without these is a graduation of four nineties, beginning at the north and south points, for the azimuths. Placed next to these are the 32 points of the compass. Next are the figure, the name, and the character of the twelve signs ; then the graduation of each as in the ecliptic. The exterior circle on the horizon represents the days of the months, so divided and adjusted to the signs,* that each day of a month is placed at the degree of a sign in which the sun is at that time. Between the divisions of the days are small figures, showing bow much the sun is fast or slow of the clock, marked , when the sun is fast of the clock, and +, when it is slow. Each tropic is represented on a terrestrial globe, by a sin- gle dark or coloured line, 23 28 from the equator ; each polar circle in the same manner, 23 28 from the pole. Peculiar to this globe are parallels of latitude, drawn to each ten degrees. At the north pole is an hour circle about two inches in di- ameter, divided into 24 parts, and numbered into two twelves, ARTIFICIAL GLOBES. 189 with a naoveable index attached to the brazen meridian. At the so-lib pole is a similar circle, and similarly divided and numbered, but without an index, time being computed from the brazen meridian. There is some diversity in globes. The description an- swers to the one present with the author. Some globes have a. quadrant of altitude, a thin strip of brass graduated into 90, equal to 90 of a great circle on the s;lobe. The circles of an artificial globe are best learned by in- spection, when the globe is at hand. For usirrg ,\ globe stand t>n the east of it, facing the gradu- ated side of the brazen meridian. This is the side to be used. To rectify the globe for the latitude of a place or any declination of the sun, is to elevate the nearest pole equd to the latitude of the place or the declination When it is rectified for a place, such place brought to the brazen meridian is at the top or highest point of the globe. For instance, to rectify the globe for the latitude of Washington, elevate the north pole till 38 53' on the lower semicircle of the brazen meridian comes to the upper side of the wooden horizon ; then Washington brought to the brazen meridian will be on the top of the globe. When the globe is rectified for the sun's declination, the sun's place in the ecliptic, brought to the meridian, is on the top of the globe. Suppose you would rectify the globe for 20, south declination of the sun, raise the south pole till 20, on the brazen meridian below the pole, come against the upper side of the horizon. This will bring the sun's place, when at the meridian, to the most elevated point of the globe. Great accuracy is not to be expected, in the solution of problems on artificial globes. The general knowledge to be obtained, however, is important. 24 190 ARTIFICIAL GLOBES. PROBLEMS TO BE SOLVED BY THE TERRESTRIAL GLOBE. PROBLEM I. To find the Latitude and Longitude of a place. Bring the place to the meridian,* Over it, on the merid- ian, is the latitude ; and at the intersection of the meridian and the equator, is the longitude. What is the latitude and longitude of Jerusalem ? Answer, about 32N. 35E. What is the latitude and longitude of Canton, in China ? 23N. 113E. PROBLEM II. To find a place, the latitude and longitude of which are given. Find the longitude on the equator, which bring to the me- ridian ; then directly under the latitude, found on the merid- ian, is the place. What place is in 33 51'S. 151 16 E. ? Port Jackson* What place is in 12 3'S. 76 55'W. ? Lima. PROBLEM III. To find the difference of latitude between two places. Bring the places successively to the meridian, and note the latitude of each. If the latitudes be of the same name, both north, or both south, subtiact the less from the greater, the remainder is the difference of latitude between them. If the latitudes be of different names, one north and the other south, their sum is the difference sought. W'hat is the difference of latitude between Baltimore and Mexico ? 20. * When a place is said to be brought to the meridian, the brazen meridian is intended. ARTIFICIAL GLOBES. 191 Give the difference of latitude between Charleston S. C. and Buenos Ayres. 67<> SO/. The difference of latitude between Richmond, Virginia, and Lima is 49 30-. PROBLEM IV. To find the difference of longitude between two places. Find the longitude of each, as before directed, and, if the longitudes be of the same name, their difference is the dif- ference sought. But if they be of different names, their sum, if le*s than 180, is the result sought ; if the sum be more than 180, subtract it from 360, the remainder is the difference of longitude between the places. What is the difference of longitude between Portsmouth, N. H. and Cadiz? 610'. Reqnired the difference of longitude between Paris and St. Louis. 92. Find the difference of longitude between Batavia and Cincinnati. 168. PROBLEM V. To find the distance between two places on the globe. With a pair of dividers, gently placed upon the globe,* take the extent between the places. Lay this extent on the equator and note the number of degrees. This number, multiplied by 69, gives the distance in statute miles. Mul- tiplied by 60, it gives the distance in geographical miles. When a globe has a quadrant of altitude, the number of degrees between places may be ascertained by laying it from one to another on the globe. What is the distance from Boston to London ? About 3340 miles. * Great care must be taken to apply the dividers laterally, and not point them against the globe. To avoid the danger of injury from dividers, the sti sight edge of a strip of paper may be used in taking the distance of objects on the globe. ARTIFICIAL CLOD K I. Give the dittance from New-York to St. Petersburg. About 4300 miles. Cape St. Rogue is distant from Cape Verd 1900 miles 1640 geo. miles. "Washington is distant from Gibraltar 3860 miles. PROBLEM VI. To find the Jlntoeci and Perioeci of any place. Bring the place to the meridian, and observe the latitude ; find the same latitude in (he opposite hemisphere, under which latitude are the Antoeci. 9 With the given place at the meridian set the index at 12, turn the globe till the index points to the opposite Id, then under the meridian at the given latitude are the Perio- eci. The people in the southern part of Chili are Antoeci, and the Chinese Tartars, Perioeci to the inhabitants of New- England. jM? PROBLEM VII. To find the Antipodes of any place. Bring the place to the meridian, note the latitude, and set the index at 12. Turn the globe till the index points to the other 12, then in the opposite hemisphere, under the merid- ian at the same latitude are found the Antipodes, of the place. Some of the New Zealanders are Antipodes to the inhab- itants of Spain. The inhabitants of the Society Islands are Antipodes to those in the interior of Africa. ARTIFICIAL GLOBES. 193 PROBLEM VIII. >v The hour of the day at any place being given, to find the time at any other place. Bring the place where the hour is given to the meridian, and set the index at the hour ; turn the globe till the other place comes to the meridian, the index will show the hour required. When it is 9 o'clock, A. M. at Boston, what is the time at Cairo in Egypt ? 3h. 47m P M. When it is noon at Washington, what, time is it at the Sandwich Islands ? 6h. 45m. A. M. PROBLEM IX. The hour of tlie day at any place being given, to find all those places, where it is any other gven hour. Bring the place to the meridian ami set the index at the hour proposed for that place ; turn the jrlobe till the index points to ibe other given hour ; the places sought will be un- der the meridian. When the time is 4 o'clock, A. M. at New- York, where is it 11, A. M.? At otc Petersburg in Russia ; in the western part of the Caspian Sea ; the eastern part of t lOh. 30m P. M. and sets at 3h. 15m, A. M of the 21st. At New-York, on the 1st of May, Arcturus rises at 4h. 23rn P. M is on the meridian at llh. 32m. P. M., and sets at 6h. 40m. of the following day. PROBLEM VIII. To find the altitude nf a star at any given time. Rectify the globe for the latitude of the place. Bringthe sun's place in the ecliptic to the meridian and set the index at 12. 1 Turn the globe till the index points to the time pro- posed Then with the quadrant of altitude, or dividers, take the nearest distance of the star from the horizon ; the num- ber of degrees on the quadrant, or in the extent of the dividers app led to the equator, shows the altitude. What is the altitude of Procyon, as seen at Washington, February 1st, at 7 o'clock, P. M. ? 32 C 40. What is the altitude oi Vega as seen from New-Haven, September 26, at 2 o'clock A. M. ? 9 30' above the western horizon. PROBLEM IX. Having the altitude of a star given, to know the time ofnigJit. Rectify the globe for the latitude of the place. Bring the sun's place in the ecliptic to the meridian, and set the index at 12. Turn the globe till the star comes to the altitude proposed ; the index will point to the hour required. What is the time of night at Philadelphia, on the 20th of ARTIFICIAL GLOBES. 201 October, when the largest star of the Pleiades is 15 P above the eastern horizon ? 8h P. M. What is the time of night at Boston, on the last day of August, when Arcturus is 10 above the western horizon? 