^iiiilniiiiimli'SiliiiSf" astronomy and the use o.in,an? ^^24 031 321 999 The original of tliis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031321999 A NEW TREATISE OH ASTRONOMY AND THE USE' OF THE GLOBES, IN TWO PARTS. OONTAININO ASTRONOMICAL AND OTHEB. DEFINITIONS ; MOTIONS AND POSITION* OF THE SUN, MOON, AND PLANETS ; KEPLEE'S LAWS AND THE THEORY Of GRAVITATION ; REFRACTION, TWILISHT AND PARALLAX ; OONNEO- TIONS PERIODS, DISTANCES, PHENOMENA, AND MAGNITUDES OF THE HEAVENLY BODIES, COMPOSING THE SOLAR SYSTEM, AC. ALSO, AN EXTENSIVE COLLECTION OF THE MOST USEFUL PROBLEMS ON THE GLOBES, ILLUSTRATED BY A SUITABLE VARIETY OF EXAMPLES, AC. DESIGNED FOR THE USE OF HIGH SCHOOLS AND ACADEMIES. BY JAMES M'INTIEE, M. D., reOFES.OR OF MiXHEMiTICS AND ^'TRONOMT IN THE CENTRAL HIOH SCHOOL O, NEW YORK: A. S. BARNES & Co., Ill & 113 WILLIAM STREET, (coRNBE or johh street.) SOLD BY BOOKSELLKBa, GENKKALLT, THKOUOUOUT THE UNITED BTATEB. 1866. Li r^ T'^ .^x ■- '■■■ i^n/ Entered, accordiiig to Act of Congress, in the year 1850, by A. S. BARNES & CO., In the Clerk's Office of the District Court for the Southern District of New- York. P. E. PRINTKR, Cor. John and Dutch-streets, N. Y. J. P. JONES & CO., ETKRBOTYPKRB. Tor. of William and 8pmce-sts., N. 1 PREFACE. The general extension of navigation and commeice over our globe, the numerous inventions and discoveries which have characterized the last and the present cen- tury, the number of travellers who have traversed the earth in all directions in pursuH.of philosophical know- ledge, the restlessness of inflamed curiosity, and even the wars, invasions and revolutions of our eventful age, have all co-operated to enlarge the sphere of human know- ledge, and consequently our acquaintance with the phe- nomena of the earth, and with the evolutions of those heavenly orbs which decorate that immense vault sur rounding our destined habitation. The learned men of the present age are better acquainted with the figure of the earth, and the planetary magnitudes and distances than their predecessors a few centuries back, were with the magnitude and position of their respective native countries. Hence, it has been found necessary to enlarge the sys- tem of school education, and to allow a liberal space to the sublime, interesting and useful science of Astronomy. We have been led into this course, not mei-ely by the VI PRErACE. desire of gratifying a liberal curiosity, but by the neces- sity of qualifying men, holding a respectable rank in society, for the discharge of the various duties of life. The philosopher, the theologian, the physician, the states- man, the merchant, and above all, the navigator, are at present supposed, to have at least, a general acquaintance with the heavenly bodies, and the unerring laws by virhich they are regulated and governed. Even well-edu- cated females are expected to have added a competent share of astronomical knowledge to the other accom- plishments of their sex. Therefore, in all our'^chools and institutes of educa- tion, male and female. Astronomy is justly becoming a favorite study, having all the advantages, we may be allowed to say, of opening to the youthful mind a view of the beautiful visions of planetary motions, and of the other charms of the science, which never fail to inspire rapturous feelings of delight, and to create a genuine taste for the beauties and sublimities of nature. Inti- mately connected with Astronomy is the Use of the Globes, the study of which is recommended by nearly all the writers on the different branches of education. A treatise on Astronomy and the Use of Globes, calculated for the use of High Schools and Academies seems to be wanted. The small compends, which are commonly met with, are too puerile and trifling, and in every view incompetent to the attainment of their object. With these impressions, and from long experience in the PREFACE. vii education of youth, the ensuing treatise has been under- taken and prepared. Part First of the present volume, it is believed, con- tains everything of importance, relating to the elements of astronomical science, and is divided into articles, each of which, for convenience in reference, is numbered, and exhibits the subject under discussion in that article. Students of ordinary attainments, can, with proper appli- cation, understand and answer nearly all the questions on the different articles, and corresponding in number, found at the foot of each page. Some knowledge of Geome- try, Trigonometry, and Algebra, is requisite' fully to com- prehend a few of the more difficult demonstrations and abstruse calculations. Part Second, contains an extensive collection of the most useful Problems on the Globes, illustrated by a suitable variety of examples, with notes and observa- tions. These problems will be found very entertaining and instructive to the young student. They explain some of the most important branches of Geography and Astronomy. A few of the most useful tables are given in this part, and the method of their calculation fully ex- plained. The design of the author in the present treatise, is to produce a work on Astronomy and the Use of the Globes, suited to the exigencies of school instruction ; to supply on the one hand the defects of the smaller compends, and on the other to convey to the pupil a comprehensive PREFACE. knowledge of these subjects in one volume of but moderate size. With what degree of judgment this at- tempt has been made, the public will determine, against whose decision there is no appeal ; but it is hoped that they will receive with indulgence a well meant effort to simplify the system of education, and thus promote the diffusion of useful knowledge. Central High School, Baltimore, Deo. 1849 :} CONTENTS. PART I. CHAP. I. Phenomena of the Heavens — Terrestrial and Celestial Globes or Spheres, Definitions of Points, Lines, Circles, and Terms, used in Observations, Computations, and in the Solution of Problems pertaining to Geography and Astronomy, 13 CHAP. II. Astronomy — Motions and Positions cf the Sun, Moon, and Planets, Different Systems, lanet's orbit are called the perihelion and aphelion ! KEPLER 3 LAWa. 41 points of the moon's orbit, or tlie apparent orbit of the sun, uie called Perigee and Apogee. These points are also called A psidus,— the one nearest to the earth, the Lower Apsis, and the one farthest from it, the Higher Apsis. The line joining these is called the Line of the Apsides. 39. Kepler's Second Law. The sun's apparent mo- tion in longitude, or the earth's real motion in its orbit, varies at different times of the year. Thus when the sun's apparent diameter is the least, which is about the 1st of July, and consequently, the earth is then in the aphelion at E, the sun's daily apparent motion in longi- tude or angular velocity, will also be the least, namely, 57' 11" in a mean solar day. But when the sun's appa- rent diameter is the greatest, which is about the 1st ot January, the earth being then in the perihelion at E', the daily motion in longitude will also be the greatest, namely, 61' 10". It is also found that the daily motions of the sun in longitude throughout the year are proportional to the squares of the corresponding appai-ent diameters ; but the apparent diameters are inversely proportional to the radii vectores ; therefore the sun's apparent daily motions, or the earth's real motions, are inversely proportional to the squares of the radii vectores or distances. Suppose the earth to pass over the portion a J of its orbit in some small period of time. Take e, the middle point of a b, and with S as a centre, and the radius vector S e as a radius, describe the arc c d, and with S D equal the mean distance or unity, describe the arc / g. It is evident that a b may be so small, that the elliptical sector S a 6 will not sensibly differ from the circular sector Sec?. Put the distance of the earth at e, or the radius vector = r, and the angle a S 6 measured by f g, the angular velocity for the short period of time == v. Now, because the circular sectors 8 f g and S c d are similar, What are the corresponding points in the moon's orbit, or the apparent 01 bit of the sun, called ? Wliat also called 3 39. Wliiiii has the sun the least apparent diameter, and when the great- est ? What is the sun's apparent daily motion in longitude, or angular velocity, at these times? To what are the daily motions of the sun throughout the year proportional ! And to what inversely proportional ? 42 AgTRONOMY. Serf:: S/2: Sc9, or S /j-: = 1 ; hence S c d = S /^f X r» ^ V ; therefore S c rf or ths eilip we have sector 8 / ff : sect, S c rf : : 1 : r*, S /, being = hatS/ff==ifffX S/== tical sector S ab = ^vr\ Again, if we suppose the ^,-' earth to pass over another portion of its orbit a' V in the same small period of time, and calling r' and v' the radius vector and an- gular velocity, we shall also have the elliptical sector S a' 6' = ■!■ v' r'\ But V : v' :: r''^ i r'^; hence v r"^ ^^ ii r'% or ^ v r^ ^ ^ i/ r^; therefore S a 6 = S a' b' ; that is, the radius vector describes equal areas in equal times, and consequently areas proportional to the times, which is Kepler's second law. 40. Kepler's Third Law. Kepler obtained his third law by comparing the periodic times of the planets and their mean distances from the sun. From these compari- sons he found that the squai-es of the periodic times are proportional to the cubes of their mean distances, or to the cubes of the semi-major axes of their elliptic orbits. This law prevails among the satellites of each secondary system, namely, that the squares of the times of their revolutions round the primary, are proportional to the cubes of their mean distances from that body regarded as their centre of motion. 41. Attraction of Gravitation. That force by which bodies near the surface of the earth are incessantly impelled towards its centre, is called Gravity, or the At- traction of Gravitation. This attractive force is mutua' Draw the Diagram, and prove that the radius vector describes areas proportional to the times. 40. How did Kepler obtain his third law 3 What did he find from these comparisons ? Does this law prevail among the satelUtes of each eeoondary system ! 41. What is gravity, or the attraction of gravitation ? FORCE OF ATTRACTION. 48 among the particles of matter, and belongs to all bodies in the universe ; therefore it is called the principle of Universal Gravitation. The planets are retained in their orbits by the attrac- tive force of the sun, which is called the Solar Attrac- tion ; and the planets are endued with the same power in attracting the sun and each other. The satellites are also retained in their orbits by the attractive force of their respective primaries. To apply the laws of universal gravitation, as established by the principles of Mechanics, in the investigation of the motions of the heavenly bodies, is an extensive and difficult science. This branch of our subject, called Physical Astronomy, will be found discussed at length in La Place's Mecardque Omeste and other similar works. The following elementary propositions are all that can be here introduced. 42. The Force of Attraction varies directly as THE Mass. From the motions produced by the action of the sun and planets upon each other, it is found that the force of attraction in these bodies, is directly propor- tional, at the same distance, to their respective masses. It is also known, that the force of attraction in several bodies, at the same distance, for another body, is propor- tional to the mass of those bodies. Hence the force of attraction of one body for another, varies as the number of similar attracting particles, or mass, of that body. 43. The Force op Attraction varies inversely as THE Square op the Distance. From the principle here laid down, Kepler's laws respecting the planetary mo- tions and periods can be established. But by assuming Why called the principle of universal gravitation ? By what force are the planets retained in their orbits ? Do the planets attract the sun and each other ? By what force are the satellites retained in their orbits ? What is said of the application of these laws in the investigation of the motions of the heavenly bodies ? 42. To what is the force of attraction of the sun and planets, at the same distance, proportional ? 43. How does the force of attraction of the same body at different dis- tances vary ! How can this principle be establislied ! 44 ASTEONOMr. this principle iiot to be true, a result would be obtained contrary to these laws, which have been confirmed by actual observations ; therefore it follows that the propo- sition must be true. The theory of gravitation as stated in the last and present articles, namely, that the force of attraction varies directly as tJie mass, and inversely as the square of the distance, was first promulgated by Sir Isaac Newton ; and hence it is sometimes called, The Newtonian Theory of Gravitation. 44. Centripetal and Pkojectile Forces. That force continually impelling a body towards the sun, or centre around which it revolves, is sometimes called the Cen- tripetal Force ; and that force which causes it to recede from thft centre, is called the Centrifugal, or Projectile Force. The nature of the orbit will depend on the intensity of the projectile force. Thus a certain intensity of force will produce a pwabola ; a less intensity, an ellipse or circle ; and a greater, an hyperbola.* 45. Quantities of Matter in the Sun and Plan- ets, OR their Relative Masses. Let S represent the sun, and E E' that portion of the earth's orbit, re- garded as circular, described in one second of time. Draw E A tangent to the orbit at E, and from E' draw E' A and E' B respectively perpen- dicular to E A and' E S. Also draw the chord E E' and S C perpendicu- lar to it at the middle point C. According to the first law of mo- tion, if the projectile force acted alone, the earth would he carried from E to A in one second of time ; but the earth is at E' ; therefore A E', or its equal E B, is the distance * Iforton's Astronomy, Article 624. 44. Describe the centripetal and projectile forces. Cfa what. iBil." the nature of the orbit depend ! , RELATIVE MASSES OP THE PLANETS. 45 the earth has been drawn in one second of time by the attrac- tive force of the sun at S. And as the distance through which a body moves in a given time is proportional to the force by which it is impelled, the versed sine E B of the arc E E' will measure the attractive force by which the earth is drawn to- wards the sun. Put D = E S the mean distance of the earth from the sun; F ^ E B the attractive force of the sun ; P = the earth's periodic time in seconds ; 1 = the mass of the sun ; TO = the mass of the earth ; iz = the ratio of the diameter to the circumference of the circle ; 2 D T .- . hence — = = the arc E E', which does not sensibly differ from the chord E E'. In the similar triangles S C E and E E' B, we have — S E : E : : E E' : E B, and 2 S E : 2 C E : : E E' : E B, 2 D ir 20" 2Dn2* or2D:_^- :: _^_ : F = -^^^ By putting / = the attractive force by which the moon is drawn towards the earth, d = the mean distance of the moon, and p = the moon's siderial revolution in seconds ; we will 2 (Z T^ find in like manner / = 5 — Now, since these forces F p-. and / are to each other directly as the masses of the sun and earth, and inversely as the squares of the distances of the earth from the sun, and of the moon from the earth (42, 43), we have — ¥: f :: d^Xl: T>^Xm, 2 D t2 2 (^ "2 „ ^„ d^ P2 , P2 ^3 pi U d^ P2 / d \^ / V \^ ^--^x-W- (it) >< i^) ■ Which formula, by substitution, will give the earth's relative mass, that of the sun being = 1. This formula will also serve for computing the mass of any of the planets that have satel- 45. Draw the iliagrara, and show how the relative raisses of the sun and planets that have eatellites. are determined. 46 A3TE0N0MT. lites, by using the planet's distance, and tliat of either of its satellites, in the first factor ; and the planet's period, and that of the satellite, in the other. The mass of a planet which has no satelhtes, and that of the moon, can only be found from the observed amount of pertur- bations produced by their action, in the motions of the other heavenly bodies. 46. Densities of the Sun, Moon, and Planets. The densities of two bodies of equal masses are to each other inversely as their volumes or magnitudes ; and the densities of two bodies of equal volumes are to each other directly as their masses. Let M and m represent the masses of two bodies, and V and v their respective volumes. Then if their masses be equal, their densities will be as « : V, or as -r^ '■ "^J ^^^ ^ ^^^ "* ^^i"g •11 1 Mm _, theij masses, their densities will be as -^r- -. — — . ihat is, the densities of bodies are proportional to their masses divided by their volumes. CHAPTER IV. DIP OP THE HORIZON, ASTRONOMICAL REFRACTION, TWILIGHT, HEIGHT OF THE ATMOSPHERE, AND PARALLAX. 47. Dip op the Horizon. Let E represent the place of the observer's eye, at the distance of e E above the earth's surface, and S any heavenly body. Draw the tangents E H and e h, which will respectively represent the visible horizons (8) at E and e. Draw E H' parallel How can the masses of the planets that have no satellites, and that of the moon, be determined 1 46. How do the densities of two bodies of equal masses vary ? How do the densities of two bodies of equal volumes vary ? Prove that the densities of two bodies are proportional to their masses divided by their volumes. DIP OF THE HORIZON. 