PkHSENTRl) BY VI '^, 1 GUY'S rXEMENTS OF ASTRONOBIY, AN ABRIDGMENT KEITH'S NEW TREATISE USE OF THE GLOBES. mmW iiltlEKICAN EDITION, WITH ADDITIONS AND IMFEOVKMENTa* %SH AN EXPLANATION OF THE ASTRONOMICAL PART OF TKK AMERICAN ALMANAC. THIRTIETH edition: PHILADELPHIA: c:harle-s desilver, 2229 CHESTNUT STREET. 1864. , ri /I rf GUY'S ■' *iJ^-r^ I'LEMENTS OF ASTRONOMY, AN ABRIDGMENT KEITH'S NEW TREATISE USE OF THE GLOBES. mWW AMERICAN EDITION, WITH ADDITIONS AND IMPROVllMEWTa* %flri AN EXPLANATION OF THE ASTRONOMICAL PART OF TKK AMERICAN ALMANAC THIRTIETH EDITION. PHILADELPHIA: CHARLE-S DESII.VER, I'm CHESTNUT STREET. 1864. ClUfceo aa'orclinsf to the ^ct of Ccngtes? in \h? y?ar 1832 ay KsY Si Jiddle. in the Clerk's Office of the Distrirt Court erf Uis Eastern I )ipiact of Pennsvlvania. Gift Ige end Mrs. Isaac R. Httt July 3, 1933 PREFACE. That Astronomy is now considered a needful and im« portant branch of knowledge for every well educated person, will be readily allowed; for however some minds, totally uncultivated, may, "witli brute unconscious gaze," raise tiieir eyes to the starry firmament, or behold the various phsenoiiiena that result therefrom, still, to those who hold a respectable rank in society, a general acquaintance at least^ with the order if the heavenly bodies, and the laws by which they are governed, must at some time necessarily become a part of their inq?uries. Hence, where it is practicable, it seems highly desirable that that which rnust be known should he begun early, or iaade a branch of school education; at least the elements of the science, or great leading principles should be tlien in^ culcated. That there are many great and scientific works, and some popular volumes already published, is well known ; ana it this compendium is added to the number, it is not for the sake of obtruding the author once more before that public which has so favourably countenanced his former works, bu^ because he has not, after a solicitous search, found any trea- tise expressly designed and practically drawn up as a doss hook for schools. He acknowledges the free use which has been allowed him of some works on the subject, from which he has ex» traxted valuable materials. Indeed, in a few instances, it will be seen that he has preferred rather to select verbatim iTorn respectable authorities, than to distort the sentencets (as is sometimes done) for the sake of an apparent originality. Par, however, from attempting to set aside the use of those v^aluable works which should have a place in every library, this is intended only to become the handmaid to them. a IV PREFACE. As the study of the same branch of science is often ccrr.- menced by persons, not only of different ages, but of ditfereni capacities, and variously circumstanced in point of assistance, so must the modes of instruction, and the treatises propor- tionabiy vary. That treatise which may be well adapted to the solitary and self-taught student, or that whlcn may, idv JLs diversified reflections, captivate a leisure hour, may not i>e the best suited to the boy who studies in conjunction with his class fellows, and with the elucidations of a master always at hand. As an elemental^ work, care has been taken to av^oid two very common evils, — that of extreme brevity on the one hand, and of a too great prolixity on the other. A mere out- line, or brief mention of a very few leading particulars, could not prove satisfactory, either to teacher or learner ; it would call forth no exertion, excite no interest, afford no pleasure, impress no lasting improvement. On the other hand, to swell the volume with complicate calculations, and by the discussion of subjects too abstruse for juvenile comprehen- sion, would occasion the Tyro to stumble at the threshold, and recoil from the study in hopeless disgust. The text or larger print, may be considered to contain the general principles and well authenticated facts; or at least, so much of tne outline of the srlence as should be first known. This therefore may be appo'iited for the iQiXxwer^s first course. The smaller print, except what refers to illustrations of the plates may be omit'.ed, or not formally insisted on, nil the second course; as it«^ontain3 matters either less known, or of less immediate importance; or else more difficult to be com- prehended. Perhaps there is not a point in which instructors more widely differ than in their opinion of the quantum proper tc be put before the pupil. The vast dissimilarity in the bulk ^of elementary treatises, on any one subject, proves the truth of this assertion. One teacher prefers a volume for his'pnpil PREFACE. ▼ that contains almost every minutia, though it may require the toil of years to wade through it ; — another presents hira with a meagre outline that will not require the labour of as many months. Wiiile this difference of opinion exists, and it will more or less ever exist, it may be desirable to meet, as much as pos- sible, the views of each. This has been attempted in some late publications ; and the plan is here followed by a distinc- tion in the type. It is herein intended, that the teocty if perused alone, should contain in itself a connected and tole^ Table complete outlirte ; and if read with the smaller type, that the work should exhibit but a more enlarged whole. This simplicity in the arrangement will, it is hoped, render it more accommodating to instructors, and suit it to the pur- poses of scholars of different classes, capacities and ages. That work must surely possess some advantages, that can be perused by the younger scholar without perplexity, and by the more advanced student without deficiency. General principles only of an art or science, it is well known, are the parts proper to be first committed to memory ; and that too, perhaps, at an age when their utility is not cnown, nor to what purposes they are applicable. This is «)est effected, as Dr. Lowth observes, " by some short and dear system." Every one is aware of the impropriety of surcharging the bodily organs, — but overloading the yet un- expanded faculties of the mind, by an attempt to fill it with a too great redundancy of ideas in a first course, is equally fruitless and injurious. It is particularly recommended that those young personb who wish to derive information from this treatise, will Tio^ only peruse it deliberately, and digest what they read, b-iv make a study of it, so as to be able to answer with consider- able correctness the questions subjoined. From a mere cur- sory perusal, neither information nor entertainment can be expected. a2 n PREFACE. It is hoped that the numerous well executed plates which accon]i)any this work will be deemed appropriate to elucidate the subjects ; and that the complete series of questions will prove generally acceptable to instructors, and contribute to facilitate their labours. It is presumed tliat most of the interesting parts of Astro nomy have been introduced. To have illustrated the method of calculating Eclipses, and the transits of Mercury and Ve- nus; or of finding tlie longitude and the periodic times and distances of Jupiter's satellites, &c. might have enhanced tlie work in the public estimation, but to the learner it would prove not only useless, but perplexing and obscure. Indeed, to have handled the subject more abstrusely, and to have written in all the technical phraseology of the science, would have been much more easy than was the frequent la- bour of verbal discrimination, of casting into sliade some parts which would only dazzle and bewilder, and of clothing other parts in a language, not less pure it is hoped, but ai •east more suited to tlie youthful comprehension. CONTENTS. CHAPTER I. Preliminary Definitions . 1 CHAPTER II. Of the Heavenly Bodies • 3 The Sun .... 5 CHAPTER in. Mercury .... 7 Venus 8 CHAPTER IV. The Earth .... 10 The Moon . . . .11 CHAPTEP V- Mars . . . . 14 Asteroids ... 15 CHAPTER VI. Jupiter 17 Jupiter's Satellites . . 18 CHAPTER VII. Saturn ... .20 Satellites of Saturn . , ib. Saturn's Ring . . 21 CHAPTER VIII. The Geor^iura Sidus, or Her- schel ." . . . ,22 The Hersohel's Satellites . 23 The Proportional Magnitude and Distance of the Planeis ib. CHAPTER IX. Comets 24 CHAPTER X. The Fixed Stars ... 26 CHAPTER XI. Constellations . . ,30 Northern Constellations , 31 Southern Constellations ' . 32 Zodiacal Constellations . . 33 CHAPTER XII. Different Systems . . . 34 | CHAPTER Xin. Of the Motions of the Planets 36 I Inferior and Supenor Con- junctions of the Planets B7 CHAPTER XiV. ITie Plane of an Orbit, Pla- nets, Ncdes, &c. . . 3^ The Transits of Mernir}' and Venus . . . ,10 CHAPTER XV. The Ecliptic, Zodiac, and Equator, on. The Earth. Mercury. Venus. Mars Jl Jupiter. b Saturn >t^ Uranu* ? Ceres. <^ Palla# ? Juno. a Vesu ELEMENTS OF ASTRONOMY. CHAPTER I. PRELIMINARY DEFINITIONS. AsTKONOMY is that branch of natural philosophy which treats of the heavenly bodies : it consists of two parts, namely, descriptive and physical A stYonomy, Descriptive Astronomy^ comprises an account of tne phenomena of the heavenly bodies. Physical Astronomy consists in the investigation of the causes of their motions, ^o,. A Circle is a plain figure, bounded by a uniform curve line, called the ciicumference, which is every where equulistant from a certain point within, called its centre, as A B C D (pi. 1. ?ig. 1.) The {.ir^umference itself is often called a circle, and also the peri phery. The Radius of a circle is a line drawii froia the centre to the circumference ; as A E, E B, or E C (fig- 1-) The Diameter of a circle is a line drawn throii^Qfh the centre, and terminated at both ends by the circum- ference, as A E C (fig. 1.) Every Diameter is double the radi!is,and divides the circle into t^vo equal parts. The terminating points of the diameter are sometimes called its Poles, as A and C. An Arc of a circle is any part of the circumference asFDG (fig. 1.) 1 2 DEFINITIONS. A Chord of a circle is a right line joining the ends of an arc ; dividing the circle into two naequal parts, as F G (iig. 1.) A Semicircle is half the circle, or a scguient cut off by the diameter, as A B C (fig. 1.) The half circumference is sometimes called the Semiorcle. A Quadrant is half a semicircle, or one fourth -part of a whole circle ; as A E B, or B E C. A quarter of the circumference is sometimes called a Quadrant All circles, great or small, are su{3posed to be di- vided into 380 equal parts, called degrees (mnrked ° ;) each degree into 60 minutes (marked ' ;) each minute into 60 seconds (marked ".) Hence a semicircle con- tains 180 degrees, and a quadrant 90 degrees. An Angle is the meeting of two lines in a point, as A (plate 1, fig. 2.) The point v/here they meet is called the angular point, and the linea A B and A C, are called sides or legs. A Right Angle is that which is made by one line perpendicular to another, or, when the angles on each side are equal to one another, they are right angles ; as the angles M and N (iig. 3.) The measure of a right angle is a quadrant of 90 degrees. An Acute Angle is less than a right angle, as the angle S (fig. 4.) An Obtuse Angle is greater than a right angle, as the angle R (fig. 4.) Parallel Lines, whether straight or circular, are lines in the same plane, which are every where at the name distance from one another; and which, though drawn ever so far, both ways, wnli never meet . thus DKFI1VITI0NS. 3 * b and c d and ef (fig. 5,) are three parallel lines: and g h and i k (iig. 6,) are two parallel j^enticircles. A Globe or Sphere is a round body, every p-ut of who^e surface is equally distant fron) a point within, called its centre. A Spheroid is a figure nearly spherical, either ob^" long or oblate. The earth is a spheroid, having its axis or diameter at the poles shorter than at tfie equator. A Gi^eat Circle, A B D E, of a sphere, is one whose plane passes through its centre C. (See plate 2, fig. 1.) A Small Circle of a sphere, F G II 1, is that whose plane does not pass through its centre. A Diavietcr, N C S, of a sphere, perpendicular \o any great circle, is called the axis of that great circle, and the extremities, N S, of the axis, are called its poles. (Plate 2, fig. 1.) Hence ihe pole of a great circle is 90" from every point of the di- emeter upon the sphere; because every angle, as NC A, beinr a figh: angle, the arc, M A, is every where 90 degrees. Any two great circles bisect each other; for the planes .'>f bo^k f^ssin;! through !he cenire of the sphere, their common se*»r"iJ, sigmtyiiig rovmgor wandering. THE SUN. The Sun is the source of light and heat, and the centre of our Solar or Planetary System. H?s f(?rm is nearly that of a sphere or globe. His diameter is about 883,210 miles, and his circumference 2,774,692 miles. According to some authorities the Sun*s diameter is 893,522 miles* For the definition ola ^^6e or sphere, see the Preliminary Dijiiiition* Chap. 1. The Sim's diameter is equal to 112 diameters oi' the earth. His distance from the earth is 95,000,000 of miles ; and he is 1,400,000 times larger than our earth. The Sun was for ages, and till lately, thought to be a globe of real hre ; but it is now supposed to be an opaque body, surrounded by a luminous atmosphere. Though to the Sun our earth is indebted for Hght and heat, life and regatation, and without its genial influence it would become a dark j^iart mass, yet Dr. Herschel supposes the Sun to be an opaque body, HrTounded by a lucid and transparent atmosphere ; that this luminary titfibrs but little in his nature from the planets ; and that it is an ia- habitable world. A number of maculss^ or dark spots, may sometime bQ seen, by means of a telescope, on different parts of the Sim's surface. These consist of a nucleus, which is much darker than the rest, surrounded by a mist or smoke ; and they are so changeable as he* quently to vary during the time of observation. Some 4>f the largest of them seem to exceed the bulk of the whole earth, and are often seen, at intervals of a fort- night, for three months together. The darker spots are termed macidse^ and the brighter faeulm. 6 THE srK. The nmculcB have been supposed by some, to be cavities in ;he bod» of the Sun ; 1ii3 nucleus being in the bottom of the excavation; and the shady zone surrounding it, the shelving sides of the cavity. Other* have sup})Osed maculae to be large portions of opaque matter monng m the iiery fluid. Some again have taken them for the smoke of vol- canoes in the Sun, or the scum floating upon a huge ocean of fluid matter. FaadcB, on the contrary, have been called clouds of light, and luminous vajx)urs. But Dr. Herschel supposes that the Sun is surround- ed by an atmosphere of a phosphoric nature, composed of various trans- parent and elastic fluids, by the decomposition of uhich, light is pro- duced, and lucid appearances formed, of different degrees and intensity. The Sun has two motions ' the one is a periodical motion, in nearly a circular direction round the com- mon centre of all the planetary motions (see the arti- cle, Centre of G^*avityyChdp.XlX.) — theother motion is a revolution upon its axis, which is completed in about twenty-five days. The Sun's motion about its axis renders it spheroidical, havmg iti diameter at the equator longer than at the poles. The method of ascertaining the Sun's revolution on his axis is, by observing the motion of some of those remar!:able spots which are seen on his disc. If these spots are observed uniformly to change their places, and to appear on one side and disappear on the other, there is not any other means of explaining sucii phe- nomeni', but that of a rotation about his axis. The time of rotation may be found by observing the aic described by any spot in a given time, and then find by pro[)ortion the time of describing the whole circle. Or the return of the spot to the same position with re- gpect to the earth. may be observed, which will give the time of an entire rotation. The Sun, if viev/ed from any other system in the universe, would appear as a fixed star does to us* MERCURY. 7 CHAPTER IIL MERCURY. . Mekcury* is the smallest of the inferior planet?/ and the nearest planet to the sun. His diaineter is above one third of the diameter of our earth, or about 3,000 milcv-. He revolves about the sun in 87 days, 23 hours, and |, at the distance of about 37.000,000 of miles from that luminary ; moving in his orbit at the amazing rate of above 112,000 miles an Ixour, or 31 miles in a sernnd. By ti^e term orhit is meant, the path descrilcd by a planet in its coarse round the sun, or by a moon round its primary planet. For an illustration of the planets' orbits, see the FrontiFDiece. Some auihorities make Mercury's diameter 200 mile, more, and others as mmh less. His mean distance from the sun is to diat of the earth from the sun, as 387 to 1,000, or considerably more than one-thiiti Though small, he has a bright appearance, with a light tint of blue; he never departs much more than 30^ from the sun, and on that account is usuall) hid ii) the splendour of that luminary. The sun's diameter will appear, if viewed from Mercur-, nearly three times as large as from l\ie. earth. And the sim'sligl taiid heat at Mercury, have be^^n calculated at above seven times those of tae eartli: upon the sui.j^NDsition that the materials of which Mercury is composed, are of the same nature as those of our globe.t Merr-iiry's diurnal motion, or time of rotation on his * Mercury, was considered, mythologically, as tl^e messenger of the gods. t These degrees of heat and light are presumed, u|X)n the long and generally received opinion, that the sun is a globe of lire. 8 VENUS. axis is 24 hours and 5 minutes, and the incliaatiori of his ajcis to his orbit is very small. Mercury changes his phases in a manner similar lo the moon, according as he is stationed with re-gard to ihe eurth and sun. Th'S planet, however, never appears to us quite full ; because when his bf' rht side is turned fully to us, he is lost in the sun's beams. Frr3i» these different phases it is clear that he does not shine by his own light ; for if so, he would appear always round. As the orbit of this planet is between the earth's or- bit and the sun, he will at times appear to pass exactly between them ; and this appearance is denominated the transit of Mercury over the sun's disc: the planet then appearing like a black spot moving across the face of the sun. As the planes of the earth and Mercury's orbits are no^ coincident, this appearaiice does not often happen. The last transit happened, Nov. 5, 1822 ; a second will happen, May 5, 1832 ; and another, Nov. 7, 1835 VENUS. Venxis is the second planet from the sun, and is easilv distinguished by her superior brightness and whiteness. Her mean distance from that lummary is abou^ 69,000,000 of miles, and she completes her an- nual revolution in less than 225 days, with a rotation about her axis in 24 hours nearly. Hence, the length of her year is not quite two-thirds nf ours Bian- shini n akesa coiTi[»leto rotation on her axis to be 24 houre Rm nutcs ; bu\ theCassinis,23hours20 minutes; and S«hroeter23 hours 21 minutes. The circumference of her orbit is at least 433,000,000 of miles. Her magi.itu le is nearly the same as that of the earth , her diameter being about 7,900 miles; and she moves m her orbit at the rate of 75,000 miles in an hour. VENUS. ** The quantity of light and heat which this p^met re- ceives from the sun, may be supposed to be double thtt of the earth. Her lustre is so great that she has been seen in the day-time, when the sun shines ; and at night she usually projects a real shade. Venus, 4hen viewed through a telescope, is neve seen to shine with a bright full face. But '^he ha phases changing like the moon ; for sometimes she ap« pears gibbous, at others, horned like the new 'moon, and her illumined part is constantly towards the sun ; which proves that she moves, not round the earth, but round the sun. Venus is a morning star when seen by us westward of the sun, for then she rises before him ; and an evening star when eastward of that luminary, for then she sets after him.* She is alternately the one and the other about 290 days. In her seasons there must be a very considerable difference ; much more, indeed, than is experienced by us. The axis of our earth is inclined only 23^ degrees, whereas that of Venus inclines about 75 degrees to the plane of her orbit. Venas appears much larger at sometimes than at others; and the great variations of her apparent diameter demonstrate that her distanco from the earth is exceedingly variable This great inequality, whh ••espect to distance between her superior and inferior conjunctions, will appear from an inspection of plate 7 fig. 2. See also page 37. The orbit of Venus, like that of Mercury, lying be- tween the earth and sun, there will happen, at times, * When a morning star, she is callerrii of a dark 7\mnd spot: this occurs only twice in aoout 120 year.-'. One was seen in England in 163U, one in 1763, and one in 1769 only P.\ J will hapj)en in the present century, viz. the fktji in 1874, the last in 1882. By ihis phaenomena astronomers have been enaWf»d toasc-?rtain the distspce of the earth from the sun; and hence' tije distances of the other planets are easily found. Kepler was the first i>eison who predict- fd the transits of Venus and Mercury over the sun £ disc. And the (irst time Venus was evei seei \i\)Ox\ the sun, v.as or Nov. 16, 1639 by OQi countryman, Mr. Ilorrox, who was educated at Emanuel Col- lege, Cancibri' V» See a fuller Illustration, Chan. XXXI CHAPTER IV, THE EARTH.* The Earth is the third planet from the sun ; its rneais distance from him being about 95,000,000 of miles its diameter is found to be 7,920 miles, and its circum- ference to be 24,880 miles. Doubtless, to a person placed on the planet Venus, the Earth wcula nave as much the appearance of a star as Venus has to us. The Earth has two constant motions ; the one about its axis, and the other through its orbit round the sun. It moves in its orbit at the rate of 68,000 miles an hour, which is nearly 20 miles each moment; and per- forms an entire revolution in nearly 365^ days, which ♦ The Earth, 'oy the ancients wp^ called Te^ ra ; an*! hy a?tronomen THE MOON. ll is the length of our year. A complete rotation upon its axis forms a natural day of 24 hours. The more exact time of its annual motion is 365 days, 5 hours, 4^ ninutes, and 49 se'^onds. Hence the division of time into ffoys and years are prescribed by the notions of the Earth ; the former depending upon the rotation of the Sarth upon its axis; the I.at'er upon its revolution in its orbit. The form of the Earth is not that of an exact globe or sphere, but of a spheroid, i. e. a little flatted at the poles, having the diameter at the equator, 26 miles ionger than at the poles The earth was formerly supp sphere next the earth, can never be really dark ; for when it is turned from the sun, it continues illuminated by light reflected from the earth, in the same manner as we are enlightened by a full moon. But the other hemisphere of the Moon has a fortnight's light, and a fortnight'* dark* aoss by turns. * The Greeks gave to the Moon the name of Sdene. 14 MARS. The sun and st?rs rise and set to the inhabitants of the Moon, in a manner similar to what they do to us ; and we are led to conclude that, like the earth, the Moon is also inhabited. Nv^ large seas or tracts of water have been observed m the Moon by Dr. Herschel, or any other astronomer, nor did he notice any indi cations of a Lunar atmosphere. Recent observations, how ever, on th^ occultations of Jupiter and Venus by the Moon, render it highly proba- ble Uiat the Moon, as well as the earth, is surrounded by an atmosphere On April 5th, 1824, Mr. Ramage, of Aberdeen, Caplain Ross, of the Navy, and Mr. Cornfield, at Northampton, observed, with excellent telescopes, the occulralion of Jupiter, and to all of them the disc of the planet appeared distorted when it approached the limb of the Moon ; aii<^ Mr. Cornfield, at Clapliam, on Oct. 30lh, 1825, observed, on the emer sion of Saturn from behind the dark limb of the Moon, lirst the diac of the planet, and then the eastern extremity of the ring decidedly flat* tened, a phsanomena perfectly analogous to what would be producer by refraction, and therefore rendering it highly probable that the Mocc is siurrounded by an atmosphere. CHAPTER V. MARS.* The orbit of Mars is next above that of the eartli, and he is the first of what are called superior planets. He is known in the heavens by a dusky red appearance. His distance from the sun is 143,000,000 of miles; and the length of his year is about 687 of our days. The cause of his dusky red colour has not been clearly ascertained: whether it arises from a thick atmosphere, or from his being of a na- ture the better to reflect the red rays of light. The mean distxince oi Mars from the sun is more than half as far again as that of our earth ♦ The ancients have given the same name to the heathen God oftoar I I ASTEROIDS. J diat is, if the distance of the earth be considered to consist of 100 parts, that of Mars would be 152. He moves in his orbit at the rate of 53,000 miles in an hour. The diurnal motion of this planet on its axis is performed in 24 hours and 39 minutes. His diameter is only 4,189 miles ; and owing to his distance he is supposed not to possess one half of the light and iieat which we enjoy. The diurnal motion of Mars is ascertained by several spots that are iteen in him, when he is in that part of his orbit which is opposite to the sun and earth. Dr. Rook first discovered them, and Cassini and Her ichel have from them, at length, determined his motion on his axis. Though Mars, when viewed through a telescope, ap pears mostly full, yet he is seen, at times, to increase and decrease somewhat like the moon ; with this excep- tfon, that he is never horned. Hence we infer that he shines not by his own light ; — that his orbit exceeds that of the earth, and includes both the earth and the sun. No satellites or moons have been discovered to attend on Mars. See plate 5. Mars, when in the part of the heavens opposite to the sun, appears about five times larger than vs hen he is near the sim ; v. hich proves that he must be much nearer io the earth in one situation than in an- Dther. This will receive illustration by an inspection of plate 7, fig, 2, where the great inequality, with respect to distance, is seen between his opposition anc cmijunciion. It is evident, also, that it is not theeardi that is in the centre of his motion, but the sun. ASTEROIDS. Between the orbits of Mars and Jupiter, four small planets, called Asteroids, have lately been discovered, viz. Vesta, Ceres, Pallas, and Juno. Vesta, though the last discovered, is nearer to Mars than the other three : its mean distance from tlic sun 16 ASTEROIDS. being 225,000,000 miles ; and the revolution through its orbit is performed in 1,326 of our days. Its incli- nation to the ecliptic is 7y degrees, being rather more tkan that of Mercury. The size of this planet is not yet ascertained. Vesta was discovered by Dr. Olbers, a physician of Bremen, m Oer naaiiy, early m 1807. This planet is much smaller than our moon. Ceres's mean distance from the sun is 263,000,000 miles, not quite three times that of the earth. Il5 time of revolution is 4 years, 7 months, and 10 days ; ks diameter 1,582 miles, and it is inclined to the eclip- tic in an angle of about IO5 degrees. Ceres was discovered by M. Piazzi, of Palermo, in Sicily, Janii gry 1, 1801. Pallas' s mean distance from the sun is nearly the same a^ that of Ceres ; not quite three times that of the earth, namely 263,000,000 miles. Its revolution is made in about four years. Its orbit is inclined to the ecliptic, in an angle of about 34^ degrees ; and its diameter is 2,280 miles, Pallas was discovered by Dr. Olbers, in March 1802. Juno's mean distance from the sun is 252,000,000 miles ; and its size nearly equal to that of Ceres. It revolves round the sun in 4 years and 4 months ; and its diameter is 1,393 miles Its inclination to the ecliptic is 13 degrees ' and it appears like a star of the eighth magnitude. Juno was discovered by M U.^rding of Lilienthal near Breinen Sept 1st, 1804 Fafr f7 n^/r s Fc^. /. 1) E^ /v^ J B ( A>^. ,f \ I ^y^ ' ^ ^- ~"x> / / \ _., -A -^'- -i^ r . i J v- JUPITER. 17 CHAPTER VL JUPITER* JupiTEii's orbit lies between those of Mars and Sa- tarn ; he is the largest of all the planets, and is easily tiistinguished by his peculiar magnitude and brilliancy. He exceeds all the planets in brightness, except some- limes Venus. The distance of Jupiter from the sun s estimated at more than 490,000,000 of miles. Jupiter's mean distance from the sun js 62 of those parts of which ce earth's distance is 10 ; hence, he is full five times farther from the en than the earth is. And if it be admitted that hght and heat dirain^ *ri in proportion as the squpxes of the distances increeise, the inha bit- tits of Jupiter receive but a 25th part of the sun's light and heat that He enjoy. See plate IB, Jupiter's diameter is more than ten times that of the < arth, it being 8P,170 miles ; and therefore his magni- ^ide is about 1,300 times that of the earth. His year is iK.-drly equal to 12 of ours, for he makes one rcvolutioT] round the sun in 4,332 days and a half.* consequently he travels at the rate of more than 25,000 miles in Kf\ hour. Jupiter rrvolves on his axis, which is perpendicular U) \tF, orbit, m less than 10 hours, at the amazing rate of "PAfiOO miles an hour, a velocity 25 times greater ihan the earth's. Hence, by this swift diurnal rota- tion, his equatorial diameter is 6,000 miles greater than his polar diameter. And as the variety in the seasons of a planet depends upon the inclination of its axis to \ts orbit, and as Jupiter has no inclination, there can be * The great heathen deity is charactenzed by this name. c 18 Jupiter's satellites. no difference in his seasons, nor any variation in the length of his days and nights. Jiipiler's days ami nighls are always 5 hours each. In length, and ftlKuji his equator ihere is perpetual summer ; and an everlasiiug wm- \fr m his polar regions. If the axis of thisplj^net were inclined lo hi? arl)if aiiy cnnsiderahle number of degrees, ii might le less hnbitabk about tlie po es ; for then each pole would be nearly six years togetli^i ~M darkness. When viewed through a telescope, Jupiter is per- ceived to be surrounded by faint substances, called zones or belts. These belts are generally parallel ts» its e<}uator, and which is very nearly parallel to the scliptic. They are subject to great variations both m number and figure. Sometimes eight have been seen at once; sometimes only one. Sometimes they continue for three months with little or no variation, and some- times a new belt has been seen in less than two hours. From their being subject to such changes, it is inffirred that they do not adhere to the body of Jupiter, but ex- ist in his atmosphere. This planet, even on the most careless view through a good telescope, appears to be oval, the longer diame- ter being parallel to the direction of the belts. Professor Struve of Dorpat, by the most accurate ad- measurements, has determined the proportion between tlie greatest and least diameters to be as 1,371, to 1,000. Jupiter's Satellites. Trfts planet has jfowr satellites revolving about him at difierent distances, and in different periods ot time; the nearest making a revolution in less than two days, and tlif) most distant in little more than sixteen: hence JUPITER S SATELLITES. 1^ 'heir relative situation changes every instant. Cons% quentlj, these satellites, like our moon, are subject to be eclij)sed, and their eclipses are of considerable im- portance to astronomers. They were first discovered by Galileo in 1610. Galileo took them, at first, for telescopic stars; but farther observar don convinced him and others that they were planetary bodies. The periodical time of the first satellite is in about one day and 18 hcuira, (he sec-ond in 3 days 15 lj(.urs , the third in 7 days 3 hours ; and the l(>urtij ui 16 days 16 hours. The angles under which the satellites appear at the mean distance of the planet from the earth, have been determined with great precision by Struve, to be first, i,01S", second 0,914", third 1,492", fourth 1,277". These numbers represent also the proportions of the diameters of the satellites. It hence appears, that the second is the smallest, the third the largest, and the fourth larger than the first. By means of the eclipses of Jupiter's satellites, a method has been obtained for determining the longi- tude of places, with facility and some accuracy; and also for demonstrating that the motion of light is pro- gressive, and not instantaneous as was once supposed. The 'velocity of light is more than a million of times greater than of a ball issuing from a cannon. Rays of light come from the sun to the earth in less than 8 minutes; which is at the rate of about 12,000,000 of oiiles in a minute. y SATELLITES OP SATURW. CHAPTER VII. SATURN* Saturn till of late years was esteemed the sixth aiu! the most remote planet of the solar system. He shine* with a pale dead leaden light. His mean distance from the sun is about 9i times farther off than that of the earth, being nearly 900,000,000 of miles. Of course the light and heat he derives from the sun, are about 90 times less than at the earth. It has been calculated, however, that the light of the sim at Saturn Is 500 times greater than that which we enjoy from our full moon While our day-light is calculated to exceed that of our full moon 90,04)0 times. The diameter of Saturn is nearly 80,000 miles, and nis magnitude almost a thousand times that of the earth. He performs his revolution in his orbit round the sun in less than 30 of our years (10,759 days,) consequently he must travel nearly 21,000 miles an hour. He revolves about his axis in 12 hours and 13^ minutes. Oassini and others attempted, but without success, to determine the rotation of Saturn about his axis; but Dr. Herschel's obs'^rvations have at length ascertained it. The Phil. Trans, of 1794 say IjO'^ 16' Q"4 ; but !ater accounts say 12^ 13i'. Satellites of Saturn. Saturn is attended by seven Satellites or Mooris, whose periodical times differ very much. The one nearest to him performs a revolution round the primary * This nair.e is given tr the supposed lather of the Heathen gods faoc J a \) Sa^ir/r/ I Yertfu o 8 Me/*rt/7\ o Q Eizrffi \ jSr jifoo/f stn ^ Jff/?fAu Saturn's ring. 21 planet in 22 hours and a half; and that which is most remote takes 79 days 7 hours. The last Sfiiellife is known to turn on its axis, and in ts rotation lo '>e subject to the same law whirh our moon obeys ; that is, it revolves in its axis in the same time in which it revolves about the planet Saturn's Ring. Saturn is also encompassed with a kind of Ring^^ or, according to Dr. Herschel, with two concentric rings, situated in one plane, which is not much inclin* ed to the equator of the planet. They may probably be of considerable use in reflecting the light of the sun to him. See plate. From numerous observations it has been concluded, that the near est is 21,(j00 miles distant from Saturn, and that the breadth of the inner nng is 20,000 miles ; that of the outer ring7,2C0 miles; and the vacant gjiace between the two rings 2,839 miles. Dr. Herschel conjectures that it is no less solid than the planet itself; and he has found that it casts a strong shadow upon the planet. The light of the nng iie has observed brighter than that of the planet : for the ring app<^ars sufficiently bright ibr observation at times, when the teld* «cope scarcely alTbrds light enough to give a fair view of Saturn. Professor Struve has made some interesting obser- vations on this planet, with a superb refracting teles- cope. — The results of his admeasurements are, that at the mean distance of the planet, llie external diameter of the external ring is 40.215 The internal diameter of the external ring is 35.395 The external diameter of the internal ring is 34.579 The internal diameter of the internal ring is 26.749 The equatorial diameter of Saturn is • . 18.045 The breadth of the external ring is • . • 2.410 The breadth of the chasm between the rings is 0.408 c2 22 THE GE0RGI17M SIDUS. The breadili of the internal ring is ... . 3.915 The distance of the ring from Saturn is . , 4.352 He adds, " it is remarkable that the outer ring is much less brilliant than the inner. The inner one- too, to- wards the plaiiet, seems less distinctly marked, and to grow fciinter ; so that I am inclined to think that the mner edge is less regular than the others." The Blng has a rotation about its axis, or, which is the same thing, revolves about the planet, in the same time that Saturn turns round on his axis. CHAPTER Vm. URANUS, OR HERSCHEL. This is the most remote planet yet discovered in on? Solar system. He appears of a bluish white colour, and can rarely be seen but by means of a telescope. He may be best perceived, by the naked eye, in a very clear nigh? when the moon is absent To Dr. Herschel the world is indebted for the discovery of this planei, on the 13th of March, 1781. The Doctor, in honou- of George II L king of England, named it the Georgiiim Sidus, (or Georgian Star,) chough by astronomers it is called the Herschel, in testimony' of re- spect to the discoverer. American astronomers call it Uranus. The distance of this planet from the sun is more than 1,800,000,000 miles ; or about nineteen times that of the earth. The distance given by some anthora, is 1,812,000,0( miles. Tli« fight and heat which he derives from the sun, are snpp ^ed ro be ahoiu the 361st part of those at our earth (for the square of 3 is 3^)1 ; wliich PHOPCKTIONAL MAGNITUDE, &:C. OF PLANETS. 23 iet; enyAmned in a futLire chapter}— that is, al^ut equal vo the effect of '^\i/-fve, a.r.d (Ih) Gporpian one hundred aud ninety parts. [See thescnleon ihe troniispi^^re.] These are cal en la led by ruulii plying the respective (hstai ices «»f the planets by 10. and dividifig by 95, the mean Jistaii; e or the eanh from the sun. For the relative magnitudes of the plane ii» .*'«« p!ate 3. CHAPTER IX. COMETS. Comets, like the orbs already mentioned, are sup posed to be planetary bodies forming" a part of our sys- tem ; for, like the planets, they revolve round the sun; not, indeed, in orbits nearly circular, but in very dif- ferent directions, and in extremely long elliptic curves, having the sun in one of theirybci / approaching some- times near the sun, at others stretching far beyond the orbit of the remotest planet. The periods of their revo- lutions are so long that only three are known with any degree of «;ertainty. Some suppose their, not adapted for the habitation of animated be- ings, on account of the great extremes of heat and cold, to which, in Siieir course, they appear to be subject. The name of Comet is derived from Cometa^ " hairy ;" because Comets appear with long tails, somewhat re- sembling hair. This appearance is supposed to be no* thing more than vapour arising from the body in a line opposite to the sun ; some indeed have been seen with- out such appendage, and as round as the regular planets. The knowledge, however, which we have of Comets, i& COMETS, 25 rery mperfect, as they afford but few observations on which to ground conjecture. By common people they are called blazing stars, and by ?ome thvy are thought to be portentous; presaging some extraordinary event. But they can have no such tendency, nor can there be any appreneusifrn that they can injure the^arth we inhabit, by coming into contact. E\f m the tail of the Comet cannot come near our atmosphere, unless it should be at its infenor conjunction very nearly at the time when it is in im node ; circumstances so extremely anhkely, that there are some mil- lions to one against such a conjunction. It was thought that the periods of three of the Comets had been dis- tinctly ascertained ; the first of these appeared in 1531, 1607, and 168:1, and it was expected to return every 75th year; and one did appear in 1758, which was supposed to be the samie. The second of them appeared in 1538 and 1661, and was again expected in 1789, but in this the astronomers were disappointed. The third was that which appeared in 1680, and its period being es- timated at 575 years, cannot, upon that supposition, return till 2^5. This Comet, at hs greatest illsiance, is 11,200,000,000 of miles from the Bun; and its least distance from the sun's centre was but 490,000 miles ; in this part of its orbit it travelled at the rate of 880,000 miles in an hour. Comets differ much in their magnitude, though most of those which have been observed are less than the moon ; but their dimensions are not determined with accuracy. The head of the Comet of 1807 was ascertained to be about 538 miles in diameter; and that of 1811, about the size of the moon. According to Sir Isaac Newton, coitiets are of an opaque nature, and consist of a very compact, durable, and solid substance, capable of bearing exceedingfy great degrees of heat and cold. The Comet seen by him in 1080, was observed to approach so near the sun that its heat was estimated by him to be 2,000 times greater ♦haxi that of red hot iron. And it has been said t6 THE FIXED STARS. that a globe of red hot iron as large as our globe wonW scarcely cool in 50,000 years. Notwithstanding ilie above supposition the apT)earancc of ihe two brilliant (vOiiiei.s,ol'lat8, s/Bems to cverturnthal theory. Of that in 1807, Dr. Iferschcl says, we are authorized to conchide that t!ie body of the Comet, on its surface is sdf luminous, from whatever cause this quality raay be fieri ved. The vivacity of the light of the Cuiriet, also, had a much greater resemblance to the radiance of a star, than to the mild reflection ofthe sun's beams upon the moon. Comets consis! (according to modern observation) ofthe nucleus, the head, the coma, and ihx'^ tail. The iiudeus is a sma'il and bri'iiant part in the centre; the head includes all the very bright surround.iig light; the coma is the hairy appearance surrounding the head ; and the taU, which is of great length, is supposed to consist of radiant matter, such asthatoftiie aurora boreahs. The tail of the Comet in 1807, was ascertained to be more than 9.000,000 of miles m length ; and that in 1811, to be full ^^04)0,000 in length. The distance of this Comet from the sun was 95,000,000 erf miles, and from the ear;h upwards of 142,C(X},CC0 of miles. 1 CHAPTER X. THE FIXED STARS. All the heavenly bodies beyond our system are called Fixed Stars, because, except some few, they never appear to move or to change their places, with regard to each other, as the planets do. As they are placed at immense distances from our system, they must be bodies of jrreat magnitude, and doi:btlsss shine by their own liglit. They are probably suns. like our sun, to different systems ol planets: each fixed star being siipposed to be ine centre of its own system. That the fixed stars shine by faeir own light is concluded; being at lach vast distances from the snn, they could not possl'oly receive froii> bim 80 strong a light as they shine with. 53o great is ihcir distance Fa^e 2S. Plaie 18. Telescopic^ Vuftrs P 5 Ihival^ ith-Ptul* THE FIXED STARS. 37 tfiAt thoiigh th« orbit of the earth is tvvire 95,()€<),0€0 of mjles atross, and we are roiiiequeiiLly 1 90,000,000 of miles nearer to some siar.^ at ont time than we are at another, yel the siars always appear in the same places, and with the same magnitude. See plate IV ii^. 2. Lei * * * represent the lixed stars, and A B C D, the earth's annr»al eoarse : then will the enrth in lliat part of its orbit at B, be i9U,000,UOO oiniues nearei iti tike fixed stars, than when at D. The distance of Sirius, or the Dog-star, the nearest o^ the fixed stars, cannot be less than two millions of millions of miles. A cannon ball flying from that star at tiie rate of 400 miles an hour, would not reach us in 570,000 years. Professor Vince says, '^ the nearest fixed star cannot he less tliaft 400,000 times larther from us than the sun is." IleiH-e 400,000, multi- plied by 95,000,0(30, give 38 millions of millioiis of miles lor the near- est fixed star. Dr. Herschel says, that several of the fixed stars revolve on tlieii exes. The fixed stars, then, are most probably suns, which, like our sun, serve to enlighten, warm, and sustain other systems of planets, and their def>endent saiellites. They are usually classed into six magnitudes, which include all that can be seen without a telescope ; the largest are called stars of the first magnitude, nnd tlia smallest, those of the sixth. There are seldom so many as a thousand visible at one time, to the naked eye, even in a clear star-light night. Tlie number of stars appears to us at limes innnmerablc ; but this it St deception, occasioned from their being observed by us in a confused! manner, or by the refraction and refieclion of the niyi^ of light, passing from lliciii through our atmospficre- Many of the fixed stars, which to the naked eye ap- pear as single stafs^ are fojirnl to consist of two, and some even if three, or more.™Not tiiat ihey are really 2S THE FIXED STAltS. double or treble, but they are stars at different cTis^ tances, which appear nearly in a right line. Tiiere arc also clusters of stars, called nebulae : the most remark- able of these is, that broad zone, called the Milky way. la this bright track. Dr. Herschel has seen 116,000 stars pass over the field of his telescope, in a quarter of n.n hour. The Magellanic clouds, near the south pole, which resemble ti^i'o whitish sfM'ts in the heavens, are of the order of nebidcB, and are welJ known to sailors. Since the introduction of telescopes, the number of fixed stars has been considered as immense ; and by the greater perfection of our glasses, stiii more stars are discovered ; so that there appear to be no ttonnds to their number, or to the extent of the universe. There are two methods of discovering which are planets, and v;hich are fixed stars : the first is by theii twinkling or not ; for every fixed star twinkles, but a planet does not. The second is by the nature of their motions : they all, indeed, appear to rise and set ; but, besides that, the planets have a motion from one part of the heavens to another, sometimes among the ^xed stars in one constellation, at other times among those of another ; whereas the fixed stars keep constantly the same relative distance from each other. Many conjectures have been offered as xo the cause of the hanklin^ nf the fixed stars; perhaps it may be the unequal refraction of light, in eoa'^equenceof inequahtiesand undulations in the atmosphere. Several stars mentioned by ancient astronomers are oot now to be found, and seveial are now observed which do not appear in their catalogues. The most ancient observationH of a new star is inat by Hip\)archus THE FIXED STARS. 29 ftbotii 120 years before Christ Some others have been noticed iii iatei times ; but the first new star we have any accurate account of, is thas wliich was discovered by Cornelius Gemma, in 1572, in the Chair of Cassiopeia. It exceeded Sirius in brightness, and was seen at mid-day t first appeared larger than Jupiter, but it gradually decayed ; after six iecn months it entirely disappeared. Some fixed stars have been noticed alternately to ap pear and disappear, and others have been subject to great periodical variations in their magnitudes. Jn 1600, a changeable bXbi was discovered by W. Jansenius, in the neck of the Swan, which appeared visible for many yeara ; but from 1640 to 1650 was invisible. It w-as seen again in 1655, increased till 166lv ihen grew less, and disaj'peared. In 1G65 re-appeared ; disappeared m. 1681. In 1715, it appeared of the sixth magnitude, as it is seen at presents To mention one more instance, among many, 3 i?/rc5 was disco vere-i by Mr. Go4>drich, to be subject to aperiodic iKiriafion. It completes aJl its phases in 12 days, 19 hours, during which lime it undergoes the Ibl- lowing changes : 1. It is of the third magnitude for about two daya 2. It diminishes in about U day. 3. It is between the fourth and fifth ajngnitudefor lessthanaday. 4. It increases in about two days. 5. \% is of the third magnitude for about 3 days. 6. It diminishes in about one day. 7. It is something larger than the fourth magnitude for a little leK;i' ihan a day. 8. It increases in about one day and three quarters to the Srsi T>oint, and so completes a whole period. See Pliil. Trans. 1785. In whatever part of the universe we are, we appear to he in the centre of a concave ; that is, a hollow sphere, where all remote objects appear at equal distances from us ; so that, whether we are on the planet Venus, or o\\ the earth, or on any planet or star in the universe, the ell eel in this particular would be the same. As a proof of this, the sun, moon, and stars, appear at equal distances; whereas the sun (as has been men- tioned) is 400 times farther off than the moon, and the fixed stars at least 200,000 times farther from us than the sun. If transplanted to a planet of any other system, su}>- D 30 CONSTELLATIONS, ^ pose to one belonging to Sirius ; then Sirins, which row appears only as a star, would prove a sun. Our sun w^ould then appear as a star, and the earth, with all the I other planets, would be invisible. ^ ' The vulgar error, that all these stars were placed in the heavens onJy to^flord us light, must be erroneous, since thojisamis of them are invisi- ble to us wiilioui the help of a telescope, and we receive more light &onj the moon, than from ail the stars together. CHAPTER XL CONSTELLATIONS. The ancients, in reducing astronomy to a science, fonned the iixedstarsintoconstellations, or collections of stars, and represented them by animals, and other figures, according to the ideas which the dispositions of the stars suggested. This arrangement took place very early ; for some kind of divisioi) ". must have been suggested by necessity, in order that astronomers might describe any particular star so as to be understood. Neither, without gome such division, could the situation of the planets have been pohit- ed out, as they are continually changmg their places. We find mention made of Orion and Pleiades by Job. Homer and IJcsiod also make mention of some of them ; but Aratus enumerates almost all the aii- cient ones. The number of the ancient constellations was about fifty, but the present number upon the globe is eighty. The heavens are usually distinguished by three re- gions^ called the Northern anil Soidhcrn lieir.ispheres, and the Zodiac, The number of the constellations^ in the northern hemisphere, is 36 ; in the southern, 32 ,• and in the zodiac, 12. Stars not comprehended in any of these, .'ire caiur«l imfoi^iud stars^ CONSTEiiLATIONS. 