9h. 45m P. M. This and the preceding problem may be applied to finding the altitude of the sun, and the time ot day, by setting the index at 12, when the sun's place is brought to the meridian, turning the globe, and taking the altitude from the height of his place and the time from the altitude, as in the case of a star. PROBLEM X. The latitude of a place being given, to place the globe so as to represent the appearance of the heavens at any hour proposed. Rectify the globe for the latitude of the place. Bring the sun's place in the ecliptic to the meridian and set the index at 12 Turn the globe eastward for the forenoon, westward for the afternoon, till the index points to the given hour. The globe will then represent the appearance of the heavens at the time proposed Represent the appearance of the heavens at Washington, March 20th. at 7 o'clock, P. M. Arcturus is rising at 25 north of east, Procyon has nearly arrived at the meridian ; Sirius is a little past ; the bright constellation, Orion, a little farther past Nearly in the same rank is Capella to the north. In front of all these and a little farther in western declination, are Aldebaran, the Hyades, and Pleiades. Represent the appearance of the heavens at Boston, Sep- tember the 23rd, 7h. 40m. P. M. Fomalhaut is a little above the eastern horizon. Altair is on the meridian ; Vega is a little declined from the zenith. The constellations, Corona, Borealis. and Bootes, with bright Arcturus, fast declining, adorn the western hemisphere. 202 ARTIFICIAL GLOBES. When the latitude and apparent time, at different places, are the same, the appearance of the heavens is the same, notwithstanding a difference of longitude ; or the same with a very trifling variation. Lisbon, in Portugal, is nearly in the same parallel of latitude, as Washington City. At 10 o'clock in the evening, therefore, the appearance of the heavens is very nearly the same at Lisbon, as at 10 in the evening observed from Washington. The general appear- ance is altered but little by a small difference of latitude. The distance from Boston to Washington will not make a great alteration. A familiar use of the globes is recommended to the student. It will greatly improve his knowledge of geography and as- tronomy. It will make him more interested in contemplating the objects of the visible heavens, a delightful and innocent amusement for the evening, or the most lonely hours of night. What is much more ; by observation on the celestial canopy, he must be irresistibly led from the greatness of the scenery to the contemplation of the immensity and infinite goodness of the GREAT AUTHOR. ASTRONOMICAL TABLES. TABLE I Mean new moon in March, with the mean anomalies of the sun and moon, and the SUB'S mean distance frm the moon's ascending node for the 19th century. Years of Christ Mean new moon in Mitch. Sun's anomaly. Moon's anomaly. Sun s mean dis- tance from node. D. H M S. S- i a 5 o / // S. o / // 1800 1801 1802 1803 1804 24 19 14 35 14 4 3 12 3 12 51 48 22 10 24 28 10 19 13 4 8 23 19 55 8 12 35 46 8 1 51 37 8 20 13 48 8 9 29 39 10 7 52 36 8 17 40 41 6 27 28 46 6 3 6 b2 4 12 53 57 11 3 68 23 11 12 1 10 11 20 3 58 28 46 59 1 6 49 46 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 29 16 45 44 19 1 34 21 8 10 22 57 26 7 55 37 15 16 44 13 8 27 51 49 8 17 7 40 8 6 23 31 8 24 45 42 8 14 1 33 3 18 31 2 1 28 19 7 8 7 12 11 13 44 18 9 23 32 23 2 25 32 47 2 23 35 35 3 1 38 22 4 10 21 23 4 18 24 10 6 1 32 50 <23 23 6 30 12 7 54 6 1 16 42 43 20 14 15 23 8 3 17 24 8 21 39 35 8 10 55 26 8 11 17 8 18 33 27 8 3 20 28 7 8 57 34 5 18 45 39 S 28 33 44 3 4 10 49 4 26 26 68 6 5 9 69 6 13 12 46 6 21 15 33 7 29 58 35 1815 1816 1817 1818 1819 9 23 3 59 27 20 36 39 17 5 25 15 6 14 13 52 25 11 4f> 32 8 7 49 18 8 26 11 29 8 15 27 20 8 4 43 11 8 23 5 21 1 13 58 64 19 36 10 29 24 5 9 9 12 10 8 14 49 15 8 8 1 22 9 16 44 23 9 24 47 10 10 2 49 58 11 11 32 59 .820 1821 1822 1823 1P24 1325 1826 1827 1828 1829 13 20 35 8 3 5 23 45 22 2 56 24 11 11 45 1 29 9 17 41 8 12 21 12 8 1 37 4 8 19 59 14 8 9 15 5 8 27 37 16 6 M 37 21 5 4 25 26 4 10 2 31 2 19 50 36 1 25 27 42 11 19 35 46 11 27 38 33 1 6 21 35 1 14 24 22 2 23 7 23 18 18 6 17 8 2 54 54 ?7 27 33 15 9 16 10 4 18 4 47 8 16 53 7 8 6 8 58 8 24 31 8 8 13 46 59 8 3 2 50 5 15 47 10 15 3 52 9 20 40 57 8 29 2 6 10 17 8 3 1 10 10 3 9 12 58 4 17 55 59 4 25 58 46 5 4 1 33 1830 1831 1832 1833 1834 23 15 37 26 13 26 3 i 9 14 39 20 6 47 19 9 15 35 56 8 21 25 1 8 10 40 52 7 29 56 43 8 18 18 54 8 7 34 45 5 15 54 13 3 25 42 18 2 5 30 23 111 7 29 11 20 55 34 6 12 44 35 6 20 47 22 6 28 50 8 7 33 10 8 15 35 58 1835 1836 1837 1838 1839 28 13 8 35 16 21 57 12 6 6 45 49 25 4 18 28 14 13 7 5 8 25 56 55 8 15 12 46^ 8 4 28 37 8 22 50 48 8 12 6 39 10 26 3* 39 9 6 20 44 7 16 8 49 6 21 45 55 5 1 34 9 24 18 59 10 2 21 46 10 10 24 33 11 19 7 35 11 27 10 22 204 ASTRONOMICAL TABLES. Yt-ars f Christ | Mean new moon Iin March Sun's anomaly Moon's anomaly. Sun's distance from node D. H. M. S g o / // S. o / // S. o / it 1840 1841 1842 1843 1844 2 21 55 41 21 19 28 21 11 4 16 58 30 1 49 37 18 10 38 14 8 I 22 30 8 19 44 40 8 9 32 8 27 22 12 8 16 38 33 3 11 22 5 2 16 59 11 26 47 16 2 24 21 10 12 12 2r 5 13 9 1 13 56 10 1 21 58 58 3 41 59 3 8 44 46 1845 1846 1847 18(8 1849 7 19 26 50 26 16 59 30 16 1 48 7 4 10 36 43 23 8 9 23 8 6 54 24 8 ?4 16 35 8 13 32 26 8 2 48 17 8 21 10 27 8 e* 31 7 27 37 37 6 7 25 42 I 17 13 47 3 22 nO 53 3 16 47 33 4 25 30 35 5 3 33 22 5 11 36 9 6 20 19 10 1850 1851 1852 1853 1854 12 16 58 2 1 46 36 19 23 19 16 9 8 7 52 28 6 40 32 8 10 26 18 7 29 42 10 8 18 4 20 8 7 20 11 8 25 42 21 fc 2 38 58 12 27 3 11 18 4 8 9 27 52 13 9 3 29 19 6 *8 21 58 7 6 24 45 8 15 7 46 8 23 10 33 10 1 53 35 1855 1856 1857 1858 1859 17 14 29 9 5 23 17 45 24 20 50 25 14 5 39 1 3 14 27 38 8 14 58 13 8 4 14 4 8 22 36 14 8 11 52 5 8 1 7 56 7 13 17 24 5 23 5 29 4 28 42 34 3 8 30 40 1 18 18 45 10 9 56 22 10 17 59 8 11 26 42 19 4 44 58 12 47 45 1860 1861 1862 1863 1864 21 12 18 10 20 48 54 29 18 21 34 19 3 10 10 7 11 58 47 8 19 30 7 8 8 45 58 8 27 8 8 8 16 23 59 8 5 39 61 23 55 50 11 3 43 55 10 9 21 1 8 19 9 6 6 28 57 11 1 21 30 46 1 29 33 33 3 8 16 35 3 16 19 92 3 24 22 9 1865 1866 1867 1868 1869 26 9 31 27 15 18 20 3 5 3 8 40 23 41 20 12 9 29 56 8 24 2 1 8 J3 17 52 8 2 33 43 8 20 55 64 8 10 11 45 6 4 34 16 4 14 22 21 2 24 10 27 1 29 47 32 9 35 37 6 3 5 10 511 7 58 5 19 10 45 6 27 53 46 7 5 56 33 1870 1871 1872 1873 1874 1 18 18 33 20 15 51 12 9 39 49 27 22 12 29 17 7 1 5 7 29 27 36 8 17 49 46 8 7 5 37 8 25 27 48 8 14 43 39 10 19 23 42 9 25 48 8 4 48 53 7 10 25 58 5 20 14 3 7 13 59 21 8 22 42 22 9 45 9 10 9 28 10 10 17 30 58 1875 187C 1877 1878 1879 6 15 49 42 24 13 22 21 13 22 10 58 3 6 59 35 22 4 32 14 8 3 59 30 8 22 21 40 8 11 37 32 8 53 23 8 19 15 33 4028 3 5 39 14 1 15 27 19 11 25 15 24 11 52 30 10 25 33 45 4 16 4t> 12 19 33 20 22 21 1 29 5 22 1880 1881 18b2 1883 1884 10 13 20 51 29 10 53 31 18 19 42 7 8 4 30 44 26 2 3 23 8 8 31 24 8 26 53 35 8 16 9 26 8 5 25 17 8 23 47 27 9 10 40 35 8 16 17 40 6 26 5 45 5 5 53 50 4 11 30 56 2789 3 15 51 10 3 23 53 58 4 1 56 45 5 10 39 46 ASTRONOMICAL TABLES, 205 TABLE I. Continued. Years of Ch.i>t Mean new moon in March. Sun's auomaly Moon's anomaly. Sun's mean dis- tance from node D. H. M S. S. ' " S. ' " S o / // 1885 1886 1887 1388 1889 15 10 52 4 19 40 37 23 17 13 16 12 2 1 53 1 10 50 29 8 13 3 18 8 2 19 10 8 20 41 20 8 9 57 11 7 29 13 2 2 21 19 1 1176 6 44 12 10 16 32 17 8 26 20 22 5 18 42 33 5 26 45 21 7 5 28 22 7 13 31 9 7 21 33 56 1890 18yl 1892 1893 1894 20 8 23 ^ 9 17 11 46 27 14 44 25 16 23 33 2 6 8 21 3B 8 17 35 13 8 6 51 4 8 25 13 14 8 14 29 5 8 3 44 56 8 I 57 27 6 11 45 32 5 17 22 38 3 27 10 43 2 6 58 48 9 16 58 9 8 19 45 10 17 2 46 10 25 5 33 11 3 8 21 1895 189H 1R97 1898 1899 25 5 54 18 13 14 42 55 2 23 31 31 21 21 4 11 11 5 52 47 8 22 7 7 8 11 22 58 8 38 49 8 19 59 8 8 16 51 1 12 35 53 11 22 23 58 10 2 12 4 9 7 49 9 7 17 37 14 11 51 22 19 54 9 27 56 56 2 6 39 58 2 14 42 45 190| 30 3 25 27 ; 8 26 39 1 6 23 14 20 3 23 25 46 TABLE II. The mean anomalies of" the sun and moon and the sun's mean distance from the moon's ascending node, for 13 mean lu- nations. No. Mean lunations. Sun's anomaly. Moon's anomaly. Suit's distance from node D. H. M. S. S. ' " S. ' " S. * ' " 2 3 4 5 29 12 44 3 59 1 28 6 88 14 12 9 118 2 56 12 147 15 40 15 29 6 19 1 28 12 39 2 27 18 58 3 26 26 17 4 25 31 36 25 49 1 21 38 1 2 17 27 1 3 13 16 2 4952 1 40 14 2 1 20 28 3 2 42 4 2 40 56 5 3 21 10 (j 7 8 9 10 177 4 24 18 206 17 8 21 236 5 52 24 265 18 36 27 295 7 20 30 5 24 37 66 6 23 44 15 7 92 50 34 8 21 56 53 9 21 3 13 6 4 54 3 6 43 3 6 26 32 3 7 22 21 4 8 18 10 4 6 4 1 24 7 4 41 38 8 5 21 52 9625 10 6 42 19 11 12 13 324 20 4 34 354 8 48 37 383 21 32 40 10 20 9 32 11 19 15 51 18 22 10 9 13 59 5 10 9 48 5 11 5 37 6 11 7 22 33 8 2 47 1 8 43 1 * 14 18 22 2 14 33 10 6 12 54 30 15 20 7 206 ASTRONOMICAL TABLES, TABLE HI. The di anon cent Jutha years. fference of new moon in March, with the corresponding lalies and distance of the sun from the node for complete aries of Julian years. Mean new moon in March Sun's anomaly. Moon's anomaly. Sun from node. D H. M. S. S. ' " S ' " ?, ' " 100 200 300 400 500 4 8 10 52 8 16 21 44 13 32 36 17 8 43 29 21 16 54 21 3 19 3 6 38" 12 9 57 18 13 16 24 16 35 30 8 15 21 44 5 43 27 1 16 :> 1 1 10 1 26 55 6 16 48 38 4 1J 27 23 9 8 54 46 1 28 22 9 6 17 49 32 11 7 16 55 600 700 800 900 1000 26 1 5 13 30 9 16 5 5 4 42 54 9 12 53 46 13 91 4 39 19 54 36 23 13 42 11 27 26 29 15 35 4 4 41 3 2 10 22 11 17 32 6 7 7 4 49 3 22 26 33 7 48 16 3 26 44 19 8 16 11 42 4 58 51 4 24 26 14 9 13 53 37 2000 3000 4000 5000 10000 27 18 9 17 12 2 29 53 25 23 34 31 10 7 55 7 20 16 50 14 8 9 21 11 13 7 43 11 17 12 23 10 22 10 45 9 14 21 30 15 36 32 11 27 35 48 5 24 4 11 17 23 20 11 4 46 40 6 27 47 14 311 37 24 54 14 9 8 7 37 6 16 15 14 TABLE IV. Days of the year, reckoned from the beginning of March. f 3 - n > ^ S t-t c a f i c wi > I e <* op 1 -r O 2! < 9 P M a y p- 1 2 3 ^1 5 1 2 3 4 5 32 33 34 35 .36 62 63 64 65 66 93 94 95 86 97 123 124 125 126 127 154 1*5 156 167 158 185 186 187 188 189 215 216 217 218 219 246 247 248 249 250 27b 277 278 279 280 307 308 309 310 ill 338 339 340 341 342 6 7 8 9 10 6 7 8 9 10 37 38 39 40 41 67 68 69 70 71 98 99 100 101 102 128 129 130 131 132 159 160 161 162 163 19J 191 192 193 194 220 ^21 222 223 224 2*1 252 253 254 255 281 282 283 2*4 285 312 313 314 315 316 34.3 344 345 346 347 11 12 13 14 1* 11 12 13 14 15 42 43 44 45 46 72 73 74 75 76 103 104 105 106 107 133 134 135 136 137 164 165 166 167 168 195 196 197 198 199 225 226 227 228 229 266 257 258 259 260 286 287 288 289 290 317 318 39 320 321 348 349 350 351 352 ASTRONOMICAL TABLES, 207 TABLE FV. Continued. 