47 to e n, and e s parallel to E S, and join C the centre of the earth, and A the point of tangency of E H. When the body S is viewed from ■-^■y E and e, the lines of vision E S and e s will be paral- lel, on account of the very yr y ^ , small elevation e E com- ^ ' pared with the great dis- tance E S ; hence the angle S E H' is equal to the angle seh. Now the angle S E H is the observed altitude of S when viewed from E, and *" s e A is the altitude when viewed from e ; S E H — H E H' = S E H' = seh; •is- but we have therefore we must subtract from the observed altitude the angle H E H', called the Dip or Depression of the Horizon, in order to obtain the apparent altitude. • Because the sum of the angles C -}- C E A is equal to a right angle, and consequently equal to the right angle C E H' ; take from each C E A, and there remains C = H E H'. Put e E = A, and C A or C e, the radius of the earth == r / and we have — E A == s/ Or -\- Uy T^ = ^^ distance to which a per- son can see on the earth at an elevation equal to h. The angle C, or the dip of the horizon, is found for various elevations hy the following proportion : C E : C A : : Radius : cosin C, or r -\- h : r : : R. : cosin C, and the results entered in a table, called a Table of the Dip of the Horizon. 48. Astronomical Refraction. It is an established fact in Optics, that a ray of light in passing obliquely out of a vacuum into a transparent medium, or out of a 47. Draw the diagram, and explain fully what is under^itood by the dip of the horizon. How is the apparent altitude obtained ? How is the distance obtained to which a person can see at a certain elevation? How iu the dip of the horizon obtained for various elevations ? 48 ASTEOXOMY. rarer into a denser medium, will become bent or refracted towards a perpendicular at the incident ray. Now, since the earth is surrounded by an atmosphere which gradu- ally decreases in density, as the ^distance from the sur- face increases, the rays of light in proceeding from the heavenly bodies into the atmosphere, and thence from one stratum of atmosphere into another, will become gradu- ally refracted towards the radius drawn from the centre of the earth to the point of incidence. Thus let S a represent a ray passing from S and enter- ing the atmosphere at a ; instead of passing on in the straight course a e, and over the head of an observer at E, it will be refracted towards the perpendicular P C as it enters the differ- ;, j>/ ent strata of the at- mosphere, in the bro- ken line a b c E to his eye. But since the number of strata infinite, or which is the same thing, the density of the atmos- phere gradually in- creases, by infinitely small degrees, from a to the surface, the number of deflections ■w ill be infinite, and the broken line a 6 c E will become a curve concave towards the earth's surface. The tangent E S' to the curve abcE at E, will point out the direction in which the ray enters the eye at E, and represent the position of the heavenly body S more elevated as at S'. Draw E S parallel to IS 48. W>ien doea a ray of light become refracted, and towards what f Towards what will the rays of light be gradually refracted, in passing through the different strata of the atmosphere ? Draw the diagram, and KEFRACTION. 49 e S, and the angle S E S' will be the increase in altitude produced by atmospherical refraction, called astronomical refraction, or simply refraction. Hence the refraction must be subtracted from the observed altitude, and added to the observed zenith distance. 49. Amount of Refraction. It is also according to an established principle in Optics, that the more obliquely a ray of light passes from a rarer into a denser medium, the greater is the refraction ; hence the refraction of the heavenly bodies is greatest when they are in the horizon, and decreases with the increase of altitude to the zenith. Mathematicians, by persevering investigations, have obtained formulas by which the astronomical refraction may be found for different altitudes from the horizon to the zenith. These foi- mulse have been proved correct by the observations of astro- nomers, except for altitudes under 10°. In such low altitudes the refraction is irregular and uncertain. From these formulae tables of refraction have been computed, adapted to the mean state of the atmosphere, namely, when the barometer stands at 30 inches and the thermometer at 50°. These are called mean refractions. To these tables, columns are annexed, con- taining the corrections to be applied to the mean refractions, for the existing state of the atmosphere at the time of obser- vation. The amount of refraction in the horizon is about 34' ; at an altitude of 45°, it is about 58" ; and in the zenith it is zero, since the rays of light from that point enter and pass through the atmosphere perpendicularly. 50. Effects of Refraction. The stars and the centres of the sun and moon appear in the horizon by show how the altitude of a heavenly body will be increased by atmo- spherical refraction. 49. What effect has the obliqiiity of a ray, in passing from a rarer into a denser medium, on its refraction ? Where is refraction the greatest ? To what state of the atrnosphere are tables of refraction adapted, and what are such refractions called ? What is the arrjount of refraction in the horizon ! At an altitude of 4.5° 1 In the zenith ? 50 ASTRONOMY. the effects of refraction, when they are really 34' below it ; hence the refraction accelerates the rising of the heavenly bodies, and retards their setting. Having this effect in rendering the sun longer visible, the length of the day will thereby be increased. Since the apparent diameter of the sun or moon is something less than 34*, the horizontal refraction, it follows that the discs of these bodies (21,) about the time of rising or setting, may be wholly visible, when they are actually below the horizon. The discs of the sun and moon, when near the horizon, appear somewhat elliptical, because the lower limb of eith,er of these bodies in that situation, is more elevated by refraction than the upper, and in consequence of which, the vertical diameter appears shortened, while the horizontal diameter remains unaffected. In the hori- zon, the vertical diameter is about one-eighth less than the whole diameter. Refraction, also, by elevating two heavenly bodies in vertical circles (1 1) which meet in the zenith, makes their apparent distance less than their true distance. 51. Twilight, ok CREPUscuLuivr. Twilight is that faint light which we perceive for some time before the sun rises and after he sets. It depends both on the re- fraction and reflection of the sun's rays in the atmosphere. Twilight begins in the evening when the sun sets, and gradually decreases till he is 18° below the horizon, when it ends. It also begins in the mojning, or it is dayireah, when the sun is within 18° of the horizon, and gradually increases till sunrise. 50, What effect lias-refraction on tlie rising and setting of the heavenly bodies ? What on the length of the day ? What- effect on the sun and moon, -when theii- upper limbs touch the horizon ? Why do the discs of the sun and moon, when near the horizon, appear elliptical ? Why is the apparent distance of two heavenly bodies less than their true distance I 51. What ia twilight, and on what does it depend I When does it be gin, and when end % HEIGHT OF THE ATMOSPHERE. 51 52. Height of the Atmosphere. From the datum stated in the last article, we are enabled to find at what height the atmosphere ceases to reflect the sun's rays. Thus let ABE represent a portion of the surface of the earth, D F G the surface of the atmosphere above it, and E F H he visible horizon touching the earth ^^ at E, the place of the observer, and intersecting the surface of the at- mosphere at F. Then another line F B S drawn from F, touching the earth in B, will be the direction of the sun when the twilight ceases, and consequently, according to ob- servation, will make with the horizon the angle H F S = 18°. From the points B, E, and F, draw to the centre C, the lines B C, EC, and F C, the latter meeting the earth in I. Now it is evident, by inspecting the figure, that the highest partjcle of the atmosphere at F, supposed capable, will reflect the light in the direction F E ; hence none of that part of the atmosphere D E F above the horizon will be illuminated, and consequently twilight will end at E. The part E I B F, though not directly enlightened by the sun, receives a degree of light by reflection from that part of the atmosphere on which he shines. Because the two angles E and B of the quadrilateral E C B F are right angles, the other two E C B and E F B will be to- gether equal to two right angles ; therefore E C B = H F S = 18°, and E C F = 9°. Then— 62 From the datum, namely, that twilight ceases when the sun is 18° below the horizo.\, find at what heiglit, by dr:iwing the diagram and work- uig the problem, the atmosphere ceases t£re of motion of the planetary system. CHAPTER VI. MERCURY. ^ 66. Remarks. Mercury, the nearest of all the planp-t.« to the sun, emits a brilliant white light with a small tint of blue, and twinkles like the fixed stars. He may be seen, when the atmosphere is favorable, a little after sun- set, and again a little before sun-rise. The observations of astronomers on this planet, on account of his proximity to the sun, and consequently his appearing _ but for a short interval above the horizon when the sun is below it, and that principally during the twilight, have been at- tended with difficulty, and considered somewhat uncer- tain. Mercury appears to us, when viewed at diffi'.rent times through a telescope of sufficient magnifying power, with all the phases of the moon, except that he never appears quite full, because his enlightened side is never directly Has any satisfactory explanation been given of ilie zodiacal light ? , 65. What has the sun for his astronomical sign, and what does it repre- sent ! 66. Which is the nearest of all the planets to the sun ? What is the appearance of Mercury ? When may he be seen S On what account have the observations of astronomers on this planet been attended with diffi- culty ! How does Mercury appear to us when viewed through a tele- scope ? OF MERCURY. 63 Opposite to us but when he is so near the sun as to be lost to our sight in the beams of that luminary. His enlightened side being always towards the sun, and his never appearing full, evidently prove that he shines not by any light of his own, but by the reflected light of the sun ; and moreover, his never appearing above the hori- zon at midnight, shows that his orbit is contained within that of the earth, otherwise he would be seen in oppo- sition (23) to the sun. 67. Period and Distance. Mercury performs his periodical revolution round the sun in 87d. 23h. 15m. 43s. = 7600543s. of our time, which is the length of his year. The earth's siderial revolution round the sun is 365d. 6h. 9m. lis. = 31558151s. Then by Kepler's third law (40) we have 315581512 : 7600543^ : : 1' : f 1522^ 1 * ^ 3 131558151 J .058005091138; and V. 05800509 1138 =.387099 nearly, the distance of Mercury from the sun, supposing the earth's distance to be 1. Hence, because the earth's distance is 24047 r (57), .387099 X 24047 = 9308.57, the distance in semi-diameters of the earth ; and 9308.57 X 3956 = 36,824,703 miles, the mean distance of Mer- cury from the sun. The distance from the foot of a perpendicular, conceived to be let fall from the centre of a planet on the plane of the eclip- tic to the centre of the sun, is called the curtate distance of the planet. Also, 87d.23h. =21 lib., and 36,824,703 X 2 X 3.1416 -H 2111 = 109,605 miles, the mean rate at which this planet moves in his orbit per hour. 68. Apparent Diameter and Magnitude. The ap- What are the proofs that Mercury shines by the reflected light of the Bun ? What is the proof that his orbit is contained within that of the earth ? 67. In what time does Mercury perform his periodic revolution ? Know- ing the earth's distance, how is Mercury's obtained ? What is the mean distance in miles ! What is the curtate distance of a planet ? At what rate per hour does he mo\ e in his orbit, and how obtained S 64 ASTKONOMY. parent diameter of Mercury varies between 5" and 12". When in his inferior conjunction (23), and at his mean distance, it is 10".75. The mean distance of the earth from the sun is 24047r, and the mean distance of Mer- cury from him is 9308.57r (67). Hence 24047r — 9308.57r = 14738.43r, the mean distance of Mercury from the earth at his inferior conjunction ; and as the apparent diameters of bodies are inversely proportional to their distances, vi^e have 24047 : 14738.43 : : 10".75 : 6".58, the apparent diameter of Mercury at a distance from the earth equal to that of the sun. And because the sun's apparent diameter is 32' 1".8, and his real di- ameter 886,144 miles (58), therefore 32' 1".8 : 6".58 : : 886,144771. : 3,034 miles, the real diameter of Mercury. Then since the magnitudes of spherical bodies are as the [7912 1 ^ ——I =(2.6)' = 17.576, which shows how many times the magnitude of the earth exceeds that of Mercury. 69. Inclination of the Orbit and Transit. The orbit of Mercury is inclined 7° to the plane of the ecliptic, and that node (22) from which he ascends northward above the ecliptic, is in the sixteenth degree of Taurus ; and consequently the descending node is in the sixteenth degree of Scorpio. The sun is in these points on the 6th of May and 8th of November ; and when Mercury comes to either of his nodes at his inferior conjunction about these times, he will pass over the disc of the sun like a dark round spot, which phenomenon is called the transit of Mercury ; but in all other parts of his orbit, he will go 68. Between what quantities does the apparent diameter of Mercury- vary ? What is it when he is in his inferior conjunction, and at his mean distance ? Knowing this and the mean distances of the earth and Mer- cury, how is the real diameter found ? How many times does the magni- tude of the earth exceed that of Mercury, and how determined ! 69. How many degrees is the orbit of Mercury inclined to the plana of the ecliptic ? In what signs and degree are the nodes ? What will occur when Mercury comes to either node at his inferior conjunction ? OF MERCURY. 65 either above or below the sun, and consequently his con- junctions will then be invisible. It is found that the longitude of Mercury's node varies but little more than 1° in a century; hence his transits can only occur, for centuries to come, in the months of May and Novem- ber, because the sun's longitude can agree with that of the nodes only in these months. 70. Rotation on the Axis, Seasons, etc. Mercury, according to Mr. Schroeter, of ' Lilienthal, performs a revolution on his axis in 24h. 5^-m. The axis is said to make a large angle with a perpendicular to the plane of the ecliptic. From the apparent diameters of Mercury taken at the time of his transits, and when at his aphelion and peri- helion distances (38) the eccentricity of his orbit is ob- tained, which is about J of his mean distance. On ac- count of this great eccentricity of the orbit. Mercury's year is divided into seasons of very unequal length. The light which this planet receives from the sun, when in the perihelion, is 10 times as great as that which the earth receives, while it is but 5 times as great when in the aphelion. This is also a consequence of the great eccen- tricity of the planet's orbit. The intensity of heat at Mercury, if it were governed by the same law as that of light, would vary of course from 5 to 10 times its intensity at the earth. But we have no reason to conclude that sen- sible heat at the planets, is in the inverse proportion to the squares of their distances from the sun. 71. Astronomical Sign. Mercury was considered the messenger of the gods. His astronomical sign ¥ is supposed to represent the caduceus with which Apollo Why will his transits occur in the months of May and November f6r centuries to come ? 70. In what time does Mercury revolve on his axis ? What part of the mean distance is the eccentricity of the orbit, and how obtained ! What is said of the seasons ? What of the light which he receives ? What of the intensity of the sun's heat at Mercury ? What is the concluding remark on tliis subject ? 1\. Describe the astronomical sign of Mercury ? 06 AaTRONOMY. furnished him. It is a rod entwined at one end by two serpents in the form of two equal semi-circles, and wing- ed at the top. The snakes are supposed to represent prudence, and the wings diligence. CHAPTER VII. VENUS. ? 72. Remarks. Venus, the next planet in order, is to appearance the largest of all the planets, and is distin- guished from them, by the brilliancy and whiteness of her light. Her orbit, including that of Mercury, is with- in the earth's orbit, for if it were not, she might be seen as often in opposition to the sun, as she is in conjunction with him ; but she was never seen in our latitude, above the horizon at midnight, or 90° from the sun. Venus, wb«sn view- fid through a teles- cope, has all the phases of the moon, though she never or seldom appears per- fectly round. (See the figures.) 73. Pekiod and Distance. Venus performs her rev- olution round the sun in 224d. 16h. 49m. 10s. = 19,411,- 750S. Hence, (67) flSiniSOV^ .378454465832117; Ul55815lJ S and V.378454465832117 = .723332, the distance of Venus from the sun, supposing the earth's distance = 1. Then .723332 X 24047r= 17394r, the distance in semi- '1% How ia Venus distinguished from the other planets ! Is her orbit within that of the earth, and if so, how known ? What is her appearance when viewed through a telescope ? 73. In what time does Venus perform her revolution round the sun I From the periodic time, determine the mean distance. OF VENUS. 