31 Northern Constellations. NUMBER OF STiUa " Ursa Minor. The Little Bear 24 Draco. The Dragon 80 Cepheus 35 Lacerta. The Lizard 16 Cassiopeia. The Lady in her Chair • . 55 Perseus • • ) Ciipiit Medusas. Medusa's Head ) Camelopardalus. The Camelopard 58 Lynx. The Lynx 44 Ursa Major. Tiie Great Bear 87 Cor Caroli. Charles's Heart Leo Minor. The little Lion 53 Coma Berenices. Berenice's Hair 43 Aster ion and Chara. The Greyhound .... 25 Bootes • 54 Corona Boreal is. The Northern Crown ... 21 Hercules. Hercules kneeling .13 Cerberus. The Three Headed Dog .... 9 Lyra. The Harp 21 Cygnus. The Swan 81 Velpecula et Aiiser. The Fox and Goose . .35 Bagitta. The Arrow 18 Delphinus. The Dolphin 18 Pegasus. The Flying Horse 89 Andromeda 66 Triangulum B^reale. The Northern Triangle . 16 Musca. The Fly Auriga. The Wagonner 66 Mons MsBnalus The Hill Maenaliis 32 CONSTELLATIONS. NUMBER OF eTl'ARS Serpens. The Serpent 64 Serpentarius. The Serpent Bearer 74 Scutum Sobieski. Sobieski's Shield .... 8 Taurus Poniatowski. Poniatowski's Bull Antinous ^4 Aquila. The Eagle 1:^ Equulus. The Colt 10 The Southern Constellations. Piscis Australis. The Southern Fish .... 24 Cetus. The Whale 97 Endanus. The River Po . 84 Orion 7S Lepus. The Hare 19 Canis Major. The Great Dog 31 Monoceros. The Unicorn 89 Canis Minor. The Little Dog 14 flydra. The Hydra 60 Sextans. The Sextant 41 Crater. The Cup 31 Corvus. The Crow • • • . 9 x\rgo Navis. The Ship Argo 64 Crux. The Cross Centaurus. The Centaur 35 Lupus. The Wolf 2\ irvra. The Altar • . • 9 Corona Australis. The Southern Crown • . . T-i i,'OMirnha Noachi. Noah's Dove 10 Robur Carolinum. The Royal Oak . ... 12 Apis. The Bee • . • • • 4 Tapf 32 PU4x 4- CONSTELLATIONS. 33 NUMBER OF STARS. Triangulum Aaslrale. The South Triangle . . 5 Apus. The Bird of Paradise 11 Pavo. The Peacock 14 Indus. The Indian 12 Grus. The Crane 13 Phccnix. The Phoenix ••.•••.. 14 Toucon. The American Goose .••».. 9 Hydrus. The Water Snake 10 Dorado. The Sword Fish 6 Piscis Volans. The Flying Fish ..... 8 Chamaeleon. The Cameleon 10 The Zodiacal Constellations. Aries. The Ram. 66 Taurus. The Bull 141 Gemini. The Twins 85 Cancer. The Crab 83 I^o. The Lion 95 Virgo. The Virgin 110 Libra. The Balance . 51 Scorpio. The Scorpion .44 Sagittarius. The Archer .... ... 69 Capricornus. The Goat 51 Aquarius. The Waterman .108 fisces. The jfishes 113 Some of the principal fixed stars are distinguished by fmrticular names, as Regulus, Arcturus, Sirius, &c. ^ others are denoted by the letters of the Greek alphaoet , the first letter being put to the greatest star in eacli constellation ; the second letter to the next greatest, and D 2 34 DIFFEREKT SYSTEMS. SO on ; and when any more letters are wanted, the Italic letters are generally used. By this contrivance the place of any particular star in the heavei^a may be found, with the greatest ease and precision. CHAPTER XII. DIFFERENT SYSTEMS. The system we have been describing, and which is now universally received, is called the Copernican. It was formerly taught by Pythagoras, a Greek philoso pher, born in the island of Samos, 590 years before Christ, and Philolaiis, his disciple, finding it impossible any other way to give a consistent account of the hea- venly motions. This system, howcA^er, was so extremely opposite tc all the prejudices of sense and opinion, that it nevei made any great progress in the ancient world till re vived by Copernicus. Ptolemy, an Egyptian philosopher, who flourished 130 years after Christ, supposed at first that the earth was perfectly at rest near the centre ; and that all the other bodies, namely, the sun, moon, planets, comet?! and fixed stars, revolved about it in circles every day- But as their retrograde motions and stationary appear- ances could not thus be solved, he afterwards supposed- them to revolve in epicycloids. Epicycloids are curves generated by the reYolixd>n of tl e pei pLc/y cfa circle along the concave or convex parts of another '•ircle. The full illustration of this motion may exceed the p^ sent comri-e- henaior of tlie learner, but he may conceive it to be n' i much unlike DIFFEEENT Si STEMS. 35 Ihe curve line, a, b, c, d, e,f, &c., plate XV. fig. 1. Now it is evident llial at the points b and c, and a] so d and e, the planet's motion would appear siaiionary and retrograde from b to c, and from d to e, and at other times direct. But though this system will not solve the phases of Venus and Mer- cuiy, and for other reasons cannot be true, it was maintained from ill? time of Ptolemy till the revival of learning in the sixteenth century. The Egyptians received also the following system : — That the earth is immoveable in the centre, about which revolve, in order, the Moon, Sun, Mars, Jupiter and Saturn ; and about the sun, revolve Mercury and Venus. This disposition will account for the phases of Mercury and Venus, but not for the apparent motions of Mars, Jupiter, and Saturn. At length Copernicus, a native of Poland, adopted the Pythagorean system, and published it to the world 'n 1530. This doctrine had been so long in obscurity, that the restorer of it was considered the inventor. Copernicus placed the Sun in the centre of the sys- tem, and about it, the other bodies in the following order : Mercury, Venus, the Earth, Mars, Jupiter and Saturn. Europe, however, was still immersed in ignorance, and the general ideas of the world were not able to keep pace with those of a refined philosophy. This occa- sioned Copernicus to have few abettors, but many op- ponents. Tycho Brahe, a noble Dane, and eminent philoso- pher, sensible of the defects of the Ptolemaic system but unwilling to acknowledge the motion of the earth, endeavoured, about 1586, to establish anew system of his own, in which the earth was supposed the centre of the sun and moon ; that Mercury, Venus, &c. re- B6 ;? Tifi: MOTIUN OJ- TTIK PLANETS. roK\;a ahoai the sun, and (i:ar tlie sun and |)laneta, ^ogethrr, turned round the eartii hi 24 hours. But as this |>j()\ «;ti to be stiil more absurd than that of Ptolemy, It w.iis sooii exploded, and gave way to the Copernican, or true solar system. S(Jnie orTyt'ho's followers, seeing the absurdily of supposing all the heavftiily i;odies daily to revolve aboiu the earth, allowed a roiary mo- tion to I he earih, in order lo account for theh* diurnal moiion, and thij was called the Senii-Tychonic sysiem. Thus the solar system, now adopted, after having been taught by Pythagoras, and revived by Copernicus, was coniirmed by Galileo, Kepler, and Descartes, and fully established by Sir Isaac Newton. See Pianeta rium, plate 6. CHAPTER XIII. OF THE MOTIONS OF THE PLANETS: DIltECT, STATIONARY, AND RETROGRADE. The planets, Mercury, Venus, the Earth, &;c. if seen from the sun, would appear to pass from star to star, through the constellations, in a uniform and regular manner. But as seen from the earth, they apparently move very irregularly ; sometimes they appear to goforxcard^ at other times to remain stationary^ and then to recede. To give some idea of this, suppose yourself placed in the centre of a arcular course, keeping your eye on the horse while going round ; rt Is evident that he would appear to run round the whole course in a regular manner. Again; imagine yourself placed at a cousiderablo distance on the outside of the coarse, and the horse's motions would OF THE MOTION OF THE PLANETS. jppear no longer uniform. On the opposite side of the course alon<^ would he seem regular : then alone would it appear the same as when vou stood in the centre. When he approached you, he would scarcely seem to move ; m that part of his course next to you, he would move in a direction coni'-ary to what he did at first ; and again, when going &om you, his motion would be scarcely visible. When the planets wee farthest from us, fheir motion Is said to be direct ; v/hen nearest to us retrograde, because they appear to be moving back again ; and vi'hen either approaching us, or goingyrom us^ we say 'hey are stationary^ because, if then observed in a line with any particular star, they will continue so for a con- siderable time ; now these appearances could not hap. pen if they moved round the earth as their centre. See plate VII. fij^. 1. Inferior and Superior Conjunctions of the Planets. When Mercury or Venus is nearest to us, that is, n a line between us and the sun (see plate VII. fig. 2.) vve say it is in inferior conjunction ; when farthest Trom us, and the sun is between us and the planet, in superior conjunction. The superior planets, namely, those whose orbits 'nclude that of the earth, have alternately a conjunction and an opposition ; a conjunction, when the sun is be- tween the earth and the planet; and an opposition, when the earth is between the sun and the planet, that is, when the planet is nearest to us, and appears to be opposite to the sun. Hence, when a planet is in conjunction, it rises and ^ets nearly with the sun ; but in opposition, it rise^ aearly vvhen the sun sets, and sets when he rises. *8 THE PLANE OF AN ORBIT, PLANETS, d^C. Ve say nmrly, because it cannot be exactly, except when tne planet is in or near its node; or, uhich is the same thing, when tht •Win, earth a/d\ [ilauet, are in a rigJu line, which seM^rn happens. As only that side of a planet which is turned to the sun can be enlightened by him it is evident, that aat viewed with a telescope from the earth, its appearance must vary ; thus Venus, just before and after her supe* rior coiijiinction, would be seen nearly with afidlface , v/hen stationary, she would appear only half enlight- ened, like the moon at the first quarter, because an equal portion of the bright and dark sides will be turn- ed towards us ; the bright parts will be decreasing till her inferior conjunction, and then only the dark side will be turned towards us, and consequently she will be for a short time invisible: by-and-by she will be- come again stationary, and appear like the moon at her third quarter. It is true, both Mercury and Venus may at times be seen even when Di their inferior conjunctions, but it can be only in their transits, which will be explahied in a future cliapter. These appearances refer to the inferior planets only, Mercury and Venus. The superior planets always ap- pear with nearly a full face. ^ CHAPTER XIV. THE PLANE OF AN ORBIT, PLANETS, NODES. ETC The earth, as seen from the sun in its periodical re- rolution, will describe a circle among the stars, which astronomers call the ecliptic ; and sometimes the sun^a THE PLAIN'E OF AN ORBIT, PLANE! b, ^^ i/ Plains THE ECLIPTIC, ZODIAC, AND EQUATOR, &C. 41 She Wt/uld, if visible, appear much larger than when she is at 4 in superior conjunction, because so much nearer in the former case than in the latter ; being in the situation a, but 27,000,000 miles from the earth E ; but at e, 163,000,000. As Venus passes from a i^lirough h c d \o e^ she may be observed by a good telescope to have all the same phrases as the moon h«? \ji [)assmg from new to full ; therefore when she is at e she is full. Also, during her journey from c througrh/to ^,she will appear to have a direct motion in her orbit ; from g to I, and from b to : to be nearly st/2tio?iary, but from h to h, her motion, thtugh sL^ll really direct, wiii apj.>ear to a spectator at E, to be goijig back again, (j7 re^rograt^e, »'« w^^ •shown before. Mercury is seen in the same manner, which i» a piixv that their orbits must be within that of the eaith- CHAPTER XV. THE ECLIPTIC, ZODIAC, AND EQUATOR, ETC. The Ecliptic is an imaginary great circle in rha heavens, which the sun appears to describe in the course of the year, among the stars. The following are the most conspicuous stars that lie near to the ecliptic: — The Ram's Horn, called, « Arie- tis — Aldebaran, in the Bull's Eye — Castor and Poliux— Regulus, or the Cor Leonis — Spica Virginis — Antares, or the Scorpion's Heart — also, which lie more distant, « Altair, in Aquila — Fomaehaut, in the Fish's Mouth, and Pegasus. The above nine stars are considered aa the most c^aspicuous near tlie moon's orbit — ^frora these the moon's distance is calculated, and i^nce tiie tables in the Nautical Almanac are constnicted for the use E 42 THE ECLIPTIC, ZODIAC, AND EQUATOR, &C of navigators. The Ecliptic is so called, becaure all the eclipsets must aecessarily happen in this line, where the sun a' ways is. The Ecliptic and Equator, being great circles, must bisect, or equally divide each other; and their inclina- tion is called the obliquity of the Ecliptic. Also the points where they intersect are called the equinocticd points, aud tlie times when the sun comes to these poinls are called the equinoxes. The Zodiac is an imaginary broad circle, or belt, surrounding the heavens, extending about 8° on each side tlie ecliptic, in which the planets, with the exception of Ceres, Pallas, and Juno, constantly revolve. The term Zcxtiac is derived from a Greek word z^Ji.^xo? ; from ^^ooi-, *'an aiiinml," because each of the twelve signs formerly represented »ome auima! ; that which ne now call Libra being by the ancients reckoiied a {)art of Scorpio. For lijc ilefinitioas of degrees, &c. see preliminary definitions. The names and characters of the twelve signs, with t'* * time of the sun's entrance into them, are as follow ; I. Aries, T, or the Ram ; March 20th. i. Taurus b, the Bull ; April 20th. 3. Gemini, n, the Twins; May 2lst 4. Cancer, 35, the Crab ; June 21st. 5. Leo, a, the Lion ; July 23d. 6. Virgo, % the Virgin; August 23d. 7. Lihra, ^, the Balance ; September 23d. 8. Scorpio, ^l, the Scorpion ; October 23d. 9. Sagittarius, /, the Archer ; November 22cr 10. (^;i[u*iconins, V3, the Goat ; December 21st 11. A(|n;i! ins, ^, the Waterman ; Januarj 20<.t 12. Pisces, X, the Fishes ; February 19th. THE ECLIPTIC, ZODIAC, AND EUUATOR, &C. 43 Dr. Wall's lines, " The Ram, ihe Bull,'* &c. are well known ; but, perhaps, to learn ihe signs in the above order will ansvvei a better purpose, and be but iitlie extra labour. The order of these is according to the motion of the sun. The Jlrsi point of Aries coincides with one of the equinoctial points, and the Jlrst pwfit oj Libra w^ith tlie other. Th<^ first six are called no?'tJie7m signs, lying on the north side of the equator ; and the last six southern^ lying on the south side. The signs Y^y ccc, X, T, ^, n, are called ascend- ingy because the sun approaches our north pole while it pnsses through them ; and ®, SI, W, — , ^, ?, are called descending, the sun receding fronn our pole as it passes through them. Each of the 12 signs of the Zodiac contains 30 de g^^ees. The Equator is either terrestial or celestial. The terresfial Equator is an imaginary great cir de of the earth, perpendicular to its axis; hence the axis and poles of the earth are the axis and poles of the equator. This circle is equally distant from the two poles, and separates the globe into the northern and southern hemispheres. The celestial Equator, called also the equinoctial, is a plane of the terrestial equator extended to the fixed %tars ; and if the axis of the earth be produced in like manner, they will be ihe poles of the celestial equator. And the star nearest to the north pole is called the pah ift%r, as P. P. iig. 2, plate II. 44 THE EPHEMERIS. OF THE EPHEMERIS. The Astronomical Ephemeris being frequently alluded to ic I lie use of the globes and the study of astronomy, a short ex planation of the astronomical part of the only work of this kinc published in this country, viz. the American Almanac, may be acceptable, taking, for example, that for the current year, 1832. The first thirty-five pages, which are occupied by the relations of the planets, the time of the entrance of the Sun into the signs of the Zodiac, the length of each of the four seasons, the ca- lendars of the Jews and Mahometans, the eclipses of the Sun, Moon, and satellites of Jupiter ; the occultations of the fixed stars by the moon, the elements of the two comets of short period, known as Encke's and Biela's : the position and magnitude of the rings of Saturn, the aspects of the planets, the height of the greatest tides, the usual height of the spring tides at several places on the American coast, the difference between the time of high water at these places and at Boston, the latitude and lon- gitude of most of the principal places in the United States, and with the length of the longest and shortest days thereat, will, it is supposed, require no illustration. Of the calendar pages, those (36 and 37) for the month of January may be taken as an example. On the top of the left hand page will be found the apparent time of the beginning and end of twihght, or the time when the Sun is 18 degrees below the horizon before sunrise, and after sunset, for every sixth day, at Boston, New York, \Vashington, Charleston, and New Orleans; which places being situated m diiferent latitudes, renders the al- manac equally useful to every part of the United States. It may however be proper to remark, that the twihght will not in general Ue sufficiently strong to be visible, unless the Sun is considerably less than 18 degrees below the horizon. On the 1st of January it appears that the twilight begins at New Orleans at 27 minutes after 5 in the morning, and ends at 27 minutes before 7 in the evening. Under the above, will be found the time of th% Moon's apogee and perigee, or the time in each lunation, when I'a^ 4-4- . ?y<^. vvoW^K }^^at^ THE EP«£MERIS. 45 ■he is faithest from, and nearest to the Earth, with the dis- tance between the Earth and Moon, at those times, in English mile<:. Next below are placed the phases of the Moon, or the mean time at Washington of her conjunction, quadratures, and oppo- eitions with tlie Sun : under these aic placed the columns of the calendar, viz. the day of the month and the corresponding day of the week, also the apparent time of the rising and setting of the Sun, and the mean time of the rising or setting of the Moon, calculated for the same cities for which the twilight was com- puted : thus, on the 2d of January the Sun rises at Boston at SI minutes after 7, and sets 31 minutes before 5 ; at New Orleans, he rises 57 minutes after 6, and sets 57 minutes before 6 ; the Moon sets the same day at Boston at 39 minutes after 4 in ihet afternoon, and at New Orleans 5 minutes after 5. By doubling the time of the Sun's rising we have the length of the night, and by doubling that of his setting, the length of the day ; hence, at Boston on the 2d of January, the length of the day, or the in- terval between the rising and setting of the centre of the Sun, exclusive of the effect of refraction, is 8 hours 58 minutes, and at New Orleans 10 hours 6 minutes : want of room is the reason assigned in the almanac for expressing the beginning and end of twilight and the rising and setting of the Sun in apparent time Apparent time is, however, readily converted into mean, by apply- ing the equation (third long column right hand page) according to the direction at the head of the column ; and mean into ap- parent, by a[ plying the equation contrary to the direction : thus, on the 2d of January the equation being 4 minutes to be added to appareat for mean time, and consequently to be subtracted from mean for apparent ; the Sun rose that day at Boston, in mean time, at 35 minutes after 7 and sat 27 minutes before 5 ; and tho Moon sat the same day, in apparent time, at 30 minutes after 4. The column of the equation of time shows the quantity by which a well regulated clock is fast or slow of the Sun, and by it watches or clocks may be regulated, by comparing them with a good dial at any time when the Sun shines tliereon, and ex* 46 THE EPHEMERIS. amining if the difference between them agrees with thtj figures in this cokimn: thus, on the first day of January 1832 ; a clock did not show true mean time unless it was 13 minutes 42 seconds faster than the time by the dial, or unless when the shadow in- dicated noon, the clock was 13 minutes 42 seconds past 12. — Foi further illustrations see the chapter on the equation of time, page 65. The second long column of the right hand page gives the mean time of the daily passage of the Moon over the meridian of Washington, or the instant her centre bears down South al that place. On the day of conjunction with the Sun, the Moon the planets, and the fixed stars come to the meridian very nearly at the same moment with him ; and if the conjunction takes place precisely at noon, the two bodies will be on the meridian precisely at the same time ; in ail other positions than when in conjunction, the Moon, planets, and stars will pass the meridian before, or after the Sun, according as the Sun's right ascension is greater or less. The mean time of the passage of any hea- venly body over the meridian, is easily found by subtracting th€ siderial time at the moment of the passage, from the right ascen- sion of that body at the same moment. The fourth, fifth, and sixth of the long columns contain the mean time of high water at Boston, New York, and Charleston, of that tide which arrives when the Moon is near to the meri dian. The 7th long column contains the remarkable days in the month, the conjunction of the Moon with fixed stars and planets, that may be occultations in some part of the United States, and other phenomena interesting to the astronomer. At the top of the right hand page, will be found the mean time of the pass- age of the planets over the meridian of Washington, with their declinations or distance from the equator at that time, on ever.v sixth day. By the assistance of this table, the places of the planets may be easily found in a celestial globe ; it being borne in mind, that north declinations are designated by the sign + and south by — . On i>ages 60, 61, 62, 63, are the Sun's declination, and the •iiisrial ume, which are given for every day, at noon, at Berlin j THE EPHEMERIS. 47 m 1 >ut six in the morning at Washington, the former in appa- rek-i, the latter in mean time ; the greatest declination (23° 27^') will be found on the 21st of June and December: about the 20th of March, and 23d of September, the declination ap- pears to be nothing ; the Sun's centre is, therefore, then but for & single moment in the celestial equator, which is vulgarly termed crossing the line ; the exact moment of the Sun having no declination, may be thus ascertained. On the 20th of ?ilarch, 1832, at apparent noon at Berlin, in Prussia, it appears by the almanac, the declination of the Sun's centre was 2' 59.2^' south, and on the 21st 20' 41.3'' north ; then by proportion as 23' 40.5'^ (the variation in 24 hours) is to 2' 59.2", so is 24 hours to 3 hours 1 minute 40 seconds ; consequently the Suii's centre was in the celestial equator at Berlin, March 20th, 3 hours 1 minute 40 seconds apparent, or 3 hours 9 minutes 14 seconds mean time in ^,he afternoon ; from which subtracting the difference of longi- tude, 6 hours 1 minute 41 seconds, (Washington being west of Berlin,) we have the corresponding time at Washington, March 20th, 9 hours 7 minutes 33 seconds, mean time, in the morning. The Sun's siderial time, is what the Sun's right ascension would be, if the Earth moved uniformly in her orbit, and in the plane of the celestial equator; it therefore is the Sun's actual right ascension, diminished or increased by the equation of time. It is of the greatest importance for the determination of the mean time of the passage of the Moon, planets, or stars over the me- ridian, by subtracting it from the right ascension of the Moon, planet, or star, at the moment of the passage. K the latter be the greater, the passage will be after ; and if less, before that of the Sun. For example, the star Aldebaran will be on tha meridian of Washington, August 28th, 1832, at 5 hours 59 mi- nutes 38 seconds mean time, in the morning, its right ascension at that moment being 4 hours 26 minutes 18 seconds; and the *iderial time 10 hours 26 minutes 40 seconds. 46 POLES AND TR0PIJ;S. CHAPTER XVI. A Degree is the 360th part of a circle ; and the measure of an angle is an arc, or part of the circum- ference of a circle, whose angular point is the centre ; and so many 360th parts as an arc contains, so many degrees the measure of an angle is said to be : Thus, lei A B (plate IX. fig. 3,) represent the plane of the ecliptic, and NC S the axis of the earth, Z C P will make an angle of 23P, be- cause the arc, Z P, contains 23i parts of ^560, the whole circle; and aa A N contains the same number of degrees as Z P, its inclination must be 23p. The Poles are the extremities of the earth's axis, (plate IX, fig. 3 ;) N the north pole, S the south pole, P the north pole star, to which, and to the opposite part of the heavens, the axis always points. These extremi- ties in the heavens appear motionless, while all the other parts seem in a continual state of revolutioju The circle of motion in the heavenly bodies seems to increase with the distance from the poles. The Tropics cire two small circles parallel to the equa- tor, at 23J degrees distance from it ; that to the north is called the tropic of Cancer, and that to the south the tropic of Capricorn. The Polar circles circumscribe the poles of the world, at the distance of 23^ degrees. That on the north is called the Arctic, and that on the south the Antarctic circle. The distance of these polar circles from the poles being fixed at23|*> (Uie same as the tropics from the equator) is because it is the line of boundary between light and darkness, when the sun is on either of the tropics, and throws his beams over and beyond the pole. Hfi^r ^^ FUtt 6\ The Meridians are so called because, as the earth revolves on his axis, when any one of them is opposite to the sun it is mid-day or noon along that line. Twen- ty-four of these lines are usually drawn on the globes^ to correspond with the twenty-four hours of the day.. Not that these are the only ones that can be imagined, for every place that lies ever so little east or west of another place has a different meridian. Suppose the upper 12 (plale IX. fig. 3.) to be opposite the sun, it will of course be noon along that line , and the«next meridian marked 1» being 15^ east, will have passed the meridian 1 hour, consequently it will there be one in the afternoon, and so on, according to the order of the figures, to the lower 12, which being the part of the earth turned directly from the sun, it will be midnight on that meridian : as you pro- ceed round, the next meridian will be one in the morning, the next two and so on, till you arrive at the upper 12, where you set ofE Hence there must be a continual succession of day and night. Note. This difference of time between places, lying under differenl meridians, i& called longitude ; or, Longitude is an arc of the equator between the me- ridian of any place and the first meridian. In English geographers the first meridian passes through London or Greenwich, and the distance is reckoned east oi west thence ; ffteen degrees of longitude being equal to one hour of time. To all places easttvard of the first meridian, the time will be before London ; if west, after London. To reduce longitude to tvme divide by 15. As the earth makes a complete revolution on its axis in 24 houis. it must pass over 360° in that time : and if you divide 360 by 24, the quo- tient, 15, will be the number of degrees passed over in an hour: hence S(P will be equal to tivo hours, 45° to three hours, &c. Then if it be 12 o'clock at London, at Barbadoes, lying nearly 60o west of London, it will be 4 houi"s earlier, or 8 o'clock in the morning. At Petersburgh, 30° east, it will be 2 hours !ater, or 2 o'clock ir th 60 LATITUDE, COLURES, &C. afternoon; and at Calcutta, almost 90° east, nearly 6 hours later in Mm i^tcrnoon. To reduce time to longitude^ multiply by 15. A captain arriving at the Bermndas, finds the difference of time I'e l^een tiiem and London to he 4 hours and 20 minutes, which, multi plied by 15 (or by 3 and 5) will give 65°. Latitude is the distance of any place from the equa- tor, either north or south, or it is equal to the elevation of the pole above the horizon. The latitude of the heavenly bodies is reckoned from the ecliptic, and ter- minates in the arctic and antarctic circles, and their longitude begins at the point Aries. The Colures are two meridians^ which pass through the poles of the world ; one of them througii the points of Aries and Libra, and therefore called the Equinoc^ tial Colure ; the other through the solstitial points, Cancer and Capricorn, and therefore called the Solsti tial Colure. The Zones are five; namely, one torrid, two temperate, and two frigid. — The torrid is all that space between the tropics, and so called from its excessive heat ; the tem^ perate zones extend from the tropics to the polar cir- cles; the frigid zones are comprised between the polar circles and the poles. Sohtltial points are the first points of Cancer and Capricorn ; so called because the sun, when he is near either of them, seems to stand still, or to be at the same height in the heavens at noon for several days together. Equinoctial points are the first points of Aries and Libra; so called, because when the sun is near either of them the days and nights are equal planets' orbits elliptical. ♦'SI As it I* presumed that the pupil will have previously gT)ne through A course of geograjihy and the globes, the above short definitions may ,be suflicieni. though ihey could not be omitted altogether. CHAPTER XVII. PLANETS' ORBITS ELLIPTICAL. The orbits or paths described by the revohiticn of the planets round the sun, are not true circles, (as plate VIII. fig. 3,) but somewhat elliptical, that is, longer one way than another. In a circle the periphery, or circumference, is equal- ly distant from a point within, called its centre, A; but an ellipsis has two points called the focuses^ ox foci, as B C. In one of these, called its lower focus, is the son. Hence, in every revolution of the planet it must b© nearer the sun in one part of its orbit than it is at an- other. Let S (plate VIII. fig, 5,) represent the sun, A B C D a planet in different parts of its orbit ; when it is nearest the sun, as at A, it is said to be in its perihelion ; when at B its aphelion; but when at C or I), its middle oi mean distance; because the distance S C oi' S D is the middle between A S, the least, and B S the greatest ; and half the distance between the two focuses is called the eccentricity of its orbits, as S E or E F. ATTRACTION OF GRAVITATION. By attraction is meant that property in bodies bj whsch they have a tendency to approach each other. 52 ATTRACTION OF GRAVITATION. Thus the magnet attracts the needle ; this is called attraction of mag vetism : and thus the feather suspended near the electrical conductor is attracted by it ; this is termed attraction of electricity. And that pro perty which connects or firmly unites the different particles of roatier, arf which the body is composed (as that of a stone,) is attraction of cofi& sioru Attraction of Gravitation is a power by which bo dies in general tend toward each other ; and the at- traction is in proportion to the quantity of matter whicli they contain ; but the earth, being so immensely large in comparison of all other substances in its vicinity, de- stroys the effect of this attaction between smaller bo- dies by bringing them all to itself. By attraction of gravitation, the sun, the largest body, attracts the earth and all the other planets, and they \gain gravitate or have a tendency to approach the sun The earth being larger than the moon, attracts her, and she gravitates towards the earth. Upon this principle, a stone, when thrown from earth, is brought by (he earth's attraciiGn and its own gravitaling power to the earth ogam. . The waters in the ocean, and indeed all the terrestrial Ix)dies, gra- vitate tow'ards the centre of the earth; and it is by this power that we stand on all parts of the earth, with our feet pointing to the centie. L'i sliort, it is by the attraction of gravity that a marble falls from the hand, a brick from the top of a building, or an apple from the tree. A.11 bo- tJies, by the power of gravity, have a tendeiicy or disposition towards rtie earth. One law of attraction is, " That attraction decreases as the squares of the distances from that centre in (^ease*^^ Any number multiplied into itself is a square number ; 'bus, th« square of 2 is 4, the square of 3 is 9 of 4 is 16, &c. Suppose a planet at P (plate X. fig. 4,) to be twice ATTRACTION OF GRAVITATION. 53 as far xiom the sun as at A ; then, as the square of the distance 2 is 4, the attraction at B will be four times i'ess than at A, or, which is the same thing, A will be attracted with four times the force it would be at B. Again, if the distance at A (fig. 5,) were four times less than at B, then, as the square of 4 is 16, the at- traction at A would be sixteen times greater than at B, The second law of gravity is, " That bodies attract mie another with forces proportional to the quantities of matter they contain.^^ All bodies of equal magnitude contain not equal quantities of matter, for a ball of cork of equal bulk with one of lead, being more porous, does not contain so much matter. So the sun, though a million of times as big as the earth, not being so compact and dense a body, contains a quantity of matter only 200,000 times as great, and hence attracts the earth with a force only 200,000 times more than the earth attracts him. Hence suppose there are in a river two boats of equal bulk at any distance, suppose twenty yards, from each other, and that a man in one boat pulls a rope which is fastened to the other, the boats will meet in a point which is half w^ay between them. If one boat were three times the bulk of the other, then the lighter would move three times as far as the heavier, ox fiftetn yards, while the heavier moved only fve. F 54 ATTE ACTIVE AND PROJECTILE FORCES. CHAPTER XVIIL OF ATTRACTIVE AND PROJECTIIJi: FORCEa The sun, being so immense a body, would, by the power of attraction draw all the planets to him, if the attractive power were not counteracted by another force. [t must therefore be observed that all simple motion is naturally rectilineal^ that is, all bodies, if there were nothing to prevent them, would move in straight lines* But the planets' motiors are circular, which is a cojn- pound of iivo forcer, the one called the attractive or centripetal force; the other the projectile or centrifugal force. Suppose a marble be shot from the hand along a smooth floor, ii it meet \vith ro impediment it will move straight forward ; this is termeii the projectile force, and its motion will be redilineal Bnt if a bail be thro'.vn }nlo the air, unless projected perpendicularly, it will not con- tinue to move in a straight line, but incline towards and fall to the earth ; for the resistance of the air, and the attraction of the earlh retard ite progress : otherwise it would continue to move in a straight line, mih. a velocity equal to that which was at first impressed upon it The joint action of the attractive or projectile force? retains the planets in their orbits ; the primaries round the sun, and the secondaries round their primaries. -■ H^hen a stone is whirled round in a sling, its motion is circular. 1/ Oic stone flics out, it will go off in a straight hne. This straight tine is what is ca''ed the tangent of a circle, as A a, B fc, &c. (I'laie V'Ul. %. 4;) lor all bodies muving m a circle have a natural tendency to i\y ofi' in tliai dire. tion. Thus a body at A will tend towards a, at B towards b, and so on, its rectilineal motion; but the central force (tlie action of the hand; acting against it, prc»orve« ns circuMr motion. The moon and all the planets move by this law ; apd ATTRACTIVE AND PROJECTILE FORCES, 5^ the attractive or centripetal force of the sun being equal to the projectile or centrifugal force of the plan- ets, they are, by attraction, prevented from moving on in a straight line, and, as it were, dravt^n towards the sun ; and by the projectile force from being overcome by at- traction. They must therefore revolve in nearly circu- lar orbits. If) for instance, the projectile force were to cease acting upon th« earth, it must fall to the sun : on the contrary, if the force of gravity .were to cease upon the earth, it would fly off into infinite space. The secondary planets are governed by the same laws in revolving round their respective primaries ; for as by the attractive pov/er of the sun, combined with the projectile force of the primary planets, they are retained in their orbits; so also the action of the pri- maries upon their respective secondaries, together with their projectile force, preserves them in their orbits. If the attractive power of the sun were uniformly the same in every part of their orbits, they would be true circles, and the planets would pass over equal portions ill equal times ; but the attractive power of the sun is not uniformly the same ; hence the orbits of the planets are not true circles, but o. iittle elliptical, and they must pass over unequal parts of their orbits in equal portions of time. By passing over equal porlions in equal times may be understood par- sing from B to C, or from C to A, in the same time as from A to D, or from D to B.— (Plate VIII. fig. 5.) By unequal portions in equal times, the centrifugal fon'e would cany a planet from A to a, in the same time as it would from B to b. And m its orbit from A to c, as soon as from B to d. A double velocity will balance a quadruple or fourfold power of gravity or attraction. — Hence, as the centri 56 ATTRACTIVE AND PROJECTILE FORCES. petal force is four times as great at A as at B, ihe cen ^rifugal force is twice as great ; and would describe flu area or space contained between the letters A S c. in the same time as the area or space B S : P. S Sjir^ ^.itU REFRACTION. 63 CHAPTER XXII. REFRACTION. The rays of light, in passing out of one medium into another of a different density, deviate from a rectilineal course ; and if the density of this latter medium con- tinually increase, the rays of light, in passing through it, will deviate more and more from a right line towards a curve, in passing to the eye of an observer. From this cause all the heavenly bodies, but the moon, except when in the zenith, appear higher than they really are. This apparent elevation of the heavenly bodies above their true altitude^ is caused by Refrac- tion. Let ABC (plate XI. %. 1.) represent the surrounding atmosphere a the true place of a star, h the apparent place. Let a ray fall from a on the surface of the atmosphere at A, and it will be refracted in lh& u'irection of the curve A D, because the density of the atmosphere in f reases as it approaches the earth's surface. Hence an observer at Y iviil see the object at b. It is in consequence of the refraction of the atmo- iphere, that all heavenly bodies, except the moon, are seen for a short time before they rise in the horizon, and also after they have sunk below it. At some periods of the year the sun appears three minutes longer, morning and evening, than he woulo do w^ere there no refraction ; and about two minutes every day at a mean rate. Hence, when the sun is at T belou the horizon, a ray of light T I, proceeding from him. comes straight to I, where failing on the atmosp«.iTe, it is turned out of its direct, or rectilineal course, ^ a5 . is so bent down to the eye of the observer at D, it %• 64 PARALLAX. the sun appears in the direction of the refracted ray above the horizon at S. The effects of refraction may be seen thus : immerse a staff m a tub of water ; if it be placed perpendicularly there will be no refraction ; that is, it will not seem bent at all : — inchne it a Uttle towards the edge uf the tub, and it will appear a little bent at the surface of the water; iftclme it still more, and the refraction will be greater. Refraction is also showTi in that well known experunent of putting »iiiy small object, as a shilling, &c., at the bottom of a basm or tub, thf n walking backward till the object is just tod sight of, and there stand- mg while another perhx^n pours water into the basin, and the money will appear Now if the edge of the basin be called the horizon, tlie wafer the atmosphere, and the shilling the moon, it is clear that it w ik be seen above the horizon when really below it. CHAPTER XXIII. PARALLAX. The Parallax of the sun and moon is the difference between the altitude of either object observed at the same instant of time by two spectators ; one on the 5?/r- face of the earth, and the other placed at the earth's The place of an object as observed from the earth's surface is calle'i its apparent place ; and as observed from the centre, its inte place. The parallax of the heavenly bodies is greatest when in the horizon; hence called the horizontal parallax. The sun's mean parallax being only 8.G, is seldom made use of in nautical calculations, except to determine the longitude, by means of . ftheerving the angular distance between the sun and moon. The fixed stars, on account of their vast distance from the earth have no parallax. As the parallax of the sun or moon or planets de presses, or causes them to appear lower than they really EQUATION OF TliMF.. 65 are, the difference must be added to their apparent al- ntudes, to obtain their true altitudes. Let C (fig. 2, plate XL) represent the centre of the earth ; F D E, part of the moon's orbit \ G d e, part of a planet's orbit; Z K, part of the starry heavens : now. to a spectator at A, upon the surface of the earth, let the moon appear at E, in the horizon of A, and it will he referred to K ; but if viewed from the centre C, \\ will be referred to I : the difference between these i)laces, or the arc i K, is called the parallax in alii tude ; and the angle A E C, is the parallactic angle. The parallax v/iil be greater or less^ as the object^ ^re more or less distant from the earth ; thus the paral-. Ux I K, of E, is greater than the parallax/' K, of c. Also, with respect to any one object, v/hen it is in ^he horizon^ the parallax is the greatest^ and dirnimshen a^ the body rises to the zenith, where the parallax h nothing. Thus, the horizontal parallax of E and e, h greater than that of D and d ; but the objects F and G, as seen from either A or C, appear in the mme pkice ■ 'Z, or in tlie zenith. CHAPTER XXIV. EQUATIOM OF TIME. OiTH summer naif year is longer 'than ilie winte? Lalf year, by about eight days ; occasioned by th^^ inequality of the earth's annual motion. This in^ equality and the obliquity of the ecliptic are the causes of the difference of time betv/een the sun and a well regulated deck. The clock keeps eQU4il time. *66 EdUATION OF TI3IE. .while the sun is constantly varying, and shows only ap parent time. The difference of these is called thv eqnution of time, E(pial time is measured hy a clock that is supposed to measure ex a( \\y 24 hours from noon to noon. And apparent time is measured hy tLe apparent motion of the sun in the heavens, or by a good sun-dial. This difference between equal and apparent time iXc- pends, /ir5f, upon the inclination of the earth's axis to the plane of its orbit; and secondly^ upon the elliptic or oval form of the earth's orbit; for the earth's orbit being an ellipse, its motion (as has been already shown) is quicker in lis perihelion than in its aphelion. The rotation of the earth upon its axis is the most equable motion in nature, and is completed in 23 hours. 06 minutes, and 4 seconds. This space is called a sidereal day, because any meridian on the earth will revolve from a fixed star to that star again in this time. Hence, if the earth had only a diurnal motion, the day wou Ul he nearly four minutes shorter than it is. But a solar, or natural day, v.'hich our clocks "are in- tended to measure, is the time which any meridian on the earth will take in revolving/ra;;i the sua to the sun igain, which is about 24 hours, sometimes a little more, sometimes less. This is occasioned by the earth's ad- vancing nearly a des^ree in its orbit, in the same time that it turns eastward on its axis ; and hence the earJh must make 7nore than a complete rotation before it can cr'me into the same position with the sun, that it had Uie day before. Some idea of fliis mny bo f^rmor] hy the hands ol a clock ; suppose both of \!iom to sot oi.i to^iiiUcv at twclvo o'clock, the mmuie hand EQUATION OF TIME, 67 must travel more than a whole circle before it will overtake the hour luiud; that is, before Ihey will be in the same relative position Again, it must be observed that only four limes a year the degrees on the ecliptic and the equation are equal ; in other words, but four times a year is the sun's longitude and right ascension the same in degrees ; and that is when he passes through the equator and the tropics, and then the sun and clocks go together, as far as re- gards this cause; but at other times they differ, because equal portions at the ecliptic pass over the meridian in unequal parts of time, on account of its obliquity. To those who are acquainted with the globes this will appear e\ i- teraber, instead of the clocks and dials agreeing, there will be a varia- tion of 6 or 8 minutes: and their times of coinciding will happen sev© fal days later in the veriial, and earlier in the autumnal equinox. If the earth's motion in its orbit v/ere uniform, whicli it would be if the orbit were circular, then the whok difference between equal time by the clock, and appa- rent time by the sun, would arise from the inclination of the earth's axis. But this is not the case; for the earth travels when nearest the sun, that is in the winter, more than a degree in 24 hours; — and when farthest from the sun, that is in summer, less than a degree in the same time. From this cause the natural day would be of the ffreatest lenofth when the earth was nearest the sun, for it must continue turning the longest time after an en lire rotation, in order to bring the meridian of any place to the SU51 again ; and the shortest day would be when ihe earth moves the slowest in her orbit. The above inequalities, combined with those arising from the inclination of the earth's axis, make up that difference which is shown by the equation table in ont of the outside columns of an Ephemeris. THE SEASONS. 69 CHAPTER XXV THE SEASONS. The axis of the earth is not upright oi perpen- dicular to the plane of the ecliptic, but inc.lines tc It 23 1 degrees, as Z C P, making an angle with it of 66J degrees, P C B, (plate IX. ng, 3.) The axis of the earth, in its annual orbit, always keeps parallel to itself. See plate XII. fig. 2, where the earth is repressnted in ibur different parts of its orbit, still preserving its parallelism ; see also plate XIIL Although the earth's orbit is 190,000,000 of miles in diameter, yet the axis of the earth always points to the same part of the heavens ; because compared with the distance of the fixed stars, 190,000,000 of miles is bu^ a mere point. As some illustration of this : suppose two parallel lines are drawn «apon an elevation, three or four yards from each other. If we look rdong them they will both seem to point directly to the moon in the ho- rizon, and perhaps three or four yards will bear as great a proportioBi to the moon's distance, as 190,000,000 of miles to the fixed stars. What a striking proof of the inconceivable distance of the fixed stars, when, notwithstanding the earth in the course of the year continues to move from one part of its orbit to the other, yet the north pole ap- pears at all times to point in exactly the same direction towards the po- lar star ! It is known that the earth has an annual course round the sun, because the sun, if seen to be in a line with a hxed star, any day or hour, will in a few weeks, by tne motion of the earth, be found considerably to the easi of such star, and he may be thus traced round the hea- vens to the same fixed star from which he set out. G 2 70 THE SEASONS. Tliose observations may be made in tlie day-time, because through the shaft of a very deep mine the stars are visible by day as well as b) nighu They are also rendered visible in ihe dny by telescopes pro- perly mted up for the purpose. The variety of the seasons depends upon the length of the days and nights, and upon the position of ihfi earth with respect to the sun. If the axis of the earth N S (plate X. fig. 1) were perpendicular to a line E Q, drawn through the cen- tres of the sun and earth, there would happen equal day and night throughout the year ; for as the sun al- ways enlightens one half, every part must be half its time in the light, and the other half in darkness. The two poles must be excepted, because to a person there situated, the sun would never appear to rise or set, but would always be mov- ing round the horizon. If the earth were thus situated, the rays would fall at all times vertically on the equator : and the heat excit- ed by the sun being greater or less, in proportion asthe rays fall more or less perpendicularly, the parts about the equator would be heated to a high degree, while the regions around the poles would be desolated by perpetual winter. The proportion of heat materially depends on the degree ofperpen dicularity of the sun's rays. Let plate X. fig. 3, represent summer anc^ winter rays in the latitude of London. It is evident thai the summer rays strike more directly, and with greater force, as well as in greater numbers, on the same place. The axis of the earth being inclined 23^° as in plate X. fig. 2, represents the position of the earth in our summer season, when all the parallel circles, except *hc equator, are divided into tivo unequal '^^rfs; and the length of their days and nights in each atitude will THE SEASONS. 