1 00 ? j* > 12 ^? $ ^C-H c_ e^ e <" > ^ 35 n -o * C ' s 5 < a A O Gi BE p 9 cr 16 17 18 19 20 16 17 18 19 20 47 48 49 50 51 77 78 79 80 81 f08 !09 110 111 112 138 139 140 141 142 169 170 171 172 173 200 201 202 203 204 230 231 232 233 234 261 262 263 264 265 291 292 293 294 295 342 323 324 326 326 353 354 355 356 357 21 22 23 24 25 21 22 23 24 25 52 53 54 5i 56 82 83 84 85 86 13 N 15 16 17 143 144 145 146 147 174 175 176 177 178 205 206 207 208, 209 235 236 237 238 239 266 267 268 269 270 296 297 298 299 300 327 328 329 330 331 358 359 360 361 362 26 27 23 29 30 26 27 28 29 30 57 58 59 60 61 87 88 89 90 91 18 19 120 121 122 148 149 150 151 152 179 180 181 182 183 210 211 212 213 214 240 241 242 243 244 271 272 273 274 275 301 302 303 304 305 332 333 334 335 336 363 364 365 366 31 31 92 153 184 245 306 337 TABLE V. The first equation of the mean to the true svzygy. s * Argument. The sun's mean anomaly. Subtract. 5 1 S. iOT. 1 2 3 H. M.. 4 H. M. S". 5 S. H. M S. 1 H. M. S. H. M. S. 000 2 3 12 3 35 4 10 53 3 39 30 2 7 45 30 1 2 3 4 5 4 18 8 35 12 51 17 8 21 24 2 6 55 2 10 36 2 14 14 2 17 62 2 21 27 3 37 10 3 39 18 3 41 23 3 43 26 3 45 25 4 10 57 4 10 55 4 10 49 4 10 3" 4 10 24 3 37 19 3 35 6 3 32 50 3 30 30 3 28 5 2 3 55 2 1 56 6 52 6 48 4 29 28 27 26 25 6 7 8 9 10 25 39 28 65 34 11 38 26 42 39 2 26 9 2 28 29 2 31 57 2 35 22 2 38 44 3 47 19 3 49 7 3 50 50 3 52 29 3 54 4 4 10 4 4 9 39 4 9 10 4 8 37 4 7 59 3 25 35 3 23 3 20 20 3 17 35 3 14 49 41 1 39 56 35 49 31 41 27 31 24 23 22 21 20 fi H 13 14 15 46 52 51 4 55 17 50 27 1 3 36 2 42 3 2 45 18 2 48 30 2 51 40 2 54 48 3 55 35 3 57 2 3 58 27 3 59 49 4 1 7 4 7 16 4 6 29 453' 4 4 41 4 3 40 3 11 59 396 3 6 10 3 3 10 307 23 19 19 5 14 49 1 10 33 I 6 15 19 18 17 16 15 208 ASTRONOMICAL TABLES. TABLE V. Continued. q ~ S. 1 2 3 4 5 S. p OQ H. M. S H. M. S. H. M. S. H. M. S. H. M. S H. M. S- | 161 17 | id 19 20 1 7 45 1 11 53 1 16 1 20 6 1 24 10 2 57 53 3 54 3 3 51 3 6 45 3 9 36 4 2 18 4 3 23 4 4 22 4 5 18 4 6 10 4 2 35 4 1 26 4 12 3 58 52 3 57 27 2 57 2 53 49 2 50 36 2 47 18 2 43 57 1 1 56 57 36 53 15 48 52 44 28 14 13 12 11 10 1 22 23 24 t>b 1 28 12 1 32 12 1 36 10 1 44) 6 1 44 1 3 12 24 3 15 9 3 17 51 3 2<- 30 3 23 5 4 6 5. 4 7 41 4 8 21 4 8 57 4 9 29 3 55 59 3 54 26 3 52 49 3 51 9 3 49 26 2 40 33 2 37 6 2 33 35 2 30 2 2 2b 26 40 2 35 36 31 10 26 44 22 17 9 8 7 6 5 26 27 28 29 30 1 47 64 1 51 46 1 55 37 1 59 26 2 3 12 3 25 36 3 28 3 3 30 26 3 32 45 3.35 4 9 55 4 10 16 4 10 33 4 10 45 4 10 53 3 47 38 3 45 44 3 43 45 3 41 40 3 39 30 ,2 22 47 2 19 5 2 15 20 2 11 35 2 7 45 17 50 13 23 8 66 4 29 000 4 3 2 1 S? S. 11 10 9 8 7 6 S. tu ft 9 A. id. cr? TABLE VI. Equation of the mnorTs raeau anomaly. Argument. Sun's meai. anomaly. Subtract D ofc S. _L_ 2 o / //jo / // 3 / // 4 1 5 S. | O ^ ?<3 000 46 4ojl 21 32 s 35 1 1 23 4|0 48 19 30 1 2 3 4 5 1 37 3 13 4 52 6 28 086 48 10 49 34 50 5o 52 19 53 40 22 21 23 10 23 57 24 41 25 24 35 2 35 I 35 34 57 34 50 22 14 21 24 2') 32 19 38 18 42 46 51 45 23 43 54 42 24 40 53 29 28 27 26 25 6 7 8 9 10 9 42 11 20 12 56 14 33 16 10 55 56 21 57 38 58 56 I 13 26 6 26 48 27 28 28 6 28 43 34 43 34 33 34 22 34 9 33 53 17 45 16 48 15 47 14 44 13 41 39 21 37 49 36 15 34 40 33 5 24 23 22 21 20 11 12 13 14 15 17 47 19 23 20 59 22 35 24 10 1 1 29 2 43 3 56 5 8 6 18 29 17 29 51 30 22 30 50 31 19 33 37 33 20 i 33 1 32 38 1 32 14 12 37 11 33 10 26 9 17 8 8 31 31 29 54 28 18 26 40 25 3 19 18 17 16 15 ASTRONOMICAL TABLES, 209 TABLE VI. Continued. 5 S. I 2 3 4 ! 5 S 1 A Q t It O / /' o / // o / // / // 1 n oq Hi 25 45 7 27 31 45 31 50 6 58 23 23 ,4 17 27 19 8 36 32 12 31 23 5 46 21 45 13 18 28 b2 9 42 32 34 30 55 4 32 20 7 1% . 19 30 25 10 49 32 57 30 25 3 19 18 28 11 20 31 57 li 54 33 17 29 51 2 1 16 46 10 -21 33 29 U' 58 33 36 29 20 1 45 15 8 (\ 22 35 2 14 1 33 52 28 45 59 26 13 28 8 23 3b" 32 15 1 34 6 28 9 58 7 U 48 7 24 38 1 16 34 18 27 30 56 45 10 7 6 25 39 29 16 59 34 30 26 50 55 23 8 5 26 40 59 17 57 34 40 26 27 54 1 6 44 4 27 42 26 18 52 34 48 25 5 52 37 053 3 28 43 54 19 47 34 54 24 39 51 12 3 21 2 29 3u| 45 19 46 45 20 40 21 32 34 58 35 r 23 52 23 4 49 45 48 19 1 40 000 1 S?l S. 1 1 | 10 | 9 8 7 I 6 S.| O I] A( Id. '1 QWJ TABLE VII. The second equation of the mean to the true syzygy. Argument. Moon's equaled anomaly. Add. I 0<3 is. o 1 2 3 4 5 S. H. ITS. | OFQ H. M. S H. M S H. M. S. H. M. S H. M. S OJO 05 12 48J8 47 8 9 46 44|8 8 59)4 34 33 30 1 2 f> 5 10 58 21 56 32 54 43 52 54 50 5 21 56 5 30 57 & 39 51 5 48 37 5 57 17 8 51 45 8 56 10 9 25 9 4 31 9 8 25 9 46 3 9 45 12 9 44 li 9 42 59 9 41 30 8 3 12 7 57 23 7 51 33 7 45 46 7 39 46 4 26 1 4 17 25 4 8 47 407 3 51 23 29 28 27 26 25 6 7 8 9 10 I 5 48 1 16 46 1 27 44 I 38 40 1 49 33 6 5 51 6 14 19 6 22 41 6 30 57 6 39 4 9 12 9 9 15 43 9 19 5 9 22 14 9 25 12 9 40 3 9 38 19 9 36 24 9 34 18 9 32 1 7 33 -36 7 27 22 7 21 2 7 14 30 7 7 50 3 42 32 *-33 3fc 3 24 42 3 15 44 3 6 45 24 23 22 21 20 11 12 13 14 15 2 23 2 11 10 2 21 54 2 32 34 2 43 9 6 47 6 54 46 7 2 24 7 9 52 7 17 9 9 27 58 9 30 32 9 32 58 9 35 12 9 37 14 9 29 33 9 26 54 9 24 4 9 21 3 9 17 51 7 1 2 B 54 8 6 47 9 6 40 6 6 32 56 2 57 43 2 48 39 2 39 34 2 30 28 2 21 19 19 18 17 16 15 1 210 ASTRONOMICAL TABLES. TABLE VH. Continued. 1823 B 1824 1825 9 10 14 33 9 10 13 9 9 45 54 9 9 31 34 9 10 16 23 6 34 59 6 19 38 6 4 16 5 29 48 55 6 32 41 1847 B 1848 1849 1850 1851 9 9 44 24 9 10 29 12 9 10 14 53 9 10 33 9 9 46 14 5 29 32 47 6 16 33 6 1 12 5 29 45 50 5 29 30 29 9 10 2 3 9 9 47 44 9 9 33 24 9 10 18 13 9 10 3 53 6 17 19 6 1 58 5 29 46 36 6 30 23 6 15 1 B 1852 1853 1854 1855 1856 9 10 31 2 9 10 16 43 9 10 2 23 9 9 48 3 9 10 32 52 6 14 15 5 29 58 54 5 29 43 32 5 29 28 10 6 11 57 18269 9 49 34 18279 9 35 14 B 1828:9 10 20 3 1829]9 10 5 43 1830J9 9 51 24 5 29 59 40 5 29 54 18 6 28 5 6 12 43 5 29 57 21 1857 1858 1859 B 1860 1861 9 10 18 335 29 56 35 3 10 4 135 29 41 14 9 9 49 53J5 29 25 52 9 10 34 4216 9 39 9 10 20 23|5 29 54 17 214 ASTRONOMICAL TABLES. TABLE X. Continued. "iears. ) Longitude, j Anomaly. Years. Longitude. Anomaly. !S ' " IS Off S. o / // S. ' " 18629 10 6 3 18639 9 51 43 B 1864'9 10 36 32 18659 10 22 12 18669 10 7 53 5 29 38 55 5 29 23 34 6 7 20 5 29 51 59 5 29 36 37 1882 1883 B 1884 1885 1886 9 10 15 13 9 10 53 9 10 45 42 9 10 31 22 9 10 17 3 5 29 27 24 5 29 12 3 5 29 55 49 5 29 40 28 5 29 25 6 186719 9 53 33 B 1868j9 10 38 22 1869,9 10 24 2 18709 10 9 43 187 1|9 9 55 23 5 29 21 16 6052 5 29 49 41 5 29 34 19 5 29 18 57 1887 B J888 1899 1890 1891 9 10 2 435 29 9 44 9 10 47 32l5 29 53 31 9 10 33 12,5 29 38 .9 9 10 18 525 29 22 48 9 10 4 33|5 29 7 26 B 18729 10 40 126 2 44 1873i9 10 25 525 29 47 22 1874 ! 9 10 11 335 29 32 1 18759 9 57 135 29 16 39 B 18769 10 42 2|6 26 B 1892 1893 1894 1895 B 1896 9 10 49 22!5 29 51 13 9 10 35 2j5 29 35 51 9 10 20 425 29 20 30 9 10 6 23|5 29 5 8 9 10 51 12|5 29 48 55 1877 9 10 27 4215 29 45 4 18789 10 13 23!5 29 29 43 18799 9 59 3.5 29 14 21 B 1880J9 10 43 525 29 58 7 1881)9 10 29 32|5 29 42 46 1897 1898 1899 1900 9 10 36 52 9 10 22 32 9 10 8 13 9 9 53 53 5 29 33 33 5 29 18 11 5 29 2 50 5 28 47 28 The sun's longitude and anomaly in Julian years. Years L ngit title. Anomal} s o i " s. o ' " 1 11 29 45 40 11 29 44 38 2' 11 29 31 21 11 29 29 17 3i 11 29 17 1 11 29 13 55 B 4! 1 50 11 29 57 42 5 11 29 47 30 11 29 42 20 6 11 29 S3 11 11 29 26 59 7 11 29 18 51 11 29 11 37 B 8 3 40 11 29 55 24 9 11 29 49 20 11 29 40 2 10: 11 29 35 1 11 29 24 40 B 20' 9 10 11 29 48 29 30 11 29 44 10 11 29 13 9 B 40 18 19 11 29 36 58 ASTRONOMICAL TABLES, 215 Years. Longitude. Anomaly. s. o n S o / n B B r B B B B 50 60 70 80 90 11 29 53 27 2 36 11 20 29 30 39 39 11 11 11 11 11 29 29 28 29 28 1 25 50 13 88 38 26 7 55 36 100 200 300 400 500 1 2 3 S 45 31 17 3 49 48 36 25 13 1 11 11 11 11 11 29 28 27 26 25' 2 4 7 9 12 24 48 12 36 B B B B B 600 700 800 900 1000 o 4 5 6 6 7 34 20 6 52 38 49 38 26 14 2 11 11 It 11 11 24 23 22 21 20 14 16 19 21 24 24 48 12 36 B B B B B 2000 3000 4000 5000 10000 1 1 2 15 22 8 16 16 54 32 10 20 5 7 10 12 24 11 11 10 10 8 ia i 21 12 24 48 12 36 The sun's mean motion in commencement of the year longitude and anomaly from the to the beginning of each month. Months Longitude. Anomaly. S. ' n S i n Jan. Feb. March \ 000 1 33 1 28 9 18 11 0000 1 33 13 1 28 9 1 April May June July Aug. 2 28 42 3 28 16 4 28 49 5 28 24 6 28 57 30 40 58 8 26 2 28 42 14 3 28 16 19 4 28 49 32 5 28 23 37 6 28 56 50 Sept. Oct. Nov. Dec. 7 29 30 8 29 4 9 29 38 10 29 12 44 54 12 22 7 29 30 3 8 29 4 8 9 29 37 21 10 29 11 21 ASTRONOMICAL TABLES. The Days. sun' s mean motion in longitude and anomaly in days. Loi igitiule. Anomaly s o / " S. o / // 1 2 3 4 5 1 2 3 4 59 58 57 56 55 8 17 25 33 42 1 2 3 4 59 58 57 56 55 8 16 24 33 41 6 7 8 9 10 5 6 7 8 9 64 53 53 ' 52 51 60 58 7 15 23 5 6 7 8 9 54 53 53 52 51 49 57 M 13 22 11 12 13 14 15 10 11 12 13 14 50 49 48 47 47 32 40 48 57 5 10 11 12 13 14 50 49 48 47 47 30 38 46 54 2 16 17 18 19 20 15 16 17 18 19 46 45 44 43 42 13 22 30 38 47 , 15 16 17 18 19 46 45 44 43 42 11 19 21 35 43 21 22 23 24 25 20 21 22 23 24 41 41 40 39 38 55 3 12 20 28 20 21 22 23 24 41 41 40 39 38 51 8 16 24 26 27 28 29 30 "31 25 26 27 23 29 37 36 35 35 34 37 45 53 2 10 25 26 27 28 29 37 36 35 34 34 32 40 48 57 i 1 33 18 1 33 13 ASTRONOMICAL TABLES 217 The sun's mean motion in longitude, anomaly, and distance from the node for hours, minutes and seconds. HT M S Longitude- and anomaly. Distance irom node. 5 7 77 -H~ Lo gitude and anomaly Distance from node. |O / // /// / n tit mi o / // /// / \n 10 2 27 51 2 36 31 16 23 15 20 29 2|0 4 55 42 5 12 32 18 51 6 23 5 3|0 7 23 32 7 47 33 21 18 57 25 41 4|0 9 51 23 10 23 34 23 46 48 28 17 5 "6 12 19 14 12 59 35 26 14 39 30 53 14 47 5 15 35 36 1 28 42 30 '33 28 7 17 14 56 18 11 37 1 31 10 20 36 4 8 19 42 47 20 46 38 1 33 38 11 38 40 9 22 10 37 23 22 39 1 36 6 2 41 16 100 ,24 38 28 25 58 40 1 38 33 53 43 52 1110 27 6 19 12JO 29 34 10 28 34 31 9 41 42 1 41 1 44 1 43 29 34 46 27 49 3 130 32 2 1 33 45 43 1 45 57 25 . 