67 diameters of the earth ; and 17394 X 3956m. = 68,810,- (564 miles, the mean distance of Venus from the sun. And since the intensity of light is reciprocally propor- tional to the squares of the distances from the source whence it emanates, we have r 1 V i— = 1 .9. [.723332 This shows that the intensity of the light of the sun at Venus, is nearly double its intensity at the earth. Venus performs her revolution round the sun in 224d. 17h. nearly =5393 A. Hence, 68,810,664 X 2 X 3.1416 _ g.^gg ^^^^ 5393 This distance is equal to the velocity per hour of Venus in her orbit. 74. Apparent Diameter and Magnitude. The greatest and least apparent diameters of Venus are 61" and 10". When she is in her inferior conjunction and at her mean distance, the apparent diameter is about 60"- Then 1— .723332 = .276668 (73) the distance of Venus from the earth at her inferior conjunction, the earth's distance from the sun being equal to unity ; and 1 : .276668 : : 60" : 16".6, the apparent diameter of Venus at a distance from the earth equal to that of the sun. Again, 32' 1".8 : 16".6: : 886144ot. : 7654 miles, the real diameter of Venus. Hence, we have r7654^ ^ ^ I7912 j " ■ making her volume about ^^ that of the earth. From the small variations in the apparent diameters of Venus at or near her inferior conjunctions, the eccentricity of her What is the mean distance in miles ? Determine the comparative in- tensities of the sun's light at Venus and the earth. What is the velocity, per hour, of this planet in the orbit ! 74. What is the apparent diameter of Venus, when in her inferior conjunction, and at her mean distance ? From this determine the real diameter. What is her volume compared witli that of the earth ? From what circumstance is her orbit found to be very nearly circular I 68 ASTRONOMY. orbit is determined to be about .00688, or less than half a mil- lion of miles ; hence, it is very nearly circular. 75. Rotation on the Axis and Seasons. Mr. Schroeter found the period of the daily rotation of Venus on her axis to be 23h. 21m. This he deduced from the different shapes which the horns assumed. He observed that the appearance of her horns varied, and after an interval of time, again assumed the same appearance. Hence, by noticing this interval, he concluded that the time of the rotation is as already stated, 23h. 2\m., and that her axis makes a considerable angle with the per- pendicular to the plane of the orbit. Some authors state that this angle amounts to 72° ; and consequently the length of her days and nights, and the vicissitudes of her seasons, are subject to great and rapid changes. 76. Morning and Evening Star. When Venus ap- pears west of the sun, or when her longitude is less than the sun's longitude, she will rise in the morning before him, and is then called a morning star ; but when she appears east of the sun, or when her longitude is greater than the sun's longitude, she shines in the evening after sunset, and is then called an evening star. This planet, when a morning star, was called by the ancient poets. Phosphorus or Lucifer, and .when an even- ing star, Hesperus or Vesper, having been regarded by them as two different bodies. Venus is a morning star for 292 days, and an evening star for the same length of time. Suppose Venus in her inferior conjunction. Put P = the periodic revolution of the earth in days, P' = the periodic rev- olution of Venus, and 1 = the circumference of the circle. Then we have, 76. What is the time of the rotation of Venus on her axis, and how deduced ? What is the inclination of her axis ? What is the conse- quence of this great incUnation of the axis ! 76. When is Venus a morning star, and -when an evening star ? What called by the ancient poets ? How long does she continue alternately a morning and an evening star ! OF VENL'3. 69 — - = the daily progress of the earth in its orbit, -pP == " " Venus in her orbit, I 1 p p' and _ _ = = the daily gain of Venus on the earth ; p p/ p p' hence, — -— — : 1 : : Icf. : d =zthe time which elapses until p p' p_p f Venus comes again to her inferior conjunction. If we substitute for P 365^ and for P' 224|, the fourth term of the above proportion will give 584 days nearly, the synodic revolution of Venus ; and 584 days — 2 = 292 days, the time which she continues alternately a morning and an even- ing star. By substituting in the same formula for P' 88, we will find the synodic revolution of Mercury about 116 days. 77. Inclination op the Orbit and Transit. The orbit of Venus makes an angle of 3° 23' 28" with the plane of the ecliptic, and the ascending node is 15° in Gemini, hence the descending node is 15° in Sagittarius ; therefore when the sun is in or* near these points of the ecliptic, and Venus in her inferior conjunction, she will pass over his disc like a dark spot, called the transit of the planet. The sun's longitude agrees with the longitude of the nodes on the 5th of June and 7th of December. Let E E' E" represent the orbit of the earth coinciding with the plane of the paper, v v' v" that part of the orbit of Venus above the plane of the earth's orbit, and v" v'" v, that part below it. When the earth is in Gemini at E, or the sun in Sagit- tarius, and Venus at v in her inferior conjunction, and in or near her ascending node, being then in a direct line between the earth and the sun, she will evidently appear like a dark spot on the sun. The same phenomena will From tlie periodic times of the earth and Venus, deduce the synodic revolution of Venus. How is the synodic revolution of Mercury found ? 77. How many degrees is the orbit of Venus inclined to the plane of the ecliptic? Wliat are the longitudes of the nodes ? 70 ASTRONOMY. occur when the earth is in Sagittarius at E", or the sun in Gemini, and Venus in or near her descending node at v". But when the earth is at E' and Venus at v, or when the earth is at E'" and Venus at «'", although in both cases she is at her inferior conjunction, there will be no transit ; because in the one case she will pass above the sun, and in the other below him. In a similar man- ner, a transit of Mercury may be illustrated. 78. FREaUENCY OP THE TRANSITS OF MeRCURY AND Venus. It has already been observed that a transit of one of the interior planets (36) cannot occur, unless the planet is in or near one of the nodes, and at the time of the inferior conjunction ; therefore, when a transit has What will occur when the sun is in or near these points, at the time Venus is in her inferior conjunction ! Draw the diagram, and illustrate a transit of Venus or Mercury. 78. When a transit has occurred at one node, of what must the fteriod, of time, that elapses be composed, before another transit can happen at the same node i OF VENUS. 71 occurred, another will not happen at the same node, till the lapse of a period of time composed of a whole num- ber of periodic revolutions of the planet and the earth, or nearly so. And again, another transit will not occur at the opposite node, till the lapse of a period of time composed of an odd whole number of half periodic rev- olutions of the planet and the earth, or nearly so. Hence let P represent the periodic revolution of the earth, P' that of an interior planet Mercury or Venus, and m and n two whole numbers, such that w P = n P' nearly ; then will m be the number of years between two consecutive transits at the same node. Or, let m and n represent two odd whole P P' numbers, such, that m, — — = n nearly, then will m he the number of half years between any two consecutive transits at opposite nodes. Let us examine the first equation : m P »re P == ji P', or n = -^^, which gives in the case of Mercury, n = — = a whole number, 88 365im 352 m 13* m , , , or = = = a whole number nearly. 88 88 88 ^ This gives for m 13, T; and the whole number of half years in the second equation will be 19, 1. Hence the transits of Mercury will occur at intervals of 13, Y, 9^, 3^, 9|-, and 3 J years, taken in order, and repeated again in the same order. The last transit of Mercury occurred May 8th, 1845 ; the next will occur November 9th, 1848. A full investigation of the same equations with reference to Venus, using 224§- in place of 88, will show that her transits will occur at i;itervals of 105|^, 8, 121^, and 8 years, taken in order, and repeated again in the same order. The last transit of Venus occurred June 3d, 1769 ; the next will occur at the opposite node, after the lapse of 105-J^ years, or December 8th, 18'74. Of -what must it be composed before a transit occurs at the opposite node ? Illustrate these principles. At what intervals will the transita of Mercury occur ? Those of Venus ? When did the last transit of Mer- cury occur, and when will the next happen i When did the List of Venus occm; and when will the next I 72 ASTRONOMY. These iuvestigations of the transits of Mercury and Venus agree in their results with those calculated from the tables of La Lande. 79. The Sun's Parallax determined by means of A Transit of Venus. A transit of Venus is a phenome- non of great importance, as furnishing the best means by which the sun's parallax may be determined. The following illustration will enable the student to understand the general principles on which the solution of this great problem depends. Let A and B represent the places of two observers, situated at opposite extremities of that diameter of the earth which is perpendicular to the plane of the ecliptic, v ,Venus passing through C D, part of her relative orbit, and in the direction from C to D, and c d ff the sun's disc, the plane of which for each observer may be regarded as perpendicular to the plane of the ecliptic. To an observer at A, the centre of the planet will appear to describe on the sun's disc, the chord c d, and to an observer at B, the parallel chord ef. Now, by knowing the exact times of the duration of the transit as observed at both these places, and also knowing the relative hourly motion of Venus in her orbit, the values of the chords c d and ef, expressed in seconds of a degree, also become known ; and hence knowing the sun's apparent diameter, the value of a h, the distance between the chords, or the difference between their versed sines, is easily found. Again, because the relative orbit of the planet, and consequently the chords c d and e f, make but a small angle with the plane of the ecliptic, a b may be regarded as parallel 79. Why is ft transit of Venus a phenomenon of great importance ? Draw the diagram, and illustrate the general principles on which the solu- tion of this great problem depends. OF \ ENUS. 73 to A B ; therefore the triangles AB v and a b v are similar, and give the proportion, a v : A v : : a b : A B ; but a v : a A :: .723 : 1 (73), &wi. a v : a A — a v = A • : : .723--- : 1—. 723 --- = .276---; hWe.723---: .276--- : : a h : AB = m a b = ^ a b nearly. And since A B measures the angle A a B, it follows that the sun's horizontal parallax, ox\AaB = ^ab nearly. We see from this method, that whatever error may be com- mitted in determining a b, the error in the parallax will be but one-fifth as great. In an exact calculation, the rotation of the earth on its axis, or whatever would affect an accurate result, must be taken into consideration. On account of the neai-ness of Mercury to the sun, and conse- quent small difference in their parallaxes, his transits are not suitable for determining the solar parallax. 80. Retrograde and Direct Motions of the interior Planets. Let S represent the sun, P an interior planet, as Mercury or Venus, E the earth, A B C a portion of the heavens, and P P' P" the planet's orbit. In an exact calculation, what must be taken into consideration ? Wliy are the transits of Mercury not suitable for def ermininjj the solar DaraUax I 4 74 ASTRONOMY. When the planet P is at its inferior conjunption, it will be invisible, because its dark side is turned towards E the earth, unless it be in one of its nodes, in which case it will be seen on the sun's disc like a dark spot. As the planet advances in its orbit from P to P', its enlightened side will become gradually visible, and it will appear west of the sun, being then a morning star. When it has arrived at P', or at its greatest western elongation (23), half its enlightened side will be seen from E, the earth, like a half moon. Now, during this motion of the planet from P to P', it will appear to an observer at E, to move from B to A in the heavens, or to go backwards, which is called its retrograde motion ; and during its motion from P' to P", it will appear to move from A to B in the heavens or forward, called its direct motion ; and when at P", it will appear in the same place in the heavens as when at P, being then in its superior conjunction. In going from P" to P'", it will become east of the sun and an evening star, and will appear to move from B to C in the heavens ; and when moving from P"' , its greatest eastern elongation, to P, it will appear to go backwards again in the heavens from C to B ; and when at P, it will again disappear, and pass by the sun. 81. Distances of Mercury and Venus, determined from their elongations. Join S P', (see last fig.) and in the right-angled triangle E P' 8, right-angled at P', we have the angle S E P' = the planet's greatest elongation, and E S ^ the distance of the sun from the earth, to find P' S the planet's distance from the sun. Mercury's greatest elongation is 28° 20', when he is in his aplielion and the earth in its perihelion ; but when Mercury is in his perilielion and the earth in its aphelion, the greatest elon- gation is 17° 36'; the mean is therefore 22° 58'. Then — 80. Draw the diagram, and illustrate the retrograde and direct motions of the interior planets. 81. What is the greatest elongation of Mercury, when he is in his aphe- lion and the earth in its perihelion ? And what is it when the planet is in the perihelion and the earth in the aphelion J From the mean of Hfce greatest elongations, determine the planet's oiatance. According to OP VENUS. 75 as Radius 90° ar. co. ... 0.0000000 is to sin SEP' 22° 58' . . 9.5912823 so is E S 24047r 4.3810609 to P' S 9383r 8.9723432 Hence 9383 X 3956™. = 37,119,148 miles, the distance of Mercury from the sun, according to this method. According to La Lande, the greatest elongations of Venus are 47° 48' and 44° 57' ; when she and the earth are in situa- tions similar to those of Mercury and the earth noticed near the beginning of this article, the mean is 46° 22' 30". Hence — as Radius 90° ar. co. ... 0.0000000 is to sm S E P 46° 22' 30" . . 9.8596611 so is E S 24047r 4.3810609 to P' 8 17406. 92r. . . . 4.2407220 Hence 17406.92 X 3956™. = 68,861,775 miles, the distance of Venus from the sun, agreeing very nearly with her distance already found by another method (73). Since these distances so nearly agree with those found by Kep- ler's third law, and since the times of the stationary appear- ances and retrogradations obtained by calculation based on the order and motions of Mercury, Venus, and the earth, in the Copernioan System, also agree with the times of observation of these phenomena, we have a strong proof of the truth of that system. 82. Astronomical Sign. The astronomical sign of Venus, ¥ , is said to represent a mirror furnished with a handle at the bottom. la Lande, what are the greatest elongations of Venus ? From the mean of these elongations, determine the distance of Venus. Do these distances of Mercury and Venus nearly agree with those found by Kepler's third law * What strong proof have we of the truth of the Copernioan sys- tem ? 82. Describe the astronomical sign of Venuj. 70 ASTRONOMY. CHAPTER VIII. THE EARTH ® 83. Remarks. The earth, or the globe which we in- habit, is the next planet above Venus. Its surface is composed of land and water, about one-fourth being land and the remainder, water. The water assumes a regular or uniform surface, but the land is irregular in its surface, occasioned by mountains and valleys. The earth is sur- rounded by an atmosphere varying in density, supposed to extend to the height of about fifty miles. By experi- ments in the science of Pneumatics, we learn that the atmosphere is an elastic medium, the density of which, being greatest at the earth's surface, decreases as the dis- tance increases. At the height of 3i miles, the density is but one-half that at the surface. The density of the atmosphere is so small at the height of 49 miles (52), that it ceases to reflect the sun's rays. 84. Period and Distance. The earth performs its siderial or periodic revolution round the sun, describing an elliptic orbit (22), in 365d. 6h. 9m. 12s., but its tropical revolution in 365d. 5h. 48??i. 48s. from any equinox or solstice (14), to the same again, which is the length of our year. Its distance from the sun, already determined (57), is 95,129,932 miles, and mbd. 6h. = 8766A.; therefore— 95,129,932X2X3.1416 ^^,^^ ., . ■ — = 68,186 miles, the mean rate 8766 of the earth's motion per hour in its orbit. S3. "Wliicli is the next planet to Venus ? Give a description of the earth's surface. To what height is the atmosphere supposed to extend ? Where is the density of the atmosphere the greatest S What is it at the height of 3| miles ? At what height does it cease to reflect the siin'a raya ? 84. In what time does the earth perform its siderial or periodic revolu- tion round the sun ! In what time its tropical revolution ? What is the length of our year ? At what rate does the earth move in its orbit per hour! OP THE EARTH 77 85. ECCENTKICITY OF THE Op.BIT. When the earth is in the periheUon, the sun's apparent diame- ter will be the greatest ; and when in the aphelion, it will be the least. The greatest i^nd least apparent diameters are respectively found to be 32' 34".6 and 31' 30".l ; hence the earth's relative distances when in these points, and consequently the eccentricity of its orbit, may be determined. Thus let e = the eccentricity, D = the greatest apparent diameter, d = the least, A = the aphelion or greatest distance, and P = the perihelion or least distance, and we shall have D : cZ : : A : P ; whence D + d : I> — d::A + F:A — F,orI> + d: B—d:: ^ + ^ : A— P , A+P , . . ; but = the semi-axis major = 1 ; and A — P = e ; wherefore I) + d : D — d : : I : e, and con- '^ , D — d sequently e = = .0108 by substitution, the eccen- tricity of the earth's orbit. Since the sun's apparent diameter is greatest about the be- ginning of January, and least about the beginning of July, it follows that 95,129,932m. X .0168 X 2 = 3,196,365 miles, which shows how much nearer the earth is to the sun in winter than summer. 