71 I ear a proportion to the greater or lesspor < n of their circuMiterence in the enlightened and dark hemisphere. I**, for instance, a b represent that circle of latitude in which London 8 situated, it is evident that about two-thirds of it is in the light, and only one-third in dai-kness; hence, the sun will be two-thirds or 16 hom-s above the horizon, and B hours below it The parallel above a ^ is entirely in the light, and from thence to the pole tliere is continual day for some time ; and at the pole the sun shines for six montiis together. During that time the south pole is involved in darkness. To those who live in equal latitudes, the one north, the other south, the length of the days to one Will be always equal to the length of the eights to the other. All parts of the globe enjoy the presence of the sun for the sanie length of time, in the course of the year. CHAPTER XXVL THE SEASONS, CONTINUED. The figure plate XII. fig. 2, represents the earth in four different parts of its orbit, or as situated with respect to the sun in the months of March, June,Sep' member, and December. The earth appearing nearei the sun in winter than in summer. We are more than 3,000,000 of miles nearer to the sjin in December than we are in June ; and as the apparent diameter of any object in creases in proportion as our distance from it is diminished, so the sun'** ipparent diameter is greater in our winter than in summer. In winter t is 32' 36", in summer but 31' 31". It is ascertained that our summer (that is, the time that passes between the vernal and autumnal equinoxes) is nearly eight days longer than our winter, or the time 72 THE SEASONS. between the autumnal and vernal equinoxes ; conse- quently the motion of the earth is shiver in summer than in Vv inter, and therefore it must be a greater dis- tance from the sun. The coldness of our northern winters (though nearer to the sun,; compared with our summers, arises from the rays falling upon us so very obliquely, as was before noticed ; and also from the lengiJi of the «?jimmer days and shortness of the nights ; for the earth and air become heated by day, more than they can cool by night. Both the hottest and coldest seasons of the year are not in the long- est and shortest days, but a month after those times ; for a body once heated does not grow cold instantaneously, but gradually, and vict versa. And as long as more heat comes from the sun in the day than is lost in the night, the heat will increase. In June the north pole of the earth inclines to the sun (plate XII. fig". 2,) and consequently brings all the northern parts of the globe into the light ; then to the people of those parts it is summer. But in December, when the earth is in the opposite part of its orbit, the north pole declines from the sun, and the south pole comes into light. It is then winter to us, and summer to the inhabitants of the southern hemisphere. In March and September the axis of the earth neither inclines to, nor declines from the sun (plate XII. fig. 2,) but is perpendicular to a line drawn from its cen- tre. It is then equal day and equal night at all places^ except at the poles, which are in the boundary of light and darkness, and the sun being directly vertical to, or over the equator, makes equal day and night at all places. In March the real place of the earth is Libra, consequently the sun wHl appear in tlie opposite sign, in Aries, and be vertical to the equator As the earth proceeds from March to June, its northern hemispherf THE moon's months, PHASES, ETC. 73 ccmes into light, and on the 21st of that month, the sun is vertical to in© tropic of Cancer. In September the sun is agam vertical to the equator, and of coursje U:e days and nights are again equal. Following the earth in its journey to December, or when it has ar- nved at Cancer, the sun appears m Capricorn, and is vertical to Hu^ tropic of Capricorn. Now the southern pole is enliglitened, and all tlw circles on that hemisphere have their larger parts in light. Of course •t is summer to the southern, and winter to the northern hemisphere. For the increase and decrease of days and nights we are indebted to the inclination of the earth's axis, and its preserving its parallelism. Hence from the 20th of March to the 21st of June the sun is vertical successively to all places between the equator and the tropic of Cancer, and consequently the days must ^ra^- ually lengthen. From June to September the sun *h again successively vertical to the same parts of the earth, but in a reverse order. From September to December the sun is sucessively vortical to ail places between the equator and the tropic of Capricorn. Vvhich causes the days to lengthen in the southern hemisphere. CHAPTER XXVn. THE MOON'S MONTHS, PHASES, ETC. The time which the moon takes in performing' her journey round the earth, is called a months of w^hich there are two kinds; a periodical month of 27 days, 7 hours, 43 minutes, and a synodical month of 29 days. 12 hours, 44 minutes, nearly. This difference arises from the earth's annual motion ia its orbit. 4 PHASES OF THE MOON. Sjip}x>se (plate Xli. fig. 1.) S the sun ; T the earth, in a part oi its (xfbit Q T L. Let E be the position of the moon. If the earlh had no motion, the moon would move round its orbit, E F G, Slc. into the po- sition of E again in 27 days, 7 hours, 43 minutes ; but while the moon IS describing her journey, the earth is passing through nearly a twelfth part of its orbit. Tliis the moon must also describe, before the Uvo t»odies can c-ome again into the same position that they before held with respect to the sim ; and this takes up so much more time as to uyike her synodical month equal to 29 days, 12 hoars, and 44 minutes. This is the cause of the division of time into monllis. N. B. The moon's orbit is elliptical. THE PHASES OF THE MOOX. The sun always enlightens one half of the moon , and though sometimes its whole enlightened hemis- phere is seen by us, yet sometimes only a part, and at other times none at all, is discernible, according to her diiferent positions in the orbit, with respect to the earth. Suppose (plate XII. fig. 1,) A B C DE, &c. to represent the mouii in different parts of her orbit round the earth, in which one half is coii- btantly seen lo be enlightened, as would appear if seen from the sun ; Uien will the enlightened parts of the outside figures represent the apv ix^arance of the moon as seen from the earth. When the moon is at E, no part of its enlightened side is visible to the earth. It is then new moon or change. And^the moon being in a line betiveen the sun and the earth, they are said to be in conjunction. The outside figure opposite E is wholly dark, to show that the moon w invisible at cliange. The whole illuminated hemisphere at A is turned to the earth, and this is called full moon, and the earth being between the sun and moon, they are said to be ii' opposition. /**i(/f' 7.i' f'/a/r // n/jrt^Ac I'lox /'ffj / 1 •v-vv,._,,^ '.,ri Ob Fin. 2. %. /•> y'^' 4 # k /^jyM/.A.LV - e,.?h;r ECLIPSES. 4 Whvn at F, a small part only will be seen fronn the dearth, and that will appear horned ; at G, one^ialf of the enlightened hemisphere is visible ; it is then said to be in quadrature. At H. three-fourths of the enlightened part are visi- ble, and it is then said to be gibbous; and at A, the jvbole enlightened face is said to hefull^ and so oi the rest. The horns of the moon ^ust £fler change, or conjunction, are turned to tlie east ; Biker full moon, or opposition, they are turned to the wpf^t The various phases of the moon are often reprf^sented by a small globe or ivoiy ball suspended by a string. Let your eye represent the &irf}i, and the candle the sun ; then moving it round you, the full aiul the change will appear, and the different degrees of illumination in her orbit as seen ll-om the earth. This will also illustrate the manner jn which the moon, by keeping the same face always towards the mrih, makes one complete revolution on her axis w'hile she makes one ii: hsi orbit The moon's apparent motion is that of rising in- the east and setting in the west, but this is owing to the revolution of the earth upon its axis. The moon's real motion round the earth is from west by south to east. Rer real motion may be known by remarking, when she is near any particular star, she vv'ill approach it from west to east, then^be in coa jimciion Vvith it, and then f^ass eastward of it. CHAPTER XXVIIL ECLIPSES, The term Eclipse implies a privation of light, and in Astronomy the obscuration of the luminaries oi ^heaven ErJipses are either of the sun or moon. 70 ECLIPSE OP THE MOON. ECLIPSE OP THE MOON, ^ An Eclip^se of the Moon is occasioned by the inter position of the earth between the sun and moon, and i*onseq'jentIy it must happen when the moon is in op- position to the sun, that is, at the full moon, as plate XIV. %. 1. If the plane of the moon's orbit coincided with thr plane of the ecliptic, there v,^oul.d bean eclipse at every opposition and conjunction ; but as that is not the case, there can be no eclipse at opposition or conjunction, unless at that time the moon be at or near the nc-de. The orbii of the moon does liot coincide ; for one-half is elevated fxiore than 5 degrees and one-third above that of tlic earth ; and the .'iher half is as much below it. Hence she mofilly passes either above (^ below the shadow of the earth. Tiie greatest distance from the node at which an eclipse of the moon can happen is 12 degrees. When she is within that distance, there will be a partial or Ictal eclipse, according as a part cr the whole disc or face of the moon falls within the earth's shadow. If the eclipse happen exactly when the moon is full in the node, it is called a centred ox total eclipse. The duration of the eclipse lasts all the time the moon is passing through the earth's shadow ; and the ^hadow being considerably wider than the moon's di- Mmeter, an eclipse of the moon sometimes lasts three or four hours. The shadow is al^io of a conical shape, and as the ?v,>)on's orhit is an ellipse, and not a circle, the moon wiii at ditTerent times be eclipsed when she is at differ tiut dii3tances from the eartlj. ECLIPSES OF THE SUN. T? md accordingly as the moon is farther from, or nearei to the earth ^e eclipse will be of a greater or less duration ; on account of the dower motion of the moon, when more distant from the earth. An eclipse of the moon always begins on the moon's feft side, and goes off on her right side. This may be conceived by pre-supjiosing that the earth casts shadow far beyond the moon's orbit; and as the moon's course is from v/est to east, her eastern edge must necessarily first enter that shadow. By knowing exactly at what distance the moon is from the earth, and of course the width of the earth's shadow at that distance, it is that all eclipses are calcu- hited with accuracy for many years before they happen. It is found also, that in all eclipses the shadow of the earth is conical, which is a demonstration that the body which casts it is of a spnerical form, for no othqr sort of figure would, in all positions, cast a conical shadow. This is mentioned as another proof that the earth is a spheri- cal body. The conical form of the shadow proves also that the sun must be a larger body than the earth ; for if two bodies were equxd to one another (as plate XIV. fig. 3,) the shadow would be cylindrical; mid if the earth were the larger body (as fig. 14,) its shadow would he oi tne figure of a cone which had lost its vertex. ECLIPSE OF THE SUN. An Eclipse of the Sun happens when the moon, pass liig between the sun and the earth (plate XIV. fig. 2, iatercepts the sun's light from coming to the earth, which can happen only at the change, or, when the moon is in conjunction. This may be illustrated by suspending a small glolw. or ivory ball, Hi a right line between the eye and the candle. The ball intercepting the light of the candle, repre8«^ir\t«j an eclipse ttf the sun ; for as light passes m a right lirie, the sun is hidden frora that part of the earth which is under tli© moon, and therefore he must b« eclijised. If the whole of the sun be obscured by the body oi H 78 ECLIPSE OF THE SUN. the moon, the eclipse is total: if only 3l part be dark- ened, it is a partial eclipse ; and so many twelfth parts of the sun's diameter as the moon cover«, sc many digits are said to be eclipsed. The word digit means a twelfth part of the diameter of either the Sim or the moon. It is only when the moon is in perigee and very near one of the nodes, that she can cover the whole disc of the sun, and produce a total eclipse ; and no eclipse of the sun can happen but when she is within 17 de- * grees of either of her nodes. At all other new moons she passes either above or below the sun, as seen from the earth ; and at all other full moons above or below the earth's shadow. An eclipse of the moon, if central, must be total ; but an eclipse of the sun may be central and not toiaL Hence there are what are termed annular eclipses, when a ring of light appears round the edge of the moon during an eclipse of the sun. It has its name from the Latin word annulus, '' a ring." This kind of eclipse is occasioned by the moon being at her greatest distance from the earth at the lime of an eclipse ; because in that situation, those who are under the point of the dark shadow will see the edge of the sun, like a fine luminous ring, all around the dark body of the moon. It is only when the moon is nearest the earth at an eclipse of the sun, that the eclipse can be total : a total ^>clipse is, therefore, a very curious and uncommon spectacle. Total darkness cannot last more than six or seven minutes. There must be two solar eclipses in a year, and there may be hut two. But there may not he one lunar eclipse POLAR DAY AND NIGHT, ETC. 70 in the course of a year. When, therefore, there are only two, they are both of the sun. There may be three lunar eclipses, and there can be no more. There may also be seven eclipses in a year ; but in this csise,Jive will be of the sun, and two of the moon. But as there are seven eclipses in the year but seldom, the mean number will be about four. The ecliptic limits of the sun are greater than those of the moon, and hence there will be more solar than lunar eclipses, nearly as three to two. But more lunar than solar eclipses are seen at any given place, because a lunar eclipse is visible to a whole hemisphere at once : whereas a solar eclipse is visible only to a part ; and therefore there is a greater probability of seeing a lunar than a solar eclipse. CHAPTER XXIX. POLAR DAY AND NIGHT, ETC. There being sometimes no night, at other times no day, for a vv'hile, within the polar circles, is thus ac- counted for. The sun being always vertical to some one point, and only one at the same time on the globe, and shining ninety degrees from that point each way, only one complete hemisphere can be at one time il- luminated. Therefore, when on the equator, his rays must extend to each pole. When he has ad- vanced one, two, or ten degrees ahorse the equator, the rays must extend the same number of degrees beyond the north pole, and consequently be withdrawn as ^0 POLAR DAY AND NIGHT, KTC. many from the south pole. And when vertical to llt^ tropic of Cancer (23g degrees north of the equator) he must shine the same number of degrees on the othci side of the pole, that is, to the polar, or arctic circle. While he thus shines there can be no night within that north polar cii^cle^ and of course no day v^^'iihiu the southern 'polar circle ; for the sun's rays, reaching but 90 degrees every way, will then extend but to the ant- arctic circle. For the reasons above given, it is evident that there can be but one day and one night at the poles, each half a year in length. For, from the moment the sun as- cends north of the equator, his rays reach over the pole y which he continues to illuminate till he returns to the equator, a period of half a year. During this time there can be no night at the north pole, nor any day at the south pole. The reverse of all this, while the sun is south of the equator, may be equally applied to the soath pole. The iiiliabiiants of the polar regions, bowever, even when the sun is absent, are not in total darkness; ioi twilight continues to enlighten them till the sun is ] 8 degrees below their horizon ; and his greatest depression is but 5? degrees more, (23 § degrees,^ equal to the inclination of the earth's axis. Besides this, the moon is above the honzon o\ the poles a fortnight together ; for as she passes through the w^hole ecliptic monihly, which lies one half north, and the otlier half south of the e) from the sun's course in the ecliptic When tb.3 sua is in the equator, he rises exactly UMBRA AND PENUMBRA, IN ECLIPSES. 81 east, and sets exactly west ; but during the summer half year be rises to the north of the east point, and sets as much north of the west ; that is, if he rises 1 0*^ north of the east, he sets 10° north of the west point &e., the place of his rising varying with his declination During the opposite half year he rises soutli of the east, and sets south of the west. It must be observed, that though we say the sun sets as many de grees N. of the W. as it rises N. of the E., &c. yet there v^dll be a srrmh variation from sun-risuig to sun-setting, as the earth is advancing in iti» orbit. This, to some, will be more clearly explained on the globe. If the sun were to remain stationary in the ecliptic, from his rising to his set ting there would be no variation. But the sun advances in the ecliptic nearly a degree in 24 hours, which, if correctly allowed for in working the problem, will show a small variation between the rising and the setting point. Hence, from the shortest to the longest day the sim sets rather more towards the nortJi than lie rises ; but from the longest to the shortest day the variation is more southerly. CHAPTER XXX. UMBRA AND PENUMBRA, IN ECLIPSES. Tke Umbra 2.nd Penumbra in an eclipse may be thus explained : (Plate XIV. fig. 5.) Let S be the sun, M die Moon, A B or C D, the surface of the earth ; then X Y Zj will be the moon's umbra, in which no part of the sun can be seen. The space comprehended between the umbra and x o k and z P g, is called the penumbra, in which part of the sun only is seen. Now it is evideiit that if A B be the surface of the earth, the space between m n, where the umbra falls. will suffer a total eclipse; the parts o m and n ^, will H 2 82 UMBRA AND PENUMBSA, IN ECLIPSES. have a 'partial eclipse; but to all the other parts of tlie earth there will be no eclipse. But as the earth is at different times at different dis- tances from the moon, suppose, again, C D to be the surface of the earth ; then as the umbra reaches but to V, the space within c^* will suffer an annular eclipse^ and the sun will appear all round about the moon in the form of a ring. The parts k c snidfg will have apar^ tial eclipse, and to the other parts of the earth there will be 710 eclipse. Hence it is evident that in this last case, supposing C D the earth, there can be no total eclipse anywhere, as the moon's umbra does not reach the earth. According to M. du Sejour, an eclipse can never .be annular longer tfian 12 minutes 24 seconds, nor total longer than 7 minutes 58 seconds. The moon's mean motion about the centre of the earth is at the rate nf about 33' in an hour; but 33' of the moon's orbit is about 2,280 miles, which therefore may be considered as the velocitj' with which the moon's shadow passes over the earth ; but this is the velocity upon ' the surface of the earth, only, where the shadow falls perpendicularly ujx)n it. In every other place the velocity of the surface will he increased. But again, the earth having a rotation about its axis, the relative ve- locity of the moon's shadow over any point of the surface will be even different from this. For if the point be moving in the direction of the Bhadow% the velocity of the shadow on that point will be diminished snd consequently the time in which the shadow passes over it will be* increased ; but if the point be moving in a contrary direction to that of the shadow (as is the case when the shadow falls on the other side of the pole) the time will be diminished. From the above it is evident that the length of a solar eclipse at any place is affected by the earth's roiatiaii about its axis. The different eclipses of the sun may be thus ex- plained : let each of the three lower circles (plate XV. fiff. 3.) represent the earth, and O R its orbit. Ijei each of the three upper circles represent the moon's Fa^e 'fJe ra^e /J Mav. /■"/at.' /.'-y I'dl'affr/l'.SfJt rf/'t//r A\t7-//f '» .V-t7.V JJec ]^hiTte~ •"" !^4^A JtjTt du,/. ^'cp , J^r p<^t. ffeh^rrritTir r/7/i/ O'eore^rhfj- Lrifte/rturff UMBRA AND PEjVUMBRA, IN ECLIPSES. 83 penumbra, P U the line described by the centres of the moon's umbra and penumbra at the earth; N the moon's node; E the earth's centre ; ^^ n the moon's penumbra ; u the umbra. Then in the first position, the penumbra p n just passes by the earth, without fall- ing upon it, and therefore there will be no eclipse. In the second position, the penumbra p n fails upon the earth, but the umbra u does not. In the third position, both the penumbra p n and the mubra u fall upon the earth ; therefore, Vi^here the penumbra falls there will be B, partial eclipse, and where the umbra falls there will be a total eclipse ; and to the other parts of the earth there will be no eclipse. As a description of a total eclipse of the sun may be interesting to the young reader, we select a few particulars of that which happened April 22d, 1715. Captain Stannyan, of Berne, in Switzerland, says, " the sun was totally dark for four minutes and a half; that a fixed star, and planet, appeared very bright;" J. C. Facis, of Geneva, says, "there was seen, during the whole time of the total immersion, a whiteness, which seem- ed to break out from behind the moon. Venus, Saturn, and Mercury were seen by many. Some persons in the country saw more than six- teen stars, and many people on the mountains saw the sky starry as on the night of a full moon. The duration of the total darkness was alxRil tiiree minutes." Dr. J. J Scheuchzer, at Zurich, says, " that both planets and fixed stars were seen ; the birds went to roost ; the bats came out of their holes, the dew fell on the grass, and a manifest sense of cold was experienced. The total darkness lasted at Zurich about four minutes." Dr. Halley, who observed this eclipse in London, says, " that about two minutes before the total immersion, the remaining part of tlie ^uii was reduced to a very fine horn ; and for the space of about a quarter of a minute, a small piece of the southern horn seemed to be cut oflffrom the rest, and appeared like an oblong star. This appearance could proceed from no other cause but the inequalities and elevated parts of the moon's surface, by which interposition, part of that exceedingly fme filament of light was intercepted. ** \ few seconds before the sun was totally hid, there discovered 84 THE TRANSIT OF VENUS. iteelf round the moon a luminous ring, in breadth about a digit, or pe» haps a tenth part of the moon's diameter ; it was of a pale whiteness, or father pearl colour, seeming to me a little tinged with the colours of the iris, whence I concluded it was the moon's atmosphere ; for it in all re- spects resembled the appearance of an enlightened atmosphere viewed from afar, but whether it belonged to the smi or the moon, I shall not take upon me to decide. " As to the degree of darkness, it was such that one might have ex- pected to see more stars than were seen in London. The planets, Jupi- ter, Mercury, and Venus, were all that were seen by some ; Capella and Aldebaran were also seen. Not was the light of the ring round the moon capable of effacing the lustre of the stars, for it was vastly inferior to that of the full moon, and so weak that I did not observe it cast a shade. I forbear to mention the chill and damp with which the dark- ness of tliis eclipse was attended ; or the concern that appeared in all 8<:»rts of animals, birds, beasts, and fishes, upon the extinction of the SUD, since ourselves could not behold it without emotion " CHAPTER XXXI. THE TRANSIT OF VENUS. The following illustration of the transit of Venus^, which is an object of great interest and utility, will now be understood : Let S (plate XIV. fig. 6.) represent the sun, and V V' Venus at the beginning and end of her transit, as she would appear from the earth's centre; also let E E' be the corresponding positions of the earth at those times. Then, if the observer would be situated at C, the venire of the earth, when Venus entered on the solar disc, she would appear as a small black spot at 5, and the true place of both her and the eastern limb of the sun would be 5. But if the observer were situated at any point on the earth's surface, as P, the apparent THE TKANSIT OF VENUS. 85 place of Venus would be at v, and the apparent place of the corresponding limb of the sun would be at P ,• md consequently Venus would appear to the eastward of the sun, by a space equal to the arc v p, which is the difference of the parallaxes of these two bodies. Hence the immersion of Venus would not take place so soon to an observer at P as to one at C, by the time she would require to describe the apparent arc v P. Now, as the transit always must take place at the inferior conjunction of the planet, the motions of both V^enus and the earth will then be from east to west, while the motion of the earth on its axis is in a con- trary direction. Consequently, while Venus and the earth move in their orbits from V to V, and from E to E', the point P, which at the commencement of the motion was w?fs^ of the centre, will at the end of it be on the east of it, as at P'. Hence the observer, who was supposed to be situated at C, would perceive Venus just leaving the sun's disc, and her apparent place would be s' ; while to the observer at P', her apparent place would be at v\ and that of the sun's western limb at P, The apparent distance of Venus from the sun at the end of tbo transit is therefore the arc v P, which is equal to the differ- ence of the parallaxes of the sun and Venus, as before. Consequently the time of the duration^ as observed at the point P, will be lessihixn the absolute duration, by the time which the planet would require to describe the two apparent arcs v P and v P, or twice the difference o£ the parallaxes of the sun and the planet. The principal use to which astronoaiers apply th^ 86 OCCULTATION OF THE FIXED STARS. transits of Venus is in determining the distance of t e sun from the earth by means of his parallax, which, on account of its smallness, they have in vain attempted to ascertain by various other methods. These transits are also applied with great effect in ascertaining th« longitude of places ; in correcting the elements of the planets, especi ally the places of the cphelia, the situation of the nodes, and the inch nations of the orbits. The transits of Mercury take place much oftener than those of Venus , but on account of his greater distance from the earth, and the small ness of his parallax from the sun, they are not susceptible of equa. utility with those of Venus, except for the determination of terrestial longitude, for which they are superior. OCCULTATION OF THE FIXED STARS. Nearly related to eclipses of the sun, is the occulta- tion of the fixed stars, which implies the obscuration of these heavenly bodies by the moon or a planet. The only method of ascertaining whether an occul- tation will happen, is that of calculating the place of the moon at the ecliptic conjunction. The course of the moon, however, affords limits to these occurrences, which enable astronomers to judge when they will take place ; for Cassini has remarked that all stars whose latitudes do not exceed 6° 36' either north or south, may suffer an occultation on some part of the earth; and if the latitudes are not more than 4° 32', the occul- tation may happen on any part of the earth. By conjuncilmi is meant having the same longitude; or answering to the same degree of the ecliptic. By latitude of a star (as has been shown in page 49) is meant its distance from the ecliptic^ either north or south. To determine when these eclipses or occultations will happen, we must compute the time of the con- 'wnction, and the true latitude of the moon at that epoch, /it^/? if6\ F/rf I X i»«^/ ^- / 1. y^ / .?', '5? / **^ :oi^'-' ^ -^5^^--.V A,; ,„,^ IV//^'^ ^^ F P Tv-^.^1 ' hth.-?hr* THE HARVEST M0C1>^ 87 tLrU then, if the diiference of the latitudes of the moon and the star exceed 1° 20', there cannot be any occult ation ; but if this difference be less than 51', there must bean eclipse of the star on some part of the earth : between these limits the occultation may oi may not take place. In very different places of the earth, a great difference will rp?ijlt fiora the change in the moon's parallax, and this difference may be evea io great as altogether to prevent the obscuration from taking plac« CHAPTER XXXII. THE HARVEST MOON. Owing to the daily progress the Moon is making in her orbit from west to east, she rises about 50 minutes later every day, when near the equator, than on the day preceding. But in places of considerable latitude there is a remarkable difference, especially about the time of harvest, when at the season of full moon she rises to us for several nights together only from IT to 25 minutes later on the one day than on that immedi- ately preceding. To those who live in the latitude of London, when the moon is in the 10th of Pisces, she nses 25 minutes later than on the day pre- ceding ; the 23d of Pisces, 20 minutes later ; the 7th of Aries, 17 minutes later; the 20th, 17 minutes 5 the 3d of Taurus, 20 minutes; and the 16th, 24 minutes later. To persons who live at considerable distances from the equator, the autumnal full moon rises very soon af- ter sun-set for several nights together ; and by thus succeeding the sun before the twilight is ended, the moon prolongs the light, to the great beneMt of those 88 THE HARVEST MOON. that are engaged in gathering in the fruits of the earth Hence the full moon at this season is called the Har- vest Moon, It is believed that this was observed by persona engaged in agricni ture at a much earlier period than that in which it was noticed by as ironoraers. The former ascribed it to the goodness of the Deiiy, noi doubting but that he had so ordered it for their advantage. About the equator, where there is no such variety of seasons, and where the weather changes but seldoiii, and at stated times, moonlight is not wanted for gather- ing the fruits of the earth, and there the moon rises throughout the year at nearly the equal intervals of 50 minutes, as before observed. At the polar circles, the autumnal full moon rises al &un-set, from the first to the third quarter; and at the poles, where the sun is for half a year absent, the win- ter full moons shine constantly without setting, from the first to the third quarter. The moon's path may be considered as nearly coin ciding with the ecliptic ; and all these phenomena are owing to the different angles made by the horizon anc? different parts of the moon's orbit, or in othjer words, by the moon's orbit lying sometimes more oblique to the horizon than at others. In the latitude of London as much of the ecliptic rises about Pisces ?ind Aries'in two hours as the moon goes through in six days ; there- lore while the moon is in these signs, she differs but two hours in rising for six days together, that is, one day with another, about 20 minutes later every day than on the preceding. These parts or signs of the ecliptic which rise with the smallest angles, set with the greatest^ and vice versa THE HARVEST IIOON. St And whenever this angle is least, a greater portion cl tne ecliptic rises in equal times than when the angle is larger. This may be seen by elevating the pole of the globe to any considerable latitude, and then turning \t round on its axis. Consequently when the moon is in those signs which rise or set with the smallest angles, she rises or sets with the least difference of time; and on the contrary, with the greatest difference in those signs which rise or set with the greatest angles. Let plate XV. fig. 2, represent the globe, the north pole being ele- vated to about 51 P, with Cancer on the meridian, and Libra rising in the east. In this position the ecliptic has a high elevation, making ac angle with the horizon of 62*^. But let the globe be turned half round on its axis till Capricorp comes to the meridian, and Aries rises in the east, then the ecliptic will have the low elevation, above the horizon (fig. 2,) making an angk of only 1.5^ with it. This angle is 47° less than the former angle, equa to the distance between the tropics. In northern latitudes, the smallest angle made by the ecliptic and horizon is when Aries rises, at which time Libra sets ; the greatest when Libra rises, at which time Aries sets. The ecliptic rises fastest about Aries, and slowest about Libra. Though Pisces and Aries .♦Tiake an angle of only about 15° with the horizon when they rise^ to those who live in the latitude of London they make an angle of 62° with it when they set. The Moon, quitting Pisces and Aries, arrives in about four- teen days at the opposite signs, Virgo and Libra, and then she differs almost four times as much in rising ; being one hour and about fifteen minutes later every day or night than on the preceding. Those who are acquainted with the globes will easily demonstrate 'iiis problem by putting small patches on the ecliptic, at distances from «aeh other equal to the moon's daily course ; which (deducting for the sHn's ad yance) iss iittlp more than 12^ Then (afl^er rectifying the glob© 1 90 THE HARVEST M00^^ for the latitude, and setting the hour-index to 12,) by turning the globe round, and observing the time of the appearing and disappearing of the patches, the variation in the time of the moon's rising or setting will b« siiown on the hour circle. As the moon can never be full but when she is op* posite to the sun, and the sun is never in Virgo or Li- bra but in our autumnal months, September and Octo- ber, it is evident that the moon is never full in the op- posite signs, Pisces and Aries, but in those two months* Therefore we can have only two full moons in a year, which rise, for a week together, very near the time of sun-set. The former of these is called the Harx>€&( Moon, and the latter the Hunter^s Moon. CHAPTER XXXIII. THE HARVEST MOON, CONTINUED. . Though there are but two full moons in the year that rise with so little difference of time, yet the phe- nomenon of the moon's rising for a week together so nearly in point of time, occurs every montii, in some part or other of her course. In Winter the signs Pisces and Aries rise about noon ; and the sun, m Capricorn, is then only a quarter of a circle distant. Therefore the TiTon, Vv'hile passing through tliem, must be only in her first quarter Hence her rising is neither regarded nor perceived. In Spring, these signs rise with the su7i, because he is then in Ihem , ftnd as the moon (-hanges while passing through the. same sign with ihe •an, it musi tlien be i?ie change, and hence invisible. In Summer, they rise about midnight, for the sun being three signs, or n quarter of a circle before them, the moon is in them, or about her Vnrd quarter. Hence rising so late, and giving but little light, her rismg passes unooser^xd. f THE HARVEST MOON. 9^ The moon goes round the ecliptic in 27 days, 8 hours but not from change to change in less than 29 days, 12 hours ; so that she must be once in every sign, and ttvice in some one sign every lunation. If the earth had no annual motion, every new moon would fall in tlie same sign and degree of the ecliptic; and every full moon in the opposite : for the moon would go exactly round the ecliptic from change to change. So that if she were once full in any sign, suppose inPisce« or Aries, she would always be full there. But in the time the moon goes round the ecliptic from any conjunc- tion or opposition, the earth goes 27i degrees, that is, almost a sign for- ward ; so that the moon must go 27i degrees more than round, before she can be in conjunction vjiih or opposite to the sun again. Hence, if she were in her conjunction at the first degree of Aries, she would, in one lunation, not only return to the same point, but repass it, and go twice over Aries to the 27h degree. To the inhabitants at the equator the north and south poles appear in the horizon ; and therefore the ecliptic makes the same angle southward with the horizon when Aries rises, as it does northward when Libra rises ; con- sequently she rises and sets not only at nearly equal angles with the horizon, but at the equal distance in time of about 50 minutes, all the year round : and hen(^e there can be no particular harvest moon about the equator. The farther any place is from the equator if it be not beyond the polar circles, the angle which the eclip- tic and the horizon make gradually diminishes when Pisces and Aries rise. This the globe itself will fully illustrate ; for the more the nortb pole is elevated, the more nearly does the ecliptic coincide with the horizon ; that is, the angle is diminished. Though in northern latitudes the autumnal full moons are in Pisces and Aries ; yet in southern lali- 92 LEAP-YEAR. tudes it is just the reverse, because the seasons are the contrary : for Virgo and Libra rise at as small angles with the horizon in southern latitudes, as Pisces and Aries do in the northern : and therefore the harvest moons are just as regular on one side of the equator as on the other. In this illusti'ation of the harvest moon, we have supposed the moon to move in the ecliptic, from which the sun never deviates ; but the orbit in which the moon really moves (as was noticed under the article Eclipses) is different from the ecliptic ; one half being elevated 5i de- grees above it, and the other half as much depressed below it. And this oblique motion causes some small difference in the time of her rising and setting from what has been above mentioned. At the polar circles, the full moon neither rises in summer, nor sets in winter. For the winter full moon being as high in the ecliptic as the summer sun, she must therefore continue, while passing through the northern signs, above the horizon ; and the summer full mooji being as low in the ecliptic as the winter sun, can no more rise, when passing through the southern signs, than he does. CHAPTER XXXIV. OF LEAP-YEAR. The time our earth takes to make one complete re volution, in its orbit round the sun, we call a year. To complete this with great exactness is a work of consi- derable difficulty. It has mostly been divided into twelve iHonths of 30 days. Pru^t^ .91' /y-'///'// LEAP- YE AK. 93 t Tlie ancient Heorew monuio jonsisled of 30 days each, except the last, which contained 35. Thus the year contained 3l5 daws. An in- tercakry month at the end of 120 years supphed the ditlereiu e. The Athenian months consisted of 30 and 29 days alteriiaiely, ao- cording to the regulation of Solon. This calculation produced a year of 354 days, and a little more than one-third. But as a soiur montk contains 30 days, 10 hours, 29 minutes, Melon, to reconcile the differ fence between the solar and lunar year, added several embolismiCt or intercalary months, during a cycle, or revolution of 19 years. The Roman months, in the time of Romulus, were only ten of 30 and 31 days. Numa Pompilius, sensible of the great deficiency of this compulation, added two more months, and made a year of 355 days. The Egyptians had fixed the length of their year to 365 days. Julius Caesar, who was well acquainted with the learning of the Egyptians, was the first who attained to any accuracy on the subject. Finding the year esta- blished by Numa ten days shorter than the solar yeai, he supplied the difference, fixed the length of the year to be 365 days, 6 hours, and regulated the months ac- cording to the present measure. To allow for the six odd hours, he added an intercalary day every fourth year to the month of -February, reckoning the 24th of that month twice, which year must of course consist of 366 days, and is called Leap-year. From him it waa denominated the Julian year. This year is also called Bissextile in the Almanacs, and the day added is termed the intercalary day. The Romans, as has been observed, inserted the intercalary day, h^ reckoning the 24th twice, and because the 24th of February in theii /calendar was called sexta calendas Marfii, the sixth of the calends oJ March, the intercalary day was called bis sexta calendas Mart it, the terond sixth of the calends of March, and hence the year of intercalation kfKd the appellation of Bissextile. We introduce in leap-year a new day in the yame month, namely, the 29th. To ascertain at any time what year is loap-year I 2 94 LEAP-YE-4B divide the date of the year by 4, if there is no r'^rnam der it is leap-year. Thus iSi4 was leap-year. But 1825 divided by 4, leaves a remainder of I, showing that it was the first year after leap-year; anil as 1S29, divided by 4, leaves 1, it will be the first after leap- year. But the true solar year does not contain exactly 365 days, 6 hours, but 365 days, 5 hours, 48 rninutrs, and 49 seconds; which to calculate for correctly, requires an additional mode of proceeding: 365 days, 6 hours, exceeds the true time by 11 minutes, 11 seconds, every year, amounting to a whole day in a little less than 130 years. Notwithstanding this, the Julian year continued in general use till the year 1582, when Pope Gregory XIII. reformed the calendar, by cutting off ten days be- tween the 4th and 15th of October in that year, and calling the 5th day of that month the 15th. This al- teration of the style was gradually adopted through the greater part of Europe, and the year was afterwards called the Gregorian year, or New style. In this country, the method of reckoning according to the New style was not admitted into our calendars until the year 1752, when the error amounted to nearly 11 days, which were taken from the month of September, by calling the 3d of that month the 14th. The error amounting to one whole day in about 130 years (by making every fourth year leap-year,) it is settled by an act of parliament that the year 1800, and the year 1900, which, according to the rule above given, are leap-years shall be computed as common years, having THE TIDES. 95 only 3o5 days in each; and that ev. .r foar hundredth year afterwards shall be a common y ar also. If this method be adhered to, the present mv)de of reckoning will not vary a single day from true time in less than 5,01)0 years: The beginning of the year was also changed, by the same act of parliament, from the 25th of March to the 1st of January. So that the succeeding months of Ja- nuary, February, and March, up to the 24th day, which would, by the Old style, have been reckoned part of the year 1752, were accounted as the first three months of the year 1753. Hence we see such a date as this, January 1, 1757-8, or February 3, 1764-5 ; that is, ac- cording to the Old style it was 1764, but according to the New^ 1765, because now the year begins in Janua- ry instead of March. CHAPTER XXXV. THE TIDES. The oceans, which cover more than one half of the globe, are in continual motion ; they ebb and flow per petually, and these alternate elevations and depressions are called the tides^ or thejlux and refiux of the sea. The ancients considered the ebbing and flowing of the tides as one of the greatest mysteries in nature, and were utterly at a loss to ac- count for it, Galileo and Descartes, and particularly Kepler, made gome successful advances towards ascertaining the cause ; but Sir [saac Newton was the first who clearly pointed out the phenomenon, and showed what were the chief agents in producing these motions- The tides are not only known to be dependent upon some fixed and determinate laws ; but t'le true cause 96 THE TIDES. of their agitation is demonstrated to be.the altractior of the sun and moon, particularly the latter; for as she is so much nearer the earth than the sun, she attracts/ with much greater force than he does, and consequently raises the water much higher; which, being a fluid, loses, as it were, its gravitating power, and yields to their superior force. Thai the tides are dependant upon some known and determinate laws, is evident from the exact time of high water being previously given in every ephemeris, and in many of the common almanacs. The moon comes every day later to the meridian than on the da/ preceding, and her exact tune is known by calculation ; and the tides in any and every place, will be found to follow the same rule ; hap- pening exactly so much later every day as the moon comes later to the meridian. From this exact conformity to the motions of the moon, we are induced to look to her as the cause ; and to infer that those phe nomena are occasioned principally by the moon's attraction. If the earth were at rest, and there were no influence from either sun or moon, it is obvious from the princi- ples of gravudtion, that the waters in the ocean would be truly spherical, as plate XVI. fig. 1 ; but daily expe- rience proves that they are in a state of continual agi tation. If the earth and moon were without motion, and the earth covered all over with water, the attraction of the moon would raise it up in a heap in that part of the ocean to which the moon is vertical, and there it would, probably, always continue, as plate XVI. fig. 2; but by the rotation of the earth upon its axis, each part of . its surface to which the moon is vertical is presented to the action of the moon, and thus are produced twr« flooas, and two ebbs. In this supposiuon we have omitted to take notice of the sun's k duence. 1 >r » THE TIDES. 97 The attractive power of the sun is to that of the moon as three to ten; hence, when the moon is at change, the sun and moon being in conjunction, or on the same side of the earth, the action of both bodies is on the same ocean of waters ; the moon raising it ten parts, and the sun three, the sum of which is thirteen parts, represented by plate XVI. fig. 4. Now it is evident that if thirteen parts be added to the attractive power of these bodies, the same number of parts must be drawn off from some other parts, as at C and D. It will now be high water under the moon at A, and low water at C and D. The attractive power of the sun, according to some authorities, is to that of the moon as two to ten^ or one-jifihy and according to others as (me-ikird. Those parts of the earth where the moon appears in the horizon, as at C and D, will have low water ; for as the waters in the zenith and nadir (A and B) rise at the same rime, the waters adjacent will press towards those places to maintain the equilibrium ; and to sup- ply the place of those, others will move the same way, and so on ; hence at the places 90° distant (C and D) the waters will be lowest. It is evident that, the quantity of water being the same, a rise cannot take place at A and B, without the parts C and D being at the same time depressed ; and in this situation the waters may be considered M partakir g of an oval form. 98 THE TIDES. CHAPTER XXXVl. THE TIDES, CONTINUED. It has been already shown, under the article gravi t^tion, that the power of gravity diminishes as the square of the distance increases; therefore not only those parts of the sea immediately below the moon must be attract ed towards it, and occasion the flowing of the tides there, as at A, fig. 4 ; but a similar reason occasions the flowing of the tides in the nadir, or that partof tiie earth diametrically opposite to it, as at B , for in the hemisphere farthest from the moon, the parts being less attracted than those which are nearer, gravitate less towards the earth's centre, and consequently must be higher than the rest ; and as every poi^tion of the earth will pass ticice through the elevated, and twice through the depressed parts, two tides will he produced each day. It has been otherwise thus explained : All bodies moving in circles have a tendency to fly off from their centres ; now as the earth and moon move round the centre of gravity, that part of the earth which is at any time turned from the moon, would have a greater centrifugd force than the side next her. At the earth's centre, the centrifugal J<)rce will balance the attractive force ,* therefore as much water is thrown off by the centrifugal force on the side which is turned from tlie moon, as is raised on the side next her by her attraction. If the tide be at high water mark in any point or har- bour that lies open to the ocean, it will presently sub- side and flow back for about six hours, and then return in the same time to its former situation, rising and fall ing nearly twice a day, or in the space of somewhav more than twenty-four hours. The interval, however, between its flux and refiun THE TIDES. 99 12 not precisely six hours, but about 12 minutes and | more, so that the time of high water does not happen at the same hour, but is above f of an hour later every day for about 30 days, when it again recurs as before ^ If the moon were stationary, there would be two tides every twenty-four hours, but as that body is daily pro- ceeding from west to east in her orbit above 12^, the earth must make more than a complete revolution on its axis, before the same meridian is in conjunction with the moon. And hence, every succeeding day the time of high water will be above f of an hour later than on the preceding. For example : If it be high water to day at noon, it will be low wa- Udf at 12 and i minutes after six in the evening ; and, consequently, after two changes more, the time of high water the next day will be above f of an hour after noon : the day following above ^ past one ;— the day after that above \ past two, and so on. Again : Suppose at any place it be high water at three in the after- noon upon the day of the new moon, the following day it will be high water about f after three ; — the day after about i past four, and so on till the next new moon. Not only when the sun and moon are in conjunction, or at the change, but when in opposition^ at the full, the tides are at the highest^ as in fig. 6. For when the moon is at full, ten parts of water are raised from that side of the earth next her, by her attractions ; and as the side which is next her is opposite to the sun, three parts must be thrown off by his centrifugal force, the sum of which will be thirteen parts next the moon. — Again, from the side opposite to the moon and under the sun, ten parts are thrown off by her centrifugal force, and three raised by his attraction, making thirteen, the same as before. 