51 39 14;0 34 29 51 36 21 44 1 48 25 16 54 15 150 36 57 42 38 57 45 1 50 53 7 56 51 160 39 25 33 41 33 46 1 53 20 58 1 59 26 17 41 53 ,24 44 8 47 1 55 48 49 222 180 44 21 15 46 44 48 1 58 16 39 2 4 38 19iO 46 49 6 49 20 49 2 44 30 2 7 14 20 ! 49 16 56 51 56 50 2 3 12 21 2 9 50 210 51 44 47 54 32 51 2 5 40 12 2 12 25 220 54 12 38 57 7 52 2883 2 15 1 23 24 56 40 29 59 8 20 59 43 1 2 19 53 54 2 10 35 53 2 13 3 44 2 17 37 2 20 13 25 26 1 1 36 11 1 4 55 55 2 15 31 35 2 22 48 1441 1 7 31 56 2 17 59 26 2 25 24 27 1 6 31 52 1 10 6 57 2 20 27 17 2 28 28 1 8 59 43 1 12 42 58 2 22 55 8 2 30 36 29 1 11 27 34 1 15 18 59 2 25 22 58 2 33 12 30 1 13 55 25 1 17 54 60 2 27 50 49 2 35 47 218 ASTRONOMICAL TABLES. TABLE XI. Equation of the sun's centre or the difference between his mean and true place. Argument. The sun's mean anomaly. Subtract. o cr? S, o / // 1 ~o / 77" 2 3 I 4 Cf / II 1 O / // 6 S. "6 / 77" S? 5*3 o 000 56 47 1 39 6 1 55 37| 1 41 12 58 53 30 i 2 3 4 5 1 59 3 57 5 56 7 54 9 52 58 30 12 1 53 3 33 5 n 1 40 7 41 6 42 3 42 59 43 52 1 55 39 1 55 38 1 55 36 1 55 31 1 55 24 40 12 39 10 38 6 37 35 52 57 7 55 iy b3 30 51 40 49 49 29 28 27 26 25 6 7 8 9 10 11 50 13 48 15 46 17 43 19 40 6 50 8 27 10 2 11 36 13 9 44 44 45 34 46 22 47 8 47 53 I 55 15 55 3 54 50 54 35 54 17 34 43 33 32 32 19 31 4 29 47 47 57 46 5 44 11 42 16 40 21 24 23 22 21 20 11 12 13 14 15 21 37 23 33 25 29 27 25 29 20 14 41 16 11 17 40 1 19 8 1 20 34 48 35 49 15 49 54 50 30 51 5 53 57 53 36 63 12 52 46 52 18 28 29 27 9 25 48 24 25 23 38 25 36 28 34 30 32 32 30 33 19 18 17 16 15 16 17 18 19 20 31 15 53 9 35 2 36 55 38 47 1 21 59 1 23 22 24 44 26 5 27 24 51 37 52 8 52 36 53 3 53 27 51 48 51 15 50 41 50 5 49 26 21 34 20 6 18 36 17 5 15 33 28 33 26 33 24 33 22 32 20 30 14 13 12 11 10 21 22 23 24 25 40 39 42 30 44 20 46 9 47 57 28 41 29 57 31 11 32 24 33 35 53 50 54 10 54 28 54 44 54 58 48 46 48 3 47 19 46 32 45 44 13 59 12 24 10 47 9 9 7 29 18 28 16 26 14 24 12 21 10 18 9 8 7 6 5 26 27 28 29 30 49 45 51 32 53 18 55 3 56 47 34 45 35 b3 36 59 38" 3 39 6 55 10 55 20 55 28 55 34 1 55 37 44 53 44 1 43 7 42 10 41 12 5 4P 4 7 2 24 1 39 58 53 8 j4 611 047 024 000 4 3 2 1 b a ep S. 11 10 9-8 7 6 O $ Add. ASTRONOMICAL TABLES. 219 TABLE XII. The suu's declination tor every degree of his longitude. Argument. The sun's longitude. d CKJ s. o 6 1 7 2 S. 8 O A crq o / // o / // O ' '/ 1 2 3 4 00 23 53 47 47 1 11 39 1 35 30 11 29 5 11 50 6 12 10 56 12 31 34 ;2 51 59 20 10 25 20 22 57 20 35 7 20 46 55 20 58 20 30 29 28 27 26 5 6 7 8 9 1 59 20 2 23 8 2 46 54 3 10 37 3 34 17 13 12 12 13 32 12 13 51 58 14 11 30 14 30 48 21 9 21 21 19 59 21 30 13 21 40 3 21 49 29 25 24 23 22 21 10 11 12 13 14 3 57 54 4 21 27 4 44 57 5 8 22 5 31 42 14 49 52 15 8 40 15 27 13 15 45 30 16 3 31 21 58 30 22 7 6 22 15 17 22 23 3 22 30 24 20 19 18 17 16 15 16 17 18 19 5 54 57 6 18 6 6 41 9 746 7 26 57 16 21 16 16 38 44 16 55 *5 17 12 48 17 29 23 22 37 18 2? 43 47 22 49 50 22 55 27 23 38 15 14 13 12 11 2U 21 22 23 24 7 49 41 8 12 17 8 34 45 8 57 5 9 19 17 17 45 40 18 1 38 18 17 18 18 32 38 18 47 38 23 6 22 23 9 39 23 13 29 23 16 53 23 19 50 10 9 8 7 6 25 26 27 28 29 9 41 19 10 3 12 10 24 56 10 46 30 1 1 7 53 19, 2 18 19 16 37 i9 30 35 19 44 13 19 57 30 23 22 20 23 24 22 23 25 57 23 27 5 23 27 46 5 4 3 2 1 30 11 29 5 20 10 25 23 28 B s S. 11 5 10 4 9 S. 3 1 0, ASTRONOMICAL TABLES. TABLE XIII. Equation of the sun's mean distance from the rsodo Argumnnt. The *u -Vs m^an anomaly. Subtract. B $ S. 1 2 3 4 _ _- 5 S. b JQ o / / o / / 2 5 2 5 2 5 2 5 2 5 / 1 2 3 4 2 4 6 9 2 4 6 8 10 47 48 49 50 51 50, 48 47 46 45 1 4 1 2 I 58 56 30 29 28 27 26 5 6 7 8 9 11 13 15 17 19 12 14 16 17 18 52 53 54 55 56 2 5 2 5 2 4 * Stf>4 2 4 44 43 41 40 39 51 52 50 48 46 25 21 ^ 22 11 10 11 12 13 14 21 U 23 25 28 30 19 21 22 24 26 57 58 58 59 2 2 4 2 3 2 3 2 3 2 2 37 36 34 33 31 44 42 40 37 35 to 19 18 17 16 15 16 17 18 19 32 34 36 38 40 27 28 30 31 34 2 2 1 2 1 2 2 2 2 2 2 2 1 2 1 2 2 30 28 27 25 24 33 31 29 27 24 15 14 !i Hi 20 21 22 23 24 42 44 46 48 50 35 36 37 39 40 2 3 2 3 2 4 2 4 2 4 69 59 58 57 56 23 21 19 17 15 22 20 18 16 13 10 9 8 7 6 25 26 27 28 29 52 54 56 58 1 41 43 44 45 46 2 4 2 5 2 5 2 5 2 5 55 54 53 52 51 13 11 ;,!<& 9 i **; 8 6 11 9 7 5 3 5 4 3 2 1 30| I 2 1 47 2 5 t 50 1 4000 S. .11 Id 9 8 7 6 S. Add. I ASTRONOMICAL TABLES. TABLE XIV. TABLE XV. The moon's lati- tude in eclipses. Argulneut. The moon's equated distance from node The moon's horizontal parallax ; the semi-diam- eters, and true horary motions of the sun and moon to every sixth degree of their mean anomalies. signs north ascending. AUOIH- ily of ^ tun & noon. Moon's or. Zdi n a i mrallax. Sun's semi-di- ameter. Moou's stmi-di- ameter . Moon's horary motion. Sun's J horary motion* Lmmialyt of sun and moon. 6 signs south descending. ~o~ [3 o / it ' ff i it i iii " 1 S. o o / // 6 12 18 24 54 29 54 31 54 34 54 40 54 47 15 50 15 50 15 50 15 51 15 51 14 54 14 55 14- 56 14 57 14 58 30 10' 30 12 30 15 30 19 30 26 2 23! 2 23 2 23 2 23 2 23 12 524 18 12 6 1 2 3| 000 5 15 10 30 15 45 30 29 28 26 4 5 6 7 20 59 26 13 31 26 36 39 26 i 25 24 23 1 6 1? 18 24 54 56> 55 6 55 17 55 29 55 42 15 52 15 53 15 54 J5 55 15 56 14 59 15 1 15 4 15 8 15 12 30 34 30 44 30 55 31 9 31 23 2 24 2 24 2 24 2 24 2 25 11 24 18 12 6 ! 10 11 12 13 14 15 41 51 47 2 52 13 57 23 1 2 31 1 7 38 1 12 44 17 49 22 21 20 19 Te 17 16 15 2 6 12 is 24 55 56 56 12 56 29 56 48 57 8 15 IS 1.5 59 16 1 16 2 16 4 15 17 15 22 15 26 15 30 15 36 31 40 31 56 32 17 32 39 33 1 2 25 2 26 2 27 2 27 2 28 10 24 18 12 6 3 6 12 18 24 57 30 57 52 58 12 58 31 58 49 |16 6 16 8 16 10 16 11 16 13 15 41 15 46 15 52 15 58 16 3 33 23 33 47 34 11 34 34 34 58 2 28 2 29 2 29 2 29 2 30 9 24 18 12 6 16 17 18 19 22 52 27 53 32 52 37 49 13 12 11 4 6 12 1.8 24 59 6 59 21 59 35 59 48 60 16 14 |l6 15 16 17 16 * 19 16 20 16 9 16 14 16 19 16 24 16 28 35 22 35 45 36 36 20 36 40 2 30 2 31 2 31 2 32 2 32 8 94 18 12 6 5 S. north descending. 11 S. south ; ascending. \ m 5 6 12 18 24 60 11 60 21 60 30 60 38 60 45 16 21 16 21 16 22 16 22 16 23 16 81 16 32 16 37 16 38 16 39 37 37 10 37 19 37 28 37 m 2 32 a 33 2 33 2 33 2 33 7 24 18 12 6 6 0|60 45|16 23116 39|37 40;2 33! 6 222 ASTRONOMICAL TABLES. TABLE XVI. Longitude on the earth changed into solar time. H. M. / M. S. // S. T. I 2 S 4 5 4 8 12 16 20 6 7 8 9 10 24 28 32 36 40 11 12 13 14 15 1 44 48 52 56 16 17 18 19 20 4 8 12 16 20 30 40 50 60 70 2 2 3 4 4 40 20 40 80 90 100 5 6 6 20 40 ASTRONOMICAL TABLES, TABLE XVII. Angle of the moon's visible path with the ecliptic. Argument. The sun's distance from the node. gns. 6 orary motion o the moon from the sun. 27 28 29 30 31 82 33 34 35 36 i JO //|O // |O n\Q ft (O '1 // |O 05 475 36 465 12 5 42 465 455 455 445 5 455 44 5 41 5 395 38 5 435 405 375 44|5 435 425 41 4; 45 395 395 38 |5 42 5 41 36 b 425 41 5 405 39 37 5 35 5 35 5 34 5 33 5 41 5 40 5 39 5 37 40 40 38 36 33 39 39 38 3521 5 32 30 27 24 18 15|5 3515 3415 33|5 32|5 31|5 31|5 30|5 29|5 295 28U5 1 1 Signs 5. if 224 ASTRONOMICAL TABLES. TABLE XVIII. Equation of time. The sun faster or slower than the clock. Bissextile. 9 Vi- ce Jan Feb. >iarch. April. May. June. M. S.|M. S|M. S.|M. S.|M. S.|M. S.. 2 3 4 6 4 v 8 4 g 36 5 c A 5 31 5 58 14 a 4 14 g 11 14 17 14 23 14 ' 28 112 cr, 27 12 g 14 12 < 1 11 47 11 32 3 a 38 3 20 3 a. 2 2 o 44 |2 ' 26 3 M 13 3 g 20 3 ~ 27 3 I 33 3 38 2 M 28 2 18 2 sr> 9 11 ft 5-9 |1 49 b ) 8 c 1C 6 o 25 6 50 7 5* 15 7 8- 40 8 * 5 14 32 14 - 35 14 i- 37 14 g- 38 14 ' 39 11 o 18 11 o" 3 10 o* 47 10 fr 31 10 ' 15 2 9 1 51 1 ? 34 i i o 1 w 17 1 ' 1 3 o 43 3 T 47 3 r 51 3 g- 53 3 ' 55 1 o 3 8 1 ? 27 1 o* 15 1 3 ' 51 fl 12 13 14 15 8 29 8 52 9 15 9 36 9 57 14 39 14 38 14 37 14 34 14 31 9 58 9 41 9 24 9 7 8 50 45 29 14 * 2 16 3 57 3 59 4 4 3 59 [0 39 27 15 2 # 11 16 17 18 19 20 10 18 10 38 10 57 11 16 11 34 14 2* 14 23 14 18 14 12 14 6 8 32 8 14 7 56 7 38 7 20 31 ^45 ;' 59 I 12 1 " 251 3 58 3 56 3 53 3 50 3 47 v 24 g 36 49 f 2 16 21 22 23 24 25 11 50 12 6 12 22 12 37 12 51 13 58 13 50 13 42 13 33 13 24 7 2 6 43 6 25 6 6 5 48 1 o 37| 1 ~> 48 1 g-69 2 10 2 ' 21 3 43 3 39 3 34 3 29 3 23 o 29 ^ 42 55 2 g- 8 2 " ' 20 26 27 28 29 30 13 4 13 16 13 27 13 38 13 48 13 14 13 3 12 51 12 39 5 29 5 11 4 52 4 33 4 15 2 31 2 41 2 50 2 58 3 6 3 16 3 9 3 1 2 53 2 45 2 33 2 45 2 57 3 9 3 20 31| 13 57 3 56| |2 38) ASTRONOMIC At TABLES. Equation of time. The sun faster or slower than the clock. Bissextile. Jniy. 1 Aug. Sept. ; Oct. Nov. Dec. M. S. M. S.|M. S.|M. S.;M. S.|M. S; 3- w 31 3 42 3 53 4 o 3 4 * 14 1 5 w 50 [5 46 5 x 41 5 f 35 b :S 29 ^ 34 . g 53 1 & I* 1 * 32 1 5fc 10 w 42 1> 1 11 -> 19 11 ! 37 11 55 [16 w 15 |16 15 16 -> 15 16 13 16 10 10 f/ . 12 9 48 9 ^ 24 8 55. 