86. Figure of the Earth. That the earth is spheri- cal, or nearly so, is not only evident from its shadow upon the moon in lunar eclipses, which shadow is always bounded by a circular line, but also from the many cir- cumnavigators who have sailed round it at different times, and the observations of persons at sea or on the shore, in viewing a vessel depart from them ; they first lose sight of the hull, while they can see the rigging and topsails ; but as she recedes farther from them, they gradually lose sight of these also, the whole being hid by the convexity of the water. 85. What are the greatest and least apparent diameters of the sun ? From these determine the eccentricity of the eartli's orbit. How much nearer is the earth to tlie sun in winter than summer ? 86. What is the figure of the earth? From what facts is it evident that the earth is spherical, or nearly so ! 78 ASTRONOMY. 87. The Earth is an Oblate Spheroid. Though the earth may be considered as spherical, yet it has been dis- covered that it is not truly so. This matter was the occasion of great disputes between the philosophers of the last age, among whom Sir Isaac Newton and James Cassini, a French astronomer, took the most active part in the controversy. Sir Isaac demonstrated from me- chanical principles that the earth was an oblate spheroid, or that it was flatted at the poles, the polar diameter or axis being shorter than the equatorial diameter. The French astronomer asserted the contrary, or that it was a prolate spheroid, the polar diameter being longer than the equatorial diameter. The French king, in 1736, being desirous to end the dis- pute, sent out two companies of the ablest mathematicians then in France, the one towards the equator, and the other towards the north pole, in order to measure a degree of a meridian in these different parts. From the results of their admeasurements, the assertions of Cassini were re- jected, and those of Newton confirmed beyond dispute. Therefore, since that time the form of the earth has been considered as that of an oblate spheroid, that is, of a solid such as would be generated by the revolution of a semi ellipse about its minor axis. 88. Diameter of the Earth. From the most accurate measurements it has been found thai the equatorial diam- eter of the earth is 7925 miles, and the polar diameter or axis, 7899 miles, the difliijrence, being 26 miles, is about jij of the equatorial diameter, called the ellipticity or 87. Is the earth truly spherical ? What did Sir Isaac Newton demon- strate concerning jt ! What were the assertions of Cassini on this suhject ? What was done, and when, "in order to ascertain its true form ? What followed the results of these admeasurements ? What has the form of the earth been' considered since that time ? 88. How long are the equatorial and polar diameters of the earth res- pectively ? What part of the equatorial diameter is the difference, and what called ? What is said of this difference, and the unevenness of the earth's surface ? OF THE EARTH. -9 oblateness of the earth. But this difference is so small, and the unevenness of the surface, arising froin moun- tains, iiills, &c., so inconsiderable, when compared with the magnitude, that in all practical sciences we may con- sider the earth as a sphere ; and hence, the artificial globes, being made perfectly spherical, are the best repre- sentations of the earth. The mean diameter is therefore 7912 miles, the radius 3956 miles, and the length of a degree of a great circle, 69 miles. 89. A Terrestrial Meridian is an Ellipse. Let E P Q, P' represent an ellipse. It is evident that the curva- ture of the arc E P diminishes from the extremity of the axis major to that of the axis minor, or from E to P, and as the curvature of the arc decreases, the radius of that arc increases ; hence, the length of a degree on the arc E P, will increase from E to P. Now, from the most accurate measurements this is found to be the case of a ter- restrial meridian from the equator to the pole ; and from the different lengths of a degree in different lati- tudes, it is proved that a meridian is an ellipse, or nearly so. If the semi- ellipse PEP' were to re- volve about P P', its minor axis, it would gen- erate a solid called an oblate spheroid, such is the form of the earth. When the revolution is made about E Q, the axis major, the solid is called a pro- ate spheroid. 90. Eccentricity of the Earth. The eccentricity of the How long ig the mean diameter ? The radius ? A degree of a great circle ? 89. Dra-w the diagram, and show how it is determined that a terrestrial meridian is an ellipse. 90. Define what is understood by the eccentricity of the earth. ASTRONOiWy. earth is the difference between its centre and one of the foci of an elliptical meridian. Thus let C (see last fig.) be the centre, and F one of the foci of the ellipse E P Q P', then will F C = the eccentricitj. If the equatorial radius E C ^ 1, we will have by the property of the ellipse F P = E ^ 1, and by the oblatenes s of the ear th ( 88), C P = 1 — sh = ilf ' but F C — Vf pa C P2 = V 1 (A 4 J2 = VTaa =.08091 = the eccentricity, the radius of the equator being unity. 91. Rotation ON THE Axis. The earth revolves once on its axis from west to east in 23h. 56m. 4s. which is the time that elapses from the passage of any fixed star over the meridian till it returns to the same meridian again. This motion of the earth, which is the most equable in nature, causes all the heavenly bodies to have an appa- rent diurnal motion in the same time, from east to west, making the vicissitudes of day and night. Besides the motion of the earth in its orbit (84), which is common to every place on its surface, the inhabitants of the equator are carried from west to east 1037 miles per hour by the daily rotation of the earth on its axis. Thus 7925 X 3.1416 24 1037 miles. 92. Inclination of the Axis and Seasons. The earth's axis makes an angle of 23° 28' with the axis of the orbit, and preserves the same oblique direction during its annual course, or keeps always parallel to itself; hence, during one part of the earth's course, the north Assuming the radius of the equator equal to unity, and knowing the oblateness, determine the eccentricity. 91. In what time does the earth revolve on its axis ? Which is the most equable motion in nature ? What causes aU the heavenly bodies to have an apparent diurnal motion from east to west ? On what do the vicissitudes of day and night depend ? How far are the inhabitants of the equator carried per hour by the rotation of the eai-th on its axis ? 92. What angle does the earth's axis make with the axis of the orbit ? What does the axis preserve during the earth's annual course ? What is the consequence of the axis preserving its parallelism J OF THE EARTH. fil pole is turned towards the sun ; and during the other part of its course, the south pole is turned towards him in like manner. This change in the position of the poles with regard to the sun, causes the variations in the lengths of days and nights, and the diflerent seasons of the year. Let S represent the sun, A B C D the earth's orbit, made sensibly elliptical, and p p' the earth's iixis making an angle of 23° 28', with the line a b passing through its centre, and per- pendicular to the plane of the orbit or ecliptic. The sun illu- minates half of the earth's surface at the same time, hence, the boundary of light and darkness, called the ch-de of illumination, is a great circle (6). It is evident that the plane of this circle ■will be perpendicular to a line drawn from the centre of the sun to the centre of the earth, called the radius vector. When the earth is in Libra at A, the sun will appear in Aries, his polar distance being 90° (16), and the angle p c S, which measures this distance, must be a right angle, hence the circle of illumination will pass through the poles/; and^y, and con- sequently will not only bisect the equator, but all the parallels What does tliis change in the position of the poles with regard to the sua cause ? Draw the diagram, and fuUy illustrate the cause of the variationa in the lengths of the day and night, and the diiferent seasons of tlie year. ' 82 ASTRONOMY. of latitude (7, 14) ; and as all places on the surface of the earth during one rotation will be as long on, one side of the circle of illumination as on the other, it follows that when the sun enters Aries, or at the time of the vernal equinox (13), he shines from pole to pole, and all the inhabitants of the earth have equal day and night. In this position of the earth, the circle of illumination will appear to the eye, placed in the plane of the ecliptic at a distance below the figure, as the circle pa p' h. While the earth advances from Libra to Capricorn, the angle p c 8 decreases, causing the north pole p to turn towards the «un, and the south pole p' from him, hence the circle of illumi- nation will cut the parallels of latitude unequally, and there- fore the length of the days in the northern hemisphere will continue to increase, and the length of those in the southern hemisphere proportionally to decrease. When the earth enters Capricorn at B, the sun will appear to enter Cancer, at which time the angle ^c^S will be the least, or 66° 32', and conse- quently the inclination of the'axis to the plane of the circle of illu- mination will be the greatest, or 23" 28', equal to ^ c a, the obli- quity of the ecliptic ; hence, when the sun enters Cancer or at the time of the summer solstice (13), the inhabitants of north lati- tude have their longest day and shortest night, and those of south latitude, their longest night and shortest day. At this time the whole of the north frigid zone (28) will have constant day, and the whole of the south frigid zone constant night. In this position of the earth the circle of illumination appears as the straight line a b. As the earth advances from Capricorn to Aries, the angle ^ c S increases, and consequently the length of the days in the northern hemisphere will decrease, and the length of those in the southern hemisphere will increase. When the earth enters Aries at C, the sun will appear to enter Libra, and then the angle pc S will be 90° ; hence, at the time of the autumnal equinox, all the inhabitants of the earth will again have equal day and night. In this position of the earth the dark hemisphere is turned towards the eye. Thus from the vernal to the autumnal equinox, it will be constant day at the north pole, and constant night at the south pole ; and in other parts of the north and south frigid zones, the time of continued day in the one and continued night in the other, will vary from 24 hours to six months^ being longer as the latitude of the place is greater OF THE MOON mi Again, as the earth advances through the other part of its orbit, or from Aries to Libra, the angle pc S will be greater than 90°, hence during this period, or from the autumnal to the vernal equinox, the north pole will be turned from the sun, and the south pole towards him, causing the night to be longer than the day in the northern hemisphere, and the day longer than the night in the southern hemisphere. When the earth enters Cancer at D, the sun will appear to enter Capricorn, at which time the angle pc S will be the greatest, or 1 13° 28', and the inclination of the axis to the plane of the circle of illumi- nation will again be equal to the obliquity of the ecliptic ; hence, when the sun enters Capricorn, or at the time of the winter solstice, the lengths of the day and night are the reverse of their lengths when the sun enters Cancer, or at the time of the summer solstice. Lastly, when the earth enters Libra the sun will again appear to enter Aries, and the circle of illumi- nation will pass through the poles ; hence, from the autumnal to the vernal equinox it will be constant night at the north pole, and constant day at the south pole. At all places situated on the equator, the lengths of the days and nights throughout the year are equal, being 12 hours each, because the equator, being a great circle, is bisected (6) by the circle of illumination. 93. Astronomical Sign. Astronomers call the earth Tellus, the astronomical sign of which © represents the terrestrial globe with its equator and axis. CHAPTER IX. THE MOON. B 94. Remarks. The moon is the nearest celestial body to the earth, and the next to the sun, from appearance, in splendor. Her apparent motion, like all the heavenly 93. Describe the astrCnomical sign of the earth. 94 Which is the nearest celestial body to the earth? 84 ASTRONOMY. bodies, is from east to west, caused by the rotation of the earth on its axis in a contrary direction. By observing her motion among the fixed stars, we will perceive that it is from west to east, and that in a period of time a little less than a month, she will have completed her circuit in the heavens. This motion of the moon round the earth is real ; besides which, she accompanies the latter in its annual revolution round the sun. The moon is a secon- dary planet, and the earth's satellite. 95. SiDERiAi, Revolution. It was observed in the last article, that the moon revolves round the earth from west to east, or from any one point in the heavens or fixed star to the same again, in less than a month. The exact time of this revolution is 21d. 7h. ASm. 5s, which period is called the moon's siderial revolution, or the periodic month. The siderial revolution is determined by observation. 96. Synodical Revolution. The synodic revolution, or the time that elapses between two consecutive con- junctions or oppositions of the sun and moon, may be deduced from the siderial revolution. Let E represent the earth, and m the moon in conjunc- tion with S the sun. After the lapse of a siderial revo- lution, the earth will have advanced in its orbit to E', and the moon to W, or the same longitude as when at m ; the line joining E and m being parallel to that joining E' and m', because two lines, supposed to be drawn from any two points of the earth's orbit to a fixed star, are sensibly parallel, on account of the immense distance to that star. What is the apparent motion of the moon, and by what caused ? In what time, and in what direction, does she complete her ch-cnit in the heavens ? Is this motion round the earth, real ? Besides tliis, what other motion has she ! Is the moon a secondary planet ? Of what planet is she the satellite ? 95. Wliat is the exact time of the moon's rerolution round the earth, and what called ? How is the siderial revolution determined ? 96. Define the synodic revolution. From what may it be deduced j OF THE MOON. 85 Now it is evident, before another junction can take place, the earth will have moved to E", and the moon to m", as represented in the figure. When the sun and moon are in conjunction, their longitudes are equal ; and before another conjunc- tion can occur, the excess of the moon's motion in lon- gitude over that of the sun's, must be 360°, or one circle. Thus put P = the periodic revolution of the earth in days, and P' == that of the moon, also in days. Then — ■■ the mean daily motion of the sun in longitude. P 1 the mean daily motion of the moon in longitude, and 1 1 ■P' P'P = the daily gain of the moon's motion in longitude over that of the sun. Hence — P-P' . , , . P' P ^ p