100 THE TIDES. If there were no moon, the sun, by his attraction, would raise a gimall tide on the side of the earth next him ; and it is evident that the ades on the opposite side would be raised as high by the centrifugal force ; for the sun and earth, as well as the earth and moonmove round their centres of gravity. The highest tides happen when the ejn and moon are either in conjunction (fig. 4.) or opposition (fig. 6,) and these are called Spring Tides ; but when the moon is in her quarters (as fig. 5,) the influences of the sun and moon counteract each other ; that is, they act in different directions ; the attraction of the one raising the waters, while that of the other depresses them. The moon of herself would raise the water ten parts under her, but the sun, being then in a line with low water, his influence keeps the tides from falling so low there, and consequently from rising so high under and oppo- site the moon. His power, therefore, on the low water being three parts, leaves only seven parts for the high water, under and opposite the moon. These are called Neap Tides* CHAPTER XXXVn. THE TIDES, CONTINUED. The tides are known to rise higher at some seasons than at others : for the moon goes round the earth in an elliptic orbit, and therefore she approaches nearer to the earth in some parts of her orbit than at others. When she is nearest, the attraction is the strongest, md consequently it raises the tides most : and when THE TIDES. 101' she is farthest from the earth, her attraction is the leasts , and the tides are the lowest. From the above theory, it may be supposed that the tides are at the highest when the moon is on the meri- dian, or due north and south. But we find that in open seas, where the water flows freely, the moon has gene rally passed the north or south meridian about three hours, when it is high water. For even if the moon^s attractions were to cease when she had passed the meri- dian, the motion of ascent communicated to the water before that time, would make it continue to rise for some time after. Much more must it do so when the attraction is not withdrawn, bui ' >nJy diminished : as a httle impulse given (o a moving ball will cans€ it to move still farther than it otherwise could have done. And expe- rience shows that the heat of tlie day is greater at three o'clock in the riiiernoon than it is at twelve ; and it is hotter in July and August than ia Jxine, because of the increase made to the heat already imparted. The tides, however, ansv/er not always to the same distance of the moon from the meridian, at the same [)lace ; but are variously aifected by the action of the sun, which brings them on sooner, when the moon is in her Jirst and third quarters ; and keeps them back later ^ when she is in her second smd fourth. Because in the former case the tide raised by the sun alone would be earlier than the tide raised by the moon, and in Die latter case later. The greatest spring tide will happen when the moon is in perigee, if other things are the same ; and the suc- ceeding spring tide when the moon is in apogee will be the least. But as the effect of a luminary is greater Uie nearer it approaches to the plane of the equator, K 102 THE TIDES. tnd as the earth is nearer the sun in winter than id summer, and still nearer in February and October tliau in March and September ; the greatest tides happen no( till some time after the avtmnnal equinox, and retirn 2 little before the vernal. In open seas the tides rise but to very small heights^ in proportion to what they do in wide-mouthed rivers opening in the direction of the stream of tide. For in channels growing gradually narrower, the water is ac- cumulated by the contracting banks. At the mouth of the Indus, the water rises and falls full thirty feet, and in the bay of Fundy seventy feet. The tide in the above instance has been compared to a moderate wind, which, though not much felt in an open plain, may yet appear with a strong and brisk current in a street, and become still more pov^ erful as the more confined. Though the tides in open seas are at the highest about three hours after the moon has passed the meridian, yet the waters, in their passage through shoals and channels, and by striking against capes and head lands, are so retarded that, to different places, the tides hap pen at all distances of the moon from the meridian, consequently at all hours of the lunar day. The tide raised by the moon in the German Ocean, when she h (hree hours past the meridian, takes twelve hours to come thence tt) liondon bridge, where it arrives by the time that a new tide is raised hx the ocean. There are no tides in lakes, because they are gene- rally so small that, when the moon is vertical, she at- tracts every part of them alike, and by rendering all the waters equally light, no part of them can be raised THE TIDES. 103 I l^her than another. The Mediterranean and Baltic soas have very small elevations, because the inlets by which they communicate with the ocean are so narrow, that they cannot, in so short a time, either receive o^ discharge enough, sensibly to raise or sink their sur^ faces. Air being lighter than water, it cannot be doubted that the moon raises n»iich higher tides in the air than in the sea. Although it has been stated that the highest tides are produced by the conjunction and opposition of the sun and moon, yet their effects zxe not immediate ; the highest tides happen not on the days of the full and change, neither do the lowest tides happen on the days of their quadratures. But on account of the continua- tion of motion these effects are greatest and least, some time after their forces are. So that the greatest spring tides commonly happen two days after the new and full moons ; and the least neap tides two days after the first and third quarters. For if the greatest elevation immediately under the moon, points to one side of the equator, the opposite greatest elevation points as much to the other side. And those places which are on the same side of the equator with the luminary, approach nearest to the greatest elevation when she is above the horizon, than to the greatest opposite elevation when she is below the horizon. This inequality is greatest when the sun and moon have the greatest declination. It is also greatest in places most remote from the equator. The nearer the place approaches to the poles, the farther it is removed from the greatest elevation on the opposite side of tlia 104 THE PRECESSION OF THE EQUINOX. equator. Thus the less tide is continually diminishing, till at last it entirely vanishes, and leaves only one tid^ in the day. Hence it is found by observation, that there is only one tide in twenty-four hours, in all places in the polar legions in w^hich the moon is either alw^ays above ot always below the horizon, during the whole rotatioo of the earth about its axis CHAPTER XXXVHL THE PRECESSION OF THE EQUINOX. It has been already observed, that the form of tlie earth is that of an oblate spheroid ; for by the earth's mo- tion on its axis there is more matter accumulated all around the equatorial parts than any where else on the earth. The sun and moon by attracting this redundancy of matter bring the equator sooner under them, in every return towards it, than if there were no such accumula- tion. Therefore if the sun sets out from any star, or other fixed point in the heavens, the moment when he is departing from the equinoctial (or from either tropic) he will come to the same equinox (or tropic) again 20 minutes, 17^ seconds of time (or which is equal to 50 ' of a degree) before he arrives at the same fixed star oi point from which he set out. For the equinoctial points recede 50" of a degree westward every year contrary to the sun's annual progressive motion. THE PRECESSION OF THE EQUINOX. 105 To prove that 20 minufes 17i seconds of lime are equal to 50" of a legree, it must be recollected that the sun goes through the wtiole ecliptic of SoO'^, in 365i days, which is not quite one degree each day, but 59' 8", (or 52" less than a degree.) Therefore, if by the rule of pro- portion ^ve sa5% as 59' 8" : 24 hours : : 50", the result will be 20 minutes 17i seconds, nearly. That the sun has a daily apparent motion in the echptic from west to east is evident from comparing the sun's right ascension every day with that of the fixed stars lying near him. For the sun is found constantly to recede from those on the west, and ap- proach those on the east ; hence his apparent annual motion is found tri be from west to east. When the sun arrives at the same equinoctial or sol- stitial point, he finishes what is called the tropical year; which, according to some authorities, is found to contain 365 days, 5 hours, 48 minutes, 48 seconds (see page 4,) and when he arrives at the same star again, as seen from the earth, he completes the sidereal year. which contains 365 days, 6 hours, 9 minutes, 14j se- conds. The sidereal year is therefore. 20 minutes, ITJ seconds longer than the solar or tropical year, and 9 minutes, 14^ seconds longer than the Julian or civil year, which is 365 days, 6 hours. So that the civil year is almost a mean between the sidereal and tropical. According to Professor Vince, a sidereal year is 365 days, 6 hours, 9 minutes, 11 seconds, .5; and a tropical year 365 days, 5 hours, 48 mi siutes, 48 seconds. As the sun describes the whole ecliptic, or 300° in a tropical year, he moves 59' 8" of a degree every day ^t a mean rate ; which is equal to 50 seconds of a de- gree in 20 minutes 17-1 seconds of time : therefore he will arrive at the same equinox or solstice when he is 50" of a degree short of the same star or fixed point in the heavens, from which he set out the year before. Sc that, with respect to the fixed stars, the sun and equi K 2 106 THE PRECESSION OF THE EQUINOX. noctial points fall back (as it were) 30° in 2,160 years This will make the stars appear to have gone 30° for- ward, with respect to the signs in the ecliptic in that time; for it must he observed, that the same signs al- ways keep in the same points of the ecliptic, without re^ gard to the place of the constellations. 50" short in one year are = P short in 72 years. For in a degree are (60 x 60) 3,600", which divided by 50", will give 72.--And P less in 72 years = 30"^ or one whole sign in 2,160 years. To explain this by a figure ; suppose the sun (plate XVII. fig. ist,) to have been in con- junction with a fixed star at S, on the first degi'ee of Taurus, 342 year?^ before the birth of Christ, or about the 15th year of Alexander the Great ; then making 2,160 revolutions through the ocliptic, he will still be found at the end of so many sid^erecd years, again at S : but at the end of so many Julian years, he will be found at J, and at the end of so many tropical years, at T. in the 1st degree of Aries, which has receded hack from S to T in that time, by the precession of the equi- noctial points tyj and =^. The arc S T will be equal to the amount of the precession of the equinox in 2,160 years, at the rate of 50" of a de- gree, or 20 minutes 17^ seconds of time annually, as above calculated From the shifting of the equinoctial points, and with them all the signs of the ecliptic, it follows that the longitude of the stars must continually increase. Hence those stars which, in the infancy of astronomy, were in Aries, are now got into Taurus; those of Taurus inio Gemini, as may be seen by inspecting the celestial globe. Hence likewise it is that the star which rose cr set at any particular time of the year, in the times of Hesiod, Eudoxus, Virgil, Pliny, &;c. by no means answers at this time to their descriptions. By comparing the longitude of the same stars, at different limes, the motion of the equinoctial points, or the precession of the equinoxes may 1>M found. Hipparchus was the first person who obse^'ved this i .otion, by com- paring his own observations with those ^vhich Tiriioc'/aris made 165 />//. / . A'pin 'dou/s V /////,s //'//// //// o/ //i( ///ir-rrs/ J/ot V, F7V/.3. . M fV 7,y. O 4 0^ E flip's ejf 7^ i^^^x^:^^ i^^nr^ PRECESSION OF THE EaUINOX. l07 vears before. From this he judged the motion to be about 1° in about 100 years ; but he doubted wheLher the observations of Timocharls were sufficiently accurate. — In the year 128 before Christ he found the longitude of Virgin's Spike to be 5 signs 24<^, and in the year 1750 its longitude was found to be 6 s. 20^ 21'. In the same year he fbmid Iko longitude of the Lion's Heart to be 3 s. 29° 50', and in 1750, it was 4 s. 26° 21'. The mean of these gives 50". 4 in a year for the precession. By comparing the observations of Albategnius, in the year 878, Avith those made in 1738, the precession appears to be 51" 9'". — ^From a com- parison of fifteen observations of Tycho, with as many made by M. de la Caille, the precession was found to be about 50" 20"'. By proceeding to shift a whole degree every 72 years, and a whole sign every 2160 years, the equinoctial points will fall back through the whole of the 12 signs, and return to the same paints again in 25,920 years ; which number of years completes the grand ce- lestial period. From the creation to the year 1819, supposing it to be (4004 -j- ]8 3) .= 5823 years, the equinoittial points have receded 2 s. 20° 51' 54" CHAPTER XXXIX. TIi£ PRECESSION OF THE EQUINOX, CONTINUED. Having thus noticed the cause of the precession of the equinoctial points, which occasions a slow deviation £if the earth's axis from its parallelism, and thereby a change of the declination of the stars from the equator together with a slow apparent motion of the stars for »vard, with respect to the signs of the ecliptic, tho •phaenomena may be explained by a diagram. Let S O N A (fig 3, plate XVII.) be the axis of the earth produced to the starry heavens, and terminating in A, *be present north pole in the heavens ; E O Q 108 PRECESSION OF THE EQUINOX. the equator ; T S5 Z the tropic of Cancer, and V T V3 the tropic of Capricorn ; V O Z the ecliptic, and B 6 it& axis, both which are immoveable among the stars. But as the equinoctial points recede in the ecliptic, the earth's axis S O N is in motion upon the earth's centre O, in such a manner as to describe the cone N O w, and S O s, round the axis of the ecliptic B O, in the time the equinoctial points move round the ecliptic, which is 25,920 years. In that length of time the north pole of the earth's axis produced, describes the circle A B C D A. in the heavens, round the pole of the ecliptic, which keeps immoveable in the centre oi that circle. The earth's axis being 23|° inclined to the axis of the ecliptic, the circle A B C D A, described by the north pole of the earth's axis, produced to A, is 47° in diameter, or double the inclination of the earth's axis. In consequence of this motion, the point A, which is at present the north pole of the heavens, and near tf a star of the second magnitude in the tail of the con- stellation called the Little Bear^ must be deserted h} the earth's axis. And this axis moving backward 3 degree every 72 years, will be directed towards the star or point B in 6,480 years from this time ; and in twice that time, or 12,960 years, it will be directed towards the star or point C, which will then be the north pole of the heavens ; although it is at present S^" south of the zenith of London, L. Then the present positions of the equator and the tropics represented by the black lines, will be changed io those represented by the dotted lines. And the sun OBLIQUITY OF THE ECLIPTIC, ETC. 10i> which in the diagram is over Capricorn, and makes the shortest days and longest nights to the northern hesni- ■sphere will then be over Cancer, and make the days longest and nights shortest. It will then require 12,960 years more (or 25,92(i from this time) to bring the north pole back quite round to the present point : and then, and not till then, will the same stars which now describe the equator, tropics^ polar circles, &c. describe them again. CHAPTER XL. THE OBLIQUITY OF THE ECLIPTIC, ETC. It may not be amiss to mention the method used by astronomers to determine the obliquity of the ecliptic ; which is, by taking half the difference of the greatest and least meridian altitudes of the sun, Eratosthenes, 230 years before Christ, found o ' " the obliquity to be Ptolemy, 140 years after Christ Copernicus, in 1500 M. De la Lande, in 1768 Not to mention many others ; and from all these united observations, It is manifest that the obliquity of the ecliptic continually decreases. Comparing the numerous observations that have been made to ascertain the true obliquity, the mean of the several results gives about 50" in a century. '* We may therefore state," says Professor Vince, "• The secular diminution of the obliquity of the ecliptic, at this time, to be 50", as determined from the most ac- curate observations ; and this result agrees very wxlj with that deduced from theory." 23 51 20 23 51 10 23 28 24 23 28 110 MAGNITUDES OF THE PLANETS. CHAPTER XLL TO FIND THE PROPORTIONATE MAGNITUDES OF THE PLANETS. To find the proportion that any planet bears to the earth, or that one globe bears to another, the diameter of each must be cubed, and the greater number divided by the less : the quotient will show the proportion that one bears to another : for all spheres or globes are in •oroporiion to one another as the cubes of their diame- ters. The cube of any number is the product of that number multiplied tvjice into itself Thus, the cube of 2 is 8 ; for 2 multiplied by 2 makes 4, and 4 maltiplied again by 2 makes 8. — So the cube of 3 is 27; fc? 3X3X3rr:27. If the diameter of the sun, as some assert, be 893,522 miles : and of the earth 7,920 miles ; then the cube of 893,522 is 713371492260872648, and of 7,920 is 496793088000, and the greater number divided by the less will give 1435952, and so many times is the bulk of the sun greater than that of the earth. TO FIXD THE PLANETs' DISTANCE FROM THE SUN. By the transits of Venus (already explained, page lOl,") the distance of the earth from the sun has been found to be about 95,000,000 of miles ; and by know- ing the earth's distance, the distances of the other pla nets are calculated. Kepler, a great astronomer, discovered that all the planets are subject to one general law, which is, that tlie squares of their periodical times are proportional to the cubes of their distances from the sun. And thi3 i»w was fully demonstrated by Sir Isaac Newton. DISTANCES OF THE PLANETS. By their periodical times is meant the time they take in revolving round the sun : thus the periodical time of the earth is 3651 days ; thai of Venus, about 224i days ; that of Mercury nearly 88 days. Therefore, if we woula find the distance of Mercury fronn the sun, we say, as the square of 365 days is to the cube of 95,000,000, so is the square of 88 days to a fourth number, which will be the cube of its distance. And if the cube root of this number be extracted, the answer will be nearly 37,000,000 of miles Thus the square of 365=133225 ; the cube of 95=857375; and the square of 88=7744. Therefore, as 133225 is to 857375, so is 7744 ^ 49836, the cube of the mean distance of Mercury. And if the root of 49836 be extracted, it will be more than. 3G|,=the mean distance of Mercury from the sun in raiUions of miles. QUESTIONS rOR EXAMINATION IN ASYRGNOMIT, Chapter I. V^'hat is Astronomy ? — Of how many parts does it consist, and what nfc they? — What does descriptive Astronomy treat of?— And what rioes physical ? — What is a circle ? What is the cu-cumference sometimes termed ? What is the radius ? — What the diameter of a circle ? Name the proportion between the diameter and radius. What is an arc of a circle ? — What is a chord of a circle ?— Does a chord mcessanly dmde a circle into two unequal or equal parts ?— What is a semicircle ? By what other name is a semicircle sometimes called ? What is a quadrant i What is the quarter of the periphery of a circle sometimes termed ? Into how many parts are all circles supposed to be divided ? — ^How are degrees marked ? — How minutes and seconds ? — Mention the num- \)eT of degrees in a semicircle and in a quadrant. — ^What is an angle / — WTiich is the angular point ? — ^Which are the legs of a right-angled triangle 1 — What is a right angle ? — What is the measure of a right angle I — What is an acuie, what an obtuse angle ? — Define what are pa- riiilei lines. — ^What is a globe or sphere ? — What is a spheroid ? — What is a great circle of a sphere ? — What is a small circle of a sphere ?— What is the diameter of a sphere to any great circle termed ? — What ari> the extremities of the diameter called ? What distance is the pole of a great circle from every part of the dia- meter ? and for what rea^^on ?— Into what parts, and whether equal 3* not, do two great circles divide each other ? and why ? What is the axis of the earth ? Chapter IL Fully define the science of Astronomy. What IB the general opinion of Astronomers \^^th reeipect to the d.'! fereni systems cf the universe ? L 113 114 QUESTIONS FOR EXA3IINATI0N. What are the sun and moon termed ? — How are stars distinguished — ^Vhence do the planets receive their hght ? — What attendants have they ? — Is there any other order ? — ^What are the names of the planets, and which are tlie Asteroids ? — Wliat are these called, and how manj moons are there ? — To what planets do they belong ? The Sun. What IS the Sun ? — Wliat his form, diameter, and circumference T What is the sun's diameter equal to ? What is his distance from the earth ; and how much larger ? What was the sun formerly thought to be ? What does Dr. Herschel suppose the sun to be ? What can be seen on the sun's surface ? AVhat is meant by maculae and faculse ? What new opinion is formed respecting it ? How many motions has the sun, and what are they ? — What does the fcun's motion about its axis render it ? Chapter III. — Mercury. Name the smallest and nearest planet to the sun ? — What is his dia- meter, and in what time does he revolve about the sun ? — At what dia- tance, and at what rate doee he move in his orbit ? What proportion do the mean distances of Mercury and the esorth from the sun bear to each other ? What appearance has Mercury ? How will the sun's diameter appear, if viewed from Mercury, and how much greater is the light and heat he receives than that ol the parth ? In what maimer does he change liis phases ? How does this planet appear to us ? — How is it known that he does not shine by his ©wn light ? When the orbit of this planet is between that of the earth and the iun, what is it denominated ? When did the last transit of this planet happen, and when will the next! i Ve7iits. Wliat is the next nearest planet to the sun, and how is she distin- guished ? — What is her dii?tance from the sun ? — In what time does she complete her annual revolution ; and in what lier rotation about her axis? QUESTIONS FOU EXAMINATION. 115 VVi.al do astronomers make a complete rotation to be ? What is iier magnitude ; \\ hat her diameter, and at what mte doen she move in her orbit? — Is her quantity of Ught and heat greater than that of the earth ? — Wliat is her appearance as seen by the naked eye ; and what, when viewed through a telescope ? — ^What is Venus deno- minated when seen by us westward of the sun ; and what when east ward ? — Is there any difference in her seasons, and w^hy ? Does she always appear of the same size, and what do her vanations demonstrate ? Are there any ti-ansits of Venus, and how^ often do they occur ? AVhen was the last seen, and when will the next happen ? — Wliat have asti'onomers ascertained by this phenomena ? — ^Who was the first person that predicted tlie transit of Venus and Mercury ? — ^Vv^hen waa the first time Venus was ever seen upon the sun, and by whom? Chapter IV. — The Earth. Which is the third planet from the sun, what its mean distance, its diameter, and its circumference ? WTiat W'Ould be the appearance of the Earth from the planet Venus ? What are the Earth's motions ? — At what rate does it move in its or- bit? — In what time does it perform an entire revolution, and what does a complete rotation form ? What is the more exact time of its annual motion ? — By what is time d'vided? — On what does the former, and on w^hat does the latter de- pend ? What is the true form of the Earth ? What form was the Earth formerly supposed to be ? and what since proved to be ? Of what service is the earth to the moon, and of what size does she appear, viewed from the moon ? The Mo&fi, To what planet is the Moon a satellite ? — ^In what time does it re* voive in its orbit ? — What is the mean distance of the Moon from the tjarth, and at what rate does she move in her orbit ? — What is her dia- meter, and bulk ? — In what time is her rotation on her axis performed, and what the length of her day and night ? — How oflen does she re- volve round the earth in a year? — What is the length of her year ? — What are the phases of the Moon? — Whence does the Moon receive her light ? — Wliat enlightens that part of the Moon which is turned 116 QUESTIONS FOR EXAMINATION. from the sun ? — Has the Moon any diversity of seasons ? — What ao thf sliades which appear on the face of the Moon result from ? What were the forrner opinions respecting the mountains of the M'jon ? — What are the present ? — What else is observed in it ? — ^\\''herj can the irregularity of the Moon's surface be most distinctly seen ? When is the Moon invisible to us ? and what is her first appearance called 2 Which hemisphere of the Moon is never completely dark, and why ? — How long is the other hemisphere enlightened ? Is the moon thought to be inhabited? — What is supposed concerning seas in the Moon, or her atmosphere ? Chapter V. — Mars. Which is the next planet to the earth, and how is he known in tne heavens ? — What is his distance from the sun, and what the length of hi« year ? lEas the cause of his dusky red colour been ascertained? — At what rate does he move in his orbit ? — In what time is the diurnal motion of this planet performed ? — What is his diameter ? — What portion of light does he enjoy ? What is the mean distance of Mars from the sun, in regard to our earth ? How is the diurnal motion of Mars ascertained ? — Who first disu covered them, and what has been since determined from them ? How does Mars appear when viewed through a telescope ? — Has he any satellites ? How does he appear when opposite the sun ? and what does it prove ? — Is the earth or sun in the centre of his motion ? Asteroids. Have any planets been discovered between the orbits of Mars anil Jupiter ?-— W^hat are their names ? — Which is the nearest to Mars ?— What is its mean distance from the sun ? — How soon is its revolution through its orbit performed? — How many degrees does it incline to the ecliptic ? By whom was Vesta discovered, and when ? What is the mean distance of Ceres from the sun ? — What its time of revolution, its diameter, and Us inclination to the ecliptic ? By whom was Ceres discovered, and when ? What is the mean distance of Pallas from the sun I — What is the tima I Fu/. / f'^u/^ 'J. /'/// J s ^^ Mry v^ I^. S. ^4iP ^^;f'f/'> 2ig. 6 TTir^ J^ftrtTt 's Corvrexitv ■X UUESTIONS Foil EXAMINATION. 117 of its revolution ? — What its diurnal motion ? — ^How great is its inclina uon to the ecliptic ? — What is its diameter ? By whom was Pallas discovered, and when ? What is the mean distance of Juno from the sun, and what is its size ^ —In what time is its revolution round the sun performed I — What its diameter ?— What is the inclination of its axis to the ecliptic ? and whaJ does it appear like ? By whom was it discovered ? Chapter VI. — Jupiter. Between what planets does the orbit of Jupiter lie ? — What his mag- nitude ? and how is he distinguished ? — What is the distance of Jupiter imm the sun ? — What his mean distance from the sun ? — How much farther than the earth, and what proportion of light and heat does lie receive ? — What is the diameter of Jupiter, and how much larger is he rhan the earth ? — What proportion does his year bear to ours ? — In what time does he make his revolution round the sun, and at what fate does he move in his orbit? — In what time does Jupiter revolve on his axis ? —Does his equatorial exceed his polar diameter ? — Does his axis incline ♦o his orbit ? — What difference in his seasons ? and what variation in his days and nights ? — What is the length of his day and night ? — What appearance has he viewed through a telescope ? To what variations are his zones or belts subject, and what are they supposed to be ? — Are they supposed to adhere to the body of tlie planet ? Jwpiter^s Satellites. How many satellites has this planet ? — In what time does the nearest make a revolution ? — What the most distant ? — ^By whom were they first discovered ? — ^What were they first taken to be ? — What are the periodical times of the first, second, third, and fourth ? — To what pui pose have their eclipses been applied ? Chapter VIL — Saturn. Wliat was Saturn formerly thought to be ? — What is his appearance 1 ^What his mean distance from the sun ? — What light and heat haa he in proportion to the earth ? — What proportion does his light bear to that of our full moon ? — What is ihe diameter and magnitude of Sa turn? — In what time does ht^ perform his revolution in his orbit?- L 2 118 QUESTIONS FOR EXAMINATION. How many miles does he travel in an hour ? — In what time doesf h« revolve about his axis ? — Who ascertained it ? Satellites of Saturn. How many Satellites or moons is Satton encompassed witti ? — Oi what use are they supposed to be 1 — What distance is the nearest, and what is its breadth ? — Of what breadth is the outer ring ? — What is the space between them ? — What is it conjectured thay are composed of ?•— in what time does the ring revolve about the planet ? Chapter VIII. — Uranus, W\\\ch is the most remote planet yet discovered ? — What appearance has he to the naked eye ? "I'VTien can it be best perceived ? — Who discovered this planet, and when ? — Why is it named the Georgium Sidus ? — What is it called by astronomers ? — What other names does it bear? What is the distance of this planet from the sun? What is the distance given by some authors ? — What light and heat does he receive, compared with the earth ? In what time does he perform his annual revolution, and at what rate does he travel ? — What is his diameter ? Tlie HerscheVs Satellites, How many Satellites has Herschel ? In what time does the nearest perform his revolution ? and in what (he most remote ? Of what use are they supposed to be ? The Proportional Magnitude and Distance of Planets* How much larger is the Earth than Mercury, Venus, Mars, or Pal- !as ? — How much larger than the Earth is Jupiter, Saturn, and Her- dchel ? — ^How do astronomers express the mean distances of the planets ? —What distance from the sun may the different planets be estimateti ft( ?— -How a e the distances calculated ? Chapter IX. — Comet s> What are Comets thought to be ? and what direction do theii or bite lake? Are they supposed to be adapted to the habitation of animated be QUESTIONS FOR EXAMINATION. 1J9 ■Jfigs ? — Whence is the name of Comet derived ? — What are their tails supposed to be ? — When could it happen that the tail of a Comet couM come near our atmosphere ? — Of how many Comets were the periods thought to be distinctly known ? — When did the first appear ? w^hen the second ? and when the third ?— -What is the greatest distance of this Comet from the sun ? and what the least distance from the suni centre ? — At what rate does it travel ? How many miles in diameter was the head of the Comet of ISO*^ as cerlained to be, and what that of 1811 ? — Of what nature are Comets ? — What did .Sir Isaac Newton estimate the head of that Comei to be, seen by him in 1680 ? Whence are we authorized to conclude that Comets receive theii light? Of what do comets consist? — ^What is the nucleus, what the head and what the coma ? — How long was the tail of the Comet of 1807 a* certained to be, and how long that of 1811 1 — What its distance from the sun, and what from the earth ? Chapter X. — The Fixed Stars. What are the heavenly bodies beyond our system called ? What is it probable they are ? By what Hght do the fixed stars shine ? How much nearer are we to some stars at one time, than at another. What is the distance of Sirius, or the Dog-star, from us ?— In what time would a cannon ball reach us from that star ? Hovi' much farther from us than the sun is the nearest fixed star ?~ Have any been observed to revolve on their axis? What is it probable the fixed stars are ? — ^Into how many magnitude« are they usually classed ? — ^What are the largest called ? — ^What the smallest ? — How many are visible to the naked eye at one time ? What is the occasion of the stars appearing to iis innumerable ? Do not some of the fixed stars, when viewed through a telescope appear double or treble ? — Wliat are clusters of stars called ? — ^Which is the most remarkable of the clusters called nebulae ? — ^AVhat has Dr Herschel remarked concerning the Milky Way ? What is observed of the Magellanic clouds ? — Have not a greater number of stars been observed since the use of telescopes ? How are planets distinguished from fixed stars ? 120 QUESTIONS FOR EXAMINATION. What is thought to occasion the twinkling of the fixed stars ? Are all stars that were known to the ancients, now to be seen t- And are not some now seen that v/ere not noticed by them ? By whom is the most ancient observation of a new star? — Which the first we have any accurate account of? Havo not some stars alternately appeared and disappeared ? What have other stars been subject to ? What star was discovered in 1600 ? — What were i^s different appear- ances ? — ^What was discovered respecting 3 Lyrae ? What appearance has the heavens to a spectator in any part of the universe ? — What proof have we of this ? — ^If transplanted to a planei l)€ longing to Siriiis, how would that star and our sun appear to us? What is the vulgar error respecting the stars ? Chapter XI. — Constellations, Into what did the ancients form the stars? For what purpose were the constellations formed ? ^ What was the ancient, and what the present number of the constel- lations ? — By what are the heavens usually distinguished ? — ^What is the number of the constellations in the northern hemisphere ? — ^What hi the southern ? and what in the zodiac ? — What are the stars called not comprehended in these. — Name the northern constellations, aiKi the southern. — Repeat the zodiacal constellations. How are some par* ticular stars distinguished ?— liow are others denoted ? Chafper XII. — Different Systems. What is the system called which has been described ? — By whoin was it formerly taught ? — By whom revived ? — ^WTial did Ptolemy sup* pose ? What are epicycloids ? What system did the Egyptians receive ? — ^Who at length adopted ihe Pythagorean ? — ^IIow did Copernicus place the sun and planets ? — What system didTycho Brahe endeavour to establish ? — By whom was the solar system first taught ? — By whom revived ?— By whom tow firmed ? — And who at length fully estabhshed it ? aUESTlONS FOK EXAMINATION. 121 Chapter XIIL — On the Motions of the Planets. How would the planets appear to move if seen from the sun ? — How >lo they appear to move as seen from the earth ? Give some illustration of the motions of the planets. WTien is their motion direct ? — When retrograde ? — When sl&- uonary ? % Inferior and Superior Conjunctions of the Planets. What is a planet in its inferior conjunction ?— When in its superior? i — ^^Vhat planets have alternately a conjunction and an opposition ?-^ I jVnd when ? — In w^hich case do they rise and set nearly vdth the sun ? ' -When is it the reverse ? — Does the appearance of a planet vary if viewed through a telescope ? — When is Venus seen with nearly a fuli J face ? — ^When only half enlightened ? I When can Mercury and Venus be seen in their inferior conjunction ? I What planets do these appearances refer to ? CHArTER XIV. — The Plane of an Orbit, Planet^ Nodes, <^c. What circle does the earth describe as seen from the sun ? In what different signs do the earth and sun appear ? What is understood by the plane of a circle ? Give some, illustration. In what do the orbit of the earth and the ecliptic vary ? Give some illustration. Do the orbits of the planets vary from the ecliptic ? — ^What is meant by the obliquity of their orbits ?— Demonstrate it by the figure. — What is meant by the line of the nodes ? — What by the ascending, and whal by the descending node ? — What is really meant by the terms plaiie and orbit ? Transits of Mercury and Venus. Define by plate VHI. fig. 1, and by plate XIV. fig. 6, the transits of Venus or Mercury. — Are there great variations in the magnitude of Venus, as seen from the earth ? — Demonstrate this by the figure, plat6 Vn[I. fig. ]. — ^What is the least distance of Venus from the earth ?- What the greatest ? Explain the phases of Venus, in her orbit, by the figure. L22 QUESTIONS FOR EXA3I1NATI0N. Chapter XV. — The Ecliptic, Zodiac, Equator, QUESTIONS FOR EXAMINATION- 123 gitude of a heavenly body usually expressed ? — Wliich of the colunms Bpeakof the rising or setting of a planet ? — Why not of both ? Chapter XVI. What is a degree ? — What is the measure of an angle ? Explain this by fig. 3, plate IX. \\Tiat are the poles ? — What parts of the heavens appear motionleas t — And wl\at part appears to have the greatest motion ?— Wiat are tht5 rn>pics? — What their distances Irom the equator ? — What are the polar cirtdes ? — What their distance from the poles ? Why is the distance of the polar circles fixed at that number of de- grees from the poles ? Why are the meridians so called ? — How many meridians arc usually drawn on the globes, and why ? — Are these ail that can be re- presented ? Explain this by fig. 3, plate IX. ^Vhat is meant by longitude ? — ^Through what place does the first meridian pass? — How many degrees are equal to an hour? — What places are before London, in time, and what afierl — How do you re- duce longitude to time ? Give the reason why 15 degrees are equal to an hour; and 30 de- grees to two hours, &c. — If 12 o'clock at London, what are the times at R'lrbadoes, at St. Petersburgh, and at Calcutta. How is time turned into longitude ? — What is meant by the latitude of a place ? — What by the latitude of a heavenly body? — What are the t-oiures ? — How many zones are there, and what are they? — ^What are the solstitial points ? And why so called ?— -What are the equinoctial points ? And why so called ? Chapter XVIL — Planets' orbits EUipticaL What are the orbits of the planets termed ? — Illustrate this by figun?* % 3, and 5, of plate Vll I. — When is a planet said to be in its perihtlion, and when in its aphelum ? — And when at its middle or mean distance t —What is termed the eccentricity of its orbit ? Attraction of Gravitation. Wliat is meant by attraction ? What is attraction of magnetism ? — What attrdfction of electricity f V\*hat of cohesion ? 124 aXTESTIONS FOR EXAMINATION. What is attraction of gravitation? In what proportion is ihLs attrac tion ? — By what kind of attraction does the sun affect the eanh, and the earth the moon ? Upon what principle does the stone fall to the earth — ^and the watem of the ocean gravitate, &c. Repeat one of the laws of attraction. — Illustrate this by the figures 4 and 5 of plate X. — What is the second law of gravity ? — Do equal mag nitudes imply equal quantities of matter? — ^With what proportion doca the sun attract the earth ? And why ? — Explain this otherwise, by boata oi" equal bulk. Chapter XVIII. — Of Attractive and Projectile Forces. Wliat power counteracts that of attraction ? — What would be the ef- fect of rectilineal motion ? — Of what are the planets' motions com pounded ? Explain this by some projectile force.— WTiat, if a ball be thrown fron^ tfie hand ? What united forces retain the planets in their orbits ? Explain the difference of a circular motion and a straight line. — Giv^ a further explanation by the figure 4, plate VIII. What results from the two forces being equal ? Wliat would result if either power were to cease acting ? By what laws are the secondary planets governed ? — Why are th* planets' orbits not true circles ? Explain by the figure, what is meant by equal portions in c^'i*^^ ♦^m^ —And by unequal portions in equal times. What power wdll a double velocity balance ? — Demonstrate this b} the figure. — What is meant by equal areas in equal times ? — What re suits from the comets' orbits being so very elliptical ? Suppose a body to receive two different impulses, what wauld be ite direction ? — Epxlain this by the figure. Chapter XIX. — The Centre of Gravtti/. Wliat la the centre of gravity? — Explain this by figure 6, plate X. If the earth were the only attendant on the sun, what motion would the sun have ? ^ What, if all the planets were on the same side of him I — Are the 8» QUESTIONS FOR EXAMINATION. 125 eondaries governed by the same laws? — ^Wliat is supposed of every system in the universe ? The Horizon. What is the horizon ? — ^To what does the rational horizon apply ^ Explain this by fig. 2, plate IV. How is this horizon represented on the artificial globe ? What does the sensible horizon respect ? — How is its extent varied ? Refer to the figure. — ^What is the extent of view, to an eye elevated five feet ? And to one elevated twenty feet ? — How do you mark the difference of the two horizons ? Why do persons oa the sensible honzon see the heavenly bodies when an the rational ? What proportion Ao^ the earth's semi-diameter bear to the sun's dis- tance?^ — And what is the result? — ^What proportion does the earth's setni-diameter bear to the moon's distance. Chapter XX. — Day and Night, What is the cause of the succession of day and night ? — Illustrate this by fig. 2, plate IV How much of a sphere does the sun illumine at one time ? — ^How much of the heavens can a spectator behold atone lime ? Explain the apparent motion of the heavenly bodies, by some fami- liar motions on our earth. How are the apparent motions of the whole starry firmament ao wonted for ? ^Vhat results from the earth's motion to persons in the latitude of London? — What, to those on the equator? ¥/hat points in the heavens keep the same positions ? — ^Why are stars rio& seen by day? — ^How many revolutions on its axis does the earfii make in a year ? — Why are we not sensible of the earth's daily motion What proof have we of other motion not being perceptible ? Chapter. XXL — The Atmosphere. What is the atmosphere ? — What does it possess t — Where is it moft epse ? And where more rare ? What does the whole mass of atmosphere contain f M 126 QUESTIONS FOR EXAMINATION. To what purposes does it serve ? — Of what appearances is it the cause What do experiments on the air-pump prove ? Without an atmosphere how would the sky appear? — ^Towhatheighi does the atmosphere extend ? — At what height does it cease to reflect the rays of hght ? — What results from the sun's rays falling upon the atmosphere before he rises ? And after he sets ? When does twilight begin ? — ^When does it end ? Chapter XXII. — Refraction. When do the rays of light deviate from a rectilineal course? — From this cause what results ? — \^Tiat is the apparent elevation called ? Demonstrate this by fig. 1, plate XL What is the consequence of this refraction ? — How much longer doeh the sun appear by this refraction ? — Explain this by the figure. How can you show the effects of refraction ? — ^Have you not another way of demonstrating it ? Chapter XXIIL — Parallax. "What is the parallax of the sun or moon ? Which is called its apparent, and which its true place ? When IS the parallax the greatest ? — And what is that parallax called ? W^at is the sun's mean parallax ? Why seldom made use of? And lor what purpose ? — Have the fixed stars any parallax ? Does the parallax of the sun or moon depress or elevate them? Ho'.v must their true altitudes be obtained ? — Illustrate this by fig. 2, plato XI.— Does distance cause the parallax to be greater or less ( — ^Where has any object its greatest and where its least parallax? -When is tli« parallax nothing ? — ^Explain this by the figure. Chapter XXIV. — Equation of Time. How much longer is the summer than the winter half year? — ^By what occasioned ? — Of what is this inequality the cause ? — ^VVhat keeps rrue time ? — And what apparent time ? — What is the difference of the^ termed? Equal time, how measured ? — and apparent time, how? Upon what does this diflerence depend ? — What motion is flie most QUESTIONS FOK EXAMINATION, 127 equable in nature ? — In what time is the earth's rotation completed ? What is this space called ? And why ? li'the earth had only a diurnal motion, what would be the length of (fie da^^ ? What is a solar or natural day? — By what is tliis difference oo casioned ? Will the hands of a clock convey any idea of this? How often are the ecliptic and zodiac coincident? — And when?— Why do they differ at other times? Explain this by the globe. — Refer also to figure 2. — What do the marks on the ecliptic represent ? — And what those on the equator ? In what quarters will the sun he faster y and in what slower than the clocks? And why? — ^Will not the elliptic forai of the earth's orbit oc- casion a variation ? What, if the differences depended solely on the inclination of the earth's axis ? — Refer to an Ephemeris for the times of the clock and dials coinciding, and say on what days. If the earth's motions in its orbit were uniform, what would result ?— What is the earth's daily course in winter, what in summer ? — From this cause, what variations are there in the natural day ? And why ? — What then are the combined causes of the inequalities of time ? Chapter XXV. — The Seasons. What IS the inclination of the axis of the earth ? — Explain this by the •plate. — What is observed of the axis of the earth ? Illustrate the earth's parallelism. WHiat is the diameter of the earth's orbit ? — To what does the axis of the earth always point, and hov/ do you account for it ? Can you illustrate this by something familiar ? WTiat proof is deduced from this ? How is the earth's course round the sun proved ? Can these observations be made in the day ? Upon what does the variety of the seasons depend ? — What, if tii6 axis of the earth were, as in the figure, perpendicular to the sun's nws Why must the poles be excepted ? What would result from such a position ? On what does the proportion of heat materially depend ? Explain it by the figure. Represent by figure 2, plate X, the position of the earth in »iii sum' wer season 128 QUESTIONS FOR EXAMINATION. Wliat is evident from the circle in the latitude of London ? — What k then the appearance at each pole ? What is observed of places in equal latiiades^ the one north, the othei south? Chapter XXVI. — Seasons, continued* What is represented by fig. 2, plate XII. ? How much nearer are w^e to the sun in December than in June *► What is the sim's apparent diameter in w^inter ? — What in summei ? What is the time we denominate our summer ? — How much longe than our winter half-year ? — ^What inference is consequent ? Whence does the coldness of our winters arise ? — When are the ?iot test and when the coldest seasons ? In June, what pole inclines to the sun ? And what results there- from? — In December what pole inclines to the sun? And where is ii then winter ? — In March and September what position has the axis ? — What lengtli are the days and nights ? In March, what is the real place of the earth? — In what sign will the 6un then appear? — On the 21st of June, where is the sun vertical? — Where in September ? — ^Where in December ? Wliat causes produce the increase and decrease of days and nights? — ^To what parts is the sun vertical, from 20th March to 21st June ? — And from June to September? To what parts is the sun vertical from 23d September to 21st De cember? — And irom December to March? — How often is the sun ver lical to ever}' part, between the tropics ? Chapter XXVIL — The Moon's Months, Phases. What kind of months are they ? — And what is the length of each ?— Wlieuce arises the difference ? Explain this by the figure. — Is the moon's orbit a circle, or an el- bpsis? How much of the moon is at one time enlightened ? — Do we alwa}^ see the whole enlightened side ? Refer agam to the figure. What is the moon's position at change ? — What, at full moon ? — What, when changed ? And wnat is the moon then said to be in ? — What, wbe « three-fburfns are sieen ? — ^What, when wholly enlightened ? rcuje 129. Plau IP. QrESTIONS FOR EXAMINATION. 129 in what directions are the horns just after the change ? — What, altei tbe full moon ? — Represent the moon's phases by a ball, or small globa Wliat is the m'>on's apparent motion ? — What the real motion ? By what may the moons real motion be known? 1 Chapter XXVIIL — Eclipses — Fi7'st, of the Moon. Wliat does the term eciipse imply ? — By what is an eclipse of the moon occasioned ? — When must an eclipse of the moon happen? — Re-, fer to the plate. — What would result if the moon's orbit coincided wilK Ae ecliptic ? How much does the orbit of the moon var;' from the ecliptic ? What is the greatest distance from the node, at which an echpse ot the moon can happen ? — When an eclipse happens full in the node, w^hat is it called? — What is the duration of an eclipse ? — Of whatshapa IS the earth's shadow? — Does not the moon's distance from the eaith vary ? How does the moon's being either nearer or more distant, affect the lengtJi of an eclipse? On which side of the moon does an eclipse begin, and on which sid« end? How may this be clearly conceived ? How are eclipses calculated ? Of what form is the earth's shadow ? — What does that aemonstrate ? — How is the sun proved to be larger than the earth ? — If the two bodies were equal, of what shape would be the shadow ? — And if the earth were the larger body, of what shape would be the shadow ? Eclipse of the Sun. When does an eclipse of the sun happen ?