59 8 33 4 ~ 24 4 X - 33 4 g- 42 * If si 4 * 58 5 3 22 5 ^ 14 5 g- 6 4 S- 58 4 ' 49 2 o 12 2 ^ 32 2 g- 52 3 g. 13 3 ' 34 12 12 12 ~> 28 12 1- 44 12 g. 59 13 ' 15 16 o 16 ~> 2 15 g- 57 15 g. 51 15 ' 44 8 o ^ 7 * 4,1 7 2-14 6 g. 46 6 ' 19 5 7 5 14 5 21 5 91 5 53 4 39 4 29 4 19 4 7 3 55 3 54 4 15 4 36 4 57 5 18 13 30 13 44 13 58 14 11 14 23 15 36 15 27 15 18 15 8 14 56 5 51 5 22 4 53 4 24 3 64 5 39 5 44 5 49 5 53 5 57 3 43 3 30 3 17 3 3 2 49 5 39 6 6 20 6 4i 7 2 14 35 14 47 14 56 15 7 15 16 14 44 14 31 14 18 14 4 13 49 3 25 2 55 2 25 1 55 1 25 5 59 6 1 6 3 6 4 6 4 2 35 2 20 2 4 1 48 1 31 7 23 7 44 8 4 8 24 8 45 15 25 15 33 15 40 15 47 15 53 13 32 13 15 12 58 12 40 12 21 55 25 0*5 35 1 5 6 4 6 4 6 2 6 5 57 1 14 57 40 22 4 9 5 9 25 9 45 10 4 10 23 15 59 16 4 16 8 16 10 16 12 12 1 11 41 11 19 10 57 10 35 1 g 2 35 2 * 4 2 f- 33 3^2 3 2.31 5 54| * 151 116 14! 1 g* 226 ASTRONOMICAL TABLES. Equation of time. The sun faster or slower than the clock. First after bissextile. :! Jan. Feb. March. | April. | May. 1 June. M, S.|M S.|M. S.jM. S.|M S|M. S. 1 2 3 4 5 4 29 4 | 57 5 * 25 5 9 7 g- 35 7 g. 59 8 ' 23 14 3511 22 14 - 37 11 - 7 14 |- 39 10 52 14 g. 40 10 36 14 ' 4010 ' 20 2 13 1 -56 1 39 1 g. 22 1 5 3 o 42 3^46 3 g- 50 3 g. 53 3 ' 55 o 41 -31 g- 19 S- 7 ' 55 11 12 13 14 15 8 46 9 9 9 31 9 52 10 13 14 39 14 38 14 35 14 32 14 28 10 3 9 46 9 29 9 12 8 54 49 33 17 2 * 13 3 57 3 59 4 4 4 43 31 19 7 0*6 16 17 18 19 20 10 33 10 52 11 11 11 29 11 46 14 24 14 19 14 14 14 8 14 8 37 8 19 8 1 7 43 7 25 28 g> 42 o 56 1 f 9 1 * 22 3 59 3 58 3 55 3 52 3 49 19 g 32 a 45 5 58 1 ' 11 21 22 23 24 25 12 2 12 18 12 33 12 47 13 1 13 52 13 44 13 35 13 26 13 16 7 6 6 48 6 29 6 11 5 52 1 o 35 1 - 47 1 58 2 g- 9 2 ' 19 3 46 3 41 3 37 3 31 3 25 1 o 24 1 ^ 37 1 g- 50 2 g. 3 2 ' 16 26 27 28 29 30 13 13 13 24 13 35 13 45 13 54 13 6 12 54 12 42 5 34 5 15 4 56 4 38 4 19 2 30 2 39 2 48 2 57 3 5 3 19 3 12 3 4 2 56 2 48 2 28 2 41 2 53 3 5 3 17 31| 14 3| | 4 1| |2 40| ASTRONOMICAL TABLES. 227 Equation of time. The sun faster or slower than the clock. First after bissextile. July. Aug. Sept. Oct. Nov. Dec. M. 'S.|M. S.IM. S.|M. S.|M. S.|M. S^ 3 j 28 3 g 39 3 50 4 < 4 3| 11 5 v 5li 5 g 47 5 42 5 'r 37 5 : ' 31 Vj 28 g 47 1 -> 6 1 |26 1 46 10 ^36 10 g- 55 11 ^ 13 11 | 31) 11 49 16 M 14 16 g 14 16 ' 13 16 12 16 ' 9 10 M 17 9 g 54 9 ^ 30 9 | 5 8 39 4 o 21 4 ^ 30 4 39 4 g. 48 4 57 5 24 5 - 16 5 g- 8 5 g- 4 * 51 2 o 6 2 ^ 26 2 g- 46 3 g. 7 3 ' 27 12 6 12 ~> 22 12 g- 38 12 -54 13 ' 10 16 o 6 16 ^ 2 15 g- 58 15 g. 52 15 ' 45 8 o 13 7 ~. 47 7 |-20 6 g- 53 6 * 25 5 4 5 11 5 18 5 25 5 31 4 42 4 32 4 22 4 10 3 58 3 48 4 9 4 30 4 51 5 12 13 25 13 39 13 53 14 6 14 19 15 37 15 29 15 20 15 10 14 59 5 57 5 29 5 4 31 4 2 5 37 5 42 5 47 5 51 5 55 3 46 3 34 3 21 3 7 2 53 5 33 5 54 6 14 6 35 6 56 14 31 14 42 14 53 15 3 15 13 14 47 14 34 14 21 14 7 13 52 3 32 3 3 2 33 2 3 1 33 5 58 6 6 2 6 3 6 4 2 391 7 17 2 24 7 37 2 9 7 58 1 531 8 18 1 36 8 39 15 22 15 30 15 37 15 44 15 51 13 36 13 19 13 2 12 44 12 25 1 3 32 2 # 28 58 6 4 6 4 6 3 6 1 5 58 1 19 1 2 45 27 9 8 59 15 56 9 1916 1 9 3816 5 9 58116 9 10 1716 11 12 5 11 45 11 24 11 2 10 40 1 SP 28 1 57 2 26 2 3 56 3 a 25 5 55j * 9! |16 13| 3 g, 53 ASTRONOMICAL TABLES. Equation of time. The sun faster or slower than the clock. Second after bissextile. B f *< - 9 Jan. ( Feb. March. | April. May. June. M. S.IM. S.|M. S.|M. S.|Ri. S. M. S. I '2 3 4 5 4 w 21 4 49 5 17 5 I 44 6 11 14 w 7 14 g 14 14 20 14 25 14 ' ! 29 12 a 32 12 g 20 12 6 11 53 11 ! 39 3 ^ 46 3 g 28 3 10 2 g 52 2 U 3 c 18 3 !l 25 3 r 31 3 37 2 34 2 25 2 !' 15 2 S' 6 1 55 6 7 8 9 10 6 o 37 7^2 7 g- 27 7 g. 52 8 ' 16 14 c 33 14 ~ 35 14 g-37 14 g. 39 14 ' 39 11 o 24 11 ^ 10 10 g- 55 10 g. 39 10 ' 23 2 16 1 ~- 59 1 5-42 1 25 1 ' 9 3 o 42 3 ^ 46 3 g- 50 3 g, 53 3 ' 55 1 o 45 1 - 34 1 5- 22 1 g. 10 ' 58 11 12 13 14 15 8 40 9 3 9 26 9 47 10 8 14 39 14 38 14 36 14 33 14 30 10 7 9 50 9 33 9 16 8 59 53 37 21 6 0*9 3 57 3 59 4 4 4 46 34 21 9 0*4 16 17 18 19 20 10 28 10 48 11 7 11 26 11 43 14 26 14 21 14 16 14 10 14 3 8 41|0 ^ 24 8 230 g 38 8 60 _ 52 7 48 1 ' 5 7 30ll 18 3 59 3 58 3 55 3 52 3 49 u I 7 30 43 f 56 1 9 21 22 23 24 25 11 59 12 15 12 30 12 44 12 58 13 55 13 47 13 38 13 29 13 69 7 11 6 53 6 34 5 1^ 1 57 1 313 46 1 ~- 433 42 1 5" 55 3 37 2 g. 63 32 2 ' 1713 27 1 . 22 1 ^ 35 1 g- 47 2 g. 2 ' 13 26 27 28 29 30 13 10 13 21 13 32 13 42 13 52 13 8 12 56 12 44 5 38 5 19 5 1 4 42 4 23 2 27 2 37 2 47 2 56 3 3 21 3 14 3 7 2 59 2 51 2 25 2 37 2 49 3 1 3 13 311 14 Oi 14 51 |2 431 ASTRONOMICAL TABLES. Equation of time. The sun faster or slower than the clock. Second after bissextile. July. Aug. Sept. | Oct. Nov. Dec. M. S.JM. S.|M. S.|M. S.|M. S.jM S. 3 OT 24 3 35 3 46 3 If 57 47 5 w 52 5 g 48 5 w 43 5 | 38 5 32 o* 24 g 43 1 ? 2 1 . 21 1 41 10 w 32 10 g 50 U g, 9 H ft 27 11 44 16 OT i4 16 14 16 .-> 14 16 ft 12 16 9 15 23 9 g' 59 9 -> 35 9 ft 11 8 45 4 18 4 ~> 28 4 ~ 37 4 g. 46 4 ' 55 5 o 26 5 ^ 19 5 11 5 g- 3 4 ' 54 2 2 ^ 20 2 g- 41 3 g. i 3 * 21 12 1 12 * 17 12 . 33 12 g, 49 13 r 5 16 6 16 ^ 2 15 2. 58 15 8 52 15 46 8 19 7 ^ 63 7 SL 26 6 I. 59 6 * 31 5 3 5 11 5 18 5 25 5 31 4 45 4 35 4 25 4 14 4 2 3 42 4 3 4 23 4 44 5 5 13 20 13 34 13 48 14 2 14 15 15 38 15 30 15 21 15 11 15 1 6 3 5 35 5 6 4 37 4 8 5 37 5 42 5 47 5 51 5 55 3 50 3 38 3 25 3 12 2 58 5 26 5 47 6 8 6 29 6 50 14 27 14 38 14 49 15 15 10 14 43 14 37 14 24 14 10 13 55 3 39 3 9 2 40 2 10 1 40 5 58 6 6 2 e s 6 4 2 43 2 28 2 13 1 57 1 41 7 H 7 32 7 53 8 13 8 34 15 20 15 28 15 36 15 43 15 50 13 4J 13 23 13 6 12 48 12 30 1 10 40 10 * 20 5<; 6 4 6 3 6 2 6 1 5 58 1 23 1 6 49 31 13 8 54 9 14 9 31 9 53 10 13 15 55 16 ^ 6 16 b 16 9 16 11 12 11 51 11 30 11 8 10 46 1 w 1 f 49 2 >. 18 2 48 3 17 5 551 * 5| |16 12) 3 46 230 ASTRONOMICAL TAfcLES. Equation of time. The sun faster or slower than the clock. Third after bissextile. 2 *< v> Jan. Feb. | March. April. May. June. M. S.|M. S.|M. S.|M. S.|M. S.jM. S. 1 2 3 4 5 4 w 14 4 42 5 . iO 5 o* 38 6 : 5 | l * , & 14 g 12 14 . 18 14 f 24 14 '' 29 12 w 35 12 22 12 9 11 f 56 11 ' 42 3 ^ 51 3 g 32 3 14 2 o 6 S 2 " 39 3 9 3 g> 16 3 " 23 3 f 29 3 '* 35 2 36 2 c 27 2 S.17 2 | 7 1 57 6 7 8 9 10 6 31 6 -* 57 7 g- 22 7 g. 47 8 ' 11 14 33 14 ~> 35 14 g- 37 14 g. 39 14 * 40 U o 2 8 11 ~ 14 10 g- 59 10 g. 43 10 ' 27 2 o 21 f ^47 1 ^ 47 1 g. 30 1 ' 14 3 40 3 ~* 44 3 g- 48 3 g. 52 3 ' 54 1 o 46 1 ~* 35 1 g- 24 1 12 1 11 12 13 14 15 8 35 8 58 9 21 9 42 10 3 14 40 14 39 14 37 14 34 14 3' 10 11 9 54 9 37 9 20 9 3 58 42 26 10 * 5 3 56 3 58 3 59 4 4 48 9 36 24 12 * 1 16 17 18 19 20 10 24 10 43 11 2 11 20 1? 38 14 26 14 22 14 16 14 10 14 3 8 45 8 28 8 10 7 52 7 33 20 g 1 35 :' 49 i i 1 3 1 "* 16 3 59 3 58 3 56 3 54 3 51 M 13 g 26 39 o* 52 1 5 21 22 23 24 25 11 54 12 10 12 ^5 12 39 12 53 13 55 13 47 13 39 13 30 13 20 7 15 6 56 6 38 6 19 6 1 c *9 1 " 41 1 53 2 g. 4 2 * 15 3 48 3 44 3 39 3 34 3 29 1 o 17 1 ~* 30 1 ST 43 1 g. 56 2 ' P 26 27 28 29 30 13 6 13 17 13 28 13 39 13 49 13 10 12 59 12 47 5 42 5 23 5 4 4 46 4 27 2 25 2 35 2 45 2 54 3 2 3 23 3 16 3 9 3 1 2 53 2 21 2 34 2 46 2 59 3 11 _31| 13 58| 4 9| |2 45| ASTRONOMICAL TABLES. 231 Equation of time. The sun faster or slower than the clock. Third after bissextile. July. Aug. Sept Oct. Nov. Dec. M. S.|M, S.JM. S.|M. S.|M. S.|M. S. 3 M 22 3 33 3 * 44 3 f 55 4*6 5 53 5 49 5 I 45 5 cT 40 5 ;S 34 91 S? 38 57 1 | 16 1 * 3b 10 27 iO S 46 11 " 4 11 if 22 11 ~ 40 16 13 16 g* 14 16 " 14 16 IP 13 16 ' 10 10 28 10 2 5 9 ; 41 9 S 4 17 8 ' 51 4 o 16 4 ~> 26 4 5- 36 4 4b 4 ' 54 5 o 28 5 ~> 21 5 g- 13 5 g. 5 4 56 1 o 55 2 ~M5 2 g- 36 2 g, 56 3 ' 17 11 o & 12 ~ 14 12 g. 30 12 g. 46 13 * 2 16 o 7 16 " 4 16 g- 15 54 15 : ' 48 8 o 25 7 ~> 59 7 g- 33 7 g. 6 6 ' 39 5 2 5 9 5 16 5 23 5 29 4 47 4 38 4 27 4 16 4 4 3 38 3 58 4 19 4 40 5 1 13 17 13 32 13 46 14 14 13 15 41 15 33 15 25 15 15 15 5 6 11 5 43 5 14 4 46 4 17 5 35 5 40 5 45 5 49 5 53 3 52 3 40 3 27 3 14 3 5 23 5 44 6 5 6 26 6 47 14 26 14 37 14 48 14 59 15 9 14 53 14 41 14 28 14 15 4 3 48 3 18 2 48 2 18 1 48 5 56 5 58 6 6 2 6 3 2 45 2 31 2 16 2 1 44 7 8 7 28 7 49 8 9 8 29 15 19 15 27 15 35 15 42 15 49 13 45 3 28 13 11 12 53 *2 35 1 18 48 18 # 12 42 6 3 6 3 6 2 6 1 5 59 1 27 1 10 53 35 18 8 50 9 10 9 29 9 49 10 8 15 54 16 16 4 16 8 16 10 12 16 11 56 11 35 11 13 10 51 1 rjo 12 1 g 42 2 12 2 ; 41 3^-11 5 56| * 0| |16 12| 3 40 232 ASTRONOMICAL TABLES, TABLE XIX. Proportional Logarithm. 1 2 3 4 5 6 7 00000'17782 14771 13010 11761 10792 9331 10000 li 35563H771014735 f2986 11743 10777 9988 9320 1 3255317639 14699 i2962 11725 10763 9976' 9310 330792! 17570! 14664 12939 11707 10749 99649300 4 ! 2954^17501jl4629J12915 1168910734 9952 9S89 5 285,3il7434! 14594112891 11671 10720 9940J9279 6 2778217368 14559 12868 11654 10706 9928 9269 7127112 17302 14525,12845 11636 10692 99169259 82653217238 1449l|l2821 11619 10678 9905.9249 9'26021.17175 14457'12798 11601 10663 98939238 10 25563 17112 14424 12776 11584 10649 9881 9228 _ .. _ *. 11 25149 17050,14390 12753J11566 10635 98699218 12124771 1699014357 12730J11549 10622 9858 9208 1324424 169301 14325 12707J11532 10608 9846 9198 14J24102 16371 I5'23802|l6812 14292 14260 ' 12685 12663 11515110594 1 1 1 498 j 10580 9834)9188 98239178 16 2352216755 14228 12640 11481 10566 9811 9168 17 23259! 16698 14196 ,12618 11464 10552 98009158 18123010 16642 14164|l2596 11447 10539 9788 9148 19|22775|16587 20'22553; 16532 14133 14102 12575 12553 11430'10525 : 11413,10512 9777 9765 9138 9129 I - 21 122341 16478 14071 12531 11397 10498 9754 9119 22J22139. 16425; 14040 ,125lO|l 1380; 10484 9742 J9109 23|2 1946! 16372 |14010 12488|11363 ! 10471 9731 9099 24 21761 16320;13979 12467 11347 10458 9720 9089 2S 21584 16269113949 12446 11331 10444 9708 9079 26,21413 2721249 28 ! 21091 16218,13920 12424 ! 1 1314 1616311389011240311298 16118 13860' 12382 11282 10431 10418 10404 9697,9070 9686 9060 96759050 29 20939! 160691 13831 12362 11266J 10391 96649041 130,20792116021113802 12341 11249,10378 9652J9031 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 233 323 _1_|JL_. 