ON. 89 ein.pses fiom full to the last quarter, and from the last quarter to new moon again. When the moon is first seen after the ckange, the line con. necting- the horns will be differently inclined to a vertical circle at ditt'erent seasons of the year. Thus about the time of the vernal equinox, the line connecting the horns will be most in- clined to a vertical circle, because this portion of the ecliptic, in which the moon is nearly situated, makes with the western honzon the greatest angle. On the contrary, about the time of the autumnal equinox, the new moon will appear most erect, or the line joining her horns the least inclined to a vertical circle. 100. Dark part of the Moon's Disc, visible. When the moon is first seen after the change, nearly the whole of her dark hemisphere is turned towards the earth ; and although this part of the moon is not immediately en- lighted by the sun, yet by the reflection of the sun's light from the earth to the moon, and from the moon again to the earth, it becomes partially visible. At the change, the moon receives light from the whole of the earth's enlightened hemisphere ; but as she ad- vances in age, she will receive less, because less of this enlightened hemisphere will be turned towards her ; and this secondary light will be farther diminished, in conse- quence of the increased size of the illuminated part of the disc. Hence this phenomenon will entirely disappear before full moon. 101. The Earth as seen from the Moon. If the two preceding articles have been well understood, it will be obvious that the earth, as seen from the moon, will assume, in the course of a lunar month, all the phases of Wliat is said of a line connecting the moon's horns, when first seen after the change, at different seasons of the year ? 100. Explain the cause why the dark part of the moon, when first seer sifter the change, is partially visible. Why does this phenomenon entirely disappear before full moon ? 101 What will the earth assume in the course of a lunar month, as seen from the moon ? 90 ASTRONOMY. the latter body as seen from the former. It is also evi- dent that when it is new moon, the earth will appear to the moon a splendid full moon, thirteen times as large (98) as the moon when full appears to us. At any par- ticular time the phase of the one body will be the oppo- site that of the other. 102. Inclination of the Orbit and place of the Nodes. The moon's orbit is not in the plane of the ecliptic, but is inchned in an angle varying from 5° to 5° 17'. From a series of latitudes and longitudes, deter- mined from the moon's observed right ascensions and declinations, we find the inclination of her orbit and the place of her nodes. The greatest of these latitudes will be the inclination of the orbit ; and when the latitude is zero, and changing from south to north, the longitude will be the place of the ascending node. The opposite point of the ecliptic will be the place of the descending node. Thus, let N A M, represent the ecliptic, and N B w, the moon's orbit referred to the celestial sphere. Since the two great circles bisect each other in the points N and n, it is evident that the arc A B, of a great circle will measure the greatest lati- tude (18), when described about N as a pole, and conse- quently will measure the angle A N B, or the inclination of the orbit to the plane of the ecliptic. When the latitude is zero, or when the moon is at N or n, the longitudes will evidently be the position of the nodes. N being the ascending and n the descending node. What is also evident in relation to this matter ? What is said of the phase of the one body, compared with that of ' he other, at the same time \ 102. What is the inclination of the moon s orbit to the plane of the ecliptic ? From what are the inclination and place of the nodes found ? Explain these principles by the diagram. OF THE MOON. 91 103. Retrograde Motion of the Nodes. The moon's nodes have a retrograde motion, amounting to about 19" 20' in a year, and consequently making a complete tropi- cal revolution in 6798 days = 18y. 224d. This varia- tion of the nodes, which is not quite uniform, is found from their repeatedly determined longitudes. 104. Same Hemisphere of the Moon always seen, AND Rotation on the Axis. By observing attentively the moon's surface and the position of the spots thereon, we find that nearly the same hemisphere is always turned towards the earth, and hence, as she revolves in her orbit from west to east round the earth in 2'7d. 7h. 43m. 5s., (95) she must necessarily make a rotation on her axis from west to east in the same interval of time. Hence, also, the inhabitants (if any) of that hemisphere turned from the earth, will be deprived of a sight of this, our planet. 105. Inclination of the Axis, Seasons, and Days. In the preceding article, we noticed that the moon always presents the same hemisphere to the earth with but slight variations. These variations are not found to arise from any want of uniformity in the motion on her axis, but from the irregularity of motion in her orbit, and the inclination of the lunar equator to the plane of the ecliptic. From accurate observations on the slight change of position of the lunar spots, it is ascertained that the axis of the moon, which maintains its parallelism, makes only an angle of 1° 30' with the perpendicular to the plane of the ecliptic, consequently she can have but little or no 103. Do the moon's nodes vaiy ? What is the amount of this variation in a year ? In what time do they make a complete revolution ? From what is this variation of the nodes found ? 104. What will we find by observing attentively the moon's surface, and the position of spots thereon ! What are the consequences of this ? 1 OS. Does the moon alw.ays present the same hemisphere to the earth without any variations ? From what do these variations arise i What is the inclination of the axis, and how ascertained ? 92 ASTRONOMY. diversity of seasons, or of length of days. It is also found that the intersection of the plane of the lunar equator with the plane of the ecliptic, is always parallel to the line of the moon's nodes. And since the moon revolves on her axis exactly in the same time in which she performs her periodic revolution round the earth, it is evident, her siderial day = 27(f. Ih. 43m. 5s., hence, her solar day = 29d. 12h. 44m., the length of the lunar month ; and hence, also, the length of her year is but a little more than 12^ of her solar days. 106. Moon's Libkations. In consequence of the irregular motion of the moon in her orbit, at one time moving slower, and at another time faster, than her mean motion, small portions of her surface on the eastern and western edges, will alternately appear and disappear. This periodical oscillation observed in the spots near these edges, is called the moon's libration in longitude. Also, in consequence of the inclination of the axis, and its remaining always parallel to itself, we will at one time see beyond ' the north pole of the moon, and at an- other time beyond the south pole. This alternate change in the appearmg and disappearing of the lunar spots near the poles, is called the moon's libration in latitude. 107. Eccentricity of the Orbit. When the moon is in perigee and apogee, .her apparent diam- eters will then be the greatest and the least, which are found to vary from one revolution to another. Of these, the greatest is 33' 31", and least 29' 22'. The' means of the greatest and least apparent diameters for one year, are respectively about 32' 59".6, and 29' 28"; hence, by using the formula in deter- Wliat is the consequence of this small inclination 1 What are the lengths of the siderial and solar days respectively ! What is the length of her year ! 106. Describe the moon's libration in longitude. Describe her libration in latitude. ltJ7. When has the moon the gi-eatest and least apparent diameters ? Do these vary from one revolution to another ! From the means of the greatest and least apparent diameters, deduce the eccentricity of her orbit. OF THE MOON. 93 oiining the eccentricity of the earth's orbit (85), we have B—d . . , , * == y. I ^ = .056, by substituting the values of D and d. Or the perigean and apogean distances may be found from the greatest and least parallaxes (55), and the eccentricity de- duced therefrom. 108. Moon's Surface and Mountains. "When the moon's disc is viewed with the telescope, numerous . spots are seen of various shapes and degrees of brightness. (See the figure.) The line of illumination is • very irregular and serrated. ■ Bright spots on the dark ™ part near this line are fre- quently observed, vs^hich gradually enlarge until they become united with the en- lightened part. From these appearances it is inferred that the surface of the moon is diversified with mountains and valleys ; and since the boundary of light and darkness is always very irregular, it follows that the moon cannot have any extensive seas, otherwise this line on the surface of water would evi- dently be a regular curve. The elevations of several lunar mountains have been com- puted. According to Dr. Herschel, the highest does not ex- ceed If miles in altitude. Professor Schroeter makes the height of some to exceed 5 miles. Several mountain ranges have the By what other method may the eccentricity be found ! 108. What are seen on the moon's disc, when viewed with a telescope ! What is said of the line of illumination, and of spots on the dark part ? What is inferred from these appearances ? From what circumstance does it follow, that the moon cannot have any extensive seas ? According to Dr. Herschel, what is the altitude of the highest lunar mountains ? What does Schrceter make the height of some ? What is said of several moun- tain r;inge.=i ? 94 ASTRONOMY. appearance of volcanic origin, tlie force of which is now be- lieved to be extinct. 109. Moon's Atmosphere. The question, whether a lunar atmosphere exists, has long been discussed by astronomers. The constant serenity of her surface, being without clouds or vapors, the want of a sensible diminution or refraction in the light of a fixed star near- ly in contact with her limb, and the want of a sensible effect on the duration of an eclipse of the sun, have induc- ed some astronomers to maintain that the moon is with- out an atmosphere, at least, of such a, nature, as apper- tains to our earth. Notwithstanding, it is maintained by others, that the above arguments are not opposed to the existence of an atmosphere of* a few miles only in height. The celebrat- ed Selenographist, Schroeter, of Lilienthal, appears to have been successful in discovering an atmosphere, while making some observations on the crescent moon. He calculated that the height to which it is capable of affect- ing the light of a star, or of 'inflecting the solar rays, does not exceed 1 mile. On the whole, it is inferred that the moon is most pro- bably surrounded by a small atmosphere. ilO. Phenomenon of the Harvest Moon. In north latitude, the rising of the moon nearly at the same time for several evenings together after the full moon, about the time of the autumnal equinox, is called the Harvest Moon. This comparatively small retardation in 'the moon's daily rising, we will now explain. 109. What arguments are used in favor of the opinion, that the moon is -without an atmosphere ? Are these arguments opposed to the exis- tence of a lunar atmosphere hut a few miles in height ? Who appears to have been successful in discovering an atmosphere ? On the whole, what is inferred ? 110. At what time does the moon rise for several evenings together, after full moon, about the time of the autumnal equinox ! What is thia peculiar rising of the moon called ? OF THE MOON. 9f Since the moon's orbit coincides nearly with th£ eclip- tic (102), her motion, in a general illustration of the phe- nomenon, may be regarded as in that circle. The dif- ferent signs of the ecliptic, on account of its obliquity to the earth's axis, make very different angles with the hori- zon as they rise and set, especially in considerable lati- tudes. Those signs which rise with the smallest angles set with the greatest angles, and vice versa ; and, when- ever these angles are least, equal portions of the ecliptic will rise in less time, than when these angles are greater ; and the contrary. In northern latitudes, the smallest angles are made when Aries and Pisces rise, and the greatest when Libra and Virgo rise ; consequently when the moon is in Pisces or Aries, she rises with the least difference of time, and she is in these signs twelve times in a year ; and when she is in Virgo or Libra, she rises with the greatest differ- ence. This peculiar rising of the moon, passes unobserved at all seasons of the year, except in the months of Septem- ber and October ; because in winter, when the moon is in Pisces or Aries, she rises at noon, being then in her first quarter ; but when the sun is above the horizon, the moon's rising is never perceived. In spring, the moon rises with the sun in these signs, and changes in them at that time of the year ; consequently, she is quite invisi- ble. In summer, when the moon is in these signs, she With what circle does the moon's orbit nearly coincide ? What is said respecting the different signs of the ecliptic, on account of its obliquity to the earth's axis ? With what angles do those signs set, whii h rise with the least ? When do equal portions of the ecliptic rise in less time ? In northern latitudes, what signs make the smallest angles with the horizon in rising ? What signs the greatest angles ? In what signs k the moon, when she rises with the least difference of time 8 And in what when she rises with the greatest difference of time ! How often is llie moon in Pisces or Aries ? In winter, when the moon is in these signs, at what time does she rise ? What is her age then ? Why is her ri ing not per- ceived ? In spring, when in these signs, why is lier rising invisible ? In summer, why does her rising pass unobserved ? And in autunui, why is this phenomenon of the moon's rising so very conspicuous ! 96 ASTRONOMY. rises about midnight, being then in her third quarter, and rising so late that she passes unobserved. But in autumn when the moon is in these signs, she rises at or about sunset, being then full, because the sun is diametrically opposite to her in Virgo or Libra, answering to the month of September or October, at which time this phenome- non of the moon's rising is very conspicuous, which had passed unobserved at all other times of the year before. In south latitude, the smallest angles are made when Virgo and Libra rise, and the greatest when Pisces and Aries rise ; so that, when the moon is in Virgo or Libra, she rises with the least difference of time ; and when she is in Pisces or Aries, she rises with the greatest differ- ence of time ; but when the moon is full in, Virgo or Libra, the sun is in Pisces or Aries, which is about the time of our vernal equinox, or the time of harvest in the southern hemisphere. Hence, the harvest moons are as regular in south latitude as in north latitude, but they take place at opposite times of the year. By elevating the pole of an artificial globe for the lati- tude of the place, and bringing the different signs of the ecliptic to the eastern edge of the horizon, these phe- nomena may be fully explained and verified. In our latitude, the least difference in the moon's risings is about 25 minutes, and the greatest Ih. 5m. 111. Astronomical Sign. The astronomical sign is the crescent D or the moon in her first quarter. In south latitude, what signs make the smallest angles in rising ! What signs the greatest angles ? In what signs is the moon, when she rises with the least difference of time in south latitude ? When is the moon full in Virgo or Libra ? What season of the year is it then in the southern hem- isphere ? Are the harvest moons as regular in south as in north latitude S How may these phenomena be fully explained and verified? Wtat are the least and greatest differences in the moon's risings, in our latitude ! 111. What is the astronomical sign of the moon ? OP MARS 97 CHAPTER X. 112. Remarks. Mars, the first planet without the earth's orbit, appears as a star of the first or second magnitude, and is easily distinguished from the other planets by his dusky red light. Mars is sometimes in con- junction with the sun, but he was never seen to transit the sun's disc. He appears sometimes round and fiill, when viewed with a good telescope, and at other times gibbous, but never horned ; therefore, from these appear- ances, it is manifest that he shines not by his own light, and that his orbit is more distant from the sun than the earth's orbit. When Mars is in opposition, or on the meridian at midnight, his apparent size is much larger than when he is near conjunction, because in the former situation, he is but about } as far from the earth as in the latter. 113. Period and Distance. Mars performs his side- rial revolution round the sun in 686d. 23h. 30m. 37s. = 59355037s. Hence, [" 59355037 1^^ 3.537461502596; l31558I5lJ and V3.53746I502596 = 1.5236, the distance of Mars from the sun or serai-axis, the earth's distance being = 1. Then 1.5236 X 24047 r = 36638 r, the distance in mean radii of the earth ; and 36638 X 3956ot. = 144,939,928 112. Which is the first planet without the earth's orbit? What is the appearance of Mara, and how distinguished ? Was he ever seen to tran- sit the sun's disc t What are his appearances when viewed with a good telescope ? What is manifest from these appearances ? Why is his ap- parent size much larger when in opposition than when near conjunction ! 113. In what time does Mars perform his siderial revolution? From this deduce his mean distance, taking the earth's mean distance equal to unity. What is his distance in miles ? 5 98 ASTRONOMY. miles, the mean distance of Mars from tiie sun. Accord- ing to this distance and the periodic time, it will be found that the planet moves in his orbit at the mean rate of about 55,000 miles per hour. Also, according to this distance, the intensity of the sun's light at Mars is not half its intensity at the earth. 114. Apparent Diameter and Magnitude. The greatest and least apparent diameters of Mars, found from observations, are respectively 23" and 3".4. His appa- rent diameter will evidently be a maximum when at his perihelion distance and in opposition, and a minimum when at his aphelion distance and in conjunction ; hence, 23" + 3".4 : 3".4 : : 1.5236 X 2 : .39244, the distance of Mars from the earth when his apparent diameter is 23". Again, 1 : .39244 : : 23" : 9".026, the apparent diameter at a distance from the earth equal to that of the sun ; hence, 32' 1".8 : 9".026 : : 886144??i. : 4161 miles = the real diameter of Mars. And = .1454, making the magnitude but a little more than | that of the earth. 115. Eccentricity of the Orbit. From the preceding article, the eccentricity of the planet's orbit may be calculated within a near degree of the truth. Thus, .39244 + 1 = 1.39244, the perihelion distance from the , 1.5236 — 1.39244 „„„ ,, ^ • •. r ... sun : and := .086, the eccentricity of the 1.5236 ' orbit nearly. 116. Inclination of the Orbit, &c. The inclinatiop At what rate per hour does he move in hia orbit ? What is the com- parative intensity of the sun's light at Mars ! 114. What is the gi-eatest, and what is the least apparent diameter of Mars ? When will he have the greatest and when tlie least apparent diameter ? • From these deduce his real diameter in miles. What is his compara- tive magnitude ? n5. How may the eccentricity of the orbit of Mars be calculated ? 