— Explam it by the figure. Illustrate it by a suspended ball or globe. If the whole of the sun be obscured, what is the eclipse teraied? — What, if only apart? What does the word digit mean ? When, only, can the moon cover the sun's whole disc ? — Within how many degrees of the node can an eclipse happen? — At all other new moons, how does she pass ? — And how at all other full moons ? — If an eclipse of the moon be central, what results? — And what, if an eclipse of the sun hv central? — What are annular eclipses? — By what occa- sioned ? — ^When only can an eclipse of the sun be to^td ? — ^How long M 2 130 QUESTIONS FOR EXAMINATION. may total darkness last? — How many soiar eclipses m a yeai musi there be ? — What is the least number there may be ? — What is the Least, and what the greatest number of lunar eclipses ? — How many ecUpse^ may happen in a year? — In this case, how many of each ? — What is the mean number of eclipses? — Why are there more solar than lunar eclipses? — And in what proportion?— Why, then, are more lunar thac ioiar eclipses seen ? Chapter XXIX, — Polar Day and Night. How are the long days and nights around the poles accounted for ?— How, when the sun is on the equator ? — How, when vertical to the tropic of Cancer ? — What is the extent of the sun's rays ? — Wliat the length of each day and night ? — And why ? Wliat benefit haA^e the polar regions from the twilight ? — How Iqng does the moon continue m their horizon ? — Explain the reason. — \Vhat third benefit do they receive? — How does the moon's track vary firom the sun's course ? When the sun is in the equator, in what point does he rise? — How, during the summer half-year ? — How during the winter half-year? Whence arises a small variation between the rising and setlinsr ?- Explam this by the globe. Chapter XXX. — Umbra and Penumbra. Explain the meaning of Umbra and Penumbra by the figure ? Which parts will suffer a total eclipse, and which a partial ? — How does the umbra fall in an annular eclipse? — And what will then be its appear- ance ? — Which parts of the earth will have a partial eclipse? — And to what parts no eclipse. How long can the annular appearance remain ? — What is the moon's mean motion? — How many miles does it answer to? — What will be the relative velocity of the moon's shadow? — ^What affects the length of a solar echpse ? Explain the different eclipses by the figure, in the 1st, 2d, and 3d po Bitions. What were the effects of a total eclipse of the sun according to Cap. tain Starmyan ? — What is Dr. Scheuchzer's accoimt ? — Relate Dr. Hai- wcy's description. aUESTIONS FOR EXAMINATION. 131 Chapter XXXI. — Transits of Venus. Illustrate a transit of Venus, by the figure. — During which conjunc- tioa does the transit take place ? — ^Vhat is the principal use to whicn astronomers apply the transits of Venus ? To what other purposes are the transits applied ^ — ^Which take place the oftener, the transits of Mercury or Venus? — And which are of the gr 3ater utility ? What is meant by the occultation of the fixed stars ? — By what me- thods are occultalions ascertained ? — ^What has Cassini remarked with respect to them ? What is meant by conjunction ? — What by latitude ? What computations are needful to determine when an occultation will happen ? Wui the appearance be different at different places upon the eart> ? — From what cause will the difference result ? — To what extent mav th^ moon's parallax affect the obscuration ? Chapter XXXIL — The Harvest Moon. How much later does the moon often nse, one day than anoth*ir ?— - Is there any difference in different latitudes ? — What is her difference in rising about the time of harvest? What is the difference to those who live in the latitude of London \ How does the autumnal full moon rise in considerable latitudes ? — Why called the Harvest Moon ? By whom were these first observed? — And to what ascribed ?— At what intervals of time does the moon rise about the equator ? — When. at the polar circles ? — How long does the moon shine within the polai circles without setting? — To what are these phenomena owing?— Wha,t is remarked of the signs Pisces and Aries ? — What difference is there in the moon's rising when in these signs ? — How do those signs af the ecliptic set, which rise with the smallest angles? Illustrate this by the figure — demonstrate it by the globe. What part of the ecliptic makes the smallest angles, in northern lati tudes ?— What, the greatest? — What angle is made by Pisces and Anes wtien rising ? — ^What angle, when setting ? — What is the moon's diffei* ence of rising when in Libra ? Demonstrate these phaenomenaon the glabe. 132 QUESTIONS FOR EXAMINATION. Why IS the moon at the full when in Pisces and Aries only in our autumnal months ?-^Whatare the two autumnal full moons called? Chapter XXXIII. — Harvest Moon continued. How often does it happen that the moon rises, for a week together, BO nearly in point of time ? What time of the day do Pisces and Aries rise in winter ? — And what IS then the moon's age ? — How do these signs rise in spring ? — And what then the moon's age ? — ^When do Pisces and Aries rise in summer? — ^What is then the moon's age ? — Why is her rising then so imob- served ? In what time does the moon go through the ecliptic ? — ^What is the time from change to change? — What results therefrom? If the earth had no annual motion, how would every new and fuU moon fall ? — And w^hy ? — ^How many degrees does the earth move du- ' ring one imiation ? — How does this affect the moon's conjunction, &c. ? — If in any conjunction she were in at the first degree of Aries, where would her next conjunction be ? — ^Why is the moon twice in some one degree every lunation ? How must the north and south poles appear to the inhabitants on tlie equator? — What angle does the ecliptic make to such ? — And what re- sults therefrom ? — AVhy have they no Harvest Moon at the equator?— WTiat effect has distance from the equator upon the rising of Pisces and Aries? Illustrate this by the globe. In what signs do the autumnal full moons happen to those in southern latitudes ? — With what angles do Virgo and Libra rise ? — What, w^th respect to hai vest moons in southern latitudes ? What circumstance may cause some small difference in the time of the moon's rising or setting ? — How much does the moon, at times, vary from the ecliptic ? To what part of the earth does the full moon not rise in summer ? — To what part does she not set in winter? — Explain the cause of this satisfactorily. Chapter XXXIV. — Leafp Year. What is the time we call a year ? — What has been the usual division * What were the ancient Hebrew months? — What the extent of tl eii atJESTIONS FOR EXAMINATION. 133 year ? — Of how many days did the Athenian months consist ? and by whom regulated ? — How did Meton attempt to reconcile the difference I — How many months composed the year in the time of Romulus? — What addition was made to them by N uma Pompilius ? — What was the length of the Egyptian year? Who first attained to tolerable accuracy ? — How did Julius Cassai regulate the months ? — How allow for the six odd hours ? — ^What was every fourth year denominated ? — ^And what is it now called ? What day did the Romans reckon twice ? — And what was such iii- tercalary day called ? — What day do we now add in leap-year? How is it ascertained Avhat years are, and what are not leap-years ?— Mention what year will and what will not be leap-years. — ^What is the length of the true solar year? — How much does 365 days 6 hours ex- ceed the true solar year ? — In how many years does it amount to a whole day ? — How long did the Julian year continue in use ? — Who reformed the calendar ? And how ? — ^How denominated ? — In what year did we adopt the new style into our calendars ? — And by what change m the days ? — Why were the years 1800 and 1900 computed as com- mon years ? — And why, every four hundredth year afterwards? What will result from this method of reckoning ? From what day w^as the beginning of the year changed? — ^How, fbi a time, did it affect the dates ? CHAFrER XXXY.—The Tides Describe the fluctuations of the ocean. What were the ancients' ideas of the tides ? — Who made some suc- cessful advances ? — And who clearly pointed out the cause ? What is the true cause of the flowing of the tides? How is the moon proved to be the cause of the tides ? What would be the appearance, if there were no influence from the %un or moon ? — What, if the earth and moon were without motion ? — What proportion does the sun's attraction bear to that of the moon? — When the moon is at change, how many parts are raised ? — If it be high water at A, fig. 4, plate XVI. what effect will it produce at C and D ? What is the attractive power of the sun and moon according to some authorities ? Explain the cause of low water at C and D. Of what form will the waters partake at full and change ? 134 QUESTIONS FOR EXAMINATION. Chapter XXXVI. — The Tides, continued. In what proportion does the power of gravity diminish ? — When there is a tide, as at A, fig. 4, plate XVI. what occasions a similar tide at B ? — From what cause will two tides be produced each day ? How has it been otherwise explained ? How often does the tide ebb and flow in twenty-four hcfurs ? — WTiai IS the interval between the flux and reflux ?— \^'Tiat is the daily varia- tion as to the time of high water ? Give an example or two. How are the tides affected at \hefuU of the moon ? — Explain this by %. 6, plate XVI. If there were no moon, how would the sun affect the tides ? — When do the highest tides happen ? — What are such tides called ?— When the moon is in her quarters, what are the influences of the sun and moon \ — ^What are such tides called ? Chapter XXXVII. — The Tides, continued. Why are the tides higher at some seasons than at others ? — ^How long is it, in open seas, after the moon passes the meridian, that the tides are at the highest ? — And why ? Illustrate this by an impulse given to a moving bali— and by the time of the greatest heat of the day — and by the increasing heat in July and August Why do not the tides always answer to the moon's uj6tance from the meridian ? — When will the greatest spring-tide happen? And why ? — VThy d^ t^^ ii^QB rise higher in channels and rivers ? To what may the tides, in the mouths of rivers, be compared ? What retards the tides in shoals and channels? — And how much are they retarded ? How long does the tide take to come to London bridge ? Have lakes any tides 1 — What seas have but small elevations ^ Give me the reason. Are there tides in the air ? How long af^er the new and full moons do the greatest spring-tides happen ? — And how long after the first and third quarters do the least neap-tides happen ? — Are the tides unequal at places remote from the fc q uator ? Where is this inequality observed ?— What has been remarJ.ed of the morning and the evening tides? QUESTIONS FOR EXAMINATION. 135 What results, when the moon's greatest elevation points to one side of the equator? Wlien and where is the inequality the greatest ?- -What is observed of the moon when she has declination ? Chapter XXXVIIL — The Precession of the Equinox » What results from the earth's motion on its axis ? — What arises from ihe attraction of the sun and moon ? — ^If the sun sets out from any star, m what time v^l he reLurn to it ? — And why? How do you prove that 20 minutes, 17^ seconds of time are equal te 50" of a degree ? — ^Wliat is the sun's apparent annual motion ? When does the sun finish the tropical year ? — And what does a tro- pical year contain ? — When does he complete his sidereal year ? — And what does it contain ? — How much longer is the sidereal year than the solar or tropical? — And than the Julian or civil year ? Are the lengths of the sidereal and solar years the same as given by another author? What is the sun's daily mean rate in a tropical }''ear ? — ^When will be arrive at the same equinox? — How long will the sun and equinoctial pomts be in failing back 30° ? — ^What will be the apparent effect upon the fixed stars ? How do you prove that 50" short in one year, are equal to a whole feign m 2160 years ?— Explain it by fig. 1, plate XVII. What results from the shifting of the equinoctial points?— What change has taken place since the infancy of astronomy ? How is the motion of the equinoctial points, or the precession of tho equinoxes, found? — ^Who first observed this motion? — And by wha means ? — With whom did Hipparchus compare his observations ? How mai>y years is the equinox in shifting a whole degree ? — How long for a whole sign ? — ^What number of years completes the grand How much have the equinoctial points receded since the creation ? Chapters XXXIX and XL. — Precession of the Eqvi» nox, continued. Explain the phasnomena by fig. 3, plate XVII. Mow do astronomers determine the obliquity of the ecliptic t^ 136 QT7ESTT0NS TOR EXAMINATION. What did Eratosthenes, Ptolemy, Cope^-^icus, and M. De la Lando find the obliquity to be ? — From these observations what its deduced ? What is the secular diminution of the ecliptic at this time ? Give a full illustration of the precession of the equinox by the tour small spheres, Plate XVII, — What does the sphere marked ' exhibit ?— What, the sphere 2?— What, the sphere 3?— What, lie sphere 4 ? ' Chapter XLI. — Proportionate Magnitudes of the Planets. How is the proportion that one planet bears to another found ? — Repeat the general law, All spheres, (J-c. What is the cube of any number ? — Demonstrate this by the cubes of 2 and 3. Cuh^ the numbers 893522, and 7920. — Divide the greater by the less. To find the Planets,^ Distances from the Sun, How is the earth's distance from the sun found? — What is its distance ? — What other calculations can be made from it ? — What general law did Kepler discover? — By whom was this law fully demonstrated? What is meant by their periodical times ? — Give instances of ^wo or three. How do we find the distance of Mercury from the sun ? — Square 365.— -Cube 95,000,000.--Square 86.— State the question, and C^rform the operation. NEW TREATISE USE OF THE GLOBES^ DESIGNED POa THE INSTRUCTION OF YOUTfL t'WnnWt PROM TEE UJSaEE WORK 07 VHOMAS KEITH. CONTENTS. CHAPTER i. lines on the Artificial Globes, Astronomical Definitions. Ac CHAFfER II. Problems performed ^^^th the Terrestrial Globe . . . CHAPTER in sVobiems performed with the Celestial Globe A NEW TREATISE ON THE USE OF THE GLOBES. CHAPTER I. Explanation of the lines on the Artificial Globes^ in- eluding Geographical and Astronomical Definitions ^ mth a few Geographical Theorems. 1 The Terrestrial Globe is an artificial repre- sentatioD of the earth. On this globe the four quar- ters of the world, the different empires, kingdoms and countries; the chief cities, seas, rivers, &;c. are truly represented, according to their relative situation on the real globe of the earth. The diurnal motion of this globe is from vvest to east. 2. The Celestial Globe is an artificial represen- tation of the heavens, on which the stars are laid down in their natural situations. The diurnal motion of this globe is from east to west, and represents the ap- parent diurnal motion of the sun, moon and stars. In using this globe, the student is supposed to be situated j[i the centre of it, and viewing the stars in the con* ,ave surface. A 2 N 2 5 DEFINITIONS, &;C. 3. The Axis of the Earth is an imaginary line passing through the centre of it, upon which it is sup- posed to turn, and about which all the heavenly bodies appear to have a diurnal revolution. This line is rep- resented by the wire which passes from north to south, through the middle of the artificial globe. 4. The Poles of the Earth are the two extremities of the axis, where it is supposed to cut the surface of the earth, one of v*^hich is called the north, or arctic pole ; the other the south or antarctic pole. The ce- lestial poles are tvt^o imaginary points in the heavens, exactly above the terrestrial poles. 5. The Brazen Meridian is the circle in which the artificial globe turns, and is divided into 360 equal parts, called degrees. In the upper semicircle of the brass meridian these degrees are numbered from to 90, from the equator towards the poles, and are used for finding the latitudes of places. On the lower semi- circle of the bras? meridian they are numbered from to 90 , from the poles towards the equator, and are used in the elevation of the poles. 6. Great Circles divide the globe into two equal parts, as the equator, ecliptic, and the colures. 7. Small Circles divide the globe into two unequal parts, as the tropics, polar circles, parallels of latitude, 6z;c. 6. Meridians, or Lines of Longitude, are semicir- cles^ extending from the north to the iouth pole, and cutting the equator at right angles. Every place upon the globe is supposed to have a meridian passing through li^ though there be only 24 drawn upon the terrestrial DEFINITIONS, &;C. 7 globe ; the deficiency is supplied by the brass meri- dian. When tne sun conies to the meridian of any place (not within the polar circles,) it is noon or mid- day at that place. 9. The First Meridian is that from v/hich geogra- phers begin to count the longitudes of places. In Eng- lish maps and globes the first meridian is a semicircle supposed to pass through London, or the royal obser- vatory at Greenwich. 10. The EauATOR is a great circle of the earth, equi- distant from the poles, and divides the globe into two hemispheres, northern and southern. The latitudes of places are counted from the equator, northward and southward, and the longitude of places are reckoned upon it, eastward and westward. The equator, when referred to the heavens, is called the equinoctial; because when the sun appears in it, the days and nights are equal all over the world, viz. 12 hours each. The declinations of the sun, stars and planets, are counted from the equinoctial northward and southward, and their right ascensions are reckoned uyon it eastward round the celestial globe from to 360 degrees. 11. The Ecliptic is a great circle in which the sun makes his apparent annual progress among the fixed stars ; or it is the real path of the earth round the sun. and cuts the equinoctial in an angle of 23° 28' ; the points of intersection are called the equinocaal points. The ecliptic is situated in the middle of the zodiac. 12. The Zodiac, on the celestial globe, is a space which extends about eight degrees on each side of th« DEFINITIOiSS, &C. ecliptic, like a belt or girdle, within which the motion of all the planets^ are performed. 13. Signs of the Zodiac. The ecliptic and zo- diac are divided into 12 equal parts, called signs, each containing 30 degrees. The sun makes his apparent annual progress through the ecliptic, at the rate of nearly a degree in a day. The names of the signs, and the days on which the sun enters them, are as fol- low : Spring Signs. HP Ariesy the E.am, 21st of March. 6 Taurus, the Bull, 19th of April. n Gemini, the Twins, 20th of May. Summer Signs. 2d Cancer, the Crab, 21st of June. SI Leo, the Lion, 22d of July. W Virgo, the Virgin, 22d of August. These are called northern signs, being north of the equinoctial. Autumnal Signs. -^ Libra, the Balance, 23d of September. ni Scorpio, the Scor- pion, 23d of October. {: Sagittarius, the Ar- cher, 22d of No- vember. These are called southern signs. The spring and winter signs are called ascending ?igns ; because when the sun is in any of these, h*'' * Except the new discovered planets, or asteroids, Ceres, FaUas, anc Juno. Winter Signs. Y^ Capricornus, the Goat, 21st December. OO- Aquarius, the Water- bearer, 20th of January, X Pisces, the Fishes, 19th February. DEFINITIONS, &C, 9 IS ascending towards our pole. The summer and au- tumn signs are called descending signs, because when the sun is in any of these, he is descending or rece- ding from our pole. 14. The CoLURES are two great circles passing through the poles of the world ; one of them passes through the equinoctial points, Aries and Libra ; the other through the solstitial points. Cancer and Capri- corn ; hence they are called the equinoctial and solsti- tial colures. They divide the ecliptic into four equal parts, and mark the four seasons of the year, 15. Declination of the sun, of a star, or planet, is Its distance from the equinoctial, northward or south- ward. When the sun is in the equinoctial he has no declination, and enlightens half the globe from pole to pole. As he increases in north declination he gradu- ally shines farther over the north pole, and leaves the south pole in darkness : in a similar manner, v/hen he *ias south declination, he shines over the south pole, and leaves the north pole in darkness. The greatest declination the sun can have is 23° 28' : the greatest declination a star can have is 90"^, and that of a planet 30° 28'* north or south. 16. The Tropics are two small circles, parallel to the equator (^or equinoctial,) at the distance of 23° 28' om it ; the northern is called the tropic of Cancer, •he southern the tropic of Capricorn. The tropics are the limits of the torrid zone, northward and southward 17. The Polar Circles are two small circles, paral * Except the planets, or asteroids, Ceres, Pallas, and Juno, which ate nearly at the same distance from the sun ; the former, in April 1802, was out of the zodiac, its latitude being 15° 20' N. 10 DEFINITIONS, diC. lei to the equator (or equinoctial,) at the distance of 66^ 32' from it, and 23'" 28' from the poles. The northern is called the arctic^ the southern the antarctic circle. 18. Parallels of Latitude are small circles drawn through every ten degrees of latitude, on the terres- trial globe, parallel to the equator. Every place on the globe is supposed to have a parallel of latitude drawn through it, though there are generally only sixteen parallels of latitude drawn on the terrestrial globe. 19. The Hour Circle on the artificial globes is a small circle of brass, with an index or pointer fixed to the north pole ; it is divided into 24 equal parts, cor- responding to the hours of the day, and these are again subdivided into halves and quarters. The hour circle when placed under the brass meridian, is moveable round the axis of the globe, and the brass meridian, in this case, answers the purpose of an index. 20. The Horizon is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars. Horizon, when applied to the earth, is either sensible or rational, 21. The Sensible, or visible horizon, is the circle which bounds our view, where the sky appears to touch the earth or sea. 22. The Rational, or true horizon, is an imaginary line passing through the centre of the earth parallel to the sensible horizon. It determines the rising and setting of the sun, stars, and planets. 23. The Wooden Horizon, circumscribing the ar* DEFINITIONS, &;C. 11 tificial globe, represents the rational horizon on the real globe. This horizon is divided into several concentric circles, which on Bardin^s New British Globes are ar ranged in the following order : TJte First is marked amplitude, and is numbered from the east towards the north and south, from tn 90 degrees, and from the west towards the north and south in the same manner. The Second is marked azimuth, and is numbt 'ed Tom the north point of the horizon towards the east and west, from to 90 degrees : and from the south point of the horizon towards the east and west in the same manner. The Thii'd contains the 32 points of the compass, divided into half and quarter points. The degrees in each point are to be found in the amplitude circle. The Fourth contains the twelve signs of the zodiac, with the figure and character of each sign. The Fifth contains the degrees of the signs, each sign comprehending 30 degrees. The Sixth contains the days of the month answering to each degree of the sun's place in the ecliptic. The Seventh contains the equation of time, or diifer- ence of time shown by a well-regulated clock and a correct sun-dial. When the clock ought to be fastoi than the dial, the number of minutes, expressing i\w. difference, is followed by the sign + ; when the clock or watch ought to be slower, the number of minutes ia the difference is followed by the sign — . The Eighth contains the twol'^'^ '•^^lendar months. 12 DEFINITIONS, 6lC» 24. The Cardinal Points of the horizon are east, west, north, and south. 25. The Cakdinal Points in the heavens are the zenith, the nadir, and the points where the sun rises and sets. 26. The Cardinal Points of the ecliptic are the equinoctial and solstitial points, which mark out the four seasons of the year ; and the Cardinal Signs are T Aries, s Cancer, =^ Lihra, and Y5 Capricorn. 27. The Zenith is a point in the heavens exactly over our heads, and is the elevated pole of our horizon 28. The Nadir is a point in the heavens exactly under our feet, being the depressed pole of our horizon, and the zenith, or elevated pole, of the horizon of our antipodes. 29. The Pole of any circle is a point on the surface of the globe, 90 degrees distant from every part of thai circle of which it is the pole. Thus the poles of the earth are 90 degrees from every part of the equator ; the poles of the ecliptic (on the celestial globe) are 90 degrees from every part of the ecliptic, and 23*^ 28' from the poles of the equinoctial ; consequently they are situated in the arctic and antarctic circles. Every circle on the globe, whether real or imaginary, has two poles diametrically opposite to each other. 30. The EauiNocTiAL Points are Aries and Libra, where the ecliptic cuts the equinoctial. The point Aries is called the vernal equinox, and the point Libra the avtumnol equinox. When the sun is in either of those points, the days and nights on every part of the t(lobe are equal to each other. 3L Tlie Solstitial Points are Cancer and Capri DEFINITIONS, <&C. 13 corn. When the sun is in, or near, these points, the variation in his greatest altitude is scarcely perceptible for several days ; because the ecliptic near these points IS almost parallel to the equinoctial, and therefore the sun has nearly the same declination for several days. When the sun enters Cancer, it is the longest day to all the inhabitants on the north side of the equator, and the sliortest day to those on the south side. When the sun enters Capricorn it is the shortest day to those who live in north latitude, and the longest day to those who live in south latitude. 32. An Hemisphere is half the surface of the globe ; ^verj great circle divides the globe into two hemi- spheres. The horizon divides the upper from the lower hemisphere in the heavens ; the equator separates the northern from the southern on the earth ; and the brasf^ meridian, standing over any place on the terrestrial globe, divides the eastern from the western hemi- sphere. 33. The IVIariner^s Compass is a representation o! the horizon, and is used by seamen to direct and as- certain the course of their ships. It consists of a cir cular brass box, which contains a paper card, divided nto 32 equal parts, and fixed on a magnetical needle that always turns towards the north. Each point oi the compass contains 11° 15' or 11^ degrees, being the 32d part of 360 degrees. 34. The Variation of the Compass is the devia- tion of ItS points from the corresponding points in the heavens. When the north point of the compass is to tne east of the true north point of the horizon, the va* b o 14 DEFINITIONS, dcC. riation is east : if it be to the west, the variation is west. The learner is to understand, that the compass does uot always point directly north, but is subject to a small (irregular) annual variation. At present, 1830, in England, the needle points about 24i degrees to the westward of the north. The compass is used for setting the artificial globe north and south ; but care must be taken to make a proper allow ance for the variation. 35. Latitude of a Place, on the terrestrial globe> is its distance from the equator in degrees, minutes, or geographical miles, &c. and is reckoned on the brass meridian, from the equator towards the north or south pole. 36. Latitude of a Star or Planet, on the celes- tial globe, is its distance from the ecliptic, northward or southward, counted towards the pole of the ecliptic, on the quadrant of altitude. The greatest latitude a star can have is 90 degrees, and the greatest latitude of a planet is nearly 8 degrees.* The sun being always in the ecliptic, has no latitude. 37. The Quadrant of Altitude is a thin flexi- ble piece of brass divided upwards from to 90 degrees and downwards from to 18 degrees, and when used is generally screwed to the brass meridian. The uppei divisions are used to determine the distances of places on the earth, the distances of the celestial bodies, their altitudes, &;c. and the lovver divisions are applied to finding the beginning, end, and duration of twilight. 38. Longitude of a Place, on the terrestrial globe^ is the distance of the meridian of that place from tho first meridian, reckoned in degrees and parts of a de- * The newly-discovered planets, or Asteroids, Ceres and PaUas^ &0. ia Dot appear to be confined within this limit. DEFINITIONS, (fec. 16 gpret on the equator. Longitude is either eastward oi westward, according as the place is eastward or west- ward of the first meridian. The greatest longitude that a place can have is 180 degrees, or half the cir- ^.umference of the globe. 39. Longitude of a Star, or Planet, is reckoned on the ecliptic from the point Aries, eastward, round the celestial globe. The longitude of the sun is what is called tiie sun's place on the terrestrial globe. 40. Almacantaes, or parallels of latitude, are ima^ ginary circles parallel to the horizon, and serve to show the height of the sun, moon, or stars. These circles are not drawn on the globe, but they may be described for any latitude by the quadrant of altitude. 41. Parallels of Celestial Latitude are small circles drawn on the celestial globe parallel to the ecliptic. 42. Parallels of DeclinatioI'T are small circles parallel to the equinoctial on the celestial globe, and are similar to the parallels of latitude on the terrestrial globe. 43. Azimuth, or Vertical Circles, are imaginary great circles passir.g through the zenith and the nadir, cutting the horizcn at right angles. The altitudes of the heavenly bodies are measured on these circles, which circles may be represented by screwing the quad- rant of altitude on the zenith of any place, and making the other end move along the wooden horizon of the globe. 44. The Prime Vertical is that azimuth circlf, which passes through the east and west points of the 16 ' DEFINITIONS, arg ] Answer. 30?° east. 2. What is the longitude of Philadelphia ? Answer 75^° west. 3. Required the longitudes of the following places Aberdeen Alexandria Barbadoes Bombay Botany Bay Canton Carlscrona Cayenne Civita Vecchia Constantinople Copenhagen Drontheim Ephesus Gibraltar Leghorn Liverpool Lisbon Madras Masulipatam Mecca Nankin Palermo Pondicherry Queda. I« What is the greatest longitude a place can have ? Problem IV., To fmd all those places that have the same longitude as a gwen place. Rule. Bring the given place to the brass meridian THE TERRESTRIAL GLOBE. 27 then all places under the same edge of the meridian from pole to pole have the same longitude. All people situated under the same meridian from 66° 28 north lati tude to 66'^ 28' south latitude, have noon at the same time ; or, if it be one, two, three, or any nimiber of hours before or after noon ivith one particular place, it will be the same hour with every other place situa- ted under the same meridian. Examples. 1. What places have the same, or nearly the same longitude as Stockholm ? Answer. Dantzic, Presburg, Tarento, the Cape of Good Hope, &a 2. What places have the same longitude as Alexan- dria ? 3. When it is ten o'clock in the evening at London, what inhabitants of the earth haye the same hour ? 4. What inhabitants of the earth have midnight whem the inhabitants of Jamaica have midnight ? 5. What places of the. earth have the same longitude as the following places ? London Quebec The Sandwich islands Pekin Dublin Pelew islands. Problem V. To find the latitude and longitude of any place. Rule. Bring the given place to th^t part of the brass meridian which is numbered from the equator to- wards the poles ; the degree above the place is the lati- tude, and the degree on the equator, cut by the brass meridian, is the longitude. This problem is only an exercise of the /rs^ and tliird. Examples. 1. What are the latitude andkngitude of Petersburg ? Aiisiver. Latitude 60^ N. longitude 30^° E. 28 PROBLEMS PERFORMED WITH 2. Required the^ latitudes and longitudes of the fol» ing places : Acapulco Cusco Lima Aleppo Copenhagen Lizard Algiers Durazzo Lubec Archangel Eisinore Malacca Belfast Flushing Manilla Bergen Cape Guardafui Medina Buenos Ayres Hamburgh Mexico Calcutta Jeddo Mocha Candy Jaffa Moscow Corinth Ivica Problem VI. Oporto. To find any place on the globe having the latitude and longitude of that place given. Rule. Find the longitude of the given place on the equator, and bring it to that part of the brass me- ridian which is numbered from the equator towards the poles; then under the given latitude, on the brass meridian, you will find the place required. Examples. 1. What place has 151 i° east longitude, and 34'^ south latitude ? Answer. Botany Bay. 2. What places have the following latitudes and lon- gitudes ? Latitudes. Longitude. Latitude. Longinide. 60° 6' N. 5° 54' W. 19° 26' N. 100' 6' W 48 12 N. 16 16 E. 59 56 N. 30 19 E. -^5 58 N. 3 12 W. 13 S. 77 55 W 52 22 N. 4 51 E. 46 55 N. 69 53 W 31 13 N. 29 55 E. 59 21 N. 18 4E THE TERRESTRIAL GLOBE. 29 r)4° 34' IS! 38'" 58' E. 8^ 32' N. 81° HE. 34 29 S. 18 23 E. 5 9S. 119 49 E. 3 49 S. 102 10 E. 22 54 S. 42 44 W 34 35 S. 58 31 W. 36 5 N. 5 22 W 32 25 N. 52 50 E. 32 38 N. 17 6 W, Problem VIL To find the difference of latitude between any two places* Rule. Bring one of the places to that half of the brass meridian which is numbered from the equator towards the poles, and mark the degree above it ; then bring the other place to the meridian, and the number of degrees between it and the above mark will be the difference of latitude. Or, Find the latitudes of both the places (by Prob^ 1.) then, if the latitudes be both north or both south, subtract the less latitude from the greater, and the re- mainder will be the difference of latitude ; but, if the latitudes be one north and the other south, add them together, and their sum will be the difference of lati- tude. Examples. 1. What is the difference of latitude between Philadelphia and Petersburgh ? Answer. 20 degrees. 2. What is the difference of latitude between Mad^. rid and Buenos Ayres ? Answer. 75 degrees. 3. Required the difference of latitude between the following places ? London and Rome Alexandria anc he Cape D^lhi and Cape Comorin of Good Hop c 2 P 2 80 PROBIEMS PERFORMED WITH Vera Cruz and Cape Horn Pekm and Lima Mexico and Botany Bay St. Salvador and Surinann Astracan and Bombay Washington and Quebec St. Helena and Manilla Porto Bello and the Straits Copenhagen and Toulon of Magellan Brest and Inverness Trinidad I. and Trincomalt Cadiz and Sierra Leone Bencoolen and Calcutta. 4. What two places on the globe have the greatest difference of latitude ? Problem VIH. To find the difference of longitude between any two places. Rule. Bring one of the given places to the brass meridan, and mark its longitude on the equator ; then bring the other place to the brass meridian, and the number of degrees between its longitude and the above mark, counted on the equator, the nearest way round the globe, will show the difference of longitude. Or, Find the longitudes of both the places (by Prob. III.) then, if the longitudes be both east or both west, subtract the less longitude from the greater, and the remainder will be the difference of longitude : but, if the longitude be one east and the other west, add them together, and their sum will be the difference of lon- gitude. When this sum exceeds 180 degrees, take it fron^ 360, and the remainder will be the difference of lon- gitude. ExAMPLiis. 1, What is the difference ^ / longitude between Barbadoes and Cape Verd? THE TERRESTRIAL GLOBE. 3] Answer. 43o 42'. 2. What is the difference of longitude between Buenos Ayres and the Cape of Good Hope ? Answer. 76° 54' 3. What is the difference of longitude between Botany Bay and O'why'ee ? Answer. 52*^ 45', or 52? degrees. 4. Required the difference of longitude between the , following places : Vera Cruz and Canton Constantinople and Batavia Bergen and Bombay Bermudas I. and I. of Rhodes Columbo and Mexico Port Patrick and Berne Juan Fernandes L and Mount Heckla and Mount Manilla Vesuvius Pelew I. and Ispahan Mount iEtna and Teneriffe Boston in Amer. and North Cape and Gibraltar. Berlin 5. What is the greatest difference of longitude com- prehended between two places? Problem IX. To find the distance betiveen any two places. Rule. The shortest distance between any two places on the earth, is an arc of a great circle contained between the two places. Therefore, lay the graduated edge of the quadrant of altitude over the two places, so that the division marked may be on one of the places the degrees on the quadrant comprehended between the two places will give their distance ; and if these defirrees be multiplied by 60, the product will give the fiistance in geographical miles ; or multiply the de- V2 PK0BLE3IS PERIORMED WITH ^rees by 69|, and the product will give the distance in Englis'i miles. Or, Take the distance between the two places with a pair of compasses, and apply that distance to the equa tor, which will show how many degrees it contains. If the distance between the two places should exceed the length of the quadrant, stretch a piece of thread over the two places, and mark their distance ; the ex- tent of thread between these marks, applied to the equator, from the meridian of London, will show the number of degrees between the two places. Examples. 1. What is the nearest distance be- tween the Lizard and the island of Bermudas 1 45^ distance in degrees. 60 2700 30 15 2745 geographical miles. 45 T distance in degrees. m 22f 405 270 34i m 3176| English miles. 2. What is the nearest distance between the island of Bermudas and St. Helena ? 131 distance in degrees. 60 4380 30 4410 geographical miles. 73i distance in degrees. 361 657 438 34i 5108i English miles. 3. What is the nearest distance between Lonrton Hnd Botany Bay. THE TERRESTRIAX GLOBE^ 38 154 distance in degrees. 60 9240 geographical miles. 154 distance in degrees 691 77 1386 924 10703 English miles. 4. What is the direct distance between London and Jamaica, in geographical and English miles ? 5. What is the extent of Europe in English miler. from Cape Matopan in the Morea, to the North Cap«^ in Lapland? 6. W^hat is the extent of Africa from Cape Verd to Cape Guardafui? 7. What is the extent of south America from Cape Blanco in the west to Cape St. Roque in the east ? 8. Suppose the track of a ship to Madras be from- the Lizard to St. Anthony, one of the Cape Verd is- lands, thence to St. Helena, thence to the Cape of Good Hope, thence to the east of the Mauritius, thence a little to the south-east of Ceylon, and thence to Madras ; how many English miles is the Land's End from Mad- ras? Problem X. A place being given on the globe, to find all places, which are situated at the same distance from it as any other given place. Rule. Lay the graduated edge of the quadrant of altitude over the two places, so that the division marked may be on one of the places, then observe what de- ^ gree of the quadrant stands over the other place ; move the quadrant entirely round, keeping the division mark- 54 PROBLEMS PERFORMED WITH ed in its first situation, and all places which pass under the same degree which was observed to stand over the other place, will be those sought. Or, Place one foot of a pair of compasses in one of the given places, and extend the other foot to the other given place : a circle described from the first place as a centre, with this extent, will pass through all the pla- ces sought. If the distance between the two given places should exceed the length of the quadrant, or the extent of a pair of compasses, stretch a piece of thread over the two places, as m the preceding problem. Examples. 1. It is required to find all the places on the globe which are situated at the same distance from London as Warsaw is ? Answer. Koningsburg, Buda, Posega, Alicant, I'ekin; and if 46 be multiplied by 116, the product ■vvui be 5336; cut alf the two right hand-hand figures, and tJie lengih of a degree in Eng- . iish mdes will be 53. Or, by the rule of three, 15- : C9im. : : lli° • 53 miles. 2. How many miles make a degree in the parallels ^'C^f latitude wherein the following places are situated? Surinam Washington Spitzbergen Barbadoes Quebec Cape Verd Havana Skalholt Alexandria Bermudas I. North Cape Paris. Problem XIV To Jlnd the hearing of one place from another. Rule. If both the places be situated on the same parallel of latitude, their bearing is either east or west from each other; if they be situated on the same me- ridian, they bear north and south from each other ; li they be situated on the same rhumb-line, that rhuml>- line is their bearing : if they be not situated on the sam) rhumb-line^ lay the quadrant of altitude over the two places, and that rhumb-line which is the nearest of being parallel to the quadrant will be their bearing. Or, If the globe have no rhumb-lines drawn on it, make a small mariner's compass (szich as in Plate I. /%•. 4.) and apply the centre of it to any given place, so that the north and south points may coincide with some meridian ; tiie other points will show the bearings of all Ihe circumjacent places, to the distance of up- THE TERKESTKIAL GLOBE. Sf^ wards of a thousand miles, if the centrical place be not tar distant from the equator. Examples, 1. Which way must a ship steer from the Lizard to the island of Bermudas ? Answer. W. S. W. 2. Which way must a ship steer from the Lizard U> the island of Madeira ? Answer. S. S. VV. 3. Required the bearing between London and the following places? Amsterdam Copenhagen Petersburg Athens Dublin Prague Bergen Edinburgh Rome Berlin Lisbon Stockholm Berne Madrid Vienna Brussels Naples Warsaw. Buda Paris Problem XV. To find the angle of position between two places. Rule. Elevate the north or south pole, according as the latitude is north or south, so many degrees above the horizon as are equal to the latitude of one of the given places ; bring that place to the brass rneri^ dian, and screw the quadrant of altitude upon the de- gree over it ; next move the quadrant till its graduated edge falls upon the other place ; then the number of degrees on ihe wooden horizon, between the graduated edge of the quadrant and the brass meridian, reckoninsj towards the elevated pole, is the angle of position be- tween the two places. 40 PROBLEMS PERFORMED WITH Examples. 1. What is the angle of position between London and Prague ? Answer. 90 degrees from the north towards the east: the quadrant of altitude will fall upon the east point of the horizon, and pass over or near the following places, viz. Rotterdam, Frankfort, Cracow, Ock- zakov, Caffa, south part of the Caspian Sea, Guzerat in India, Madras. and part of xae island of Ceylon. Hence all these places have tin? •same angle of position from London. 2. What is the angle of position between London and Port Royal in Jamaica ? Answer. 90 degrees from the north towards the west ; the quadrant of altitude will fall upon the west point of the horizon. 3. What is the angle of position between Philadel- phia and Madrid ? Answer, 65 degrees from the north towards the east ; the quadrant af altitude will fall between the E. N. E. and N. E. by E. points of the horizon. 4. Required the angles of position between London and the following places? Amsterdam Copenhagen Rome Berlin Cairo Stockholm Berne Lisbon Petersburg Constantinople Madras Quebec Problem XVL Tojlnd the Antoeci, Periceci, and Antipodes to ike inhabitants of any place. Rule. Place the two poles of the globe in the hori zon, and bring the given place to the eastern part ol the horizon ; then, if the given place be in north lati tude, observe how many degrees it is to the northward of the east point of the horizon ; the same number of ilegrecs to the southward of the east point will show THE TEKHESTRIAL GLOBE. 4! the Antosci ; ao equal number of degrees, counted froui the west point of the horizon towards the nortlj, will ghow the Perio^ci ; and the same number of degrees, counted towards the south of the west, will point out the Antipodes. If the place be in south latitude, the same rule will serve by reading south for north, and the contrary. Or thus : For the AniCBci. Bring* the given place to the brass meridian and observe its latitude ; then in the opposite hemisphere, under the same degree of latitude, yoo will find the Antoeci. For the Periceci. Bring the given place to the brass meridian, and set the index of the hour circle to 12c turn the globe half round, or till the index points to the other 12; then under the latitude of the given place you will find the Perioeci. For the Antipodes. Bring the given place to the brass meridian, and set the index of the hour circle to 12, turn the globe half round, or till the index points to the other 12 ; then under the same degree of latitude with the given place, but in the opposite hemisphere^ ^ou will find the Antipodes. Examples. 1. Required the Antoeci, Perioeci, and Antipodes, to the inhabitants of the island of Bermu- das? Answer. Their Antosci are situated in Paraguay, a little N. W. ot Buenos Ayres ; their Perioeci in China, N W of Nankin ; and their Antipodes in the S. W. part of New Holland. 2. Required the Antoeci, Perioeci, and Antipodes t(^ the inhabitants of the Cape of Good Hope ? d 2 Q 2 42 PROBLEMS PERFORMED WITH 3. Captain Cook, in one of his voyages, was in 50 degrees sjuth latitude and 180 degrees of longitude ; in what part of Europe were his Antipodes ? 4. Required the Antoeci to the inhabitants of the Falkland islands? 5. Required the Perioeci to the inhabitants of the Philippine islands ? 6. What inhabitants of the earth are Antipodes to those of Buenos Ayres ? To find at tvJiat rate per hour the inhabitants of any given jjlace are carried^ from west to east, by the re- volution of the earth on its axis. Rule. Find how many miles make a degree of longitude in the latitude of the given place (by Prob lem XIII.) which multiply by 15 for the answer. Or, look for the latitude of the given place in the table, Problem IX., against which you will find the number of miles contained in one degree ; multiply these miles by 15, and reject two figures from the right hand of the product ; the result will be the answer. Examples. 1. At what rate per hour are the in- habitants of Madrid carried from west to east by the revolution of the earth on its axis? Answer. The latitude of Madrid is about 40° N. where a degree of iongilude measares 46 geograj)hic;al, or 53 English miles (see Exampk I. Prob. XITI.) Now 46 multiplied by 15 produces 690; and 53 multi- plied by 15 produces 795; hence the inhabitants of Madrid are carried C90 geographical, or 795 English miles per hour. By the Table. Against the latitude 40 you will find 45-96 geogra- phical miles, ?ind 52-85 English miles : Hence, 44-95 X 15 = 689-40 and 52-85 X 15 = 792-75, by rejecting "^^ two right- hand (igures from each product, the result will be CS' geographical miles, and 792 English miles, agreemg nearly with thf Above. THE TERRESTRIAL GLOBE. 43 2. At what rate 'per hour are the inhabitants of the following places carried from west to east by the revo- lution of the earth on its axis ? Skalholt Philadelphia . Cape of Good Hope Spitzbergen Cairo Calcutta Petersburgh Barbadoes Delhi liondon Quito Batavia. Problem XVIII. A particular place, and the hour of the day at thai place being given, to find what hour it is at any other place. Rule. Bring the place at which the time is given to the brass meridian, and set the index of the hour circle to 12 ; turn the globe till the other place comes to the meridian, and the hours passed over by the in- dex will be the difference of time between the two places. If the place where the hour is sought lie to the east of that wherein the time is given, count the difference of time forward from the given hour; if it lie to the west, reckon the difference of time backward. Or, w^ithout the hour circle. Find the difference of longitude betw^een the two places (by Problem VIII.) and turn it into time by al- lowing 15 degrees to an hour, or four minutes of time fo one degree. The difference of longitude in time will be the difference of time between the two places, with which proceed as above. Degrees of longitude may be turned into time by multiplying by 4 ; observ- ing that minutes or miles of longitude, when multipJ»*M 44 PROBLEMS PERFORMED WITH by 4, produce seconds of time ; and degrees of lonj/' tuile, when multiplied by 4, produce minutes of time. Some globes have two rows 6f figures on the hour cirrle, others buJ one ; this difference frequently occasions confusion ; and the manner •ji which authors in general direct a learner to solve those problems wherein the hour circle is used, serves only to increase that confusion. m this, and in all the succeeding problems, great care has been taken to render the rules general for any hour circle whatsoever. Examples. 1. When it is ten o'clock in the morn- ing at London, what hour is it at Petersburgh ? Anstver. The difference of time is two hours ; and, as Petersburg la eastward of London, this difference must be counted forwaid, so that It is 12 o'clock at noon at Petei-sburg. Or, the difference of longitude between Petersburgh and London ia 30^ 25', which multiplied by 4 produces two hours 1 mm. 40 sec. the difference of time shown by the clocks of London and Petersburgh . hence as Petersburgh lies to the east of London ; when it is ten o'clock in the morning at London, it is one minute and 40 seconds past 12 al Petersburgh. 