3 4 2 \ Q , 7 j 30 20792' 16021; 13802 12341 L1249 10378'i )652j9031 31120649.1597313773112320 11233jl0365|964;|902J 32 20512115925 13745!l2300|11217J10352|9630;90 ,2 3320378 15878 13716 12279:11201 10339 961 9;9002 3420248 15832 L3688 12259 11186'! 0326-9608 8992 35 20122'l5786 13660 12239 11170 | 10313;9597|8983 1 1^ 36^20000 15740' 13632 122 18 11154 10300J95868973 37 19881 I5695'l3604; 1219811 1138 10287 ',9575i8964 38 19765 15651 13576(1^178 11123U0274 9564:8954 39.19652, 15607 13549:1^159 11 107 10261 95538945 4019542 15563! 13522, 12139 11091 10248J9542 8935 41|19435 15520.1349512119 1 1076 10235 9532 8926 42J19331 15477 43 19228S15435 13468 12099 13441>12080 11061 '(10223 9521 11045l0210 i 95iO 8917 8907 44-19128 45J 19031 15393 15351 134l5jl206l|ll030 13388|12041jllOl5 10197 10185 9499 9488 8898 8889 46 18935 15310 13362 120221 10999 10172 9478[8879 47'l8842 15269 13336 12003 ! 10984 10160 9467 8870 48 18751 15229133101198410969 10147 9456 8861 49 18661 15189 1328411965 10954 1013519446 8851 50 18573 15149 13259 ; 'l 1946 10939 10122J94358842 51 18487 15110 13233 1 1927 10924 10110 19425 8833 52 18 403] 15071 13208 11908 10909 10098|94 148824 53 1832011503213183 11889 10894 1008594048814 5413239 149941315811871 10880 1007319393 ,8805 55 18159 14956 13133 11852 10865 10061 J9383 8796 56 18081 14918 13108 11834110850 10049J9372 8787 57 18004 ! 14881 13083 11816 10835 1003619362 8778 58 17929;14844 13059 11797 10821 10024*9351 8769 59 1785514808 13034 1177910806 S 00? 2 934: 8760 60 17782' 14771 1301C 111761 107 92J 10000983 1 8751 234 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 8 9 8239 8231 8223 8215 8207 8199 10 11 7368 7361 7354 7348 7341 7335 12 Id 14 15 16 ! 2 2 4 5 8751 8742 8733 8724 8715 8706 7782 7774 7767 7760 7753 7745 6990 6984 6978 6972 6966 6960 6642 6637 b631 6625 6620 6614 6320 6316 6310 6305 6300 6294 6021 6016 6011 6006 6001 5997 5740 5736 5731 5727 5722 5718 6 7 8 9 10 8697 8688 8679 8670 8661 8191 8183 8175 8167 8159 7738 7731 7724 7717 7710 7328 7322 7315 7309 7302 6954 6948 6942 !6936 6930 6609 6603 6598 6592 6587 6289 6284 6279 6274 6269 5992 5987 5982 5977 5830 6824 6818 6812 6500 6494 6489 6484 6478 6188 6183 6178 6173 6168 5897 5892 5888 5883 5878 5624 5620 5615 5611 5607 ASTRONOMICAL TABLES* Table of Proportional Logarithms. 8 9 10 7570 11 12 13 14 15 5878 16 5607 30 8487 8004 717516812 rt478 6168 31 8479 7997 7563 7168 6807 6473 6163 5874 5602 32 8470 7989 7556 7162 6801 6467 6158 5869 5598 33 8462 7982 7549 7153 6795 6462 6153 5864 5594 34 8453 7974 7542 7149 6789 6457 6148 5860 r 589 33 8445 7966 7535 7143 7137 6784 6451 6143 5855 5585 36 8437 7959 7528 f>778 f>446 6138 5850 5580 37 8428 7951 7522 7131 6772 6441 6133 5846 5576 38 8420 7944 7515 7124 6766 6435 6128 584 5572 39 8411 7936 750d 7118 b761 6430 6123 5836 5567 40 8403 7929 7501 7112 6755 6425 6118 5832 5563 41 8395 7921 7494 7106 6749 6420 6113 5827 5559 42 8386 7914 7488 7100 6744 r 414 6108 5823 5554 43 8378 7906 7481 7093 6738 6409 6103 818 5550 44 8370 7899 7474 7087 6732 6404 6099 5813 5546 45 8361 7891 7467 7081 6726 6398 6094 5809 5541 46 47 48 8353 8345 8337 78P4 7877 7809 7461 7454 7447 7^75 7069 7063 6721 6715 6709 6393 6388 6383 6089 6084 6079 5804 5537 580015533 5795-5528 49 8328 7862 7441 7057 6704 6377 6074 5790 5524 50 8320 7855 7434 7050 6698 6372 6069 5786 5520 51 8312 7847 7427 7044 6693(6367 6064 r>781 5516 52 8304 7840 7421 7038 6687 6362 6059 5777 5511 53 8296 7833 7414 70326681 6357 60r>5 5772 5507 54 8288 7825 7407 7026 6676 6351 6050 5768 5503 55 8280 7818 7401 7020 6670 6346 6045 5763 5498 56 57 8271 8263 7811 7803 7394 7387 7014 17008 6664 6659 6341 6336 6040 035 5758 5754 5494 5490 58 8255 7796 7381 700* 6653 6331 6030 6749 5486 59 60 8247 8239 7789 7782 73746996 1-36816990 6648 6642 f'325 6320 tJ025 6021 5745 5740 5481 5477 ASTRONOMICAL TABLtl. Table of Proportional Logarithms. J 3! 4: 5i ~6 ; 9! 10 11 12 13 14 15 16 17 18 19 20 17 5477 5473, 546* 5464 5460; 5456 5452 5447 5443 5439 5435 5430 5426 5422 5418 5414 5409 5405 5401 5397 5393 18 5229!' 5225.^ 522 i* 5217'^ 5213;< 5209 < 5205 < 5201 - 5197 5i93| 5189; 5!85 5181! 5177) 5173 5169 5165 5161 5157 5153 5149 19 1994- I990i 1986 1983 4979 4975 4971 4967 4964 4960 4956 4952 4949 4945 4941 4937 4933 4930 4926 4922 49 18 20 477 1< 4768' 4764/ 4760- 4757 4753 4750 4746 4742 4739 4735 21 4559 ' 4556^ 4552^ 4549^ 4546^ 4542^ 4539 4535' 4532 4528 4525, 4522 4518 4515 4511 4508 22 | 1357 ^ 1354|< 4351 < 4347 4344 4341 4338 4334 4331 4328 4325 23 4164: 4161 4158 4155 4152 4149 4.45 4142 4139 4136 4133 4130 4127 4124 4120 4117 24 3979: 3976 3973 3970 3967 3964 396 i| 5958 3955 3952 r^949 25 >802 3799 3796 3793 3791 3788 3785 :3782 3779 3776 ,773 4732 4728 4724 4721 4717 432 i 4318 4315 4311 4308 .3946 3943 3940 3937 3934 3931 3928 3925 3922 3920 3770 3768 3765 >762 ^759 4714 J4710 14707 14703 |4699 4505 4501 4498 4494 4491 4305 4302 4298 4295 4292 4289 4286 4282 4279 4276 4272 426S 4266 426: 426C 4114 4111 4108 4105 4102 3756 3753 3750 3747 --745 21 22 22 24 25 26 21 2* 2< S< 5389 5384 538C 5376 >5372 J5368 364 I535S tp33 )|535] 5145 5141 5137 5133 5129 5125 U5122 Moll 8 Hfilll t|511C 4915 4911 4901 4904 490C 4896 489S 488< 488 |488J 14696 ;4692 4689 14685 14682 4488 4484 4481 4477 4474 4099 4096 4092 4089 4086 408S 408C ,407^ IJ4074 14071 3917 3914 391 1 3908 ..905 13902 1 389S 3896 t'"89, 389C 3742 3739 37:36 3733 JS730 >4678 'J4674 M4671 )|466S |466^ 4471 4467 4464 (4461 l;4457 !3727 :3725 3722 ,3719 )!3716 ASTRONOMICAL TABLES. 331 Table of Proportional Logarithms. 17 | 13 19 J 20 21 I 22 I 23 I 24 25 3053515110488146644457426014071,38903716 31:5347 5106 4877 466044544256 4068 J3887 3713 32 5343 5102 4874 4657 44504253 ! 40653884 37 10 335339 5098 487046534447 4250J4062388 113708 345335 50944866 4650 4444 4247 1 4059 138 7 8 3705 355331,5090 4863:4646 4440 4244J4055 13875 3702 36 5326 5086 4859;4643 4437 4240 4052;3872 3699 37 5322 5083J4855 | 4639'4434 4237 4049,3869 3696 38 5318 5079 4852 4636J4430 4234 4046 13866 3693 39 53 14 5075 4848J4632 442714231 ; 4043 3863 3691 40153105071 4844462944244228404038603688 _l i ! 41 '53065067 4841 4625 4420 4224 403713857 3685 42^5302 5063 4837 4622 441 7|422 1 4034 3855 3682 43:5298:505914833 4618441414218 4031,3852 3679 44!5294;5055i4830i4615441042l5 ! 4028l3849!3677 45 5290i5052 4826 46 1 1 4407J4212j4025!3846J3674 1 A ar\r\ I A ncii 4652855048 47 528 1 15044 48 19 4604 44004205401 9;38403668 48 527715040 48 15 4601 4397 J420240 1613837^665 49|5273:50364811 50 5269J5032 4808 4594 439041 964010 383 1 $660 4822 4608 44044209 14022 3843 3671 4597 43944199i4013|3834|3663 51 5265 5028 4804 4590 4387,4193 4007 13828!3657 52 526 1 5025 4800 4587 438441 904004i3825l3654 52575021 52535017 4797 4584438041864001,3822*3651 479345804377 55524915013 4789 4577 4374 418 i!5009 5245 5241 5237 52334998 500547824570 4367 5002 4778 4566J4364 4171 4775 4563:436 1 4183 ! 3998|3820|3649 99513817:3646 4786 4573 4370 4177!3992|3814|3643 41743988,381113640 60 5229 4994J477 14559 3985j3808|3637 ,_ 4167J3982I38053635 I4357|4164i3979i3802[3632 238 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 26 I 27 ! 28 i 29 I 30 0363213468331031583010286827302596 31 32 33 34 2467 1 3629 3465 3307 31553008J2866 2728 2594 2465 2 3626 3463 3305 31533006*2863 2726J2592 2462 3 3623 3460 3302 3 1 50 3003i286 1 2723 I2590J2460 43621J3457 33003148 3001j2859272l'2588 i 2458 53618 '3455,3297 3 1 45 299812856 27 1 9 2585>2456 299812856 271 9 12585 _. | j 63615!3452 ; 32943143299628542716|25832454 7 36 12)3449 3292 3 14Q 2993 2852 27 14^58 12452 8 36 10 3447 3289 3138 2991 2849 27 1212579 2450 9 3607 3444 3287 3 135 2989 2847 27 10J2577 2448 1036043441,3284313329862845270725752446 1 1 3601 13439 3282 3 13012984 2842 2705 J2572I2443 123599J3436 3279 3128 2981 2840 2703,25702441 13 3596;3433 3276 3125,2979 2838 2701 2568 2439 143593J3431 3274 31232977 2835 2698 2566 2437 1 5 359013428 327 1 3 1 20^2974 2833 2696 '2564 2435 ! 16 3587(3425 326931 18 2972 2831 2694 2561 2433 1 7 3585;3423 3266 3 1 1 5 2970 2828 2692 2559 243 1 18 35823420326431 132967 2826 26902557 2429 93579 3417 3261 31 102965128242687 2555 2426 20 357 6 J34 1 5 3259 3 1 08 2962,282 1 2685 2553 2424 21 3574|3412'32563l05|296o!2819 ( 2683|2551 2422 22 357 1 13409 3253 3103 J2958 28 1 7|268 1 2548 2420 23I3568J3407J3251 3101 i2955 : 28 1512678 25462418 24|3565!3404|3248;3098'2953 i 28 12J2676 25442416 25 i 3563 i '34013246J3096'2950 | 28102674 2542,2414 26i356o'3399 3243'3093 ; 2948 2808J2672 2540 ! 2412 27,3557 3396 3241i3091j2946j2805 2669 2538:2410 28,3555^3393,323813088 2943 ! 2803 2667 2535J2408 29,35523391 3236;3086.2941 2801 2665,2533 ! 2405 30|35493388i3233i3083i2939i2798 1 2663i253ll24Q3 ASTRONOMICAL TABLES* 239 Table of Proportional Logarithms. 26 3549 27 28 29 30 | 31 1 - _ 32 I 33 34 338832333083 29: 92798 2663125^1 2403 11 3546 3386 3231 3081 29.i62796'2660!2529;2401 |3544i3383 3228 3078 29.34 2794 2658 12527 J2399! _ '3541 i3380 3225 3076 2931 : 2792'2656 2525 2397 4 3538!3378 3223 3074*2929 2789 2654 2522!2395 353533753220307129272787265225202393 >|3533 3372 ! 32 1 8 3069 2924 2785 2649 ! 251 8 239 1 r|3530;3370 3215 3066 2922 27822647 ,2516j2389 3527i3367 3213 3064 2920 2780 2645 25142387 J93525J3365 32103061 29172778 264^25122385 (40 3522J3362 ,3208 3059 29 15 2776 2640 2510 2382 41 3519 3359'3205 3056 291327732638 2507 12 35 16 3357 3203 3054 29 10 27 7 126 06 2505 237 6 |43 351 4 3354 32003052 2908 2769 26342503 2. 78 44 351 113^52 319800492905 27.66 26322501 3508,3349 3195 3047 290. 46 '3506 3346 3 193 2764 2629^2499(2372 30442901 2762 2627 2497 47 3503 3344 3190:^042 2898 2760 262524952:368 48 3500 3341 3 188 '30. >9 2896 2757 262 J2492 2366 149 3497 3338 3 1 85i3037 2894 2755 262 1 J2490 I 2364 1 3495 3336 3 1 83 3035 289 1 2753;26 1 8J2488 2362 2^80 2374 2370 151 3492'3333;3180'30322889|275o|2616 24862:^60 |52 3489 333l!3178 ! 