116. What is the inclination of the orbit of Mars to the eclijitic, and OF MARS. 99 of the orbit of Mars to the plane of the echptic is 1° 51', and the ascending node 18° in Taurus. He revolves on his axis, which is inclined to the axis of the ecliptic 30° 18', in 24A. 39m. 21s. ' Hence, this great obliquity of his equator to the orbit, will occasion a great diversity of seasons, and a great inequality in the length of his days and nights. The great eccentricity of the planet's orbit will cause a great difference in the length of his seasons, the spring and summer in the northern hemisphere being 372, and the autumn and winter 296 martial days long. 117. Telescopic Appearances OF Mars. When Mars is viewed with a good telescope, spots are seen on his surface, which retain their size and form, and their ap- pearances, with some slight variations of color. Some spots are of a reddish color, and therefore conjectured to be land, while others are greenish, and thence supposed to be water. Remarkable white spots (see the figure) are often seen near the poles of the planet. These vary in size, and after long ex- posui-e to the sun, sometimes disappear, for which reason they are believed to be snow. From observations on these spots, the obliquity of the axis to the orbit, and the time of rotation thereon, have been found. 118. Astronomical Sign. The astronomical sign of Mars, i , represents a spear and shield, the emblems of war. the place of the node ? What is the inclination of his axis, and the time of rotation tliereon ? What will this great obliquity of the equator to the orbit occasion ! What will the great eccentricity of the orbit cause ! What are the lengths of hie seasons in martial days ? ll"?. Give a description of tlie spots seen on the surface of Mars. Describe particularly the spots seen near the poles of the planet. What have been found from observations on these spots ? 118. What is the astronomical sign of Mars ! 100 ASTRONOMY. CHAPTER XI. ASTEROIDS VESTA, JUNO, CERES, PALLAS, ASTRjEA, HEBE, FLORA, IRIS, AND METIS. 119. Remarks. The planets Vesta, Juno, Ceres, and Pallas, of this group, sometimes called Asteroids, have been discovered about the beginning of the present cen- tury ; the others, within the last three years. Although these planets are situated between the orbits of Mars and Jupiter, yet on account of their smallness, they can- not be seen without the aid of a telescope. Their orbits cross each other, though not in the same plane. There is much uncertainty concerning their actual magnitudes ; and the inclinations of their axes, and rotations thereon, have not yet been determined. It is the opinion of some philosophers, that a large planet, which once existed between the orbits of Mars and Jupitei", burst in pieces by some internal force capa- ble of overcoming the mutual attraction of the fragments, and therefore gave rise to these small planets under con- sideration. 120. Vesta. The planet Vesta was discovered by Dr. Olbers, a physician of Bremen, in Germany, on the 29th of March, 1807. She revolves round the sun in 1325^^ days, in an orbit inclined to the ecliptic 7° 8', and at a mean distance of nearly 225,000,000 miles. Her diameter is estimated at only 270 miles. 121. Astronomical Sign. On the altar of Vesta, the goddess of fire and patroness of the vestal virgins, a per- il 9. Name the Asteroids. Where are they situated, and why can they not be seen without the aid of a telescope ? What is said of theu- orbits S What is the opinion of some philosophers concerning their origin ? 120. By whom and when was Vesta discovered ? What is her period J Inclination of her orbit ! Mean distance ? And diameter ! 121. What have astronomers adopted as her sign ? ASTEKOrDS. 101 petual flame was maintained ; hence astronomers have adopted an altar, fi as her astronomical sign, on which a fire is blazing. 122. Juno. The .planet Juno was discovered by M. Harding, of Lilienthal, near Bremen, on the 1st of September, 1804. She revolves in her orbit round the sun in 1593 days, at the mean distance of nearly 254,000,000 miles. Her orbit, which is very eccentric, is inclined to the ecliptic in an angle of 13° 2'. The diameter of Juno is stated to be 460 miles. 123. Astronomical Sign. Juno, the queen of the heavens, has for her astronomical sign, 5 , a mirror crowned with a star, the emblems of beauty and power. 124. Ceres. Ceres was discovered at Palermo, in Si- cily, by M. Piazzi, on the 1st of January, 1801. She performs her revolution round the sun in 1684 days, at a mean distance from him of about 263,000,000 miles. Her orbit, which is inclined to the ecliptic 10° 37', is but moderately eccentric. The diameter of this planet is given equal to that of Juno, viz : 460 miles. 125. Astronomical Sign. The astronomical sign of Ceres, the goddess of corn and harvests, called Bona Dea, is a sickle, ? , the instrument of the harvest. 126. Pallas. Pallas was discovered at Bremen, by Dr. Olbers, the discoverer of Vesta, (120), on the 28th of March, 1802. She performs her revolution round the sun in 1686 days, at the mean distance from him of about 263,000,000 miles. The eccentricity of her orbit, which 7 2.2. By whom and when was Juno discovered ! What is her period ! Mean distance ? Inclination of the orbit ? And diameter ? 123. What is the astronomical sign of Juno? 124. By whom and when was Ceres discovered ? What is her period ! Mean distance ? Inclination of the orbit ? And diameter ? 125. What is the astronomical sign of Ceres ? 126. By whom and when was Pallas discovered ? What is her period ? Mean distance ? IncUnation of the orbit, and its eccentricity ? 102 ilSTKONOMY. is inclined to the plane of the ecliptic 34° 35' nearly, is i the semi-axis or mean distance from the sun. Lament has stated the probable diameter of Pallas, which is the largest of the five, to be 670 miles. 127. Astronomical Sign. Pallas, the reputed goddess of wisdom and war, has for her astronomical sign, 2 , the head of a spear. 128. AsTR/BA, Hebe, Flora, Iris, and Metis. Astraea, the fifth Asteroid, was discovered by Mr. Hencke, of Dresden, December 15th, 1845. This planet revolves round the sun in 1566 days, in an orbit inclined to the ecliptic 7° 45', and at a mean distance of 253,000,000 miles. Mr. Hencke, the discoverer of Astraea, discovered, on the 1st of July, 1847, the sixth Asteroid, called Hebe. It resembles in appearance a star of the ninth magnitude. Mr. Hind, secretary of the Royal Astronomical Society, England, soon after the discovery of Hebe, added Flora and Iris to the same family group. And lastly, on the 25th of April, 1848, Mr. Graham, of Mr. Cooper's Obser- vatory, Markee Castle, Sligo, discovered Metis, the ninth Asteroid. The elements of these four planets have not yet been computed with sufficient accuracy, to warrant their record. Several other Asteroids may exist. 129. Astronomical Sign of Aste^a. A star, *, is the astronomical sign of Astraea, the goddess of justice. 130. Ultra-Zodiaoal Planets. The great inclina- tions of the orbits of Juno, Ceres, and Pallas, to the plane How does Pallas compare in magnitude with the other asteroids ? What is her diameter according to Lamont ? 127. What is the astronomical sign of Pallas ? 128. What is said of Astriea ! By whom discovered, and when ? What is her period ? Inclination of the orbit ? And mean distance ? Who discovered Hebe, and when? Who discovered Flora and Iris! When was Metis, the ninth Asteroid, di?cov«ved and bv whom ? 129. What is the astronomical sign of Astrsea? 130. What planets are called ultra-zodiacal, and on what account! JUPITEll AND HIS SATELI.rTES. 103 of the ecliptic, being respectively 13° 2', 10° 37', and 34° 35', will cause that they are found, sometimes, beyond the limits of the zodiac (10) ; and hence they are called ultra-zodiacal planets. CHAPTER XII. JUPITER "K AND HIS SATELLITES. 131. Remarks. Jupiter, the largest of all the planets, and the most brilliant in appearance, except sometimes V^enus, may, on those accounts, be distinguished by his great magnitude and peculiar brightness. When Jupiter is opposite to the sun, that is, when he comes to the me- ridian at midnight, he is then nearer to the earth than he is for some time before or after conjunction ; and conse- quently, at the time of opposition, he appears larger and shines with greater lustre than at other times. Some- times Jupiter appears nearly as large as Venus, though his nearest distance from the earth is fifteen times the nearest distance of Venus from our planet. 132. Period and Distance. Jupiter performs his si- derial revolution round the sun in 4332 or the polar diameter is Jy less than the equatorial diameter. 147. Astronomical Sign. The astronomical sign of Saturn is ^ , supposed to represent the original form of a sythe with which he was armed, an emblem of the rav- ages of time. 148. Satellites of Saturn. It has been already- observed, that Saturn is attended by no less than seven satellites or moons, which supply him with light during the sun's absence. The 6th of these satellites in the order of their distances from the primary, was discovered by Huygens, a Dutch mathematician in the year 1655. The 3d, 4th, 5th, and 7th, were discovered by John Dominic Cassyii, a celebrated Italian astronomer, between the years 1671 and 1685. The 1st and 2d, were discovered by Dr. Herschel in the years 1787 and 1789. Large telescopes are required for the observations of these sat- ellites, particularly the 1st and 2d, the discovery of which was a fruit of Dr. Herschel's large reflecting telescope of 40 feet focus. The times of their revolutions round Saturn and their respective distances from him, are as follows : 146. What is the inclination of the orbit of Saturn to the ecliptic, and the place of the node ? In what time does he rcTolve on his axis ! What is the inclination of his axis to the axis of the orbit ? What is the oblateness of this planet ? 147. Describe the astronomical sign of Saturn. Of what is it an em- blem ! 148. How many satellites attend Saturn ? By whom, and when was the 6lh discovered ! By whom, and when, were the 3d, 4th, 5th, and 7th discovered ? By whom, and when, were the 1st and 2d discovered ! What is said of the telescopes reqmred for the observations of these sat- ellites, particularly the Ist and 2d 9 SATUEN- -HIS SA'l rELi SAT. D. H. M. s. 1 sid. rev. 22 37 23 2 ti tt 1 8 53 9 3 CI tt 1 21 18 26 4 " " 2 17 44 51 5 tt tt 4 12 25 11 6 tt tt 15 22 41 13 1 " " V9 7 54 37 TES AND RINGS. 113 MILES. dist. from S. 120,000 154,000 189,000 " " 244,000 341,000 791,000 " 2,306,000 149. Magnitudes, &o. The satellites of Saturn, owing to their great distance from us, appear very small, and consequently, their real magnitudes are not well known. The 7th is the largest, and according to Sir John Herschel, is nearly equal in size to the planet Mars. From the 7th, or most distant, they are said to diminish inward. The orbits of the satellites are in the plane of Saturn's ring, except that of the 7 th, which is considerably inclined to it ; and since the ring coincides with the planet's equator, which latter plane makes an angle of 29° (146) with Saturn's orbit, it fol- lows that they will be but seldom eclipsed, and only when Saturn is in or near one of the nodes of their orbits. As the 7th satellite exhibits periodical variations of bright- ness, it is inferred, that like our moon, it rotates on an axis in the same time that it revolves round Saturn. 150. Saturn's Rings. Huygens first discovered Sa- turn's ring, which Dr. Herschel afterwards, by the assis- tance of his powerful telescopes, found to be double, or to consist of two concentric rings. The ring casts a shadow on the planet, and is likewise obscured on that side opposite to the sun by the planet's shadow ; hence, the general conclusion is that it is a so!'i opaque body, shining by reflecting the light of the sun. Give the times of their revolutions round Saturn, and their respective distances from him. 149. Why are the magnitudes of Saturn's satellites not well known ? "Wliich is the largest, and what is its size according to Sir John Herschel ? Explain the reason why they are but seldom eclipsed. "Wliat is inferred from the periodical change of brightness observed in the 7th ? 150. "Who first discovered Saturn's ring ? Who afterwards found it to be double ! What is the general opinion respecting the nature of tie 117,000 miles 20,000 151,000 17,000 155,000 2,000 176,000 10,500 114 ASTRONOMY. It has been observed, that this most extraordinary appendage is very thin. According to Sir John Herschel, its thickness does not exceed 100 miles. From the micro- metrical measurements of Professor Struve, the othei dimensions are as follows : Interior diameter of the interior ring, Distance of the edge of the interior ring from the planet, - ... .Exterior diameter of the interior ring. Breadth of the interior ring, Interior diameter of the exterior ring. Interval between the rings. Exterior diameter of the exterior ring. Breadth of the exterior ring, - The interval between the rings can only be seen by teles- copes of great power. It appears under the form of a black line, as represented in the figure (143). 151. Inclination and Rotation of the Rings. From observations, it has been found that the plane of the rings coincides with the plane of Saturn's equator, and therefore is inclined to the plane of the orbit 29°. The ascending node of the ring is 20° in Virgo. From the motion of lucid spots on the surface of the ring, it has been inferred that it rotates on an axis per- pendicular to its plane, and passing through the centre of the planet. The time of this rotation, which is from west ti east, is lOA. 29m., equal the time of Saturn's rotation 0-1 his axis. 152. Apparent Forms of the Rings. Since the tfane of the ring, which continues parallel to itself, is i r.clined to the orbit under an angle of about 28° 40' ; rinff, and on what based ? What is the thickness of the ring according to Sir John Herschel ! From the micrometrical measurements of Professor Struve, what are the other dimensions ! 161. Wliat is said respecting the inclination of the ring, and the place of the ascending node ? What has been inferred from the motion of lucid spots on Its surface ? What is the time of this rotation f 152. Explain the reason why Saturn's ring appeals elliptical. SATURN HIS SATELLITES AND RINOS. 115 anil since this latter plane nearly coincides with the ecliptic (146), it follows that it can never be seen from the earth but under different degrees of obliquity, vary- ing from about 60° to 90° with its axis ; hence, it will not appear circular in its form, which it really is, but elliptical. And as the orbit of Saturn is very large, com- pared with the earth's orbit, the eccentricity will vary according to the distance of the planet from one of the nodes of the ring. Let S represent the sun, ah c d the orbit of the earth, and A B C D the orbit of Saturn. If A and C be the nodes of the ring, it is evident that when the planet is at A or 0, the plane of the ring will pass through the sun, and hence, the edge will only be illuminated. In this position, the ring can o^ly be seen with a telescope of high power, appearing like a line of light on the disc of the planet, and extending some dis- tance on each side of it. According to what will its eccentricity vary ? Draw the diagram, and show the difierent apparent forms of the ring. 116 ASTRONOMY. As the planet advances in the orbit from A or C, the illumi- nated plane of the ring will become more visible ; and when at B or D 90° from the node A or C, the ring will appear most open, or to the greatest advantage. 153. Disappearances of the Ring. If the tangent parallels e h and f ff (see the last figure) be drawn at an equal distance from the node A, it will be found, taking the diameter of the earth's orbit equal 2, and Saturn's distance from the sun equal 9.54 (144), that the arc e f will contain 12° very nearly. Now since the planet revolves round the sun in 29 years, 167 days (144), he will pass through the portion ef or ff hin nearly one year, or while the earth passes , through the whole orbit, abed. This being understood, it is evident there will be occasional disappearances of the ring from the fact that the earth will sometimes be on the dark side of the plane of the ring, or on the opposite side from the sun. Thus, if the planet come to e, when the earth is at any posi- tion between c and d, it is evident that in some position between e and A, the plane of the ring will pass between the sun and the earth, and therefore there will be a disappearance. When the planet has arrived at A, the earth will be at some position between a and b, immediately after which time there will be another disappearance, which will continue until the earth comes to a position between b and c, or on the same side of the plane of the ring with the sun. In like manner there will be ■V)ccasional disappearances of the ring, when the planet is pass- ing through the portion g h oi the orbit. When Saturn's lon- gitude is within 6° of either node of tlie ring, or within 6° of 170°, or 350° (151), one of these disappearances may be expected ; and as the planet revolves round the sun in 29 years 167 days, about 14^ years will elapse from the occurrence of a disappearance at one node till another takes place at the opposite node. The last disappearance happened in April, 1848, the next will occur in 1863. When the planet's longitude is 80° or 260°, the ring will be in a position most advantageous for observation. 163. Draw the tangent parallels ef and g h'm the last figure, and show from what fact there will be occasional disappearances of the ring. Give thf different positions of the planet and the earth, when these disappear- ances will occur. When may a disappearance be expected ? When a disappearance has occuned at one node, what time will elapse befoiw UK ANUS AND HIS SATELLITES. 