2. When it is two o'clock in the afternoon at Alex andria in Egypt, what hour is it at Philadelphia? Ansiver. The difference of time is seven hours ; and because Phila^ deiphia lies to the westward of Alexandria, this difference must be reckoned backward, so that it is seven o'clock in the morning at Phila rhia. Or, The longitude of Alexandria is ^ The longitude of Philadelphia is Diflference of longitude Difference of longitude in time 7 h. 1 m. 48 aec ; trie clocks at Philadelphia are slower than those of Alexandria ; heiic# when it is two o'clock in the afternoon at Alexandria, it is 58 ra. 12 sec. paf»t six in the morning at Philadelphia, 3. When it is noon at London, what hour is it at Cri* cutta? 30O 16' E. 75 11 W. 105 27 4 THE TERRESTRIAL GLOBE. 4e5 4. When it is ten o'clock in the morning at London, what hour is it at Washington? 5. W^hen it is nine o'clock in the morning at Jamai ca, what o'clock is it at Madras ? 6. My watch was well regulated at London, and when I arrived at Madras, which was after a ilve months' voyage, it was four hours and fifty minutes glower than the clocks there. Had it gained or lost during the voyage? and how much? Problem: XIX. A particular place and the hour of the day being given^ to find all places on the globe where it is then noon, or any other given hour. Rule. Bring the given place to the brass meridian^ and set the index of the hour circle to 12 ; then, as the difference of time between the given and required places is always known by the problem, if the hour at the required places be earlier than the hour at the given place, turn the globe eastward till the index has passed over as many hours as are equal to the given difference of time ; but, if the hour at the required places be latier than the hour at the given place, turn the globe westward till the index has passed over as many hours as are equal to the given difference of time ; and, in each case, all the places required will be found under the brass meridian. Or, without the hour circle. f Reduce the difference of time between the given place and the required places into minutes* these mi- 46 PROBLEIVIS PERFORMED WIFH nutes, divided by 4, will give degrees of long.tude ; if there be a remainder after dividing by 4, multiply it bj 60, and divide the product by four, the quotient will bo minutes or miles of longitude. The difference of longitude between the given place and the required places being thus determined, if the hour at the re- quired places be earlier than the hour at the given place, the required places lie so many degrees to the vvesiward of the given place as are equal to the differ- ence of longitude ; if the hour at the required places be later than the hour at the given place, the required places lie so many degrees to the eastward of the given place as are equal to the difference of longitude. Examples. 1. When it is noon at London, at what {)laces is it half past eight o'clock in the morning? Answer. The difference of time between London, the given place, tnd the required places, is 3^ hours, and the time at the required places (s earlier than that at London ; therefore the required places lie 3i hours SNestvvard of London; consequently, by bringing London to the brass meridian, setting the index to 12, and turning the globe eastward till the lindex has passed over 3i hours, all the required places will be under Jie brass meridian, as the eastern coast of Newfoundland, Cayenne, pari .of Paraguay, &c. Or, The difference of time between London, the given place, and the required places, is 3 hours 30 min. 3h. 30 m. The difference of longitude between the 60 given place and the required places is 52^ 30* The hour at the required places being earlier 4)120 ra, than that at the given place, they lie 52<3 30* westward of the given place. Hence, all 520 — 2 places situated in 52^ SO' west longitude froiD 60 London, are the places sought, and will hs found to be Cayenne, »it this cannot be representod hv esevating or depressinj^ the pcle. 62 PROBLEMS PERFORMED WITH below the pole, the appearance will be exactly the same. The latitude of London is about 5H° north ; if T^-r- *don be brought to the brass meridian^ and the north LK>le be elevated 51|^° above the norih point of the wocaen horizon, then the wooden horizon v/ill be vus irz-^ horizon of London; and, if the artificial globe be placed exactly north and south by a mariner's coiapa3.s- or by a meridian line, it will have exactly the posiUo.i which the real globe has. Now, if we imagine Lne^ to be drawn through every degree within the torrid zona, parallel to the equator, they will nearly represent th« sun's diurnal path en any given day. By comparing these diurnal paths with each other, they will be fo'ind to increase in length from the equator porthvz&rd, ami to decrease in length from the equator sou.ihv/srd ; consequently, when the sun is going north from tha equator, the days are increasing in length to us ; ar.si when going from the equator, the days are d'i^crea^- ing. The sun's meridian altitude, for any day, may be found by counting the number of degrees from thj parallel in which the sun is on that day, towards the horizon, upon the brass meridian ; thus, when the sun is in th^t parallel of latitude which is ten aegrees north af the equator, his meridian altitude will be 48|^°. Though the wooden horizon be the true horizon of the given place, yet it does not separate the enlightened hemispiiere of the globe from the dark hemisphere, ivhen the pole is thus elevated. For instance, when the Bun is in Aries, and London at the meridian, all the places on the globe above the horizon beyond those meridians THE TERRESTRIAL GLOBE. 63 which pass through the east and west points thereof, reckoning towards the north, are in darkness, notwith- standing they are above the horizon : and all places below the horizon, bettveen those same meridians and* the southern point of the horizon, have day-light, not- withstanding they are below the horizon of London* Problem XXIII. The month and day of the month being given^ to find all places of the earth where the sun is vertical on that day ; those places where the sun does not set, and those places whei^e he does not rise on the given day. Rule. Find the sun's declination (by Problem XX») for the given day, and mark it on the brass meridian; turn the globe round on its axis from west to east, and all the places which pass under this mark will have the sun vertical on that day. Secondly. Elevate the north or south pole, accord- ing as the sun's declination is north or south, so many degrees above the horizon as are equal to the sun's de- clination : turn the globe on its axis from west to east; then, to those places which do not descend below the horizon, in that frigid zone near the elevated pole, the sun does not set on the given day : and to those places which do not ascend above the horizon, in that frigid zone adjoining to the depressed pole, the sun does not rise on the given day. Or, by the analemma. Bring the analemma to that part of the brass meri- dian which is numbered from the eq^iator towards the 64 PROBLEMS TERFORMED WITH poles, the degree directly above the day of the montn on the brass meridian, is the sun's declination. Ele- vate the north or south pole, according as the sun's de- clination is north or south, so many degrees above the horizon as are equal to the sun's declination ; turn the globe on its axis from v^est to east, then to those place? which pass under the sun's declination, on the brass meridian the sun will be vertical; to those places (in that frigid zone near the elevated pole) which do not go below the horizon, the sun does not set; and to those places (in that frigid zone near the depressed pole) which do not come above the horizon, the sun does not rise on the given day. Examples. 1. Find all places of the earth where the sun is vertical on the 11th of May, those places in the north frigid zone where the sun does not set, and those places in the south frigid zone* where he does not rise. Answer. Tlie sun is vertical at St. Anthony, one of ihe Cnpe Verd islands, the Virgin islands, south of St. Domingo, Jamaica, Golconda, &.C. All the places within eighteen degrees of the nortl? pole will have constan- day ; and those (if any) within eighteen degrees of the south pole will have constant night 2. Whether does the sun shine over the north or south pole on the 27th of October, to what places will he be vertical at noon, what inhabitants of (he earth will have the sun below their horizon during several revolutions, and to what part of the globe will the sun never set on that day ? 3. Find all the places of the earth where the in- habitants have no shadow whea the sun is on theit meridian on the first of June. THE TERRESTRIAL GLOBE. b5 4. What inhabitants of the earth have their shadows directed to every point of the compass during a revo- lution of the earth on its axis on the 15th- of July? 5. How far does the sun shine over the south pole on the 14th of November, what places in the north frigid zone are in perpetual darkness, and to what places is the sun vertical ? 6. Find all places of the earth where the rrioon will be vertical on the 3d of June 1827. Problem XXIV, A place being given in the torrid zone, to find those ttco days of the year on which the sun will be vertical at that place. Rule. Bring the given place to that part of the brass meridian which is numbered from the equator towards the poles, and mark its latitude ', turn the globe on its axis, and observe what two points of the ecliptic pass under that latitude : seek those points of the ecliptic in the circle o'f signs on the horizon, and exactly against them, in the circle of months stand the days required Or, by the analemma. Find the latitude of the given place (by Problem 1 ) and mark it on the brass meridian ; bring the analem- ma to the brass meridian, upon which, exactly under the latitude, will be found the two days required. Examples. 1. On what two days of the year will the sun be vertical at Madras ? Answer On the 25th of April and on the 18th of August. f2 s2 t>6 PROBLEMS PEKFORMED WITbfl 2 Oa what two days of the year is the sui; vertica at the following places ? O'vvhy'hee St. Helena Sierra Leone Friendly Isles Rio Janeiro Vera Ouz Straits of Alass Quito Manilla Penang Barbadoes Tinian Isle Trincomale Porto Bello Pelew Islands., Problem XXV. The month and the day of the month being given (at any place not in the frigid zones,) to find what other day of the year is of the same length. Rule. Find the sun's place in the ecliptic for the given day, (by Problem XX.) bring it to ibe brass me ridian, and observe the degree above it ; turn the globe on its axis till some other point of the ecliptic falls un- der the same degree of the meridian : find this point 3f the ecliptic on the horizon, and directly against it you will find the day of the month required. This Probleni may be performed by the celestial globe in the samt Vianner. Or, by the analemma. Look for the given day of the month on the analem- ma, and adjoining to it you will find the required day t)l the month. Or, without a globe. Any two days of the year which are of the same length, will be an equal number of days from the longest or shortest day. Hence, whatever number of days the THE TERRESTEIAL GLOBE. 67 given day is before the longest or shortest day, just so many days will the required day be after the longest or shortest day, et contra. Examples. 1. What day of the year is of the same length as the 25th of April 1 Answer. The 18th of August. 2. What day of the year is of the same length as the 25th of May? 3. If the sun rise at four o'clock in the morning at London on the 17th of July, on what other day of the year will it rise at the same hour 1 4. If the sun set at seven o'clock in the evening at fuondon on the 24th of August, Oii what other day of the year will it set at the same hour 1 o. If the sun's meridian altitude be 90° at Trinco- ' male, in the island of Ceylon, on the 1 2th of April, on what other day of the year will the meridian alti- tude be the same ? 6. If the sun's meridian altitude at London on the 25th of April be 51° 35', on what other day of the year will the meridian altitude be the same ? 7. If the sun be vertical at any place on the 15th of April, how many days will elapse before ho is verti- cal a second time at that place 1 8. If the sun be vertical at any place on the 20th of August, how many days will elapse befoie he is vertical a second time at that place ? 68 PROBLEMS PERFORMED WITH Problem XXVI. The months day^ and hour of the day being given, tojind where the sun is vertical at that instant. Rule. Find the sun's declination (by Problem XX.) and mark it on the brass meridian ; bring the given place to the brass meridian, and set the index of the hour-circle to twelve ; then, if the given time be before noon, turn the globe westward as many hours as it wants of noon ; but, if the given time be past noon, turn the globe eastward as many hours as the time is past noon ; the place exactly under the degree of the sun's declination will be that sought. Examples. 1. When it is forty minutes past six o'clock in the morning at London on the 25th of April, where is the sun vertical? Answer. Here* the given time is five hours twenty minutes before noon; hence the globe must be turned towards the west till the indei !ias passed over five hours twenty minutes, and under the sun's decJi nation on the brass meridian you will find Madras, the place required. 2. When it is four o'clock in the afternoon at Lon- don on the 18th of August, where is the sun vertical ? Answer. Here the given time is four hours past noon; hence the globe must be turned towards the ensi, till the index has passp^i over four hours, then, under the sun's declination, you will find Bar- tmdoes, the place required. 3. When it is three o'clock in the afternoon at Lon- don on the 4th of January, where is the sun vertical? 4. When it is three o'clock in the morning at Londora on the 11th of April, where is the sun vertical ? 5. When it is ihirty-seven minutes past one o'clock THE TEBKESTRIAL GLOBE. 6^ AL the afternoon at the Cape of Good Hope on the 5th cf February, where is the sun vertical ] 6. When it is eleven minutes past one o'clock in the iifternoon at London on the 29th of April, where is the Bun vertical ? 7. When it is twenty minutes past five o'clock in the afternoon at Philadelphia on the 18th of May, where is the sun vertical ? 8. When it is nine o'clock in the morning at Cal- cutta on the 11th of April, where is the sun vertical? Problem XXVIL The month, day, and hour of the day at any place being given, to find all those places of the earth where the sun is rising, those places where the sun is setting, those places that have noon, that particular place where the sun is vertical, those places that have morn' ing twilight, those places that have evening twilight, and those places that have midnight. Rule. Find the sun's declination (by Problem XX.) and mark it on the brass meridian ; elevate the north or south pole, according as the sun's declination is north or south, so many degrees above the horizon as are equal to the sun's declination ; bring the given place to the brass meridian, and set the index of the hour- circle to twelve ; then, if the given time be before noon, turn the globe westward as many hours as it wants of noon; but, if the given time be past noon, turn the globe eastward as many hours as the time is past noon : keep the globe in this position ; then all places along the western edge of the horizon have the sun rising ; 70 PROBLEMS PERFORMED WITH those places along the eastern edge have the sun set ting ; those under the brass meridian above the hon zon, have noon ; that particular place which stands under the sun's declination on the brass meridian, has the sun vertical ; all places below the western edge of the horizon, within eighteen degrees, have morning twilight ; those places which are below the eastern edge of the horizon, within eighteen degrees, have evening twilight ; all places mider the brass meridian below the horizon, have midnight ; all the places above the horizon have day, and those below it have night or twilight. Examples. 1. When it is fifty-two minutes past four o'clock in the morning at London on the fifth of March, find all places of the earth where the sun is rising, set- ting, &c. &;c. Ansiver. The sun's declination will be found to be 6p south ; there fore, elevate the south pole 67° above the horizon. The given time be- jig seven hours eight minutes before noon ( = 12 h. — 4 h. 52m.j the globe must be turned towards the tbest, till the index has passed over seven hours eight minutes. Let the globe be fixed in this position , then, The sun is rising at the W'estem part of the Wliite Sea, Petersburgh, the Morea in Turkey, &c. Setting at the eastern coast of Kamtschatka, Jesus island, Palmerston island, &c. between the Friendly and Society islands. Noon at the lake Baikal in Irkoutsk, Cochin China, Cambodia, Sunda islands, &c. Vertical at Batavia. M&rmng twilight at Sweden, part of Germany, the southern part of Italy, Sicily, the western coast of Africa along the ^Ethiopian Ocean &c. 4 Evening Iwiligld at the north-west extremity of North America, the Sandwich islands. Society islands, &c. Midnight at Labrador, New- York, western part of St. Domingo, ChiU, aiid the western coast of South America. THE TERRESTRIAL GLOBE. 71 Oayat the eastern part of Russia in Europe, Turkey Egj'^pt, trie Cape ct'Good Hope, and all the eastern part of Africa, almost the whole of Asia, &c. .^ Nighi at the whole of North and South America, the western part ol Africa, the British isles, France, Spain, Portugal, &c. 2. When it is four o'clock in the afternoon at Lon-* don on the 25th of April, where is the sun rising", set- ting, n the 27th of July, where is the sun rising, setting, &c. &c. ? Problem XXVIIL To find the time of the sun^s risings and settings and length of the day and nighty at any 'place not in ike, frigid zones. Rule. Find the sun's declination (by Problem XX.) and elevate the north or south pole, according as the 7<5 PROBLEMS PERFORMED WITH declination is north or south, so many degrees above the horizon as are equal to the sun's declination; bring the given place to the brass meridian, and set the in- dox of the hour-circle to twelve ; turn the globe east- ward till the given place comes to the eastern semi- circle of the horizon, and the number of hours passed over by the index will be the time of the sun's setting . deduct these hours from twelve, and you have the tin^e of the sun's rising ; because the sun rises as many hours before twelve as it sets after twelve. Double the time o{ the sun's setting gives the length of trie day, and double the time of rising gives the length of the night. By the same rule, the length of the longest day, at all places not in the frigid zones, may bt readily fomid ; for the longest day at all places in north latitude is on the 21st of June, or when the sun enters Cancer and the longest day at all places in south latitude is on the 21 st of I >e- <;omber, or when the sun enters the sign Capricorn. Ok, Find the latitude of the given place, and elevate tlie north or south pole, according as the latitude is north or south, so many degrees above the horizon as are equal to the latitude; find the sun's place in the ecliptic (by Problem XX.) bring it to the brass nieridian, and set the index of the hour circle to twelve ; turn the globe westward till the sun's place come to the western semicircle of the horizon, and the number of hours passed over by the index will be the t*jme of the sun's setting , and these hours taken from twelve will give the time of rising; then, as before, double the time of setting gives the length of the day, and double the time of rising gives the length of the night. the terrestrial globe. ts Or, by the analemma. tind the latitude of the given place, and elevate ih north or south pole, according as the latitude is nortl yr south, the same number of degrees above the hori zon ; bring the middle of the analemma to the brasi^ meridian, and set the index of the hour-circle to twelve*. rurn the globe icestward till the day of the month on fhe analemma comes to the western semicircle of the horizon, and the number of hours passed over by the in- dex will be the time of the sun's setting, &;c. as above. Examples. 1. ¥/hat time does the sun rise and set at London on the 1st of June, and what is the length of the day and night? Answer. The sun sets at 8 min. past 8, and rises at 52 min. past 3, die 'eiigth of the day is 16 hours 16 minutes, and the length of the nighl 7 Ii< -irs 44 minutes. The learner will readily perceive that if the tinie at Y hich the sun rises be given, the time at which it sets, together wit)i .he length of the day and night, may be found without a globe ; if the Ion- th of the day be given, the length of the night and the time the sun !'iso>4 ami sets may be found ; if the lengili of the night bo given, the leiijfth of thQ day and the time the sun rises and sets are easily knowa 2. At what time does the sun rise and set at the l<»)!owing places, on the respective days mentioned, and vvLat is the length of the day and night? Lr ndon, 17th of May (riaraltar, 22d July E^'inburgh, 29th January li tany Bay, 20th Febru- ary R' kin, 20th April Cape of Good Hope, 7tb ' December Cape Horn, 29th January Washington, 15th Decern. Petersburgh, 24th October Constantinople, 18th Aug. 3. Find the time the sun rises and sets at every pi ce on the surface of the globe on the 21st of March^ an \ likewise on the 23d of September. S T 74 PROBLEMS PERFORMED WITH 4. Required the length of the longest day and short* est night at the following places : London Paris Pekin Petersburg Vienna Cape Horn Aberdeen Berlin Washington Dublin Buenos Ayres Cape of Good Hope Glasgow Botany Bay Copenhagen. 5. Required the length of the shortest day and longeit flight at the following places : London Lima Paris Archangel Mexico O'why'hee O Taheitee St. Helena Lisbon Quebec Alexandria Falkland islands. 6. How much longer is the 21st of June at Peters* burg than at Alexandria ? 7. How much longer is the 21st of December at Alexandria than at Petersburgh? 8. At what time does the sun rise and set at Spitz- bergen on the 5th of April. Proble3i XXIX. The length of the day at any place ^ not in the frigid zones, being given, to find the huvbs declination and the day of the month. Rule. Bring the given place to the brass meridian and set the index to twelve : turn the globe eastward till the index has passed over as many hours as are equal to half the length of the day ; keep the globe from revolving on its axis, and elevate or depress one of the poles till the given place exactly coincides wnth the eastern semicircle of the horizon ; tiie distance of THE TERRESTRIAL GLOBE, 75 uie elevated pole from the horizon will be the sun's declination : mark the sun's declination, thus found, on the brass meridian : turn the globe on its axis, and observe what two points of the ecliptic pass under this mark ; seek those points in the circle of signs on Khe horizon, and exactly against them, in the circle cf Sionths, stand the days of the months required. Or, Bring the meridian passing through Libra to coincide ivith the brass meridian, elevate the pole to the latitude of the place, and set the index of the hour-circle to twelve ; turn the globe eastward till the index has passed over as many hours as are equal to half the length of the day, and mark where the meridian pass- ing through Libra is cut by the eastern semicircle of the horizon ; bring this mark to the brass meridian, and tne degree above it is the sun's declination ; with which proceed as above. Or, by the analemma. Bring the middle of the analemma to the brass meri- iian, elevate the pole to the latitude of the place, and «et the index of the hour-circle to twelve ; turn the globe eastward till the index has passed over as many hours as are equal to half the length of the day ; the two days, on the analemma, which are cut by the east- ern semicircle of the horizon, will be the days required ; and, by bringing the analemma to the brass meridian, the sun's declination will stand exactly above these 76 PROBLEMS PERFORMED WITH Examples. 1. What two days in the year aie each sixteen hours long at London, and what is the sun's declination ? Answer. The 24th of May and the ITthof July. The sun's decliiif> tion is about 21° north. 2. What two days of the year are each fourteen hour^ long at London 1 3. On what two days of the year does the sun set at half-past seven o'clock at Edinburgh ? 4. On what two days of the year does the sun rise at four o'clock at Petersburg ? 5. What two nights of the year are each ten hours long at Copenhagen ? 6. What day of the year at London is sixteen hours and a half long ? Problem XXX. To find the length of the longest day at any place in the north frigid zone. Rule. Bring the given place to the northern point of the horizon (by elevating or depressing the pole,) and observe its distance from the north pole on the brass meridian ; count the same number of degrees on the brass meridian from the equator, towards the north pole, and mark the place where the reckoning ends ; turn the globe on its axis, and observe what two points of the ecliptic pass under the above mark ; find thosp points ot the ecliptic in the circle of signs on the hori- zon, and exactly against them, in the circle of months, you will find the days on which the longest day begins and ends. The day preceding the 21st of June is THE TEKEESTHIAL GLOBE. T"/ that or which the longest day begins at the given place, and the day following the 21st of June is that on which Bring the given place to that part of the brass men dian vjhich is numbered from the north pole towards tlie equator, and observe its distance in degrees from the pole ; count the same number of degrees on the brass meridian from the equator towards the south pole, and mark where the reckoning ends ,* bring the ana- lemma to the brass meridian, and the two days which stand under the above mark will point out the begin ning and end of the longest night. THE TERRESTRIAL GLOBE. 79 Examples. 1. What is the length of the longest night at the North Cape, in the island of Maggeroe,in latitude 71° 30' north? Ansiver. The place is 18p from the pole ; the longest night begins on the 16ih of November, and ends on the 27th of January : the night is therefore seventy-three days long, that is, the sun does not rise during Bevent}'-three revohitions of the earth on its axis. 2. What is the length of the longest night at tho north of Spitzbergen ] 3. The Dutch wintered in Nova Zembla, latitude T6 degrees north, in the year 1596 ; on what day of the month did they lose sight of the sun ; on what d^v of the month did he appear again ; and how many days were they deprived of his appearance, setting aside tiie effect of refraction ? 4. For how many days are the inhabitants of the northernmost extremity of Russia deprived of a sight of the sun 1 Proelem XXXIL To find the number of days which the sunrises and sets at any place in the north ^frigid zone. Rule. Bring the given place to the northern point of the horizon, (by elevating or depressing the pole,) and observe its distance from the north pole on the brass meridian ; count the same number of degrees on the brass meridian from the equator towards the poles northward and southward, and make marks where the reckoning ends ; observe what two points of the eclip- * The same might be found for a place in the south frigid zone, wora that zone inhabited. 8G PROBLEMS PERFORMED WITH tic nearest to Aries pass under the above marks ; these pojnts will show (upon the horizon) the end of the lon- gest night and the beginning of the longest day ; dur- ing the time between these days the sun will rise and set every twenty-four hours; next observe w^hat two points of the ecliptic, nearest to Libra, pass under the marks on the brass meridian ; find these points, as be- fore, in the circle of signs, and against them you will find the day on which the longest day ends at the given place, and the day on which the longest night begins ; during the time between these days the sun will rise and set every twenty-four hours. Or, Find the length of the longest day at the given place (by Prob. XXX.) and the length of the longest night (by Prob. XXXI.) add these together, and subtract the bum from 365 days, the length of the year, the remain- der will show the number of days which the sun rises and sets at that place. Or, by the analemma. Find how many degrees the given place is from thy^ north pole, and mark those degrees upon the brass meridian on both sides of the equator ; observe what four days on the analemma stand under the marks on the brass meridian; the time between those two days on the left hand part of the analemma (reckoning to- wards the north pole) will be the number of days on which the sun rises and sets, between the end of the V>ngest night and the beginning of the longest day THE TERRESTKIAL GLOBE. 81 and the time between the two days on the right-haod part of the analemma (reckoning towards the south pole) wall be the number of days on which the sun rises and sets, between the end of the longest day and the beginning of the longest night. Examples. 1. How many days in the year does tlio sun rise and set at the North Cape, in the island of Maggeroe, in latitude 71^ 30' north? Answer. The place is 18^^ from the pole, the two points .ir. the ecliptic, nearest to Aries, which pass under IS^o on the brass meridian, are 8° in CX, answering to the 27th of Januaiy, and 24^ in y, answering to the 14lh of May. Hence the san rises and sets for 107 days, ' viz. from the end of the longest night, which happens on the 27th of Janu- ary, to the beginning of the longest day, which happens on the 14th of May. Secondly, the tw^o points in the ecliptic, nearest to Libra, whicli pass under 181° on the brass meridian, are 8^ in Q, answering to \\\e 30th of July, and 24^ in V(\ , answering to the 15th of November. Hence the sun rises and sets for 108 days, viz. from the end of the longest day, which happens on the 30ih of July, to the beginning of the longest night, which happens on the 15th of November ; so that the whole time of the sun's rising and setting is 215 days. Or, thus : The length of the longest day, by Example 1st, Prob. XXX. is 77 days ; the length of the longest night by Example 1st, Prob. XXXI. ia 73 days ; the sum of these is 150, which, deducted from 365, leaves 215 days as above. 2. How many days in the year does the sun rise and set at the north of Spitzbergen ? 3. How many days does the sun rise and set at Green- land . in latitude 75^ north ? 4. How many days does the sun rise and set nt the !Jorthern extremity of Russia in Asia T S2 PROBLEMS PERFORMED WITH Problem XXXIII. To find in what degree of north latitude^ on any lay between the 21 st of March and the 21st of June ^ or in what degree of south latitude, on any day between the 2Sd of September and the 21st of December, the sun begins to shine constantly without setting ; and also in what latitude in the opposite hemisphere he begins to be totally absent. Rule. Find the sun's declination (by Prob. XX.) and count the same number of degrees from the north pole towards the equator, if the declination be north, or from the south pole, if it be south, and mark the point where the reckoning ends ; turn the globe on its axis, and all places passing under this mark are those in which the sun begins to shine constantly v/ithoul setting at that time : the same number of degrees from the contrary pole will point out all the places where twilight or total darkness begins. Examples. 1. In what latitude north, and at what places, does the sun begin to shine without setting dur- ing several revolutions of the earth on its axis, on the 14th of May] Answer. The sun's declination is 18P north, therefore all places in latitude 71 ^^ north will be the places sought, viz. the North Cape in Lapland, the southern part of Nova Zembla, Icy Cape, &c. 2. In what latitude south does the sun begin to shine without setting on the 18th of October, and in what latitude north does he begin to be totally absent ? A.nsu)€r. The sun's declination is 10^ south, therefore he begins tc shine constantly in latitude 80^ south, where there are no inhabitanta THE TERSESTRIAL GLOBE. S'A knowTi, and to be totally absent in latitude 80^ nortti it Spits- bergen. 3 In what latitude does the sun begin to r iiuie with* out setting on the 20th of April? 4. In what latitude north does the sun begin to shinin without setting on the 1st of June, and in w^hat degree of south latitude does he begin to be totally absent? Problem XXXIV. Any number of days, not exceeding lrj6, being given, to find the parallel of north latitude in which the sun does not set for that time. Rule. Count half the number of days from the 21st oi June on the horizon, eastward or westward, and op- posite to the last day you will find the sun's place in the circle of signs : look for the sign and degree on the ecliptic, which bring to the brass meridian, and observe the sun's declination ; reckon the same number of de- grees from the north pole (on that part of the brass me- ridian which is numbered from the equator towards the poles) and you will have the latitude sought. Examples. 1. In what degree of north latitude, and at what places, does the sun continue above the horizon for seventy-seven days ? Ar^jwer. Half the number of days is 38^, and if reckoned backward or towards the east, from the 21st of June, will answer to the 14th of May ; and if counted forward, or towards the west, will answer to the ^Oth of July ; on either of which days the sun's declination is I8j de- grees north, consequently the places sought are 18i degrees from the iiorth pole, or in latitude 7U degrees nortli ; answering to the North Cape in Lapland, the south part of Nova Zembl^ Icy Cape, &c. 2o in what ^egxQQ of north latitude is the longest 'lay \M days, or 3216 hours in lenjrth 7 'r<4. PKOBLEMS PEHFORMED WITH 3. In what degree of north latitude does the sun continue above the horizon for 2160 hours ? 4. In what degree of north latitude does the sun con ^inue above the horizon for 1152 hours'? Problem XXXV. To find the beginning, end, and duration of twilight at any given place on any given day. Rule. Find the sun's declination for the given day ihy Problem XX.) and elevate the north or south pole, according as the declination is north or south, so many degrees above the horizon as are equal to the sun's de^ clination ; screw the quadrant of altitude on the brass meridian, over the degree of the sun's declination : bring the given place to the brass meridian, and set the index of the hour-circle to twelve : turn the globe east- ward till the given place comes to the horizon, and the hours passed over by the index will show the time of' the sun's setting, or the beginning of evening twilight : continue the motion of the globe eastward, till the given place coincides with 18° on the quadrant of altitude below the horizon, and the hours passed over by the index, from 12, will show when evening twilight ends. The time when evening twilight ends, subtracted fro.n 12, will show the beginning of morning twilight. Or, thus : Elevate the north or south pole, according as the la- titude of the given place is north or south, so many degrees above ihe horizon as are equal to the latitude ; ^m\ tiie sun's place in *he ecliptic, bring it to thebrasa THE TERRESTRIAL GLOBE. 85 meridian, set the index of the hour-circle to twelve and screw the quadrant of altitude upon the brass me- ridian over the given latitude : turn the globe westward on its axis till the sun's place comes to the western edge of the horizon, and the hours passed over by the index will show the time of ihe sun's setting, or the beginning of evening twilight ; continue the motion of the globe westward till the sun's place coincides with 18^ on the quadrant of altitude below the horizon, the time passed over by the index of the hour-circle, from the time of the sun's setting, will show the duration of evening twilight. Or, by the ana lemma. : Elevate the pole to the latitude of the place, as above, and screw the quadrant of altitude upon the brass me- ridian over the degree of latitude ; bring the middle of the analemma to the brass meridian, and set the in- dex of the hour-circle to twelve ; turn the globe west- ward till the given day of the month, on the analemma, comes to the western edge of the horizon, and the hours passed over by the index will show the time of the sun's setting, or the beginning of evening twilight : continue the motion of the globe westward till the ^ivcn day of the month coincides with 18° on the quadrant below the horizon, the time passed over by the index, from the time of the sun's setting, will show the duration of evening tv/ilight. Examples. 1. Required the beginning, end, and duration of morning and evening twilight at London on the 19th of April? h U 86 PROBLEMS PEKFORMED WITH Answer. The sun sets at two minutes past seven, and evening twi- light ends at nineteen minutes past nine ; consequently morning twh light begins at (12 n. — 9 h. 19 ra. =) 2 h. 41 m. and ends at (12 h. — 7 h 8 m. =) 4 h. 5S m. ; the duration of twilight is 2 h. and 17 minutes. 2. What is the duration of twilight at London on the 23d of September, what time does dark night begin, and at what time does day break in the morning? Answer. The sun sets at six o'clock, and the duration of twilight is two hours ; consequently 1 he evening twilight ends at eight o'clock, and tlie morning twilight begins at four. 3. Required the beginning, end, and duration of morning and evening twilight at London on the 25th of August ? 4. Required the beginning, end, and duration of morning and evening twilight at Edinburgh on the 20th of February ? 5. Required the beginning, end, and duration of morning and evening twilight at Cape Horn on the 20th of February ? 6. Required the beginning, end, and duration of morning and evening twilight at Madras on the 15th of June ? Problem XXXVL To jind the beginnings end, and duration of constant day or twilight at any place. Rule Find the latitude of the given place, and add 18° to that latitude; count the number of degrees correspondent to the sum, on that part of the brass me- ridian which is numbered from the pole tov/ards the equator, mark whore the reckoning ends, and observe wliat two point? of the ecliptic pass under the marR; THE TERRESTRIAL GLOBE. 87 that, point wherein the sun's declination is increasing will show on the horizon the beginning of constant twilight; and that point wherein the sun's declination is decreasing, will show the end of constant twilight. Examples. 1. When do we begin to have constant day or twilight at London, and how long does it con- tinue ? A7iswer. The latitude of London is 5U degrees north, to which add 18 degrees, the sum is 69^, the two points of the ecliptic which pass under 69i are two degrees in n, answering to the 22d of May, and 29 degrees in go, answering to the 21st of July ; so that, from the 22d ot May to the 21st of July the sun never descends 18 degrees below the horizon of London. 2. When do the inhabitants of the Shetland islands cease to have constant day or twilight? 3. Can twilight ever continue from sun-set to sun- rise at Madrid ? 4. When does constant day or twilight begin at Spitzbergen? 5. What is the duration of constant day or twilight at the North Cape in Lapland, and on what day, after their long winter's night, do the sun's rays €rst enter the atmosphere 1 Problem XXXVII. To find the duration of twilight at the north pole. Rule, Elevate the north pole so that the equator may coincide with the horizon ; observe what point of the ecliptic nearest to Libra passes under 18^ below the horizon, reckoned on the brass meridian, and ^n^^ the day of the month correspondent thereto, the time elapsed from the 23d of September to this time v/ill be 88 PROBLEMS PERFORMED WITH the duration of evening twilight. Secondly, observe what point of the ecliptic, nearest to Aries, passca under 18° below the horizon, reckoned on the bras.^ meridian, and find the day of the month correspondent thereto ; the time elapsed from that day to the 21st of March will be the duration of morning twilight. Example. What is the duration of twilight at th*^ north pole, and what is the duration of darl^ ni^bt there ? Answer. The point of the ecliptic nearest to Libra Vvhich passes under 18 degrees below the horizon, is 22 degrees in 11], answering to the 13th of November ; hence the evening twilight continues from the 23d of September (the end of the longest day) to the 13th of Noveni- ber, (the beginning of dark night) being 51 days. The point of the ecliptic nearest to Aries which passes under 18 degrees below the hori- ' zon is 9 degrees in OX, answering to the 29th of January ; hence th(^ morning twilight continues from the 29th of January to the 21st of March (the begimimg of the longest day) being 51 days. From the 23d of September to the 21st of March are 179 days, fpm which deduct 102 ( z= 51 X 2,) the remaindei is 77 days, the duration of total dark- ness at the north pole ; but, even during tiiis short period, the moon and the Aurora Boreaiis shine with uncommon splendour. Problem XXXVIII. To find in lohat climate any given place on the giobe is situated. Rule. 1. If the place be not in the frigid zone find the length of the longest day at that place (bj Problem XXVIII.) and subtract twelve hours there- from ; the number of half hours in the remainder will show the climate. 2. If the place be in the frigid zone,* find the length * The climates between the polar circles and the poles were un- known to the ajicient geographers ,* they reckoned only seven climates THE TERRESTRIAL GLOBE. 8li of the longest day at that place (by Problem XXX.) and if that be less than thirty days, the place is in tho twenty-fifth climate, or the ^rs^ within the polar circle. [f more than thirty and less than sixty, it is in the twenty-sixth climate, or the second within the polar circle ; if more than sixty, and less than ninety, it is in the twenty-seventh climate, or the third within the polar circle, &c. Examples. 1. In what climate is London, and what other remarkable places are situated in the same climate ? Answer. The longest day in London is 16^ hours, if we deduct 12 therefrom, the remainder wdll be 4i hours, or nine half hours ; hence London is in the ninth climate north of the equator ; and as all places in or near the same latitude are in ihe same climate, we shall /uid Amsterdam, Dresden, Warsaw, Irkoutsk, the southern part of the pe- ninsula of Kamtschatka, Nootka Sound, the south of Hudson's Bay, the north of Newfoundland, &c. to be in the same climate as London. 2. In what climate is the North Cape in the island of Maggeroe, latitude 71° 30' north? north of the equator. The middle of the first northern climate they made to pass through Meroe, a city of Ethiopia, built by Cambyses on an island in the Nile, nearly under the tropic of Cancer ; the second through Syene, a city of Thebais in Upper Egypt, near the cataracts of the Nile ; the third through Alexandria ; the fourth through Rhodes ; the fifth through i?ome or the Hellespont; the sixth through the mouth of the Borysthenes or Diiieper ; and the seventh through the Riphhcean mounialns, supposed to be situated near the source of the Tanais or Doa river. The southern parts of the earth being in a great measure un known, the climates received their names from the northern ones and not from particular towns or places. Thus the climate, which was supposed to be at the same distance from the equator southward Meroe w^as northward, was called Antidiameroes, or the opposite tliraate to Meroe ; Antldiasyenes was the opposite climate to Syenes te. A 2 TJ 2 90 PROBLEMS PESFOJRMEr WITH Answer. The length of the longest day is 77 days ; these days dU vided by 30, give two months for the quotient, and a remainder of 17 days ; hence the place is in the third climate within the polar circle, or the 27th climate reckoning from the equator. The southern part oi' Nova Zembla, the northern part of Siberia, James' Island, Baffin's Bay the northern part of Greenland, &c. are in the same climate. 8. In \vhat climate is Edinburgh, and what other places are situated in the same climate 1 4. In what climate is the north of Spitzbergen F 5. In what climate is Cape Horn? 6. In what climate is Botany Bay, and what other places are situated in the same climate ? Problem XXXIX. To find the breadths of the several climates between the equator and the 'polar circles. Rule. For the northern climates. Elevate the north pole 23 J° above the northern point of the horizon ; bring the sign Cancer to the meridian, and set the in- dex to twelve ; turn the globe eastward on its axis till the index has passed over a quarter of an hour ; observe that particular point of the meridian passing through Libra, which is cut by the horizon, and at the point of intersection make a mark with a pencil ; continue the motion of the globe eastward till the index has passed over another quarter of an hour, and make a second m.ark : proceed thus till the meridian passing through Libra* will no longer cut the horizon ; the several * On Adams' and Gary's globes, the meridian passing through Lihr^ IS divided into degrees, in the same m^anner as the brass meridian is di« vided ; the horizon will, therefore, cut this meridian in the several de- grees answering to the end of each climate, without the trouble of bring* mg it to the brass meridian, or markmg the globe. THE TESRESTPaAL GLOBE. 91 marks brought to the brass meridian will point out the latitude where each climate ends. Examples. 1. What is th'e breadth of the ninth noi tb climate, and what places are situated w-ithin it? Answer. The breadth of the 9th climate is 2^ 57' ; it begins in Mh tude 49° 2' north, and ends in latitade 51^ 59' north, and all places siui- ated within this space are in the same climate. The places will b€ nearly the same as those enumerated in the first example to the preced- ing problem. 2. What is the breadth of the second climate, and in what latitude does it begin and end ? 3. Required the beginning, end, and breadth of the fifth climate ? 4. What is the breadth of the seventh climate north of the equator, in what latitude does it begin and end, and what places are situated within it ? 5. What is the breadth of the climate in which Pe- tersburg is situated ? 6. What is the breadth of the climate in which Mount Heckla is situated ? Problem XL.' To find that part of the equation of time which depends on the obliquity of the ecliptic. Rule. Find the sun's place in the ecliptic, and bring it to the brass meridian ; count the number of degrees from Aries to the brass meridian, on the equator and on the ecliptic ; the difference, reckoning four minutes of time to a degree, is the equation of time. If the number of the degrees on the ecliptic exceed those on the equator, the sun is faster than the clock ; but if the 92 PROBLEMS PERFOKMED WITH number of degrees on the equator exceed those on thft ecliptic, the sun is slower than the clock. Note. The equation of time, or differ- ence between the time shown by a well- .egulated clock, and a trae sun-dial, de- pends upon two causes, viz. the obliquity of the ecliptic, and the unequal motion of the earth in its orbit. The former of these causes may be explained by the above Problem. If tw^o suns were to set off at the same time from the point Aries, and move over equal spaces in equal time, the one on the ecliptic, the other on the equator, it is evident they would never come to the meridian together, ex- cept at the time of the equinoxes, and on the longest and shortest days. The an- nexed table shows how much the sun is faster or slower than the clock ought to be, so far as the variation depends on the obliquity of the ecliptic only. The signs of the first and third quadrants of the ecliptic are at the top of the table, and the degrees in these signs on the left hand ; m any of these signs the sun is faster than the clock. The signs of the second and third quadrants are at the bottotn of the table, and the degrees in these signs at the right hand ; in any of these signs the sun is lower than the clock. Thus, when the sun is in 20 degrees o)l }^ ox 1T[, it is 9 minutes 50 seconds faster than the clock, and, when the sun 18 in 18 degrees of 05 or VJ, it is 6 mi- BUtes 2 seconds slower than the clock. Sui^ faster than the Clock in op b n IQu bo ~r\- ^ t 3Qu M. S. M. S. M. S. 8 24 8 46 30 1 20 8 35 8 36 29 2 40 8 45 8 25 28 3 1 8 54 8 14 27 4 1 19 9 3 8 1 26 5 1 39 9 11 7 49 25 6 1 59 9 18 7 35 24 7 2 18 9 24 7 21 23 8 2 37 9 31 7 6 22 9 2 56 9 36 6 51 21 10 3 16 9 41 6 35 20 11 3 34 9 45 6 19 19 12 3 53 9 49 6 2 18 13 4 11 9 51 5 45 17 14 4 29 9 53 5 27 16 15 4 47 9 54 5 9 15 16 5 49 55 4 50 14 17 5 21 9 55 4 31 13 18 5 38 9 54 4 12 12 19 5 54 9 52 3 52 11 20 6 10 9 50 3 32 10 21 6 26 9 47 3 12 9 22 6 41 9 43 2 51 8 23 6 35 9 38 2 30 7 24 7 9 9 33 2 9 6 25 7 23 9 27 1 48 5 26 7 36 9 20 1 27 4 27 7 49 9 13 1 5 3 28 8 19 5 43 2 29 8 13 8 56 22 1 30 8 24 8 46 2Qu m a 55 t 4Qu X ^^ Q Sons lawer than the CL0C9. -^j THE TERBESTRIAL GLOBE. 93 Examples. 1. What is the equation pf time on the 17th of July? Answer. The degrees on the equator exceed the degrees on t}?e ecliptic by t^b ; hence the sun is eight minutes slower than the clock. 2. On what ft)ur days of the year is the equation of time nothing ? 3. What is the equation of time dependant on the obliquity of the ecliptic on the 27th of October? 4. When the sun is in 18° of Aries, what is the equation of time ? Problem XLL To find the sun's meridian altitude at any time of the year at any given place. Rule. Find the sun's declination, and elevate the pole to that declination ; bring the given place to the brass meridian, and count the number of degrees on the brass meridian (the nearest) to the horizon ; these degrees will show the sun's meridian altitude. Note. The sun's altitude may he found at any particular Tioiur, in the following manner. Find the sun's declination, and elevate the pole to that declination ; bnng the given place to the brass meridian and set the index to 12; then, if the given time be before noon, turn the globe W3stward as many hom*s as the time wants of noon; if the given time be past noon, turn the globe eastward as many hours as the time is past noon. Keep the globe fixed in this position, and screw the quadrant of altitude on the brass meridian over the sun's declination ; bring the graduated edge of the quadrant to coincide i^ath the given place, and the number of degrees between that place and the horizon will show the sun's al titude. Or, Elevate the pole so many degrees above the horizon 94 PROBLEMS PERFOEMED WIPH as are equal to the latitude of the place ; find the sun'd place in the ecliptic, and bring it to that part of the brass meridian which is numbered from the equator to- wards the poles ; count the number of degrees con- tained on the brass meridian between the sun's place and the horizon, and they will show the altitude. To find the sun's altitude at any hour, see Problem XLIV. Or, by the analemma. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place ; find the day of the month on the analemma, and bring it to that part of the brass meridian which is numbered from the equator towards the poles ; count the number of degrees contained on the brass meridian between the given day of the month and the horizon, and they will show the altitude. To find the sun's altitude at any hour, see Problem XLIV. Examples. 1, What is the sun's meridian altitude at London on the 21st of June? Answer. 62 degrees. 2. What is the sun's meridian altitude at London on the 21st of March? 3. What is the sun's least meridian altitude at Lon- don? 4. What is the sun's greatest meridian altitude at Cape Horn ? 5. What is the sun's meridian altitude at Madras on the 20th of June ? 6. What is the sun's meridian altitude at Bencoolen on the 15th of January ? THE TERRESTRIAL GLOBE. 95 Examples to the note. 1. What is the sun's altitude at Madrid on the 24th of August, at 11 o'clock in the morning? Ansvoer. The sun's declination is lit degrees north ; by elevating lii«» north pole lU degrees above the horizon, and turning the globe so that Madrid may be one hour westward of the meridian, the sun's alti- tude wall be found to be 57i degrees. 2. What is the sun's altitude at London at 3 o'clock in the afternoon on the 25th of April ? 3. What is the sun's altitude at Rome on the 16th of January at 10 o'clock in the morning? 4. Required the sun's altitude at Buenos Ayres on the 21st of December at two o'clock in the afternoon? Problem XL IT. ^Vken it is midnight at any place in the temperate or torrid zones, to find the sun^s altitude at any place (on the same meridian) hi the north frigid zone, where the sun does not descend below the horizon. Rule. Find the sun's declination for the given da} and elevate the pole to that declination j bring the place (in the frigid zone) to that part of the brass meridian which is numbered from the north pole towards the equator, and the number of degrees between it and ihe horizon will be the sun's altitude. Or, Elevate the north pole so many degrees above the horizon as are equal to the latitude of the place in the 96 PROBLEMS PERFORMED WITH frigid zone ; bring the sun's place in the ecliptic to the brass meridian, and set the index of the hour-circle to twelve ; turn the globe on its axis till the index points to the other twelve ; and the number of degrees be- tween the sun's place and the horizon, counted on the brass meridian towards that part of the horizon marked north, will be the sun's altitude. Examples. 1. What is the sun's altitude at the North Cape in Lapland, w^hen it is midnight at Alexan- dria in Egypt on the 21st of June ? Answer. 5 degrees. 2. When it is midnight to the inhabitants of the island of Sicily on the 22d of May, what is the sun'? altitude at the north of Spitzbergen, in latitude 80*^ north ? 3. What is the sun's altitude at the north-east of Nova Zembla, when it is midnight at Tobolsk, on the 15th of July? 4. What is the sun's altitude at the north of Baffin's Bay, when it is midnight at Buenos Ayres, on the 28th of May 7 Problem XLIII. To find the Burl's amplitude at any place. Elevate the pole so many degrees above the horizon as are equal to the latitude of the given place ; find the sun's j)lace in the ecliptic, and bring it to the eastern semicircle of the horizon ; the number of degrees from tlie sun's place to the east point of the horizon will be the lisiiig amplitude ; bring the sun's place to the v/est' THE TERRESTRIAL GLOBE. 9? em semicircle of the horizon, and the number of de grecs from the sun's place to the west point of the hori- zoD will be the setting amplitude. Or, by the analemma. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place ; bring the day of the month on the analemma to the eastern semicircle of the horizon : the number of degrees from the day of the month to the east point of the horizon will be the rising amplitude : bring the day of the month to the western semicircle of the horizon, and the number of degrees from the day of the month to the west point of tiie horizon will be the setting amplitude. Examples. 1 . What is the sun's amplitude at Lon- don on the 21st of June? Answer. 39^ 48' to ihe north of the east, and 39^ 48' to the north of the west. 2. On what point of the compass does the sun rise and set at London on the 17th of May? 3. On what point of the compass does the sun rise and set at the Cape of Good Hope on the 21st of De- cember? 4. On what point of the compass does the sun rise aod set on the 21st of March ? 5. On what point of the compajss does the sun rise and set at Washington on the 21st of October? 6. On what point of the compass does the sun rise and set at Petersburg on the 18th of December? T. On December 22d, 1827, in latitude 31^ 38' S. and longitude 83° W., if the sun set on the S. W. point ji the compass,' what is ihe variation ? t X 08 PROBLEMS PERFORMED WITH 8. On the 15th of May 1827, if the sun rise E. by N. in latitude 33° 15' N. and longitude 1S° W., what is the variation of the compass? Problem XLIV. To find the sutCs azimuth and his altitude at any place^ the day and hour being given. Rule. Elevate the pole so many degrees above the ' horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridian, over that latitude ; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to twelve ; then if the given time be before noon, turn the globe eastward* as many hours as it wants of noon ; but, if the given time be past noon, turn the globe westward as many hours as it is past noon, bring the graduated edge of the quadrant of alti- tude to coincide with the sun's place, then the number of degrees on the horizon, reckoned from the north or south point thereof to the graduated edge of the quadrant, will show the azimuth ; and the number of degrees on the quadrant, counting from the horizon to the sun's place, will be the sun's altitude. * "Whenever the pole is elevated for the latitude of the place, the pro- per motion of the globe is from east to west, and the sun is on the east Bide of the brass meridian in the morning, and on the west side in the aftemooii ; but when the pole is elevated for the sun's declination, th« motion is from west to east, and the place is on the w^est side of the me ndian in the m>rmng, aiid en the east side in the aflemoon. the terrestrial globe. 99 Or, by the analemma. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridian, over that latitude ; bring the middle of the analemma to the brass meridian, and set the index of the hour-circle to twelve ; then, if the given time be before noon, turn the globe eastward on its axis as many hours as it wants of noon ; but, if the given time be past noon, turn the globe westward as many hours as it is past noon ; bring the graduated edge of the quadrant of altitude to coin- cide with the day of the month on the analemma, then the number of degrees on the horizon, reckoned from > the north or south point thereof to the graduated edge of the quadrant, will show the azimuth ; and the num- ber of degrees on the quadrant, counting from the ho- rizon to the day of the month, will be the sun's altitude. Examples. 1. What is the sun's altitude, and his azimuth from the north, at London, on the 1st of May, at ten o'clock in the morning? Ansroer. The altitude is 47^, and the asimuth from the north 136^ ©r from the south 44*^. 2. What is the sun's altitude and azimuth at Peters- burg on the 13th of August, at half past five o'clock in the morning ? 3. What is the sun's azimuth and altitude at Anti- gua, on the 21st of June, at half past six in the morn- ing, and at half past ten ? 4. At Barbadoes on the 21st of June, re({uired the sun's azimuth and altitude at 8 minutes past 6^ and at 100 PROBLEMS TERFORMED WITH J past 9 in the morning : also at i past 2, and at 5'3 minutes past 5 in the afternoon. 5. On the 13th of August at half past eight oxlock m the morning, at sea, in latitude 57° N. the observed azimuth of the sun was S. 40° 14' E., what was the sun's altitude, his true azimuth, and the variation of the compass? 6. On the 14th of January, in latitude 33° 52' S., at half past three o'clock in the afternoon, the sun's magnetic azimuth was observed to be N. 63° 51' W. ; what was the true azimuth, the variation of the com- pass, and the sun's altitude ? Problem XLV. The latitude of the place, day of the month, and the sun^s altitude being given, to find the sini's azimuth, and the hour of the day. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridian, over that latitude ; bring the sun's place in the ecliptic to the brass meridian, and set the index of the hour- circle to twelve ; turn the globe on its axis till the sun's place in the ecliptic coincides vjiih. the given degree of altitiide on the quadrant ; the hours passed over by the index of the hour-circle will show the time from noon, and the azimuth will be found on the horizon, as in the preceding problem. Or, by the analemma. Elevate the pole to the latitude of Ihe place, and screw the ouadrant of altitude ove^ that latitude : bring THE TERRESTRIAL GLOBE. 101 ibe middle of the analeiiima to the brass meridian, and set the index of the hour-circle to twelve ; move the globe and the quadrant tiJl the day of the month coin- cides with the given altitude, the hours passed over by the index will show the time from noon, and the azi- muth will be found in the horizon as before. Examples. 1. At what hour of the day on the 21st of March is the sun's altitude 22 J° at London, and what is his azimuth? The observation being made in the afternoon. Answer. The time from noon will be found to be 3 hours 30 mi- nutes, and the azimuth 59° ]' from the south towards the west Had the observations been made before noon, the time from noon would have been 3^ hours, viz. it would have been 30 minutes past eight in the morning, and the azimuth would have been 59° V from the south towards the east. 2. At what hour on the 9th of March is the sun's al- titude 25° at London, and what is his azimuth ? The observation being made in the forenoon. 3. At what hour on the 18th of May is the son's al- titude 30° at Lisbon, and what is the azimuth '? The observation being made in the afternoon. 4. Walking along the side of Queen-square in Lon- don on the 5th of August in the forenoon, I observed the shadows of the iron-rails to be exactly the same length as the rails themselves ; pray what o'clock was it, and on what point of the compass did the shadows of the rails fall ? 5. At what hour of the day on the 20th of Septem- ber, is the sun's altitude 21° at Quebec, and what is its azimuth, the observation being made in Xhe morninof ? ^02 PROBLEMS PERFORMED WITH 6. At what hour on the 15th of June is the sun s a] titude 30^ at Philadelphia, and what is the azimuth the observation being made in the afternoon ? Problem XLVI. Given the latitude of the place, and the day of the month to fuid at what hour the sun is due east or west. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to twelve ; screw the quadrant of altitude on the brass meridian, over the given latitude, and move the lower end of it to the east point of the horizon ; hold the quadrant in this position, and move the globe on its axis till the sun's place comes to the graduated edge 'of the qua drant ; the hours passed over by the index from twelve will be the time from noon v/hen the sun is due east, and at the same time from noon he will be due west. Examples. 1, At what hour will the sun be due east at London on the 19th of May ; at what hour will he be due Vv est ; and what will his altitude be at these times? Answer. The time from 12 when the sun is due east, is 4 hours 54 minutes ; hence the sun is due east at six minutes past seven o'clock in the morning, and due west at 54 minutes past four in the afternonn ; the sun's altitude will be found at the same time, as in Problem XLIV In this example it is 25° 26^ 2. At what hours will the sun be due east and west at London on the 21st of June, and on the 21st of De* cember ; and what will be his altitude above the horl zon on the 21st of June ? THE TERRESTRIAL GL JB® 1 03 3. Find at what hours the sun will be due east and ^esif not only at London, but at every place on the surfavze of the globe, on the 21st of March and on the 23d of September? 4. At what hours is the sun due east and west at Buenos Ay res on the 21st of December ? Problem XLVII. Given the sun^s meridian altitude, and the day of the montk, to find the latitude of the place. Rule. Find the sun's place in the ecliptic, and bring it to that part of the brass meridian which is numbered from the equator towards the poles ; then, if the san was south of the observer when the altitude ' was taken, count the number of degrees from the sun's place on the brass meridian towards the south point of the horizon, and mark Vv^here the reckoning ends ; bring this mark to coincide with the south point of the hori- zon, and the elevation of the north pole will show the latitude. If the sun was north of the observer when the altitude was taken, the degrees must be counted in a similar manner, from the sun's place towards the north point of the horizon, and the elevation of the south pole will show the latitude. ^R, WITHOUT A GLOBE. Subtract the sun's altitude from ninety degrees, the remainder is the zenith distance. If the sun be south when his altitude is taken, call the zenith distance north; bui, if north, call it south; find the sun's de- 104 PROBLEMS PERFORMED WITH clination in an ephemeris or a table of the sun's tie^ ciinatioxi, and mark whether it be north or south ; then, if the zenith distance, and declination have the same name, their sum is the latitude, but, if they kave con- trary names, thei-r difference is the latitude, and it is always of the same name with the greater of the two quantities. Examples. On the 10th of May, 1827, I observed the sun's meridian altitude to be 50°, and it was south of me at that time ; required the latitude of the place ? Answer. 57^ 29^ north. By calculation. 90O 0' 50 S., sun's altitude at noon. 40 N., the zenith's distance. 17 29 A":, the sun's decUnation 10th May 1827. • 67 29 N., the latitude sought 2. On the 10th of May, 1827, the sun's meridian at- titude was observed to be 50°, and it was north of the observer at that time ; required the latitude of the place? Answer. 22° 23^ south. By calculaiion. 990 0' 50 N.y sun's altitude at noon. 40 S., the zenith's distance. 17 29 .Y., the sun's declination 10th May 1897. 22 31 S., the latitude sought. 3. On the 5th of August, 1827, the sun's meridian altitude w^as observed to be 74° 30' north of the ob- server : what was the latitude? THE TERRESTRIAL GLOBE. 105 4. On the 19th of November, 1827, the sun's meri- dian altitude was observed to be 40° south of the ob- server ; what was the latitude ? 5. At a certain place, where the clocks are two hours faster than at London, the sun's meridian altitude was observed to be 30 degrees to the south of the observer on the 21st of March ; • required the place ? 6. At the place where the clocks are 5 hours slower than at London, the sun's meridi"an altitude was ob- served to be 60"^ to the south of the observer on the 16th of April, 1827 ; required the place 1 Problem XLVIII. The length of the longest day at any place, not within the polar circles, being given, to find the latitude of that place. Rule. Bring the iirst point of Cancer or Capricorn to the brass meridian (according as the place is on the north or south side of the equator,) and set the index of the hour-circle to twelve : turn the globe westward on its axis till the index of the hour-circle has passed over as many hours as are equal to half the length of the day : elevate or depress the pole till the sun's place (viz. Cancer or Capricorn) comes to the horizon ; then the elevation of the pole will show the latitude. Note. This problem will answer for any day in the year, as weL as the longest day, by bringing the sun's place to the brass meridian and proceeding as above. Or, Bring the middle of the analemma to the brass meridian, and set the index of the hour-circle to 12 ; turn the globe westward on its axis till the index has passed over as many hours as are equal to half the length of the day ; elevate or depress the pole *4li the day of Ih* A 06 PROBLEMS PERFORMED WITH month coincides with the horizon, then the elevation of the pole wii» show the latitude. Examples. 1. In what degree of north latitude. and at what places is the length of the longest day 16^ hours ? Answer. In latitude 52*^, and all places situated on, or near that pa- rallel of latitude, have the samelengtii of the day. 2. In what degree of south latitude, and at what olaces is the longest day 14 hours 1 3. In what degree of north latitude is the length of the longest day three times the length of the shortest night ? 4. There is a town in Norway w^here the longest day is five times the length of the shortest night ; pray what is the name of the town ? 5. In what latitude north does the sun set at seven o'clock on the 5th of April ? 6. In what latitude south does the sun rise at five o'clock on the 25th of November ? 7. In what latitude north is the 20th of May 16 hours long? 8. In what latitude north is the night of the 15th of August 10 hours long? Problem XLIX. The latitude of a place and the day of the month being given, to find how much the sun'^s declination must vary to make the day an hour longer or shorter than the given day. Rfle. Find the sun's declination for the given day, and elevate the pole to that declination^: bring the THE TESEESTKIAL GLOBE. lOT given pla:5e to the brass meridian, and set the index of the hour circle to twelve : turn the globe eastward on its axis till the given place comes to the horizon, and observe the hours passed over by the index. Then, if the days be increasing, continue the motion of the globe eastward till the index has passed over another half hour, and raise or depress the pole till the place comes again into the horizon, the elevation of the pols will show the sun's declination when the day is an hour longer than the given day ; but, if the days be decreas- ing, after the place is brought to the eastern part of the horizon, turn the globe westward till the index has passed over half an hour, then raise or depress the pole till the place comes a second time into the hori- zon, the last elevation of the pole will show the sun's declination when the day is an hour shorter than the given day. Or, Elevate the pole to the latitude of the place, find the sun's place in the ecliptic, bring it to the brass meri- dian, and set the index of the hour-circle to twelve ; turn the globe westward on its axis till the sun's place comes to the horizon, and observe the hours passed over by the index ; then, if the days be increasing, continue the motion of the globe westward till the in- dex has passed over another half hour, and observe what point of the ecliptic is cut by the horizon ; that point will show the sun's place when the day is an hour longer than the given day, whence the declination is readily found : but, if the days be decreasing, turn the globe eastward till the index h,)s passed over half an 108 PROBLEMS PEi? FORMED WITH hour, and observe what point of the ecliptic is cut bj the horizon ; that point will show the sun's place when the day is an hour shorter than the given day. Or, by the analemma* Proceed exactly the same as above, only, instead of bringing the sun's place to the brass meridian, bring the analemma there, and instead of the sun's place, use the day of the month on the analemma. Examples. 1. How much must the sun's declina- tion vary that the day at London may be increased one hour from the 24th of February '? Answer. On the 24th of February the sun's declination is 9^ 38' *oulh, and the sun sets at a quarter past five ; when the sun sets at three quarters past five, his dechnation will be found to be about 4io south, answering to the tenth of March: hence the declination has decreased 5^ 23', and the days have increased 1 hour in 14 days. 2. How^ much must the sun's declination vary that the day at London may decrease one hour in length from the 26th of July ? Answer. The sun's declination on the 26th of July is 19° 38 north, and the sun sets at 49 min. past seven; when the sun sets at 19 mui. past seven, his declination will be found to be 14^ 43' north, answering to the 13th of August : hence the declination has decreased 5° 55*, anii the days have decreased one houi in 18 days 3. How much must the sun's declination vary from the 5th of April, that the day at Petersburg may in- crease one hour? 4. How much must the sun's declination vary fiora the 4th of October, that the day at Stockholm may de- crease one hour ? 5. What is the difference in the sun's declinatioa, THE TERRESTRIAL GLOBE. 109 wlier^ he rises at seven o'clock at Petersburg, and whew he sets at nine ? Problem L. To find the svnh right ascension^ oblique ascension^ ob- lique descension, ascensional difference, and time of rising and setting at any -place. Rule. Find the sun's place in the ecliptic, anci bring it to that part of the brass meridian whicli is numbered from the equator towards the poles ; the de- j^ree on the equator cut by the graduated edge of the brass meridian, reckoning from the point Aries east- ward, will be the sun's riglit ascension. Elevate the poles so many degrees above the horizon > as are equal to the latitude of the place, bring the sun's place in the ecliptic to the eastern part of the horizon, and the degree on the equator cut by the horizon, reckoning from the point Aries eastward, will be the sun s oblique ascension. Bring the sun's place in the ecliptic to the western part of the horizon, and the de- gree on the equator cut by the horizon, reckoning from the point Aries eastward, will be the sun's oblique de •ac en si on. Fmd the difference between the sun's right and ob- lique ascension ; or, which is the same thing, the dif ference between the right ascension and oblique de- scension, and turn this difference into time by multi- plying by 4 : then, if the sun's declination and the latitude of the place be both of the same name, viz. both north or both south, the sun rises before six and sets after six, by a space of time equal to the ascca^ k V . ilO PROBLEMS PERFORMED WITH sioDa! difFerence ; but if the sun's declination and tb€ latitude be of contrary names, viz. the one north and the other south, the sun rises after six and sets before Bix. Examples. 1. Required the sun's right ascension, oblique ascension, oblique descension, ascensional dif- ference, and time of rising and setting at London, on the 15th of April ? A/nstver. The right ascension is 23^ 3(y, the oblique ascension is 9*^ 15*, the ascensional difference (23^30'— 9^ 45'=) 13o 45', or 55 minutes sf tir le ; consequently (he Bun rises 55 minutes before 6, or 5 min. past 5, and sets 55 min. past 6. The oblique descension is 37° 15' ; conse- qaently the descen^sional difference is (37° 15'— 23° 30' = ) 13° 45*, the same as the ascensional difference. 2. What are the sun's right ascension, oblique ascen- sion, and oblique descension, on the 27th of October at London ; what is the ascensional difference, and at what time does the ^\in rise and set? 3. V/hat are the sun's right ascension, declination, oblique ascension, rising amplitude, oblique descen- sion, and setting amplitude at LfOndon, on the 1st of May ; what is the ascensional difference, and at wha* time does the sun rise and set ? 4. What are the sun's right ascension, declination iblique ascension, rising amplitude, oblique descen- sion, and setting amplitude, at Petersburg, on the 21st of Jwrie; what is the ascensional diiference, and what time does the sun rise and set ? 5. Wh?it are the sun's right ascension, declination, obli'iuc ascension, rising amplitude, oblique desccn- Bion, and setting amplitude, at Alexandria, on the 2lflft THE TERRESTRIAL GLOBE. Ill of December ; what is the ascensional difference and what lime does the sun rise and set T Problem LI. Given the day of the month and the sun^s amphludt at sunrise to find the latitude of the place of olh servation. Rule. Find the sun's place in the ecliptic, and bring it to the eastern or western part of the horizon, (according as the eastern or western amplitude i.' given,) elevate or depress the pole till the sun's i)la^e coincides with the given amplitude on the horizon, then the elevation of the pole will show the latitude Or, thus : Elevate the north pole to the complement* of the amplitude, and screw the quadrant of altitude upon the brass meridian over the same degree : bring the equi- noctial point Aries, to the brass meridian, and move tlie quadrant of altitude till the sun's declination foi ihe given day (counted on the quadrant) coincides with the equator ; the number of degrees between the point Aries, and the graduated edge of the quadrant, will be the latitude sought. ExA3iPLES. 1. The sun's amplitude at sunrise was observed to be 39° 48' from the east towards the north, on the 21st of June ; required the latitude of the place ! *The complement of the amplitude is found by subtracting the amph- l>litude from 90°. This rule is exactly the same as above ; for it in Jbrraed from a right-angled spherical triangle, the basio being the com piement of the amplitude, the perpendicular the latitude of *he p.are, aiK^ the hypothenuse the complement of the smi's dejiinaiioii. U2 PROBLEMS PERFORMED WITH Answer. 5P 32' north * 2. The sun's amplitude was observed to be 15^ 30 from the east towards the north, at the same time his declination was 15° 30' ; required the latitude ? 3. On the 29th of May, when the sun's declination was 21° 30' north, his rising amplitude was known to De 22° northward of the east ; required the latitude ? 4. When the sun's deplination was 2° north, his ris- ing amplitude was 4° north of the east ; required the latitude ? Problem LII. Given two observed altitudes of the sun, the time elapsed between tJiem, and the sun^s declination, to find the latitude. Rule. Find the sun's declination, either by the globe or an ephemeris ; take the number of degrees contain- ed therein from the equator with a pair of compasses, and apply the same number of degrees upon the meri dian passing through Libraf from the equator northward or southward, and mark where they extend to: turn ihe elapsed time into degrees, :j: and count those de- grees upon the equator from the meridian passing through Libra ; bring that point of the equator where the reckoning ends to the graduated edge of the brass meridian, and set off the sun's declination from that * See. Keith's Trig(mometry^ fourth edition, page 285. t Any meridian will answer the purpose as well as that which passes through Libra ; on Adams' and on Gary's globes this merdian is divided ike the brass meridian. \ See ihe method of turning time into degrees. Prob. Xf X. THE TERRESTRIAL GLOBE, llt^ point along the edge of the meridian, the same way as before : then take the complement of the first altitiiile from the eq ator in your compasses, and, with one foot in the sun's declination, and a fine pencil in the other foot, describe an arc ; take the complement of the second altitude in a similar manner from the equator, and with one foot of the compasses fixed in the ^'econd point of the sun's declination, cross the former arc ; the point of intersection brought to that part of the brass meridian which is numbered from the equator towards the poles, will stand under the degree of lati- tude sought. Examples. 1. Suppose on the 4th of June, 1827, in north latitude, the sun's altitude at 29 minutes past 10 in the forenoon, to be 65° 24', and at 31 minutes past 12, 74° 8' : required the latitude? Answer. The aun's declination is 22^^ 22' north, the elfipsed time two honrs two niin. answering to 30° SC ; the complement of the fli'^i altitude 24° 36', the compiement of the second altitJide 15^ 52^ and tha latitude sought 36° 57' north. 2. Given the sun's declination 19° 39' north, bis al- titude in the forenoon 38° 19', and, at the end of one hour and a half, the same morning, the altitude was 50° 25' ; required the latitude of the place, supposing \t to be north ? 3. When the sun's declination was 22° 40' north, his altitude at 10 h. 64 m. in the forenoon was 53° 29', uml at 1 h. 17 m. in the afternoon it was 52° 48' , re- quired the latitude of the place of observation, sup- |>osing it to be north? 4. In north latitude, when the sun's declination waa 22^' 23' south, the sun's altitude in the afternoon was k 2 Y 2 114 PROBLEMS PEKFORMED WITH -observed to be 14° 46', and after 1 h. 22 m. had elapsed, his altitude was 8° 27'- required the latitude? Problem LIII. The day and kour being given when a solar eclipse will happen^ tojind where it will be visible. Kjjle. Find the sun's declination, and elevate (he pcle agreeably to that declination ; bring the place at which the hour is given to that part of the brass meri^ dian which is numbered from the equator towards the poles, and set the index of the hour-circle to twelve ; ^hen, if the given time be before noon, turn the globe westward till the index has passed over as many hours as the given time wants of noon ; if the time be past noon, turn the globe eastward as many hours as it is past noon, and exactly under, the degree of the sun's declination on the brass meridian you will find the place on the globe where the sun will be vertically eclipsed :* at all places within 70 degrees of this place, the eclipse may t be visible *^pecially if it be a total eclipse. ExA3iPLE. On the 11th ol February, 1804, at 27 ruin, past ten o'clock in the morning at London, there was an eclipse of the sun, where was it visible, sup '^ T>ie effect of parallax is so great, that an eclipse may not be visi Me even where the sun is vertical. t When the moon is exactly in the node, and when the axis of th» tiioon's shadow and penumbra pass through the centre of the earth, tii& ?>readih of the earth's surface under the penumbral shadow is 70° 2^ uut the breadth of this shadow is variable; and if it be * •* accurately determined by calculation, it is impossible to tell by ihr ^lobe to what txtent an eclipse of the sun will be visible. THE TERRSSTEIAL GLOBE. 115 posing the moon's penumbral shadow to extend north- ward 70 degrees from the place where the sun was vertically eclipsed? Answer. London, &c. Problem LIV. The day and hour being given when a lunar eclipse will happen, to find where it will he visible. Rule. Find the sun's declination for the given day and note wiiether it be north or south ; if it be north, ele- vate the south pole so many degrees above the horizon as are equal to the declination ; if it be south, elevate the north pole in a similar manner ; bring the place at which the hour is given to that part of the brass meri- dian which is numbered from the equator towards the poles, and set the index of the hour-circle to twelve then, if the given time be before noon, turn the globe westward as many hours as it wants of noon ; if after noon, turn the globe eastward as many hours as it is past noon ; the place exactly under the degree of the sun's declination will be the antipodes of the place where the moon is vertically eclipsed, set the index of the hour-circle again to twelve, and turn the globe on its axis till the index has passed over twelve hours , then to all places above the horizon the eclipse will be visible ; to those places along the western edge of the horizon, the moon will rise eclipsed ; to those along the eastern edge she will set eclipsed ; and to that place immediately under the degree of the sun's declination reckoning towards the elevated pole, the moon will be vertically eclipsed. 116 > lOBLEaiS PERFORMED WITH ExAMPLK. ')n the 2Gth of January, 1 804, at 58 mm past spveii m the afternoon at London, there was an eclipse of th srioon ; where was it visible? Aisioer. ft \va^ visible to the whole of Emope» Afnca, and ibo coiitnieni of Asia. Problem LV. To find the time of the year when the Sun or Moon ivih be liable to be eclipsed. Rule 1. Find the place of the moon's nodes, th< time of new moon, and the sun's longitude at that time by an ephemeris; then if the sun be within 17 de- grees of the moon's node, there will be an eclipse of the sun. 2. Find the place of the moon's nodes, the time of full moon, and the sun's longitude at that time, by an ephemeris: then, if the sun's longitude be within 12 degrees of the moon's node, there will be an eclipse of the m.oon. Or, without the ephemeris The mean annual variation of the moon's nodes is 19*^ 19' 44" and the place of the node for the first of January 1827 being 2° 2' in =g=, its place for any otlic rime may therefore be found. ExAMPLES.1.0nthe9thof June, 1827, there will bo a full moon, at which time the place of the moon's node is 7° in ^ and the sur.'s longitude b(, 17'^ 48'; will an eclipse of the moon happen at that time ? Ansicer. Here the sun's longitude is not within 12 degrees of th« THE TERRESTRIAL GLOBE. 117 iDoon's node, therefore there will be no eclipse of the moor. — ^When Jhe sun is in one of the moon's nodes at the time of full moon, the moon is in the otiier node, and the earth is directly between them. 2. There will be a new moon on the 7th of June, 1827, at which time the place of the moon's node will be =^, 12° 43' and the sun's longitude b 15^ 54'; will there be an eclipse of the sun at that time? 3. There will be a new moon on the 18th of De- cember 1827, at which time the place of the moon's node will be ^ 2° 24' and the sun's longitude ^ 25^ 51' ; will there be an eclipse of the sun at that time ? 4. On the 3d of November, 1827, there v/ill be a full moon, at which time the place of the moon's node will be =- 4"^ 56', and the sun's longitude =-= 10'' 18' ; will there be an eclipse of the moon at that time 1 5. On the 25th of April, 1827, there will be a new moon, at which time the place of the moon's node is d^ 15° 19' and the sun's longitude ^ 4° 29' ; will there be an eclipse of the sun at that time? 6. On the 20th of October, 1827, there will be a new moon, at which time the place of the moon's node IS =-=5° 38' and the sun's longitude W 26° 19'; will there be an eclipse of the sun at that time ? Problem LVL To explain the phenomenon of the harvest moon* Definition 1. The harvest moon, in north latitude is the full moon which happens at, or near the time of the autumnal equinox; for, to the inhabitants of north latitude, whenever the moon is in Pisces or 4ries (and «he is in these signs twelve times in a year,) there is 116 PROBLEMS PERFOHMED WITH very little difference between her times of rising itii several nights together, because her orbit is at these times nearly parallel to the horizon. This peculiai rising of the rnoon passes unobserved at all other times of the year except in September and October ; for there never can be a full moon except the sun be directly opposite to the moon ; and as this particular rising of the noon can only happen when the moon is in X Pisces or <^p Aries, the sun must necessarily be either in W Virgo or t^h Libra at that time, and these signs answer to the months of September and October. Definition 2. The harvest moon, in south latitude, is the full moon which happens at, or near, the time of the vernal equinox ; for, to the inhabitants of south la- titude, w^henever the moon is in tt)^ Virgo or r^ Libra her orbit is nearly parallel to the horizon : but when the full moon happens in ^j^ Virgo or =^ Libra, the sun must be either in X Pisces or T Aries. Hence it ap- pears that the harvest moons are just as regular in south latitude as they are in north latitude, only they happen at contrary limes of the year. Rule for FERroRMiNo the problem. — L For north latitude. Elevate the north pole to the latitude of the place, pui a patch or make a mark in the ecliptic on the point Aries, and upon every twelve degrees pre- ceding and following that point, till there be ten or ele- ven marks ; bring that mark which is the neisrest to Pisces to the eastern edge of the horizon, and set the index to 12 ; turn the globe westward till trie other marks successively come to the horizon, and observe THE TERRESTRIAL GLOBE 119 tiie hours passed over by the index ; the intervals of time between the marks coming to the horizon v/ill show the diurnal difference of time between the moon's rising If these marks be brought to the western edge of the horizon in the same manner, you will see the diurnal difference of time between the moon's setting; for, when there is the smallest difference between the .^mes of the moon's rising, there will be the greatest iiliV'-ence between the times of her setting; and, on he 1 o.^trary, when there is the greatest difference be- iweei: the *imes of the moon's rising, there v/ill be the least difTeLMi-^c between the times of her setting. Note. As tile v^Ok I's Dodes vary their position and form a complete revohition in about i*-ii"^fc9n years, there will be a regular period if all the varieties which can mppen in the rising and setting of ihe mcK>« during that time. The ibii v^mg table (extracted from Ferguson's As- tronomy,) shows in what ye^irs ti e harvest moons are the least and most beneficial, wath regard to the ti nesof their rising, from 1823 to I860. The columns of yea^^ under tn 3 letter L are those in w'hich the har- vest moons are least beneficial, Iscause ihey fall about the descending node ; and those under M are t te mo^st beneficial, because they fall a i z .22 PROBLEMS PERFOHMED WITH m. 3 sec. past five o'clock in the morning at Green- wich ; where was it visible? Answer. In this example the longitude of the sun exceeds the loiw l^tude of Jupiter, therefore Jupiter was a morning star, his declination being 19=^ 16' S. and his longitude 7 signs 29^ 46', by the Nautical Al- manac : his right ascension and the sun's right ascension may be found by the globe ; for, if Jupiter's longitude in the ecliptic be brought to the brass meridian, his place will stand under the degree of his declina- tion ;* and hits right ascension will be found on the equator, reckoning from Aries. This eclipse was visible at Greenwich, the greater part of Europe, the west of Africa, Cape Verd islands, &c. 2. On the 5th of January, 1827, at 44 min. 2 sec past seven o'clock in the morning, at Greenwich, there will be an immersion of the first satellite of Jupiter; where will the eclipse be visible ? Jupiter's longitude at that time being 6 signs 13^ 41' and his declination 4'' 10' south. 3. On the 5th of June, 1827, at 14 min. 8 sec. past eight o'clock in the evening, at Greenwich, there will be an emersion of the first satellite of Jupiter ; where will the eclipse be visible? Jupiter's longitude at that time being 6 signs 4*^ 31' and his declination 0° 30' south. 4. On the 2d of December, 1827, at 39 min. 4 sec. oast six o'clock in the morning, at Greenwich, there will be an immersion of the first satellite of Jupiter ; . ivhere will the eclipse be visible ? Jupiter's longitude * This is on supposition that Jupiter moves in the ecliptic, and, as he deviates but little fherefrom, the solution hy this methoove the horizon of the place, and the sim as much below it." THE TERRESTRIAL GLOBE. 1 23 at that time being 7 signs 3° 59' and his declination 1^ 5' north. Problem LVIII. To place the terrestrial globe in the sun-shine, so that it may represent the natural position of the earth. Rule. If you have a meridian line* drawn upon a horizontal plane, set the north and south points of the wooden horizon of the globe directly over this line ; or, place the globe directly north and south by the ma- riner's compass, taking care to allow for the variation ; bring the place in which you are situated to the brass meridian, and elevate the pole to its latitude ; then the globe will correspond in every respect with the situa- tion of the earth itself. The poles, meridians, parallel circles, tropics, and all the circles on the globe, will correspond with the same imaginary circles in the heavens ; and each point, kingdom, and state, will be turned towards the real one, which it represents. While the sun shines on the globe, one hemisphere will be enlightened, and the other will be in the shade ; thus, at one view, may be seen all places on the earth wliich have day, and tliose which have night.f If a needle be placed perpendicularly in the middle of the enlightened hemisphere, (which must of course * As a meridian line is usetiil for fixing a horizontal dial, and fij^r placing a globe directly north and south, &c. the different methods of drawing a line of this kind will precede the problems on dialling. tFor thip part of the problem it would be more convenient if the globe could ^*e properly supported without the frame of it, because the shadow of its stand, and that of its horizon, will darken several parts ol Lhe surface of the globe which would otherwise be enlightened i:4 PROBLEMS PEftFOKMED WITH he upon the parallel of the sun's declination for th« lar time, aa showTi by a siui-dial ; and, therefore, to agree with » good clock or watch, il must be cx)rrected by a table of equation of time See a table oi'tliis kind among tlie succeedi*-, Algorab, in the Crow. «, ArcturuSj in Bootes. £, Fewtiemm^riar, in Virgo. Problem LXIII. To find the latitude and longitude of a star,^ Rule. Place the upper end of the quadrant of alti- tude on the north or south pole of the ecliptic, ac- cording as the star is on the north or south side of the ecliptic, and move the other end till the star comes to the graduated eilge of the quadrant : the number of de- grees between the ecliptic and the star is the latitude ,' and the number of degrees on the ecliptic, reckoned eastward from the point Aries to the quadrant, is the longitude. Or, Elevate the north or south pole ^Q\° above the horizon, according as the given star is on the north or * The latitudes and longitudes of the planets must be found from on ephemeris. 130 PROBLEMS PERFORMED WITH south side of the ecliptic; bring- the pole of the eclip tic to that part of the brass meridian which is numbei ed from the equinoctial towards the pole : then th*» ecliptic w^ill coincide with the horizon ; screw the quadrant of altitude upon the brass meridian over the pole of the ecliptic ; keep the globe from revolving on its axis, and move the quadrant till its graduated edge comes over the given star : the degree on the quadrant cut by the star is its latitude ; and the sign and degree on the ecliptic cut by the quadrant show its longitude- ExAMPLES. 1. Required the latitude and longitude df » Aldeharan in Taurus ? Anmer. Latitudfe 5° 28' S. longitude 2 signs 6° 53'; or 6° 53' in Gemini. 2. Required the latitudes and longitudes of the fol lowing stars ? «, Markab, in Pegasus. ^, Scheat, in Pegasus. «, Fomalhaut, in the S. Fish. », Deneb, in Cygnus. «, Altai?*, in the Eagle. &i Albireo, in Cygnus. «, Vega, in Lyra. y, Rastaben, in Draco. », Antares, in the Scor pion. «, Arcturus, in Bootes. '3, Pollux, in Gemini. p, Rigely in Orion. Problem liXIV. The right ascension and declination of a star, the moon^ a planet, or of a comet, being given, to find its place on the globe* Rule. Bring the given degrees of right ascension to that part of the brass meridian w^hich is numbered from the equinoctial towards the poles : then under THE CELESTIAL GLOBEo 131 the given declination on the brass meridian you will find the star, or place of the planet. Examples. 1. What star has 261^ 29' of right as- cension, and 52° 27' north declination ? Answer, & in Draco. 2. On the 31st of January, 1825, the moon's right ascension was 91° 21', and her declination 23^ 19'; find her place on the globe at that time. Answer. In the milky way, a little above the left foot of Castor. 3. What stars have the following right ascensions md declinations? Right Ascensions. Declinations. 55° 26' N. 38 N. 50 N. 34 8. 29 N. 27 S. 4. On the 1st of December, 1827, the moon's right ascension at midnight will be 50° 58', and her de ciination 16° 58' N.; find her place on the globe. 5. On the 1st of May, 1827, the declination of Ve- nus will be 1° 11' S. and her right ascension O'^ 4', find her place on the globe at that time. 6. On the 19th of January, 1827, the declination of Jupiter will be 4° 21' S, and his right ascension 12^ 55'; Snd hifs place on the globe at that time. 7° 19' 55 11 11 59 25 54 19 46 32 9 53 64 23 76 14 8 ight Ascensions. Declinationg. 83° 6' 34° 11' S. 86 13 44 55 N. 99 5 16 26 S. 110 27 32 19 N. 113 16 28 30 N. 129 2 7 8 N.^ 132 PROBLEMS PERFORMED WITH Problem LXV. The latitude and longitude of the moon^ a star or a planet^ given, to find its place on the globe. Rule, Place the division of the quadrant of al r.itude marked G, on the given longitude in the ecliptic, and the upper end on the pole of the ecliptic ; then, under the given lalitude, on the graduated edge of the qua- drant, you will find the star, or place of the moon oi planet. Examples. 1. What star has signs 6° 16' of Ion gitude, and 12° 86' N. latitude! Answer, r in Pegasus. 2. On the 5th of June, 1827, at midnight, the moon's longitude will be 6' 23° 41'; and her latitude l^ 49 S.; find her place on the globe. 3. What stars have the following latitudes and longi- tudes? Latitudes. 12° 35' S. 5 29 S. 31 8 S. 22 52 N. 16 3 S. Longitudes. | 1" ir 25' 2 6 53 2 13 56 2 18 57 2 25 51 Latitudes. 89^ 33' S. 10 4 N. 27 N. 44 20 N. 21 6 S. Longituden. 3» 11° 13 3 17 21 4 26 57 7 9 22 11 50 4. On the first of June, 1827, the longitudes anci latitudes of the planets will be as follow : required their places on the globe? Longitudes. ? 2» 0° 54' ? 1 7 1 J 2 22 12 Latitudef?. 0*-^ 29' S. 1 52 S. 46 N. Lonsn tudes. Latitudes. U G'' 4^^ 28' r27'N. ^^ 3 5 47 32 S. fj< 9 27 52 21 5 S the celestial globe. 133 Problem LXVI. The day and hour^ and the latitude of a place being given, to find what stars are risings setting, culmina' Ung, <§fc. Rule, Elevate the pole to the latitude of the place find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to 12 ; then, if the time be before noon, turn the globe east ward on its axis till the index has passed over as many hours as the time wants of noon ; but, if the time be past noon, turn the globe westward till the index has passed over as many hours as the time is past noon : then all the stars on the eastern semi-circle of the ho- rizon will be rising, those on the western semi-circle will be setting, those under the brass meridian above the horizon will be culminating, those above the hori- zon will be visible at the given time and place, those below will be invisible. If the globe be turned on its axis from east to west, those stars which do not go below the horizon never mi at the given pkce ; and those which do not come above the horizon never rise ; or, if the given latitude be subtracted from 90 degrees, and circles be described on the globe, parallel to the equinoctial, at a distance from it equal to the degrees in the remainder, they will be the circles of perpetual apparition and occulta tion. Examples. 1. On the 9th of February, when it is nine o'clock in the evening at London, what stars are m 2 A 184 PROBLEMS PERFORMED WITH nsing", what stars are setting, and what stars are on iht meridian ? Answer. Alphacca, in the northern Crown is rising ; Arcturjs and Mirach, in Bootes, just above the horizon ; Sirius on the meridian ; Pfocyon and Castor and Polhix a little east of the meridian. The con- ftellations Orion, Taurus, and Auriga, a little west of the meridian : Markab, in Pegasus, just below the western edge of the horizon, &c. 2. On the 20th of January, at two o'clock in the morn- mg at London, what stars are rising, what stars are jsetting, and what stars are on the meridian ? Answer. Vega in Lyra, the head of the Serpent, Spica Virginis, &«. are rising ; the head of the Great Bear, the claws of Cancer, &c. on the meridian ; the head of Andromeda, the neck of Cetus, and the body of Columba Noachi, &;c. ere setting. 3. At ten o'clock in the evening at Edinburgh, on the 15th of November, what stars are rising, what stars are setting, and what stars are on the meridian? 4. What stars do not set in the latitude of London, and at what distance from the equinoctial is the circle of perpetual apparition ? 5. What stars do not rise to the inhabitants of Edin- burgh, and at what distance from the equinoctial is the circle of perpetual occultation 1 6. What stars never rise at Otaheite, and what stam never set at Jamaica? 7. How far must a person travel southward frono London to lose sight of the Great Bear ? 8. What stars are continually above the horizon at the north pole, and what stars are constantly below the horizon thereof? THE CELESTAL GLOBE, 135 PROBLFa>I LXVIL Fhe latitude of a place ^ day of the months and hour being giveuj to place the globe in such a manner as to represent the heavens at that time ; in order to find out the relative situations and names of the constella- tions and remarkable stars. Rule. Take the globe out into the open air, on a clear star-light night, where the surrounding horizon is uninterrupted by different objects ; elevate the pole to the latitude of the place, and set the globe due north and south by a meridian line, or by a mariner's com pass, taking care to make a proper allowance for the variation ; find the sun's place in the ecliptic, bring it to the brass meridian and set the index of the hour- circle to 12 ; then, if the time be after noon, turn the globe westward on its axis, till the index has passed over as many hours as the time is past noon ; but, if the time be before noon, turn the globe eastward till the index has passed over as many hours as the time wants of noon ; fix the globe in this position, then the flat end of a pencil being placed on any star on the globe so as to point towards the centre, the other end will point to that particular star in the heavens. Problem LXVIII. To find when any star^ or planet, will rise^ come to the meridian, and set at any given place. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place , find 136 PROBLEMS PERFORMED WITH the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to 12. Then if the star or planet be helow the horizon, turij the globe westward till the star or planet comes to the eastern part of the horizon, the hours passed over by the index will show the time from noon when it rises ; and, by continuing the motion of the globe westward till the star, &c. comes to the meridian, and to the west- ern part of the horizon successively, the hours passed over by the index will show the time of culminating and setting. If the star, &c. be above the horizon and east of the meridian, find the time of culminating, setting, and rising, in a similar manner. If the star, &;c. be abcme the horizon west of the meridian, find the time of set- ting, rising, and culminating, by turning the globe westward on its axis. Examples. 1. At what time will Arcturus rise, come to the meridian, and set, at London, on the 7th of September ? Answer. It will rise at seven o'clock in the morning, come to the meridian at throe in the afternoon, and set at eleven o'clock at night 2. On the 1st of August, 1805, the longitude of Ju- piter was 7 signs 26 deg. 34 min., and his latitude 45 min. N. ^ at what time did he rise, culminate, and set, at Greenwich, and whether was he a moruing or an evening star? Answer. Jupiter rose at half past two in the afternoon, came to the meridian at ahoui ten minutes to seven, and set at aqupr'.er past eleven in the evening. Here Jupiter was an evening star, because he set after ihesiin. THE CELESTIAL GLOBE, 137 3. At what time does Sirius rise, set, and come to the meridian of London, on the 31st of January ] 4. On the 1st of January, 1627, the longitude of Venus will be 8 signs 27 deg. 10 min. and her latitude 1 deg. 29 min. N.; at what time will she rise, culminate, fand set at Paris, and whether will she be a morning or an evening star 1 5. At what time does Aldebaran rise, come to the meridian, and set at Dublin, on the 25th of November? 6. On the first of February, 1827, the longitude of Mars will be 11 signs 26 deg. 26 min., and latitude deg. 32 min. S. ; at what time will he rise, set, and come to the meridian of Greenwich ? Phoblem LXIX. To find the amplitude of any star, its oblique ascension and descensiony and its diurnal arc for any given day. Rule. Elevate the pole to the latitude of the place, and bring the given star to the eastern part of the ho- rizon ; then the number of degrees between the star and the eastern point of the horizon will be its rising amplitude ; and the degree of the equinoctial cut by the horizon will be the oblique ascension : set the index of the hour-circle to 12, and turn the globe westward till the given star comes to the western edge of the ho- rizon ; the hours passed over by the index will be the star's diurnal arc, or continuance above the horizon. The setting amplitude will be the number of degrees between the star and the western point of the horizon, and the oblique descension will be represented by that m2 2 a2 138 PROBLEMS PERFORMED WTTH degree of the equinoctial which }^ intersected by the horizon, recKoning from the point Aries. Examples. 1. Required the rising and settin-^ am- plitude of Sirius, its oblique ascension, oblique descen- sion, and diurnal arc, at London ? Answer. The rising amplitude is 27 deg. to the south of the east setting amplitude 27 deg. south of the west ; ohlique ascension 120 deg^ oblique descension 77 deg.; and diurnal an- 9 houi"s 6 minutes. 2. Required the rising and setting amplitude of AI- debaran,its oblique ascension, oblique descension, and diurnal arc, at London ] 3. Required the rising and setting amplitude of Arcturus, its oblique ascension, oblique descension, and diurnal arc, at London 1 4. Required the rising and setting amplitude of y Bellatrix, its oblique ascension, oblique descension, and diurnal arc, at London ] Problem LXX. To find the distances of the stars from each other in degrees. Rule. Lay the quadrant of altitude over any two stars, so that the division marked o may be on one of the stars ; the degrees between them will show their distance, or the angle which these stars subtend, as seen by a spectator on the earth. Examples. 1. What is the distance between Vega in Lyra, and Altair in the Eagle 1 Answer. 34 degrees. 2. Required the distance between ^ in the Bull's Horn and y Bellatrix in Orion's shoulder ? THE CELESTIAL OLOBF. 139 3. What is the distance between s in Pollux, and • in Procyon ? 4. What is the distance between m, the bnghtest of the Pleiades, and 3 in the Great Dog's Foot? 5. What is the distance betvveen « in Orion's girdle and s' in Cetus ? 6. What is the distance between Arcturus in Bootes, and ^ in the right shoulder of Serpentarius'i Problem LXXI. To find what stars lie in or near the moon's path^ or what stars the moon can eclipse, or make a near ap^ proach to. Rule. Find the moon's longitude and latitude, or her right ascension and declination, in an epheineris, for several days, and mark the moon's places on the globe ; then by laying a thread, or the quadrant of alti- tude, over these places, you will see nearly the moon's path, and consequently, what stars lie in her way. Examples. 1. What stars were in, or near, the moon's path, on the 10th, 11th, 13th, and 16th of De- cember, 1805] 10th, )'s longitude £\ 20^ 12' latitude 3° 34' S. 11th, . . nj 4 22 . - 4 25 S. 13th, . . =- 1 39 - . 5 15 S. 16th, . . m, 10 11 . - 4 26 S Answer, The stars will be found to be Cor Leonis or Regulus, Spi- es Virginis, » in Libra, &c. See page 47, White's Ephemeris. 2. On the 1st, 2d, 3d, 4th, and 5th of April, 1827 what stars will lie near the moon's way ? 140 PROBLEMS PERFORMED WITH 1st, )'s right ascension, 72° 6' declination 19° 55'N 2d, - - 84 41 . - 19 59 N, Sd, - . 97 14 . . 19 9N. 4th, - 109 44 . . 17 28N 5th, - . 122 8 . . 14 58 N Problem LXXII. Given the latitude of the place and the day of the months to find what planets will be above the horizon after sun-setting. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place ; find the sun's place in the ecliptic, and bring it to the western part of the horizon, or to ten or twelve degrees Delow ; then look in the ephemeris for that day and month, and you will find what planets are above the horizon, such planets will be fit for observation on that night. Examples. 1. Were any of the planets visible after the sun had descended ten degrees below the horizon of London, on the 1st of December, 1805 ? Their lon- gitudes being as follow: ^ 8» 22° 30' 4 8' 15° 27' ^s longitude at ? 9 23 40 1? 6 24 50 midnight 0' Q'^ ^ 8 25 21 JJ{ 6 24 5 Answer. Venus and the moon were visible. 2. What planets will be above the horizon of Lon .ion when the sun has descended ten degrees below, on the 1st of January, 1827 1 Their longitudes being }is follow : THE CELESTIAL GLOBE. 141 ^ 8 17^' 51' 4 6' 12^13 )'s longitude an ^8 27 10 ^321 midnight ir 5° 9' J 11 2 48 iji 9 23 22 Peoblem LXXIIL Given the latitude of the place^ day of the month, and hour of the night or morning, to find what planets will be visible at that hour. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place ; find the sun's place in the ecliptic, bring it to the brass me- ridian, and set the index of the hour-circle to 12 : then, if the given time be before noon, turn the globe eastward till the index has passed over as many hours as the time wants of noon ; but if the given time be past noon, turn the globe westward on its axis till the index has passed over as many hours as the time is past noon : let the globe rest in this position, and look in the ephemeris for the longitudes of the planets, and, ii any of them he in the signs which are above the horizon, such planets will be visible. Examples. 1. On the 1st of December, 1805, the longitudes of the planets, by an ephemeris, were as follow ; were any of them visible at London at ^\q o'clock in the morning ? ^ 8^ 22° 30' 4 8' 15° 27' ^s longitude at ? 9 23 40 T? 6 24 50 midnight 0' 9° 15'. J 8 25 21 JJi 6 24 5 Answer. Saturn and the Georgium Sid us were visible, and both nearly in the same point of the heavens, near the eastern horizon j Sa- lum was a little to the north of the Georgian 143 PROBLEMS PERFORMED WITH 2. On the first of June, 1827, the longitudes of the planets in the fourth page of the Nautical Almanac ar 5 a« follow : will any of them be visible at London at ten o'clock in the evening] ¥ 2' 0° 54' 4 6' 4° 28' )'s longitude at ? 1 7 1 ^ 3 5 47 midnight 5- 0^ 25'. ^ 2 22 12 )ii 9 27 52 Problem LXXIV. The latitude of the place and day of the month hein^ given, to find how long Venus rises before the sun when she is a morning star^ and how long she sets after the sun when she is an evening star. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place ; find the latitude and longitude of Venus in an ephemeris, and mark her place on the globe ; find the sun's place in the ecliptic, and bring it to the brass meridian ; then, if the place of Venus be to the right hand of the me- ridian, she is an evening star ; if to the left hand she is a morning star. When Venus is an evening star. Bring the sun's place to the western edge of the horizon, and set the index of the hour-circle to 12 ; turn the globe westward n its axis till Venus coincides with the western edge of the horizon ; and the hours passed over by the index will show how long Venus sets after the sun. ' When Venus is a morning star. Bring the sun's place to the eastern edge of the horizon, and set the index of the hour-circle to 12; turn the globe eastward on its axis till Venus comes to the eastern edge of the THE CELESTIAL GLOBE. 143 nonzon, and the hours passed over by the ndex will show how long Venus rises before the sun. Note. The same rule will serve for Jupiter^ by wark' ing his place instead of that of Venus. Examples. 1. On the first of March, 1805, the longitude of Venus was 10 signs, 18 deg. 14 min., or 18 deg. 14 min. in Aquarius, latitude deg. 62 min. south : was she a morning or an evening star ? If a morning star, how long did she rise before the sun at I^ndon ; if an evening star how long did she shine after the sun set ? Answer. Venus was a morning star, and rose three quarters of an lOur before the sun. 2. On the 25th of October, 1805, the longitude of Jupiter was 8 signs 7 deg. 26 min., or 7 deg. 26 min. in Sagittarius, latitude deg. 29 min. north : whether was he a morning or an evening star ? If a morning star, how long did he rise before the sun at London ? [f an evening star, how long did he shine after the sun set ? Answer. Jupiter wa« an evening star, and set 1 hour and 20 mm. after the sun. 3. On the 1st of January, 1827, the longitude of Venus will be 8 signs 27 deg. 10 min., latitude 4 deg. 29 min. north : will she be a morning or an evening star ? If she be a morning star, how long will she lise before the sun at London ? If an evening star, how long will she shine after the sun sets ? 4. On the seventh of July, 1827, the longitude of Jupiter will be 6 signs 5 deg. 46 min., latitude 1 deg, 19 min north ; will he be a morning or an evecing 144 PROBLEMS PERFORMED WITH atar ? If he be a morning star, how long will he rise before the sun ? If an evening star, how long will he shine after the sun sets 7 Problem LXXV, The latitude of a place and day of the month being given to find the meridian altitude of any star or planet* Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the given place ; then, For a star. Bring the given star to that part of the brass meridian, which is numbered from the equinoc tiai towards the poles; the degrees on the meridiar contained between the star and the horizon will be the altitude required. For the moon or a planet. Look in an ephemeris for the planet's latitude and longitude, or for its right as- cension and declination, for the given month and day, and mark its place on the globe ; bring the planet's place to the brass meridian ; and the number of degrees between that place and the horizon will be the altitude. Examples. 1. What is the meridian altitude of Al- debaran in Taurus, at London? Answer, 549 2&. 2. What is the meridian altitude of Arcturus in Bootes, at London ? :^. On the first of February, 1827, the longitude of Jupiter will be 6 signs 14 deg. 25 min., and latitude i deg. 27 min. north : what will his meridian altitude be at London ? 4. On the first of November, 1827, the longitude of THE CELESTIAL GLOBE. £45 Saturn will be 3 signs 20 deg. 18 niin. and latitude deg. 21 min. south : what will his meridian altitude be at London ? 5 On the first of April, 1827, at the time of thi^ moon s passage over the meridian of Greenwich, hei right ascension is 61° 49', and declination 19"^ 40' N. required her meridian altitude at Greenwich? 6. On the 21st of December, 1827, the moon wil^ pass over the meridian of Greenwich at 56 minutes j.ast two o'clock in the evening ; required her meridiaF altitude? The )'s right ascension at noon being 44° 49', declination 15° 51' N« Daatmidnight 50 68 - - - 16 58 N. Pkoblei^ LXXVI. To find all fJiose places on the earth to which the moon will be nearly vertical on any given day. Rule. Look in an ephemeris for the moon's lati- tude and longitude for the given day, and mark her [dace on the globe (as in Prob. LXV.) ; bring this place to that part of the brass meridian which is num- bered from the equinoctial towards the poles, and ob- serve the degree above it ; for all places on the earth having that latitude will have the moon vertical (or nearly so) when she comes to their respective meri* dians. Or : Take the moon's declination from page VI. of the Nautical Almanac, and mark whether it be north or south, then, by the terrestrial globe, or by a map, find all places having the same number of degrees of latitude as are contained in the moon's declination n 2B 146 PKOBLEMS PERFORMED WITH and those will be the places to which the moon will be successively vertical on the given day. If the moon's declination be north, the places will be in north latitude • i{ the moon's declination be south, they will be in south latitude. Examples. 1. On the 15th of October, 1805, the m3on's longitude at midnight was 3 signs 29 deg. 14 min., and her latitude 1 deg. 35 min. south; over what places did she pass nearly vertical ? Answer. From the moon's latitude and longitude being given, her declination may be found by the globe to be about 19^ north. The moon was vertical at Porto Rico, St. Domingo, the north of Jamaica, O'why'hee, &c. 2. On the 9th of September, 1827, the moon's lon- gitude at midnight will be 1 sign 10 deg., and her latitude deg. 22 min. south ; over w^hat places on the earth will she pass nearly vertical ? 3. What is the greatest north declination which the moon can possibly have, and to what places will she be tiien vertical ? 4. What is the greatest south declination which the moon can possibly have, and to what places will she be Uien vertical? Problem LXXVII. Given the latitude of a place, day of the month, and ths altitude of a star, to find the hour of the night, and the starts azimuth. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude : find the sun's place in the ecliptic THE CELESTIAL GLOBE. 147 bring it to the brass meridian, and set the index of the hour-circle to 12 ; bring the lower end of the quadrant of altitude to that side of the meridian on which the star was situated when observed ; turn the globe west- ward till the centre of the star cuts the given altitude on the quadrant; count the hours which the index has passed over, and they will show the time from noon when the star has the given altitude : the quadrant will intersect the horizon in the required azimuth. Examples. 1. At London, on the 28th of Decem- ber, the star Deneb m the Lion's tail, marked /S, was observed to be 40 deg. above the horizon, and east of the meridian : what hour was it, and what was the star's azimuth ? Answer. By bringing the sun's place to the meridian, and turning the globe westward on its axis till the star cuts 40 deg. of the quadrant east of ike meridiauy the index will have passed over 14 hours ; conse- quently, the star has 40 deg. of altitude east of the meridian, 14 hours fix>m noon, or at two o'clock in the morning. Its azimuth will be 62| deg. from the south towards the east. 2. At London, on the 28th of December, the star /3, in the Lion's tail, was observed to be westward of the meridian, and to have 40 deg. of altitude : what hour was it, and what was the star's azimuth \ Answer. By turning the globe westward on its axis till the star cuti 40 deg. of the quadrant west of the meridian, the index will have passed over 20 hours ; consequently, the star has 40 deg. of altitude west of the meridian, 20 hours from noon, or at eight o'clock in the morning. Its azimuth will be 62i deg. from the south towards the west. 3. At London, on the 1st of Septemberj the altitude of Benetnach in Ursa Major, marked », was observed to be 36 degrees above the horizon, and west of the meridian ; what hour was it, and what was the star'a azimuth? 148 PROBLEMS PESFORMED WITH 4. On the 21st of December, the altitude of Sinus, when west of the meridian at London, was observed te be 8 deg. above the horizon ; what hour was it, and what was the star's azimuth? 5. On the 12th of August, Menkar in the Whale's jaw, marked «, was observed to be 37 deg. above the horizon of London, and eastward of the meridian ; what hour was it, and what was the star's azimuth ? Problem LXXVIIL Given the latitude of a place, day of the month, and hour of the day, to find the altitude of any star, and its azimuth. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude ; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to 12 ; then, if the given time be before noon : turn the globe eastward on its axis till the in- dex has passed over as many hours as the time wants of noon ; if the time be past noon, turn the globe west- ward till the index has passed over as many hours as the time is past noon : let the globe rest in this posi- tion, and move the quadrant of altitude till its gradua- ted edge coincides with the centre of the given star; the degrees on the quadrant, from the horizon to the itar, will be the altitude ; and the distance from tne aorth or south point of the horizon to the quadrant, C'i'^anted on the horizon, will be the azimuth from the m ith or south. THE CELESTIAL GLOBE. 149 Examples. 1. What are the altitude and azimuth of Capeila at Rome, when it is &ve o'clock in the morn- ing on the 2d of December? Anffiver. The altitude is 41 deg. 58 min. and the azimuth 60 deg. 50 min. from the north towards the west 2. Required the altitude and azimuth of Altair in Aquila on the 6th of October, at nine o'clock in the evening, at London 1 3. On what point of the compass does the star Alde- baran bear at the Cat)e of Good Hope, on the 5th of March, at a quarter past eight o'clock in the evening; and what is its altitude 1 4. Required the altitude and azimuth of Acyone in the Pleiades marked ^, on the 21st of December, at four o'clock in the morning, at London Problem LXXIX. €Hven the latitude of the place, day of the month, and azimuth of a star, to find the hour of the night and the starts altitude. Rule, Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude ; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the honr-circle to twelve ; bring the lower end of the qua- drant of altitude to coincide with the given azimuth on the horizon, and hold it in that position ; turn the globe westward till the given star comes to the graduated %^gQ of tlie quadrant, and the hours passed over by the index will be the time from noon ; the degrees on the n2 2 b2 £50 PROBLEMS PERFORMED WITH quadrant, rfeckoning from the horizon to the »tar, wiL be the ali'tude. Examples. 1. At London, on the 28th of Decem- ber, the azimuth of Deneb in the Lion's tail marked i, was 62 J deg. from the south towards the west; whs I hour was it, and what was the staf's altitude ? Answer, By turning the globe westw^ard on its axis, the index wiil ' pass over 20 hoars before the star intersects the quadrant; therefore the lime will be 20 hours from noon, or eight o*clocii in the morning ; and the star's altitude will be 40 deg. 2. At London, on the 5th of May, the azimuth of Cor Leonis, or Regulus, marked «, was 74 deg. from the south towards the west ; required the star's altitude, and the hour of the night ? 3. On the 8th of October, the azimuth of the star marked /s, in the shoulder of Auriga, was 50 deg. from the north towards the east; required its altitude at Lon- don, and the hour of the night ? 4. On the 10th of September, the azimuth of the star marked «, in the Dolphin, was 20 deg. from the south towards the east ; required its altitude at London, and the hour of the night 1 Problem LXXX. Two stars being given, the one on the meridian, and the other on the east or ivest part of the horizon, to find the latitude of the place. Rule. Bring the star which was observed to be on the meridian, to the brass meridian ; keep the globe from turning on its axis, and elevate or c.epress the pole till the other star comes to the easter i or wester© THE CELESTIAL GLOBE. 161 part of the horizon ; then the degrees from the ele^. vated pole to t^ie horizon will be the latitude. KxA3iPLEs. 1. When the two pointers of the Great Bear, marked « and ^, or Dubhe and /s, weie on the meridian, I observed Vega in Lyra to be rising ; re- quired the latitude? Answer, 27 deg. north. 2. When Arcturus in Bootes was on the meridian, Altair in the Eagle was rising; required the latitude ? 3. When the star marked /3 in Gemini was on the meridian, « in the shoulder of Andromeda was setting; required the latitude? 4. In what latitude are « and /6, or Sirius and 3 in Canis Major rising, when' Algenib, or «, in Perseus, h on the meridian? PllOBLE3I LXXXI. The latitude of the place, the day of the month, and two stars that have the same azimuth, being given, to find the hour of the night. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude ; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to 12 ; turn the globe on its axis from east to west till the two given stars coincide with the gra- duated edge of the quadrant of altitude ; the hours passed over by the index will show the time from noon , and the common azimuth of the two stars will be found on the horizon. 152 PROBLEMS PERFORMED WITH Examples. 1. At what hour at London, on the 1st of May, will Altair in the Eagle, and Vega in the Haq); nave the same azimuth, and what will thai azimuth bet Ansv^er. By bringing the sun's place to the meridian, <&:c. and turn- ing the globe westward, the index will pass over 15 hours before the stars coincide with the quadrant; hence they will have the same azi- muth at 15 hours from noon, or at three o'clock in the morning ; and the azimuth will be 42^ deg. from the south towards the east 2. On the 10th of September, what is the hour at London, when Deneb in Cygnus, and Markab in Pe- gasus, have the same azimuth, and what is the azimuth 1 3. At what hour on the 15th of April will Arcturus and Spica Virginis have the same azimuth at London, and what will that azimuth be ? 4. On the 20th of February, what is the hour at Edinburgh when Capella and the Pleiades have the same azimuth, and what is the azimuth 1 5. On the 21st of December, what is the hour at Dublin when « or Algenib in Perseus, and /s in the Bull's horn, have the same azimuth, and what is the azimuth ? Problem LXXXIL The latitude of the 'place ^ the day of the months and two stars that have the same altitude, being given, to find the hour of the night. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude upon the brass meridian over that latitude ; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to 12 ; turn the globe on its axis from east THE CELESTIAL GLOBE* 153 to west till the two given stars coincide with the given altitude on the .graduated edge of the quadrant; the hours passed over by the index will be the time from noon when the two stars have that altitude. Examples. 1. At what hour at London, on the 2d of September, will Markab in Pegasus, and o» in the head of Andromeda, have each 30 deg, of altitude? Answer. At a quarter past eight in the evening. 2. At w^hat hour at London, on the 5th of January, will «, Menkar, in the Whale's jaw, and », Aldebaran, in Taurus, have each 85 deg, of altitude ? 3. At what hour at Edinburgh, on the 10th of No- vember, will «, Altair, in the body of the Eagle, and c, in the tail of the Eagle, have each 35 deg. of altitude ? 4. At what hour at Dublin, on the 15th of May, will »7, Benetnach, in the Great Bear's tail, andy, in the shoulder of Bootes, have 56 deg, of altitude? Problem LXXXIII. The altitudes of two stars having the same azimuth^ and that azimuth being given, to find the latitude of the 'place* « Rule. Place the graduated edge if the quadrant of altitude over the two stars, so that each star may be exactly under its given altitude on the quadrant; hold the quadrant in this position, and elevate or depress the pole till the division marked o, on the lower end of the quadrant, coincides with the given azimuth on the ho rizon : when *his is effected, the elevation of the pole will be the latitude. ^54 PKOBLEMS PERFORMED WITH Examples. 1. The altitude of Arcturus was ob served to be 40 deg. and that of Cor. Caroli 68 deg. their common azimuth at the same time was 71 deg from the south towards the east; required the latitude! Answer. 5H deg. north. 2. The altitude of « in Castor was observed to be 40 (leg.y and that of 3 in Procyon 20 deg. ; their common azimuth at the same time was 734 deg. from the south towards the east ; required the latitude ? 3. The altitude of «, Dubhe, was observed to be 40 deg.^ and that of r in the back of the Great Bear 29 J deg,^ their common azimuth at the same time was 30 deg. from the north towards the east ; required the la- titude 1 4. The altitude of Vega, or » in Lyra, was observed to be 70 deg., and that of « in the head of Hercules .39J deg*, their common azimuth at the same time was 60 deg. from the south towards the west ; required the latitude 1 Problem LXXXIV. The day of the month being given, and the hour when any known star rises or sets, to find the latitude of the place. Rule. Find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour- circle to 12 ; then, if the given time be before noon, turn the globe eastward till the index has passed over as many hours as the time wants of noon ; but, if the given time be past noon, turn the globe westward til; the index has passed over as manv hours as the time THE CELESTIAL GLOBE. 155 IS past noon; elevate or depress the pole till tivo can tre of the given star coincides with the horizon; then the elevation of the pole will show the latitude. Examples. 1. In what latitude does ^, Mirach, io Bootes, rise at half past twelve o'clock at night, on the (enth of December ? Answer. 5U deg. north. 2. In what latitude does Cor Leonis, or Regiilus, rise at ten o'clock at night, on the 21st of January? 3. In what latitude does ^, Rigel in Orion, set at four o'clock in the morning, on the 21st of December? 4. In what latitude does s, Capricorn us, set at eleven o'clock at night, on the 10th of October? Problem LXXXV. To find on what day of ike year any given star passes the meridian at any given hour. Rule. "Brmg the given star to the brass meridian, and set the index to 12 ; then, if the given time be before nocn, turn the globe westward till the index has passed over as many hours as the time v/ants of noon , but, if the given time be past noon, turn the globe eastward till the index has passed over as many hours as the time is past noon ; observe that degree of the ecliptic which is intersected by the graduated edge of the brass meridian, and the day of the month answering thereto, on the horizon, will be the day required. Examples. 1 . O/i what day of the month does Pro- tyon come to the meridian of London at three o'clock m the morning? AnSiVer, Here the time k nine hours before noon , the globe must li^yG PROBLEMS PERFORMED WITH tlierefbre be turned nine hours towards the west, the point of the ev^lip lir: intersected by the brass meridian will then be the ninth ol f, an Bwering nearly to liie first of December. 2. On what day of the month, and in what month floes «, Alderamin, in Cepheus, come to the meridian of Edinburgh at ten o'clock at night ? Answer. Here the time is ten hours after noon; the globe mu* til ere fore beturn;Hi ten hours towards the east, the point of the ecliptic- intersected by the brass meridian will then be the 17th of 11]^, answering U' Lhe ninth of September. S. On what day of the month, and in what month does i^y Deneb, in the Lion's tail, come to the meri dian of Dublin at nine o'clock at night ? 4. On what day of the month, and in what month, does ilrcturus in Bootes come to the meridian of Lon- don at noon ? 5. On what day of the month, and in what month, does^^in the Great Bear come to the meridian of Lon- don at midnight? 6. On what day of the month, and in what month, does Aldebaran come to the meridian of Philadelphia at five o'clock in the morning at London ? Problem LXXXVI. The day of the month being given, to find at what hour any given star covies to the meridian. Rule. Find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour- r^ircle to 12 ; turn the globe westward on its axis till the given star comes to the brass meridian, and the hours passed over by the index will be the time from uoon when the star culminates. the celestial globe. 157 J3r, without the globe. Subtract the right ascension of the sun for the given day from the right ascension of the star, and tne remain- der will be the time of the star's culminating nearli^. If the sun's right ascension exceeds the star's add 24 hours to the star's before you subtract. Examples. 1. At what hour does Cor Leonis, or Regulus, come to the meridian of London on the 23d of September ? Answer, The index will pass over 211 hours ; hence this star cul- minates or comes to the meridian 2H hours after noon, or at three tjuarters past nine o'clock in the morning. 2. At what hour does Arcturus come to the meri- dian of London on the 9th of February ? Answer. The index will pass over 16i hours ; hence Arcturus cul minates 16i hours after noon, or at half past four o'clock in the morn- ing. 8. Required the hours at which the following stars come to the meridian of London on the respective days annexed : Bellatrix, January 9th. Menkar, Pvlay 18th. ' Draco, Sept. 22d. » Dubhe, Dec. 20th. 3 Mirach, October 5th. Aldebaran, Feb. 12th. ^ Aries, November 5th. « Taurus, January 24th 4. At what time will Sirius come to the meridian of Greenwich on the 18th of December, 1827, his right ascension being 99^ 15' 26", and the sun's right aai- tension 265° 29' 0''. o 2C k68/ PE0BLEM6 PERFORMED WITH Problem LXXXVII. ' Given the azimuth of a knmvn star^ the latitude^ and the houry to find the star's altitude and the day of the month. Rule. Bring the pole so many degrees above the horizon as are equal to the latitude of the given place, screw the quadrant of altitude upon the brass meridian over that latitude, bring the division marked o on the lower end of the quadrant to the given azimuth on the horizon, turn the globe till the star coincides with the graduated edge of the quadrant, and set the index of the hour-circle to 12 ; then if the given time be before noon, turn the globe westward till the index has passed over as many hours as the time wants of noon ; if the given time be past noon, turn the globe eastward till the index has passed over as many hours as the time is past noon ; observe that degree of the eclij)tic which is intersected by the graduated edge of the brass meri' dian, and the day of the month answering thereto, on the horizon, will be the day required. Examples. 1. At London, at ten o'clock at nigjit, the azimuth of Spica Virginis was observed to be 40 ^Gg. from the south towards the west ; required its alti- tude, and the day of the month ? Answer. The star's altitude is 20 deg. and the day is the 18ih of June. The time being ten hours past noon, the globe must be turned ten hours towards the east. 2. At London, at four o'clock in the morning, the THE CELESTIAL GLOBE. 159 Jizimutli of Arcturus was 70 deg". from the south to- wards the west ; required its altitude, and the day of the month ? Answer. Here the time wants eight hours of noon, therefi>r^ th<» globe must be turned eight hours westward j the altitude of the stai will be found to be 40 deg., and the day ilie 12th of April. 3. At Edinburgh, at 11 o'clock at night, the azimuth of « Serpentarius, or Ras Alhagus, was 60 deg. from the south towards the east; required its altitude, and the day of the month ? 4. At Dublin, at two o'clock in the morning, the azimuth of 3 Pegasus, or Scheat, was 70 deg. from the north towards the east ; required its altitude, and the day of the month ? Problem LXXXVIII. The altitudes of two stars being given, to find the latu tude of the place. Rule. Subtract each star's altitude from 90 de- grees ; take successively the extent of the number of degrees, contained in each of the remainders, from the equinoctial, with a pair of compasses ; with the com- passes thus extended, place one foot successively in the centre of each star, and describe arcs on the globe with a black-lead pencil ; these arcs will cross each otlier in the zenith ; bring the point of intersection to that part of the brass meridian which is numb'^red from the equinoctial towards the poles, and the degree above it will be the latitude. Examples. 1. Atsea^in north latitude, I observed 160 PROBLEMS PERFORMED WITH the altitude of Capella to be 30 deg., and that of Alde- baran 35 de^. ; what latitude was I in ? Ansiver. With an extent of 60 deg. (=90O— 30O) taken from UTie equinoctial, and one foot of the compasses in the centre of Capella, de- scribe an arc towards the north ; then with 55 deg. (=90° — 35"^,) takers in a similar manner, and one foot of the compasses in the centre of A* debaran, describe another arc, crossmg the former ; the point of inter* gection brought to the brass meridian will show the latitude- to be 20i ^eg. north. 2. The altitude of Markab in Pegasus was 30 deg*, and that of Altair in the Eagle, at the same time, was 65 deg. ; what was the latitude, supposing it to be north ? 3. In north latitude the altitude of Arcturus w^as ob- served to be 60 deg., and that of 3 or Deneb, in the Lion's tail, at the same time, was 70 deg. ; what wag the latitude? 4. In north latitude, the altitude of Procyon was observed to be 50 deg. and that of Betelgeux in Orion, at the same time, was 58 deg. ; required the latitude of the place of observation ? Problem LXXXIX. The meridian altitude of a known star being given at anyplace in north latitude^ to find the latitude* Rule. Bring the given star to that part of the brass meridian which is numbered from the equinoctial to- wards the poles; count the number of degrees in the given altitude on the brass meridian from the star to- wards the south part of the horizon, and mark where tne reckoning ends ; elevate or depress the pole till this maik coincides with the south point of the horizon, THE CELESTIAL GLOBE. 161 and the elevation of the north pole above the north point of the horizon will show the latitude. Examples. 1. In what degree ol north latitude is the meridian altitude of Aldebaran 52^ deg. ? Answer. 53 deg. 36 min. north. 2. In what degree of north latitude is the meridian altitude of 3, one of the pointers in Ursa Major, 90 deg. 1 3. In what degree of north latitude is ^', in the head of Draco, vertical when it culminates? 4. In what degree of north latitude is the meridian altitude of • or Mirach in Bootes, 68 deg. ? Problem XC. The latitude of a place, day of the month, and hour of the day, being given, to find the nonagesimal de- gree* of the ecliptic, its altitude and azimuth, and the MEDIUM CCELI. Rule. Elevate the north pole to the latitude of the given place, and screw the quadrant of altitude upon the brass meridian over that latitude ; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour-circle to 12 ; then, if the given time be before noon, turn the globe eastward till \he index has passed over as many hours as the time wants of noon ; but, if the given time be past noon, * The nonagesimal degree of the ecliptic is that point which is the most elevated above the horizon, and is measured by the angle which the ecliptic makes with the horizon at any elevation of the pole i or, it is the distance beneath the zenith of the place and the pole of the echp- tic. This angle is frequently used in the calculation of solar eclipses. The medium caeli, or mid-heaven, is that point of the ecliptic whitn is Apcfo. the meridian. o2 2c 2 162 PROBLEMS PERFORMED WITH turn the globe westward till the index has past over as many hours as the time is past noon, and fix the globe in this position ; count 90 deg, upon the ecliptic from the horizon, (either eastward or westward) and mark where the reckoning ends, for that pomt of the ecliptic will be the nonagesimal degree, and the degree of the ecliptic cut by the brass meridian will be the medium cceli : bring the graduated edge of the qua- drant of altitude to coincide with the nonagesimal de- gree of the ecliptic thus found, and the number of de- grees on the quadrant, counted from the horizon, will be the altitude of the nonagesimal degree ; the azimuth will be seen on the horizon. Examples. 1. On the 21st of June, at forty-hve minutes past three o'clock in the afternoon at London, required the point of the ecliptic which is the nonage- simal degree, its altitude and azimuth, the longitude of the medium ci^li, and its altitude, &:c. Ansicer. The noDagesimal degree is 10 deg. in Leo, its altitude is 54 deg., and its azimuth 22 deg. from the south towards tlie west, oi nearly S. S. W. The mid-heaven, or point of the eclittic under the brass meridian, is 24 deg. in Leo. and its altitude above (he horizon, is 52 deg. The degree of the equmootiai cut by the brass meridian reck- oning from the pomt Aries, is the right ascension of the mid-heaven,- which in this example is 146 deg. The rising point of the echptic will be found to be 10 deg. in Scorpio, and the setting point 10 deg. in Tau- rus, If the graduated edge of the quadrant be brought to comcide with the sun's place, the sun's altitude will be found to be 39 deg. and his ttzimuth 78i deg. from the south towards the west, or nearly W. by S. 2. At London, on the 24th of April, at nine o'clock in the morning ; required the point of the ecliptic which is the nonagesimal degree, its altitude and azimuth, the point of the ecliptic which is the mid-heaven, dec. &c« ' THE CELESTIAL GLOBE. . l63 3. At Unierick, in 52 deg. 22 min. north latitude, on the 15th of October, at five o'clock ii] the afternoon , required the point of the ecliptic which is the noimge- simal degree, its altitude and azimuth, the point of the ecliptic which is the mid-heaven, &.c. (fee. 1 4. At Dublin, in latitude 53 deg. 21 min. north, oa the 15th of January, at two o'clock in the afternoon ; re(|uired the longitude, altitude, and azimuth, of the nonagesimal degree ; and the longitude and altitude of the mediun cceli, &c. dtc. ? Problem XCl The latitude of a place, day of the month, and the hour^ together with the altitude and azimuth of a star, being given, to find the star. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, and screw the quadrant of altitude on the brass meridiao over that latitude ; find the sun's place in the ecliptic bring it to the brass meridian, and set the index of the hour-circle to 12 ; then, if the given time be before noon, turn the globe eastward till the index has passed over as many hours as the time wants of noon , but, if the time be past noon, turn the globe westward till the index has passed over as many hours as the time is past noon ; let the globe rest in this position, and bring the division marked O on the quadrant to the given azi- muth on the horizon ; then, immediately under the given altitude on the graduated edge of the quadran* you will find the star. Examples. 1. At London, on the 21st of Decern 164 PROBLEMS PERFORMED \V rrn ber, at four o'clock in the morning, the altitude of a star was 50 (leg., and its azimuth was 37 deg. from the south towards the east ; required the name of the star ? Answer. Deneb, or o in the Lion's tail. 2. The altitude of a star was 27 deg., its azimuth 76J deg. from the south towards the west, at eleven o'clock in the evening at London, on the 11th of May ; what star was it ? 8. At London, on the 21st of December, at four o'clock in the morning, the altitude of a star was 8 deg., and its azimuth 51 deg. from the south towards the west ; required the name of the star ? 4. At London, on the 1st of September, at nine o'clock in the evening, the altitude of a star was 47 deg.^ and its azimuth 73 deg. from the south towards the east : required the name of the star 1 Problem XCIL To find the tune of the moon's southings or coming to the meridian of any place^ on any given day of the month. Rule. Elevate the pole so many degrees above the horizon as are equal to the latitude of the given places- find the moon's latitude and longitude, or her right as- cension and declination, from an ephemeris, and mark her place on the globe ; bring the sun's place to the brass meridian, and set the index of the hour-circle to 12 ; turn the globe westward till the moon's place comes to the meridian, and the hours passed over by the index will show the time from noon when the moon will be upon the meridian. the celestial globe. 165 Or, without the globe. Find the moon's age, which multiply by 31, and cut off two figures from the right hand of the product, the left hand figures will be the hours; the right hand figures must be multiplied by 60, for minutes. Or, correctly, thus : Take the difference between the sun's and moon's right ascension in 24 hours ; then, as 24 hours dimi- nished by this difference is to 24 hours, so is the moon's right ascension at noon, diminished by the sun's, to the time of the moon's transit. Examples. 1. At what hour, on the 10th of April, 1827, will the moon pass over the meridian of Green- wich ? The moon's right ascension at midnight being 185 deg. 28 min., and her declination 5 deg. 49 min. south. Ansv^er. By the Globe.— The moon comes to the meridian about midmght By usi^ng the Nautical Almanac. Sun's right ascension at noon 10th April = 1 h. 13' 15" 7 Ditto .... llthApril = l 16 55 5 Increase of motion in 24 hours . 3 39 8 Moon*s right ascension at noon 10th April = 178o 47' 32" Ditto . , . . 11th April = 192° 16' 45" Increase in 24 hours .... 13° 29' 13" equal to 53' 56'',- hence 59' 56" diminished by 3'" 39", leaves SC 17" the moon motion exceeds the sun's in 24 hours. 166 PROBLEMS PERFORMED WITH ^loon's right asnension 178^ 4? X 4 = • 11 h. 55 8^ Sun's right ascension . = 1 13 J 5.7 10 41 52.3 24h -50' 17" : 24h. : : 10^ 41' : llh. 4' the true time of the moon's p£t» sage over the meridian in the morning, agreeing within one minute of the Nautical Almanac. 2. At what hour, on the 1st of January, 1827, will the moon pass over the meridian of Greenwich, the moon's right ascension at noon being 328 deg. 43 min., and declination 7 deg. 15 min. south. 3. At what hour, on the 12th of March, 1827, will the moon pass over the meridian at Greenwich, the moon's right ascension at midnight being 164 deg. 41 min., and declination 1 deg. 43 min. north? 4. At what hour, on the 17th of October, 1827, will the moon pass over the meridian of Greenwich, the moon's right ascension at noon being 163 deg. 28 min., and declination 2 deg. 33 min. north ? Problem XCIII. The day of the months latitude of the place y and time of high water at the full and change of the moon be- ing given, to find the time of high water on the given day. Rule. Find the time at which the moon comes to he meridian of the given place by the preceding pro- blem, to which add the time of high water at the given place at the full and change of the moon, and the sum will show the time of high water in the afternoon. If ♦ When the sun*s right ascension is greater than the moon's, 24 hours must be added to the moon's right ascension before you subtract. THE CELESTIAL GLOBE. 167 the sum exceed 12 hours, subtract 12 hours and 24 minutes from it, and the remainder will show the time of high water m the morning ; but if the sum exceed 24 hours, subtract 24 hours and 48 minutes from it, and the remainder will show the time of high water in the afternoon. Examples. 1. Required the time of high water at Tendon Bridge on the 2d of April, 1827, the moon's right ascension at that time being 78 deg. 23min ,and her declination 20 deg. 4 min. north ? Answer^ By the Globe. — ^The raoon comes to the meridian at 4h 39* Time of high watei at the full and change at London -3 Time of high water in the moimng .... 7 39 2. Required the time of high water at Hull, on the 25th of May, 1827, the moon's right ascension at noon being 58 deg. 34 min., and her declination 18 deg. 50 min. north? 3. Required the time of high water at Liverpool, on the 22d cf June, 1827, the moon's right ascension at noon being 68 dieg. 2 min., and her declination 19 deg 39 min. north ? 4. Required the time of high water at Limerick, on the 19th of August, 1827, the moon's right ascension at noon being 111 deg. 20 min., and her declination 17 deg. 10 min. north? 5. Required the time of high water at Bristol, on the 9th of September, 1827, the moon's right ascension at noon being 31 deg. 51 min., and her declination 13 deg. 6 min. north ? 6. Required the time of hig:h water at Dublin, oa , fc68 PROBLEMS PERFORMED WITH the 12th of October, 1827, the moon's right ascension at noon being 102 degrees 57 m^n., and her declinatio'. 18 deg, 3 min. north? Problem XCIV. To describe the apparent path of any planet^ or of a comet amongst the fixed starsy ^c. Rule. Draw a straight line o, o, to represent the ecliptic, and divide it into any convenient number of equal parts. Set off eight of those equal parts north- ward and southward of the ecliptic at each end thereof; and draw lines, as in the figure Plate V.; these will re- present the zodiac. Find the planet's geocentric lati- tude and longitude in an ephemeris, or in the Nautical Almanac, and mark its place for every month, or for several days in each month, beginning at the right hand of the ecliptic line, and proceeding towards the Find the latitudes and longitudes f of the principal stars in the several constellations near which the planet passes, and set them off in a similar manner from the right hand towards the left ; you will thus have a com- plete picture of any part of the heavens, with the posi- ♦The young student will recollect, that the stars appear in a con- trary order in the heavens to what they do on the surface of a globe In the heavens we see the concave part, on the globe the convex. This manner of delineating the stars will be found extremely useful, and will enable the student to know their names and places sooner than by the globe. tThe places of the stars may likewise be laid down by their righ. Bscensions and declinations, by drawing a portion of the equinoctial rastead of the ecliptic. THE CELESTIAL GLOBE. 169. fions of the several stars, dec. as they appear to a spec- tator on the earth. Example. Delineate the path of the planet Jupiter for the year 1811 ; the latitudes and longitudes being as follow :* Longitudes. Latitudes. Jan. 1st. I«2r45' 0«57'S. 1 \^b. 7th 1 22 1 1 25th 123 58 Inarch 1st 1 24 29 25th 128 16 April 1st 1 29 35 25th May 1st 13th 25th June 1st 25th 2 4 30 2 5 49 2 8 31 2 11 17 2 12M 2 18 27 2 21 49 47S. 43S. 42 S. 37S. 36 S. 32S. 31S. 30 S. 29S. 28S. 26S. 25S. Longitudes. Latitudes. July 25th 2^25^1' 0^24'S. Aug. 7th 2 27 36 19th 2 29 48 25th 3 48 Sept. 7th 3 25th 3 Oct. 7th 3 25th 3 Nov. 1st 3 ^ 19th 3 -25th 3 Dec. 13th 3 25th 3 2 45 4 50 5 44 6 15 6 10 5 12 4 40 2 34 57 23 S. 22 S. 22 S. 21 S. 21 S. 20 S. 19 S. IBS. 17S 16 S. 14 S. 12 S. July 7th Jupiter's path, when delineated, will be south of the ecliptic in the order A, B, C, D, E, F, G, H. Thus, he will appear at A on the 1st of January, at B on the Ist of March, at C on the 1st of April, at D on the 1st of May, at E on the 1st of June, at F on the 7th of July, at G on the 25th of August, and at H on the 25th of October. On the 25th of August, when Jupiter ap- l>ears at G, he will be a little to the right hand of the star marked y, in Gemini ; when he arrives at H, which Will happen on the 25th of October, he vjiW ap'parently return again to G, a small matter above his former path, * As Jupiter performs his revolution round the sun in 11 years 315 days, he will have nearly the same longitUvle in the years 1823 and 1835, consequently lie will pass through the same constellations as are deli- a<^ated in Plate V. V 2D 170 PROBLEMS PERFORMED, <&C. where he will be situated on the 25th of December. Jupiter will not be visible during the whole of hjs ap- parent progress from A to H, being too near to the sun during the months of May and June. In the same manner the places and situations of tiie stars may be delineated ; thus, Aldebaran, the princi- pal star in the Hyades, will be found by the globe, (or a proper table) to be situated in 7^ of n and in 5|° of south latitude ; Betelgeux in Orion's right shoulder in about 26° of n and 16° of south latitude, and its place may be laid down on a map by extending the line of its longitude, as from L, till it meets a straight line passing through 16, 16, on the sides of the map. In the same manner any other star's situation may be de- scribed ; thus the Hyades will appear at Q, the Pleia- des at P, &c. and Bellatrix, 4 ' — ■ _ _ f I I^ORD'S HISTORY. j I A MODERN HISTOHY, j I FROM THE TIME OF LUTHER TO THE FALL OF NAPOLEON. J J For the use of Schools and Colleges, i i BY JOHN LORD, A.M., | 5 Lecturer on History. / 5 Bound in half morocco. Price $1 50. f f PIM^OCK'S SCHOOL HISTOKIES. I I — I I PINNOCK'S ENGLAND, f J REVISED EDITION. J i PINNOCK'S IMPROVED EDITION OF DR. 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