3030j28872748!261424842o57 153 3487 3328 '3 1 75, S027 '28 84*2746 (2612 2482 2355 l!34843325 3173M025 2882 2744 26 10^2480 2353 >:3481j3323;3170[3022|2880 2741 2607 i2477 2351 56 347913320 3168JS020J2877 2739|2605!24752349 57 3476i3318 3165!?018i2875 2737.260 ^i247:V2:H7 58|347333153163l3015|28732735!2601i24712345 59J3471 1 3313;3160|3013|287027^2|2599l24692M3 60;3468|3310i3158i3Q10i2868j27JO|2596i2467|2341 340 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 35 36 37 38 39 40 41 42 43 2341 2219 2100 1984 1871 1761 1654 1549 1447 1 2339 2217 2098 1982 1869 175S 16521547 1445 2 2337 2214 2096 1980 1867 175*7 1650|1546 1443 3 2335 2212 2094 1978 18oo 1756 1648 1544 1442 4 2333 2210 2092 1976 1863 1754 1647 1542 1440 5 2331 2208 2090 1974 1862 1752 1645 1540 1438 6 2^28 2206 20 8 1972 1860 1750 V643 1539 1437 7 2326 2204 2086 197*. 1858 1748 1641 1537 1435 8 324 2202 2084 1968 1856 1746 1640 1535 1433 9 2322 2200 2082 1%7 1854 1745 1638 1534 1432 102320 2198 2080 1965 J852 1743 1636 1532 1430 112318 2196 2078 1963 1851 1741 1634 1530 1428 122316 2194 2076 1961 1849 1739 1633 1528 1427 132314 2192 2074 1959 1847 1737 1631 1527 1425 14J2312 2190 2072 1957 1845 1736 1629 1525 1423 152310 i 2188 2070 1955 1843 1734 1627 1523 1422 1012308 2186 2068 195o 1841 1732 1626 ;522 1420 17?306 2184 2066 1951 1839 1730 1624 1520 1418 182304 182 2064 1950 1838 1728 1622 1518 1417 192302 2180 2063 1948 1836 1727 1620 1516 1415 202300 ~>178 2061 194b 1834 1725 1619 1515 1413 21 2293 2176 2059 1944 1832 1723 1617 ,513 1412 22 2296 2175 2057 1942 1830 1721 1615 1511 1410 2;; 2294 2173 2055 1940 1828 1720 1613 1510 1408 24 2292 2171 2053 1938 1827 1718 1612 1508 1407 25 2289 2169 2051 1930 1825 1716 1610 1506 1405 26 2287 2167 2049 4934 1823 1714 1608 1504 1403 2-7 * 6 285 2165 2047 1933 1821 1712 1606 1503 1402! 28 22832163 2045 193 11819 1711 1605 1501 1400] 29 30 2281 2879 2161 2159 2043 2041 1929|l817 1927|1816 1709 1707 1603 16011 1499 1498 1398/ 1397 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 24* 35 36 | 37 38 39 40 41 42 43 30 2279 21592041 1927 1816 1707 1601 1498 1397 31 2277 215712039 195 1814 1705 1599 1496 1395 3212275 2155|2037 1923 1812 1703 1598 1494 1393 33 2*73 2153 2035 1U21 1810 1702 1596 1493 1392 34 2271 2151 2034 1919 1808 1700 1594 1491 1390 35 2269 2149 2032 1918 1806 1698 1592 1489 1388 36 2267 2H7 2030 1916 1805 1696 1591 1487 1387 37 226* 2145 2028 1914 1803 1694 1589 1486 1385 38 2263 2143 2026 1912 1801 1693 1587 1484 1383 36 2261 2141 2024 1910 1799 1691 1585 1482 1382 40 2259 2139 2022 1908 1797 1689 1584 148! 1380 41 2257 2137 2020 1906 1795 1687 1582 1479 1378 42 2255 2135 2018 1904 1794 1686 1580 1477 1377 43 2253 2133 2016 1903 1792 1684 1578 1476 1375 44 2251 2131 2014 1901 1790 1682 1577 1474 1373 45 2249 2129 2012 1899 788 1680 1575 1472 1372 46 2247 2127 201 1897 1786 1678 1573 1470 1370 47 2245 212& 2009 1895 1785 1677 1572 1469 1368 48 2243 2123 2007 1893 1783 1675 1570 1467 1367 49 2241 2121 2005 1891 1781 1673 1668 1465 1365 50 2239 2119 2003 1889 1779 1671 1566 1464 1363 51 2237 2117 2001 1888 1777 1670 1565 1462 1362 52 2235 2115 1999 1886 1775 1668 1563 1460 1360 1 53 2233 2113 1997 1884 1774 1666 1561 1459 1359 54 2231 2111 1995 1882 1772 16S4 1559 1457 1357 55 2 C 229 2109 1993 1880 1770 1663 1558 1455 1355 56 2227 2107 1991 1878 1768 1661 1556 1454 1354 57 2225 2105 1989 1876 1766 1659 1554 1452 1352 58 2223 2103 1988 1875 1765 1657 1552 1450 1350 59 2221 2101 1986 1873J1763 161-5 1551 1449 1349 60 2218|2099 1984ll87l'l76lil654 1549 1447 1347 242 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 44 45 46 47 48 49 50 51 52 1347 11249 1154 1061 969 880 792 706 622 1 1345 1248 1152 1059 968 878 790 704 620 2 1344 1246 1151 1057 966 877 789 703 619 2 1342 1245 1149 1056 965 875 77 702 617 4 1340 1213 Ii48 1054 963 874 786 700 616 5 1339 1241 1146 1053 962 872 '85 699 615 6 1337 1240 1145 1051 960 871 783 697 613 7 1336 1238 1143 1050 959 869 782 696 612 8 1334 1237 1141 1048 957 868 780 694 610 9 1332 1235 1140 1047 956 856 779 693 609 10 1331 1233 1138 1045 9M 865 777 692 608 11 1329 1232 ;137 1044 95^ 863 77b 690 606 12 1327 1230 1135 1042 951 862 775 689 605 13 1326 1229 1134 1041 950 860 773 687 6u3 14 1324 1227 1132 1039 948 859 772 686 602 15 1322 1225 1130 1038 947 857 770 685 601 16 1321 1224 11^9 1036 945 856 769 683 599 17 1319 1222 1127 1034 944 855 767 682 o98 18 1318 1221jll2b 1033 942 853 766 680 597 19 1316 12191124 1031 941 852 764 >7y 595 20 1314 1217 1123 '030 939 850 763 78 594 21 1313 1216 1121 10$8 938 849 762 676 592 22 1311 1214 1119 1027 936 847 760 675 591 23 1309 1213 1118 1025 935 846 759 673 590 24 3308 1211 1116 1024 933 844 757 672 588 25 1306 1209 1115 1022 932 8431 756 670 587 26 1304 1208 im 1021 i 93 > 841* 754 669 r>86 27 1303 120ft 1112 1019 929 840 733 668 584 28 1301 1205 1110 1018 927 83P 751 666 583 29 1300 1203 1109 1016 926 837| 750 665 581 301298 1201 1107 1015 924 835 749 663 580 ASTRONOMICAL TABLES. Table of Proportional Logarithms. 243 44 45 46 47 48 49 50 51 52 30 1-98 1201 1107 1015 924 835 749 663 580 31 1296 1200 1105 101 3j 923 834 747 662 579 32 1295 1,98 1104 1012! 921 833 746 661 577 33 '295 1197 1102 1010 920 831 744 659 576 34 1291 119511101 1009 918 830 743 68 574 35 1290 1193 1099 10u7 917 828 741 656 573 36 1288 1192 1098 1005 915 827 740 655 572 37 1287 1190 1096 1004 914 825 739 654 570 38 1285 1189 1095 1002 912 824 737 652 569 39 1283 1187 1093 1001 911 822 736 651 568 40 128:,! 1186 1091 999 909 821 734 6i9 566 41 1280 1184 1090 998 908 819 733 648 565 42 1278 1182 1088 996 906 818 731 647 563 43 1277 1181 1087 995 905 817 730 645 562 44 1275 1179 1085 993 903 815 729 644 561 4511274 1178 1084 992 902 814 727 642 559 | 1272 1176 1082 990 900 812 726 641 558 47 1270 1174 1081 989 899 811 724 640 557 48 1269 1173 1079 987 897 809 723 638 555 49 1267 1171 1078 986 .896 808 721 637 554 50 1266 1170 1076 984 894 806 720 635 552 51 1264 1168 1074 983 893 805| 719 634 551 52 1262 1167 1073 981 s:u 803| 717 633 550 &3 1261 1165 1071 980 890 802 716 631 548 54 1259 1163 1070 97.8 888 801 714 630 547 55 1257 1162 1068 977 887 799 713 628 546 56 1256 1160 1067 975 885 798 712 627 544 57 1254 1159 1065 974 884 796 710 626 543 58 1253 1157 i064 972 883 795 709 624 542 59 1251 1156 1062 971 881 793 707 623 540 60 I249lll54il061 969 880 792 706 621 539, 344 ASTRONOMICAL TABLES. Table of Proportional Logaritknvs. 53 1 54 1 55 1 56 I 57 1 58 ~~ r~ \~~\~\ 539l458l378l300l223lt47 5911 73ii30 53154 498)418 55 339 8 i 57 j 58 i-59 ""H"K 1851110! 36 1 2 537456 5361455 377 375 298.222|146 297220J145 72 31 71 ''32 4971416 495415 337 336 260|l84!|09 2581182 108 35 34 3 535|4S4 374 296 2191144 69||33 494 414 336 257181 1061 33 4 5 532 452 451 373 371 294 293 218 216 142 141 68134493 67 '35!491 412333 441 332 2561180 255 179 105' 32 104' 30 6 i, i31 450 370 292 215|140 6> 36490 410 331 253 177 103 7 529 448 369 291214139 64 37'489408 329252 176 101! 28 8 528 447367 2891213 137 63 38|487 407 328251 175 100 27 9 527 446 366 088211 136 62 39486 406 327 '250 174 99 25 10 525j444 365 287210 135 61 ] 40 484 404 248 172 98 24 11 12 524J443 522442 363 362 285'209 284 208 134 132 60 41 58 42 483403 482402 r .247 3231246 171 170 96 95 23 22 13 14 15 521 520 518 440 439 438 3611283 3601282 358J280 206 205 204 131; 57||43480 130 56 44 '479 129; 55'j45j478 400|322i244j 169 399320243167 398 ! 319 242 166 94 93 91 21 19 18 16 517 436I357|279 203 127 53 |46i476 396 3181241 165 90 17 17 18 516 514 4353561278201 434 3541276 200 126 125 52 i47'475 51 48i474 39513161239 164 394 13 15 238' 162 89 16 88 15 19 513 432 353275.199 124 50 491472 392J314i237|16l 87 13 20 512 431 352J274 197122 49 ! 47 391,313 236J160I 85 12 21 510 430 350 273 196' 121 47 51 470 390311 234 1 59' 84 11 22 509428349271 1951120 *6 52468'388310 233157 83 10 23 507'427 348270194119 45 531467 387,309 232il56 82 8 24 06|426 346269i 192 117 44 54 466 386 3071230' 155 80 7 25 505 424 345267 191 116 42 55 464384 306j229|154 79 6 20 503 423 344 '266 190 115 41 r>o 463383 305!228l 152^ 7B 5 27 502:422 343 265 189 1 14 401157 ,462!382,304i227; 151 77 4 28 501 420 341 264 187 112 39|I58'460!381 302'225 150 75 2 29 499 419 340 262 186 111 38i'59!459|379 301 224 149' 74 1 30 4t>8 418j339|26ljl85lll0i 36|l60!458i378|300|223JU7l 73 INDEX. [ A. ] Page. AIR. tide in * ' . / ' 94 Annular eclipses . .Jr... ,^>-.- i-V.*.: 98 Anomalies ,*".;<. .... .:;*'' -. * f ! 108 Anomalistic year . ... TV'; > rf -,';; . 45 Aphelion, motion of . . . . . . . 45 110 place of ....... 46 revolution of . . ^' V .." '"' ''. . 46 Artificial globes .' , . .'V '' ... 187 Ascending node of the moon, sun's distance from . . 124 Asteroids &"= ; '. ; /'/.*, '? ; *f . 60 hypothesis of . r . '. ' ' '" "" . 60 Astronomical tables . , ;^'.'" >' . 203 Astronomy, term explained . ***^ ,-T , . *"* Atmosphere refraction of . *, *'k - ' 4 . H ^W Axis of the earth, position of '-' .". - .... V , .:, . . 43 affects eclipses '.*.* ^ .; . 104 [ B. ] Binary stars . .,.-> . . . fc . 162 Brahe Tycho, system of , "- *.--4 , ^.'''^ . xiv Brewster, Dr. hypothesis of the sun's heat ... 29 [ c. ] Calendar, Julian ^;*. > ^ - . '*.* '**:'. 137 Gregoriaa < . '^ .' . . . 137 Catalogue of eclipses f ' ' '*;,. >/ . . ;, 105 Causes of planetary motion .' **f " N> , 75 Centrifugal and projectile forces, how different . ; . # ^ Centripetal and projectile forces compared <" ' J . . 78 Ceres --^^ . : ^-' '-: r \ ;"'.',- . . 59 Chaldean period ^ w'.^% .* . .134 Characters . . . . . , , 24 Circles of the earth ... . .38 31 246 Page. Circumference of the earth's orbit . . , . 46 Coiour of Mars and of the mon eclipsed . . 