117 CHAPTER XIV. URANUS 1^ AND HIS SATELLITES. 154. Remarks. Uranus was discovered on the 13th of March, 1781 , by Dr. Herschel, who named it Georgium Sidus, through respect to his patron, King George III, On the continent, it was generally called Herschel, in honor of its illustrious discoverer, and of late, astrono- mers have adopted the name Uranus, from the circum stance that the other planets have been named after heathen deities. Uranus, though large, on account of his great distance from the sun, can scarcely be distinguish- ed by an unaided eye, even in a clear night, and in the moon's absence. 155. Period and Distance. Uranus performs his siderial revolution round the sun in 30686^. 19A. 42wi. =: 84 years, Q\ days, of tropical mean time, and hence, ' 30686.821 11^ (84.014469)* = (7058.431)* = 365.2564 J ' ^ ' 19.18239 = semi-axis of the orbit, the earth's mean dis- tance being =1 ; therefore 95,129,932ot. X 19.18239 — 1,824,819,456 miles, the mean distance of Uranus from the sun. And 30686fi?. 19fA. : lA. : : 1824819456??i. X 2 X 3.1416 : 15567 miles, the planet's hourly mean motio'i another occurs at the opposite node ? When did the last disappeara-.xv; happen \ When will the next ? "What is the planet's longitude, wlhn is the ring in a position most advantageous for observation % 154. "When, and by whom was Uranus discovered? What named'! Hi rschel give it ? What was it called on the continent ? From what circumstance have astronomers adopted the name Uranus ? Can Urai u^ be distinguished by the unaided eye ? 155. In what time does Uranus perform his siderial revolution! What is the length of the semi-axis of his orbit ? What is his mean distance from the sun in miles? What is the planet's hourly mean motion in the orbit ? 118 ASTRONOMY. in the orbit. The intensity of the sun's h"ght at Uranus is but (tstHsj)^ = 3T8 of what it is at the earth. 156. Apparent Diameter AND Magnitude. The ap- parent diameter of Uranus when at his mean distance from the earth, is 4", and when in opposition, it is about 4".l; hence 1 : 19.18239 — 1 : : 4".l : 74".5478, the apparent diameter of Uranus at a distance from the earth equal to that of the sun. Then 32' 1".8 : 74".5478 ; . 886,144771. ' 34,374 miles, the real diameter of Uranus ; and (VfiV)' = (4.344)' = 82, which shows how many- times his magnitude is greater than that of the earth. 157. Inclination op the Orbit, &c. The inclina- tion of the orbit of Uranus to the plane of the ecliptic, is but 46' 28", and the ascending node 13° in Gemini. Uranus doubtless revolves on an axis as the other planets do, but owing to his very great distance from us, astronomers have not been able to detect spots or any periodical changes on his surface, by which they might determine the period of his rotation. La Place was of the opinion that the time of his diurnal motion is but little less than that of Jupiter or Saturn (134, 146), and that his axis is nearly perpendicular to the plane of the ecliptic. 158. Astronomical Sign. Uranus has for his astro- nomical sign, ¥, the initial of the discoverer's name, with <♦ tsall, the emblem of a planet, suspended from its cross- bar. 159. Satellites of Uranus. Uranus is attended by i»'.i satellites, all of which were discovered by Dr. Her- '''''i? '. is the comparative intensity of the sun's light at Uranus ? iit. Whit is the apparent diameter of Uranus ■when in opposition! From this deduce the real diameter. Also the comparative magnitude. IS'?. What is tlie inclination of the orbit of Uranus to the plane of the ecliptic, and the place of the node ? AVlat is said respecting the period of his rotation ? Wliat was La Place's opinion on this subject ? 158. Describe the astronomical sign of Uranus. ' "19 How many satellites attend Uranus ? By whom were they dia- URANUS — AND HIS SATELLITES, 119 ichel, to whose genius we are indebted for the discovery of the planet itself The second and fourth were detect- ed in 1787, and the other four in 1798. They are dis- cernible only with telescopes of the highest power. Their siderial revolutions round Uranus, and their res- pective distances from his centre, are as follows : SAT. H. M. MILES. 1 si d. rev. 5 21 25 dist. from U. 225,000 2 8 16 56 5 " 292,000 3 ( tt 10 23 4 " 341,000 4 13 11 8 59 " 391,000 5 38 1 48 " 782,000 6 107 16 40 " 1,564,000 These satellites are said to move in orbits nearly circular, and lying in the same plane, which is nearly perpendicular to the ecliptic, a remarkable peculiarity, being inclined about 79° to that plane. Their motion is retrograde, or contrary to the order of the signs, another singular anomaly, as all the other planets and satellites move from west to east, or according to the order of the signs. Their magnitudes' cannot be less than tb«se of the satellites of Saturn, probably greater, otherwise they could not be seen at a distance so immense from our planet. The plane' in which these satellites move will pass through the sun but twice in the course of a year of Uranus, hence they can he eclipsed only at intervals of 42 years. In these eclipses, the satellites will be seen to ascend from the shadow of the planet, in a direction nearly perpendicular to the orbit covered, and when I Give the times of their sideriat rfivoliri ions round the primary, and their respective distances from him. Wii"! is said of their orbits ? Tlieir motion ? Their magnitudes i And their eclipses ! fi" ASTHONOMY. CHAPTER Xy. NEPTUNE. JaO ? EM ARKS. All the planets not only gravitate to the sun, but to one another, hence their motions are affected by these attractions of gravitation. From the ■^ low 1 elements of the orbit of a planet, and the attrac live influence of all the other known planets, its place cin be previously calculated for a certain time, and con- s^'^uently compared with its place found by observation at that time. It was found that the observed places of Uranus did not agree with those determined by calcula- tion, and hence some observing astronomers, most con- versant with this subject, were led to believe that these perturbations in the motions of Uranus w^ere produced by the action of a still more distant planet. M. Le Verrier, a French astronomer, on the 31st of August, 1846, in his third paper on this interesting sub- ject, made known the elements of the orbit of the sup- posed planet, and the method by which he arrived at the value of the unknown quantities. Le Verrier " leaves an impression on the mind of the reader, by the undoubt- ing confidence which he has in the general trdth of his theory, by the calmness and clearness with which he lim- ited the field of observation, and by the firmness with which he proclaimed to observing astronomers, ' Look in the place which I have indicated, and you will see the planet well.' "* On the 23d of September follow- * Mr. Ally's lecture before the Royal Ast. Soc, England. 160. From what data can the place of a planet be calculated for a cer- taJ'i time, that its place may be compared with that found by observation at the same time ? Did the observed places of Uranus agree with those fi^'Und by calculation ? What were some astronomers led to believe in o-'.sequence of the perturbations of Uranus ? Who made known the elements of the supposed planet, and when ? What did Le Verrier pro- claim to observing astronomers S NKi'TUNE. 121 ing, these directions of Le Verrier reached Dr. Galle, of the Berlin Observatory, and guided by them, he discover- ed the expected new planet on the evening of the same day. It is but justice to notice that Mr. Adams, of St. John's College, Cambridge, in England, without any previous knowledge of M. Le Verrier's labors, had made calcula- tions on this subject, and had arrived at similar conclu- sions, in consequence of which. Professor Challis, of Cam- bridge Observatory, was searching for the planet, when, on the 29th of September, having received the more pointed directions of the French astronomer, he changed his plan of observing, and on that evening discovered a star with a visible disc, which' was the new planet. The planet at first was named Le Verrier, in honor of its dis- tinguished discoverer, but it has since received the name of Neptune, which meets with the more general approba- tion and assent of astronomers. 161. Period, Distance, &o. The elements of the orbit of the new planet as made known by M. Le Verrier, previous to discovery, are, periodic time, 217 years, mean distance, or semi-axis major, 33, the earth's dis- tance being unity; hence, 95,129,932 »i. X 33 = 3,139,- 287,756 miles, the mean distance from the sun. Eccen- tricity, .10761, longitude of perihelion, 284° 45', mean longitude, Jan. 1, 1847, 318° 47', and mass .0001075, or twice the mass of Uranus. The period obtained from observation since discovery, is 167 years, and distance 30. These discrepancies in the elements have led some astronoiflers, and particularly. Professor Peirce, of Cambridge, Mass., to believe that Neptune is not the planet Guided by these directions, who discovered the new planet, and when ! Who made calcniatious on this subject, and arrived at similar conclusions Wiat was the new planet called at first ! What name since received ? 161. What are the elements of the new planet, as made known jire- vious to discovery ? What the period and distance, obtained from obser- vation, since discovery ? What have these discrepancies led some as- tronomers to believe ? 6 122 asthonomy. of theory, but of accident, or that " the planet Neptune is not the planet to -which geometrical analysis had directed the tele- scope." The astronomical sign of Neptune, if one has been adopted, has not come to our knowledge. 162. Bode's Law of the Planetary Distances. Professor Bode, a German philosopher, towards the end of the last century, from a close examination of the known distances of the planets from the sun, discovered the following empirical law, namely : assume 3 6 12 24 48 96 192 add 444 444 4 4 results 4 t" 10 16 28 52 100 196 The terms of the last series, beginning with Mercury, will very nearly express the proportional distances of the planets of our system from the sun, thus : Mercury. Venus. Earth. Mars. Asteroids. Jupiter. Saturn, Utanns. Neptune. 4 7 10 16 28 52 100 196 388 The great interval between the orbits of Mars and Jupiter, led Kepler to conjecture that tliere must be a planet revolving in the intermediate space. This curious law of the planetary distances, induced some astronomers, about the beginning of the present century, to make diligent search for the supposed planet. Four very small planets were soon discovered as the result of their labors (tl9).- 8ince 1845, five more have been added to the same family group. 163. Tables relative to the Sun, Moon, and Planets. The following tables contain the principal elements of the planetary orbits. Also, the diameters, volumes, masses, &c., of the sun, moon and planets. Give the remark of Professor Peirce on this subject. 162. Explain Bode's law of the planetary distances? What was Kepler's conjecture, and what led to it ! TABULAR VIEWS OF THE SOLAR SYSTEM. 123 Planet's Name. Siderial Period. Semi-axis maj. Mean distance frotij the sun in miles. Inten'y ufliBhU D. H. M. S. Mercury, 87 23 15 43 .387099 36,824,000 6.677 Venus, 224 16 49 10 .723332 68,810,000 1.911 Earth, 365 6 9 12 1.000000 95,130,000 1.000 Mars, 686 23 30 37 1.523600 144,940,000 .431 Asteroids (P) 1686 7 19 12 2.772600 263,000,000 .130 Jupiter, 4332 14 2 8 5.202776 494,866,000 .037 Saturn, 10759 5 16 30 9.538786 907,540,000 .Oil Uranus, 30686 19 42 — 19.182390 1824,819,000 .003 Neptune, 167 years. 30,000000 2853,900,000 .001 Planet's Name. Mercury, Venus, Earth, Mars, Asteroids(P) Jupiter, Saturn, Uranus, Neptune, [ncLin. of orbit to the Ecliptic. o / II 7 9 3 23 28 1 51 6 34 35 49 1 18 51 2 29 36 46 28 Long, of Ascend'g the Node. o ' /I 45 57 31 74 51 55 48 3 172 38 30 98 26 19 111 56 37 72 59 35 Eccentricity of the Orbit. .2055150 .0068607 .0167835 .0933070 .2419980 .0481621 .0561505 .0466108 .1076100 Mean daily mo- tion in LoiiK. 4 5 33 1 36 8 59 8 31 27 12 49 4 2 59 1 42 21 Planet's Name. Mercury, Venus, Earth, Mivs, Ast's.(P) Jupiter, Saturn, Uranus, Neptune, Sun, Moon, Apparent diameter at Mean Dis. Kent Diam in Miles. / II 6.5 3034 16.6 7654 7912' 5.8 4161 670 36.9 88932 16.2 71668 3.9 34374 32 1.8 886144 31 7 2162 Volume. 0.057 0,905 1.000 0.145 1404.928 744.000 82.000 1404928.000 0.020 i_ 2 2 5 8 10 1 4 12 11 1 3 5 5 i 2680337 1_ 10 4 8 ^1 3 5 X 17 9 18 26*520200 Rotation on the Axis. 24 5 28 23 21 7 23 56 4 24 39 21 9 55 50 10 29 17 25 10 27 7 43 5 163. What do the tables under this article contain i 124 astronomy. 164. Proportional Magnitudes op the Planets REPRESENTED TO THE Eye. The magnitudes of the primary planets proportional to each other, and to a sup- posed globe of 12 inches in diameter for the sun, are represented to the eye in the frontispiece to this work. Also, a delineation of the apparent magnitudes of the sun, as seen from the different planets. According to these proportional magnitudes of the planets, the distance of Mercury from a sun of 12 inches in diameter, would be 42 feet, Venus 78 feet, the Earth 108 feet. Mars 163 feet, the Asteroids 297 feet, Jupiter 558 feet, Saturn 1024 feet, Uranus 2059 feet, and Neptune 3221 feet. In ac- cordance with this representation, the moon's distance from the earth would only be about ,3i inches CHAPTER XVI. ■ COMETS. 165. Remarks. Comets are bodies which occasion- ally visit our system: The sun is the centre of their attraction. They appear in every part of the heavens, and move in all directions. Their orbits are so very eccentric, that when they are in those portions of them, which are farthest from the sun, they become invisible, and after traversing regions far beyond the orbit of the remotest planet, unseen for years, they make their ap- 164. According to the proportional magnitude of the planets repre- sented in the frontispiece, how large is the sun ! What will be the dis- tances of the several planets from this supposed sun ? What the moon's distance from the earth ? 165. What are comets ? 'What is the centre of their attraction ? In what part of the heavens do they appear, and in what directions do they move ! What is said of the eccentricity of their orbits ? COMETS. 125 pearance again. Some, after visiting our system, pass off into boundless regions of space and never return. The general opinion is, that they shine by reflecting the light of the sun. They are visible but for a short time, and only when near their perihelion. Many, on account of their dim- ness cannot be seen by the unassisted eye ; others, on the con- trary, are splendid in their appearances. 166. Parts op a Comet. Comets are composed of three principal parts, namely, the nucleus, the head, and tail. (See the drawing.) The most brilliant central and condensed part is called the nucleus, around which is a nebulous envelope to a considerable extent, called the coma, from its hairy appearance, (the word comet is de- rived from coma, hair,) which, with the nucleus, composes the head of the comet. The luminous train which pro- Great Comet of 1811. ceeds from the head, in a direction opposite to the sun, and expands sometimes to a great distance, is called the tail of the comet. Ordinarily, the tail is curved, having the concave side towards that part of the orbit from which the comet is just receding. The smaller comets, have frequently short tails, and some are entirely desti- tute of these appendages. What of some after visiting our system ? How do they shine S How long are they visible, and when ? What is said of many, and others ? 166, Of how many principal parts are comets composed ? Name them ? Describe the nucleus. What is the derivation of the word comet? Describe the coma. The head. The tail. What is said of small comets ? 126 ASTRONOMY. 167. Orbits of Comets. Comets move in very eccen- tric orbits, as already noticed. The eccentricity of some of their orbits is so great, that that part which is near their perihelion, or which is descrj.bed during the visibility of the comet, does not sensibly differ from a parobala, having the sun in the focus. If some comets, as is assert- ed, move in hyperbolas, they can never visit our system but once, and after having passed their perihelia, must either move off indefinitely, or advance in their way to another system, at an inconceivable distance. The elements of a comet's orbit, are the same as those of a planet's orbit, but the computation of the former is much more difficult and laborious than that of the latter, since the periodic time and semi-axis major are unknown. Notwithstanding, the elements of the orbits of about 150 comets have been com- puted and registered, with a view to detect their future returns. When a comet appears, if the elements of its orbit agree or nearly agree with any set of elements in the catalogue, it is presumed that the same comet formerly noticed, has returned again. The orbits of comets are generally inclined under large angles with the ecliptic. t 168. Physical constitution of Comets. As to the nature of these mysterious bodies, philosophers seem to know but little or nothing. Some suppoSe them to be wholly gaseous. On the other hand, it has been main- tained that the nucleus at least, is solid and opaque Stars have been seen through the nebulosity, and some astronomers assert that they have seen them through the nucleus. The tail becomes more attenuated and en- larged, in proportion to its distance from the head of the comet. 167. What is said of the orbits of some comets as to their great eccen tricity ? What is said of those comets asserted to move in hyperbolas ? Why is the computation of the elements of a comet's orbit more difficult than that of the elements of a planet's orbit ? Of how many have the elements been computed ? With what view are these elements registered ! 