56 Colures ... - . 39 Comets ... 158 tails of . . ... 159 Conjunction of the sun and moon with the moon's nodes . . 99 Constellations . . . , . 164 Copernican system . .... . . . x iv Copernicus - - . . xv Curves, looped considered ..... 74 Cycle of the moon . . . . . 135 Cycle of the sun . ' . . . , 134 [ D. } Days - 139 Depression of the horizon * . . ''"."'* '/; *86 Diameter of the earth . . x . , . <: ; -* 3$ Diony si an period . . . *.'*. 134 Distance of the planets from the sun . . .^^ . 159 Dominical letter . . . ; V 140 Dominical letters, table of . . 142 t E. ] Earth . 38 circles of . . 38 diameter of . 38 figure of . .38 irregularity of motion first discovered . 42 latitude of how determined . . 175 longitude of how determined . . 177 motions of . 41 motion of not perceptible . "V 47 orbit of 42 position of axis . 43 prospect of the heavens at . . . . 74 zones of . . 40 Earth's shadow extent of . . . ''*'', 9S at the moon ... .97 Eclipse of June 16, 1806 . . 100 Eclipses . . , , 95 annular anil total ..... 98 catalogue of ..... 105 duration of ..... 104 limit from the node . . , 96 long absence of . . . . . . 1W number of . . . 99 partial, total, and central . . 96 period of . . . 99 INDEX. 247 Eclipses, projection of solar ' - m . . . 125 projection of lunar . -;. ; ' ^ *h 1 rr^S-^t 131 series of . . ; ^ siu' ** total darkness in . -_ . . ' . .; 103 Ecliptic . "I . . , -,y j 39 obliquity of . , . .""" > 144 Elements in the projection of a solar eclipse . . f 4 * 155 in the projection of a lunar eciipie . . . 131 of Herschel Y . /J . .>;,. 68 of Jupiter " \ . . V* v, 62 of Mars , . . .+**.*, ,^. 57 of Mercury .... .^ 33 of Saturn .... , 65 of Venus . '. . . '" ,' " 35 Epact .* [ ty* . t . 135 Equation of time . . . n: * r ! ' -<:; 78 Equinoxes, precession of . '*.;< :. fi i/ .*:* : -.? ; 47 Explanation of tables . . . ' .. " .-*.-. . : 108 { P. 3 Ferguson s observations on tides . . . . !. 94 Fixed stars . . .' ' '.' '' *J . 161 Full moon calculated . . . . > : V- ; 117 r r i [ tr. ] Galaxy . . . . .' 168 Galileo discovered the satellites of Jupiter . :.*>*': ' vj r 63 Georgium Sidus .... ' , 67 Globes, artificial . . , - , ^ 187 problems solved by . . . . . 190 celestial problems by . . *' ir i^ '' ^ ^ ' 1 197 Glossary . . :f # '*'."'': J^ /? : 17 Golden number . . *V. .. 4,' 135 Greeks computed time . . . ". : 136 [ H. ] Harvest mon .... ., 84 table of . . . . V' V r 88 Heavens, concavity of . ,^ . '.*'*' : ; . Si prospect of at the earth . . ."~ 74 at Herschel . . ' r ;*^ W$$ 75 at Jupiter . . .**i' : ;.', . 76 at Mercury . . * . ' v *' 73 at the sun .' . . * ^ 7 g Herschel's hypothesis of the sun V. . ..^^ . 27 Herschel, the planet . . n !. !C : t 6' elements of . . ?^ v3 *^ prospect of the heavens at ,, ", . . , 75 tatellitesof . """!, .'* . ^ 68 Hoar 139 248 IKDEX. -Indiction, Roman . . . .'''.135 Inferior planets ... .36 [ J. ] Jews computed time . '. *, . . 135 Julian calendar "', '. .". . >';** ^^ period '"; ' ' \ ; ! ." 134 Juno . " ' t . 5g Jupiter . '. . *;' \* | s 67 elements of .'.-.. 62 prospect of the heavens at 75 satellites of * . '.', . , . 63 spots on V '*. . 62 t K. ] Kepler discovered the cause of the tides p 39 explained the motion of the earth . v- ' *i-j x 43 laws of . .. .. .< :v n k . 31 I L. ] Latltude :... .*. ''/. 40 on the earth how determined . . . 175 Laws of Kepler . , . . ^j Letter Dominical .... 140 LettPis Dom.nical, tibie of . . . . . 142 Librntions of the moon " * , . . . 55 Light, progressive . . . . , 30 refraction of . . . , , jg9 zodiacal . '.' . . J *"..'" 173 Limit of eclipses . / '. '.' . ^<-^ ^ Logarithms, proportional . . . . 112 Longitude . . . . , 40 on the earth how determined ' 4 177 of the sun . . ' . ' \" 121 Looped curves considered ..... 74 Lunar year . . .136 Lunation .... log [ M. ] Magnitude of stars < . . . .163 Mars . . 56 colour of, and of the moon eclipsed . 56 elements of . . . . t ^ Mercury . ' . > pj elements of . ' '. " . ''' \ 33 elongation of . . . 1 ' .: 3$ phases of . / . > 3^ prospect of the heavens at 'i'^ : V ; ''. . 73 retrograde motion of . **^-v ;;e^ ^ ^- 1 - 36 Page. Milky way 168 Months ' ~< i ' ,; V" 138 Moon . Y "\ 48 appearance of when eclipsed '."*'; .t ... , ^ 97 appears large near the horizon . . .;. . -, ^ 54 atmosphere of . '"'..: $1 cycle of % I MM . > , v : ., Y 135 dark parts of .....* f ^ . 4 .'->'*^ 51 diameter of * . , /v ^ . 49 eclipsed colom of ^ , > ; , * -?K ^ 6 harvest .- . . 3 '- '"*'" ^ irregularities of surface ... . $1 keeps the same surface to the earth ... : - .. . , 48 librations of . . . ,,- ,'i' . ; . ; 55 magnitude compared with the earth ,* ' 49 motion in her prbit . , r /I. ..': ' ./, 84 new. and full calculated * ^ '^ ; '.i>' ^^ orbit, of . j vi ^ 53 parallax of . ,. ? , ,^ ,, , . . ,.,,;, 148 phases of ' - . , . ->:!/ 50 quantity of her light , , . . t ', f , 4 r-^,, 'i\*>w! 53 rcTolutions of . . _, '.\-^' -. ,- 48 shines not by her own light . . , :^-'; 49 Boon's nodes, motion of . . _y * .-ifJ- 99 shadow, extent of ^, . . , ' \ 98 on the earth . . . . 101 JMotion of the aphelion . . . ' . 45 J10 of the moon in her orbit '. . , . 84 Motions of the earth ' .* - * ' * ' *' >- Sc 41 not perceptible . ' /' ;-* . 47 Movement of the solar system ^^ * u . : ;;r . 1< 168 , Neap tides . . v . 93 Nehutae , y C . .,'"*? 169 New moon calculated . C V - ., '' ',- ; 117 -New stars . .,- -.^i' -,*' : '' *">..-. 167 Newton, Sir Isaac, on the heat of Mercury . -. . 32 -Nodes oi the moon, motion of ,. ^^ IV 99 in conjunction with the sun. v? . -*.J? '* ? ! "> 99 t o. ] .Oblique sphere . . ' - ..'*>" " >"* 42 Obliquity of the ecliptic . '. '. . VJ< * ' :< * 3 144 Orbit of the earth '*> ' : , "> \ ->i: ; 42 circumference of ' ,- ^ 46 diameter of . . . . 46 rtriis of the planets elliptical . . , . 3136 Page. [ p. ] Pallas ". - . . 59 Parallax . . . . .147 of the moon . . ""' .' ..... *.."'" . i4g of the sun . . .'" . 150 Penumbra ... ".'*' "*' '.""' 99 extent on the earth . . . . >' - 102 Phases of Mercury and Venus . . . : "Y '' 37 of the moon . . . . . 50 Planetary motion, causes of . . . . . 7 ft table of . . . . . 69 Planets . . V . 31 distance from the sun . -' '-* > . . 150 inferior . . . . . ' 36 primary and secondary eclipse each other ~ .* J 95 retrograde motion of . . - . - * . 37 shine by the sun's light . . -. . 9ft Polar circles . . . . , 39 Precession of the equinoxes . . . . : "*fc 4 '-"' 47 Projectile force . , . , * v }J ^ 75 Projection of lunar eclipses . . . . . " 131 of solar eclipses . . . . . 125 Proportional logarithms . . ' . . 112 Ptolemy, system of ' ''' v Refraction of light . . . ^. Tj> 169 of the atmosphera . . ' _., .^.,. 170 table of . 172 Retrograde motion of the planets 37 Ring of Saturn ..... 64 Roman Indiction ... . 136 Romans computed time . . . 137 [ s. 3 Satellites, secondary planets ... .31 ofHerschel . . , . . vJ/ 68 of Jupiter .... ;.*" 63 of Saturn . :-. 66 Saturn . . 64 elements of '*% ' ' **> ring of : 64 satellites of ... .66 spots on ... 65 Seasons of the year . . . 43 explained by figure .- . . . 44 i n different hemispheres ,tt-i &'*., * 4546 INDEX. 51 Shroetr, notice of his discoveries . * V - Secondary planets * * ' * \ >-; 31 Shadow of the earth, extent of #*"" . 1 . v:fe- 96 of the earth at the raooa - . . , ' ' 97 of the moon, extent of . .. . 98 of the moon, extent on the earth * ".'. ;/ .* v 101 Sidereal year ".*. .' . / i *&' : 45 Soiar system V -V- * Sfi 25 adrancement of in space . *."'*' - #p , 168 Sphere ,*=' *. 41 oblique *'.*i "* * 42 parallel ",* *j . r *, . 42 right * Vi. ^ -V , ';-/ ^ Spots on Jupiter v ^ *^ *' 62 on Satura ^.J^ r ^ , ., .. V 65 on the Sua ^ v *''AV " 3 on Venus * . . * ": !." 34 Springtides . ij .*" . ^' 93 Stars, binary - ;; v ' R -I - * ' ** >? ^^ clusters of 169 fixed ;v# ' > ; . " 161 magnitude of , 163 new ;% ^ .v ' 167 Style, alteration of '. . . . ' ' . ? '. 137 Summer, why warmer than winter . . . . ' 46 Sun '..*>. ,; ^2 . . .'^" 25 causes a tide "' >. ^ ; 93 parallax of " f -4 ' '."- *'* '*-*>< 15 prospect of the heavens at . ..^ .'. J r . 73 spots on iji . , f ^.: . - ,* 30 Sun's distance from the moon's ascending node * f * ^* , 124 li^ht progressive . ,^ ' ^ ?''*'. .<'''* 30 place calculated . !'rH, * t ' . |121 System solar . . ^ -^i . - 25 movement of in space *Vf ^ ^^ Tables, astronomical ... ;* .* 'V . 203 Table of constellations . 'V . ."", ^ ,'" " '+' : : 165 harvest moon . $y . ,J ' . ;. 88 planets , . . ''.." "' . 69 refraction . , ( . . / ( , 172, Tables used in calculating eclipses, explained I. , * '. 108 IT. in iv. '.-';" 109 V VI VII. . 110 VIII IX. X. . Ill XL XII. XIII. XIX. 112 Tails of comets . 159 Tides . . * at the poles ^ . . -91 caused by the sun - . . ... 93 in the air . . 94 little or none in small seas ., ' - : . 94 Mr. Ferguson's observations on - vW ? ^ 94 of great utility - - - - - 95 single - 91 spring and neap V .^- . 93 Time, divisions of . . . ,- , _ 1^4 equation of *$, ... 78 equ ation of, short tabl .... 83 Transit of Venus , J" . 150 Tropical year . 7 .' . 45 Tropics * ... 39 Twilight 172 tTranus, Herschel . . .- ^>! / 57 [ v. 3 Vesta . .- , ' .- 5 8 Venus . , ^-.-., 33 elements of . . ^ . *#. 35 elongation ef . . . . 35 Mercury and - -' . ' . . 33 mountains of . ^ - - 34 retrograde motion of , - - ' 3T spots on . ; V ' ^i' 34 transit of . r> ; k . f .-if- 150 [ W. ] Week Year 45 how computed , . 136 seasons of . - - , : . 43 Zodiac .-'i . . .'V . 39 Zudiacallight - . -_ . 173 Zones . ' / ^ *' w - 40 UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUJ| UU lilt last daiL jtampud below. DEC 5 1947 6 1947 JUL2 9 1953 Ltt 5Dec'53WB l -100m-9,'47(A5702sl6)476 VB 17017 2643 THE UNIVERSITY OF CALIFORNIA LIBRARY " - I"- 3 * "1 Si