168. What is known of the nature of comets ? What have some sup- poseil them to be ? What has been maintained of the nucleus i COMETS. 127 Comets have passed so near some of the planets, that had they been possessed of a density approaching that of anj' other heavenly body, they would have disturbed these planets, but not the slightest perturbations have been detected in them ; hence, it is inferred that the quantity of matter in a comet must be very small. 169. Distances and Dimensions of Comets. We will here notice some particulars respecting two or three of the most remarkable comets. One of these was the great comet which appeared towards the close of the year 1680. At its perihelion, it was but 146,000 miles from the sun's surface, and at its aphelion, 13,000,000,000 miles from that luminary. Its period is supposed to be about 575 years. When nearest the sun, its velocity has (_.ri_ Ll CljmeT til 1^4_i_ been computed at 1,240,000 miles per hour ! Its nucleus was calculated to be 10 times as large as the moon, and its tail when longest, 124,000,000 miles. A comet very remarkable for its peculiar splendor, appeared in 1811. The diameter of the inner nucleus was 2600 miles, and that of the head, 132,000 miles. The greatest length of the tail was 132,000,000 miles. From the most accurate observations on its motion, its period is calculated at about 3000 years. Some astron- omers compute it to exceed 4000 years.. We will mention one other, the great comet of 1843. Have the planets been disturbed when comets passed near them What is the inference f 169. What were the perihelion and aphelion distances of the great comet of 1680 ? What its period ? Its velocity when nearest the sun ? How large was the nucleus ! How long was the tail ? Give the dimen- sions of the great comet of 1811. Its period. 128 ASTRONOMY. (See the drawing.) This comet of which we are treat ■ ing, was remarkable for its near approach to the sun. According to Professor Norton, of Delaware College, when at its perihelion, which was February 27th, 5 P. M., Phil, time, it was but 520,000 miles from the sun's centre, or less than 100,000 miles from his surface. 170. Halley's Comet. The periodic times of but few comets have been determined. Dr. Edmund Halley, a celebrated English astronomer, having calculated the elements of the orbit of a comet, which appeared in the year 1682, found that it was identical with the comets of 1456, 1531, 1607, and therefore predicted its return in 1758. Thus giving to it a period of about 75^ years. Subsequently, Clairaut, an eminent French mathemati- cian, having found from laborious and intricate calcula- tions, that the attractions of Saturn and Jupiter would prolong its period, predicted that it would not reach its perihelion until the 13th of April, 1759. It appeared about the end of December, 1758, and arrived at the perihelirai on the 13th of March following, but one month sooner Than the time fixed by Clairaut. This comet came again to its perihelion on the 16th of November, 1835, but nine days after the time fixed by Pont6coulant, a distinguished French astronomer. The motion of this comet in the orbit, which is inclin- ed 18° to the ecliptic, is retrograde. Its perihelion dis- tance is 57,000,000 miles, and aphelion distance, 3400,- 000,000 miles, nearly equal twice the distance of Uranus. What was remartaBle of the great comet of 1843 ? When did it come to its perihelion, and what was its distance then from the sun i 110. Who calculated the elements of the orbit of a comet which ap- peared in 1682 ! What did Dr. Halley find and predict ? What is the period of this comet ? Wliat did Clairaut subsequently find and predict concerning it ! How much sooner did it come to the perihelion, than the time fixed by Clairaut ? When did this comet come again to its peri- helion, and how long after the time fixed by Pontecoulant? What is said of ita motion ? What are the perihelion and aphelion distances ? COMETS. 129 it is called Halley's Comet, from the fact that Halley first ascertained the elements of its orbit, and correctly pre- dicted the time of its return. 171. Encke's Comet. A comet was discovered at Marseilles, on the 26th of November, 1818, by M. Pons, the elements of the orbit of which, and periodic return, were ascertained by Professor Encke, of Berlin ; hence, it is called Encke's Comet. It was considered identical with the comets seen in 1786, 1795, and 1805. It is re- markable for the shortness of its periodic revolution, which it aicoomplishes in 1207 days, or nearly 3^ years, and hence, it is also called the Comet of short period. This comet has reappeared in 1822, 1825, &c., as predict- ed. It came again to its perihelion near the close of the year 1848. The inclination of its orbit to the ecliptic is 13i°, the perihelion ■ is about the distance of Mercury from the sun, and the aphelion that of Jupiter. Encke's comet is small and has no tail ; (see the drawing) it s of feeble light, and in- | visible to the naked eye, ' except in favorable circum- stances. There is a singu- lar peculiarity attending this comet, namely, that its period is continually short- ening, and its mean distance from the sun gradually les- sening. Professor Encke accounts for it by a resist- ance offered to the motion of the comet, arising from Why called Halley's comet ! 171. "When and by whom -was Encke's comet discovered, and why so called ? With the comets seen in what years was it considered identical ? For what is it remarkable ? What is its period, and what also called ? When did it last come to its perihelion ? What is the incUnation of its orbit ? What are the perihelion and aphelion distances ? Can it be seen by the naked eye? What singular peculiarity attends this comet! How does Professor Encke account for this ? 6* 130 ASTRONOMY. a very rare etherial medium in space. Sir John Herschel has advanced the opinion that, " it will probably fall ultimately into the sun, should it not first be dissipated altogether, a thing no way improbable." 172. Game art's Comet. This comet was discovered by M. Biela, at Josephstadt, in Bohemia, on the 27th of February, 1826, and ten days afterwards, by M. Gam- bart, at Marseilles. Gambart calculated its parabolic elements, and found from the catalogue of comets, that it had been seen in 1789 and 1795. The periodic time is 2460 days, or 6f years. According to this prediction, it appeared in the latter part of 1832, but not in 1839, owing to the unfavorable situation of the earth. It was seen at its last return in the beginning of 1846. It is called Gambart' s Comet, sometimes, Biela' s Comet. The inclination of the orbit of this comet, is 13°, the perihe- lion is just within the earth's orbit, and aphelion beyond Jupi- What opinion has Sir John Herschel advanced on this subject ? 172. When, and by whom was Gambart's comet discovered ? Who calculated its parabolic elements i What is its period i When was it last seen ? COMETS. 131 ter's orbit. It is small, without either tail, or any appearance of a nucleus, and is not discernible without a telescope. 7he preceding figure represents the orbits of the three comets, whose periodic times have been accurately determined. S, represents the sun, the small circle, the orbit of the earth, and the large circle that of Jupiter. 173. Number of Comets. The number of comets which have been observed at different times since the Christian era, is probably seven or eight hundred ; and although many of them may have been reappearances of the same comet, yet vphen we consider, that, before the invention of the telescope, none but the largest and most conspicuous had been noticed, the actual number may be some thousands. Nevertheless, owing to the long periods of many of them, and the comparatively short time which they are observable, the orbits and periods of but three are known with certainty. Besides these three, which we have described in the preceding articles, there are some others, which are supposed to be identical with former comets, but which have not yet returned to verify the predictions concerning them. CHAPTER XVII. FIXED STABS. 174. Remarks. Having treated of those heavenly bodies belonging to the solar system (35), and having wiven their positions, connexions, periods, distances, mag- What are the perihelion and aphelion distances ? Of what is it desti- tute ? 173. What is the number of comets probably observed since the Chris- tian era ? What may be the actual number ? Why are the oibits and periods of but three known with certainty ? What is supposed of some others ! 174. What orbs do we now come to notice ! 132 ASTRONOMY. nitudes, and phenomena, derived from the most accurate observations of modern times, we now come to notice those orbs which lie at a distance far beyond this system. These are the Fixed Stars, so called, because they are known to keep nearly in the same position, and at the same apparent distances from each other. They have an apparent motion from east to west, in common with the other heavenly bodies, caused by the diurnal motion of the earth on its axis from west to east. A fixed star twinkles, and thereby may be distinguished from a planet which does not. Various hypotheses have been given explanatory of the cause of this phenomenon, which is now generally acknowledged as a consequence of the unequal refraction of light, produced by inequalities and undulations in the atmosphere. 175. Number of Stars and their Classification. The number of 'fixed stars which are visible to the naked eye, in both hemispheres, is about 4000. Of this number, not quite 2000 can be counted above the horizon at any given place. Besides these discernible by the unaided eye, the telescope brings into view innumerable multi- tudes of others, and every increase of its power greatly increases the number. These are, therefore, called Tel escopic Stars. The stars, on account of their various degrees of brightness, and apparently various magnitudes, are divid- ed into classes. Those which appear the largest, are called stars of the Jirst magnitude ; the next to these in appearance, stars of the second magnitude ; and so on to the sixth magnitude, which are the smallest that can be Wiat called, and why ? How may a fixed star be distinguished from a planet ? What is the generally acknowledged cause of this phenome- non, or twinkling of the fixed stars ? 175. What is the number of stars visible to the naked eye in both hemispheres ? How many may be counted above the horizon at any given place ? What are telescopic stars ! How are the stars, on account of their various degrees of brightness, and apparently various magni- tudes, divided \ Describe the different classes or magnitudes ! FIXED STARS. 133 seen by the naked eye. But few eyes can distinguish those belonging to this magnitude, even in the clearest night. The classification is continued under the powei of the telescope, down to the 16th magnitude. There are about 17 stars of the first magnitude, 76 of the second, 223 of the third, and so on, the numbers of each class in- creasing very rapidly to the sixth magnitude. 176. Arrangement of the Stars into Constella- tions. The ancients divided the heavens into three principal regions. 1st, the zodiac, 2d, all that part of the heavens on the north side of the zodiac, and 3d, all that part on the south side of it. These, in ord*r to dis- tinguish the stars from one another, they again sub-divid- ed into groups of stars, or Constellations. According to their superstitious notions, these constellations were con- ceived to represent the outlines of certain animals, im- aginary beings, or figures, and thus were named accord- ingly. This, no doubt, was done for the sake of conve- nience, that a person may be directed to any part of the heavens where a particular star is situated. It is desirable that a more scientific and definite division of the celestial sphere could be arranged, than the present unnatu- ral and mythological division into figures, "like to corruptible man, and to birds, and four-footed beasts, and creeping things." The zodiacal constellations are 12, the northern 34, and the southern 47, making in all 93. Of these, 48, in- cluding those of the zodiac, were formed in ancient times, the rest within the last two or three centuries. Which are the smallest that can be seen by the naked eye ? How far IS the classification continued under the power of the telescope ? How many stars of the first, second, Chi, ch. \ Lamda, 1, 4-, Psi, ps, ft. Mu, m, a^ Omega, 6, 178. The Milky Way. — Nebula. That bright lumi- nous zone in the heavens, visible to every observer, is called the Galaxy, but more frequently the Via Lactea, or Milky Way, from its resemblance to the whiteness of milk. This band encircles the whole sphere of the hea- vens, and cuts the ecliptic nearly in the solstitial points at an inclination of about 60°. It varies in breadth from By whom was this useful method first introduced ? When are the numbers 1, 2, 3, &.c. used ? 178. Describe -.the galaxy or milky way. What does it encircle, and .. jw does it cut the ecliptic ! Does it vary in breath and brightness ! FIXED STARS. 139 about. 5° to 15°, and also in brightness, being more lumi- nous in some parts than others. Its whiteness, so per- ceptible in a clear night, is caused by the joint light of the vast number of small stars in close proximity, of which it is composed. The Milky Way when examined by powerful telescopes, is found, according to Sir John Herschel, " to consist entirely of stars scattered by mil- lions." Besides the Milky Way,- which may be considered as a nebulous belt, there are various spots, resembling white clouds, seen in the starry heavens by the telescope. These are properly called Nehula, and are arranged into two classes, resolvable and irresolvable. The resolvable nebulae have been separated into stars by means of the telescope, but the irresolvable have not, though submit- ted to the space-penetrating power of the largest tele- scopes yet constructed. From recent observations made by Lord Rosse's telescope of 6 feet reflector, and 54 feet focus, some nebulae hitherto con-' sidered irresolvable, have been separated into clusters of stars. It is expected that new discoveries will be made by this won- derful instrument, not only in -the nebulae, but in every other heavenly body the subject of observation. 179. Groups and Clusters op Stars. Every atten- tive observer of the heavens, in a clear night, will per- ceive that the stars are irregularly distributed in the con- cave firmament. In some places, they appear collected together into groups, while in others, they are more scat- tered and indiscriminately arranged. Of these groups the most conspicuous and beautiful is that called Pleiades, which, within its small compass, ex- By what is its whiteness caused ? Of what does it consist aoxjording to Sir John Herschel ? What are nebulie ? How arranged ? Describe each class. What is said of recent observations made by Lord Rosse's tele- 179. What will every attentire observer of the heavens perceive? How do they appear in some places ? Which is the most conspicuous and beautiful group I 140 ASTRONOMY. hibits through a telescope of moderate power 50 or 60 distinct stars. This group is in the constellatioi. Taurus, and to the unassisted eye, consists of six or seven stars close together, and nearly at the same apparent distance from each other. The constellation Coma Berenices situated north of Virgo, is another gi'oup, more diffused than the Pleiades, and to the naked eye composed of larger stars. In the constellation Cancer, there is a group called Prcesepe, or the Bee-hive, of a nebulous appear- ance, w^hich the telescope easily resolves into small dis- tinct stars. Another spot is found in the sword-handle of Perseus, which exhibits, through a telescope of great power, a group of stars smaller in size than those com- posing the other groups already noticed. Besides groups of stars, there are found in the noctur- nal heavens, many clusters, which differ from groups in their elliptical or round figures, and in the crowded and condensed appearance of the stars composing them, es- pecially towards the centre. None but telescopes of great power will show them to consist of separate and distinct stars. 180. Variable and Temporary Stars. Some stars are subject to periodical changes in their brightness, and are therefore called Variable Stars. The star o Ceti was discovered about the close of the 16th century to be of this kind. From the time of its greatest brightness, being then a star of the second magnitude, it decreases during three months, when it becomes invisible ; after the lapse of five months, it reappears, and in about three months is again restored to its former brightness. The period of this star is therefore eleven months. A varia- ble star has been noticed in the constellation Hydra, and another in the Swan. There are many stars known to Where is the group Pleiades ? Describe it. Describe the gi-oup Coma Berenices. The group Praesepe. Where is there another group ? How do clusters diiFer from groups ? 180. What are variable stars? What is said of the star o Ceti ! What is its period ! What others have been noticed ! FIXED STARS. 141 vary in lustre, without becoming entirely invisible. The most remarkable of these is Algol or » Persei, which re- tains its magnitude for 2d. 12h., and then in 4 hours diminishes to a star of the fourth magnitude, when it begins to increase, and in the succeeding 4 hours regains its original brightness, performing its period in about 2 days 20 hours. Several instances are on record, of new stars having appeared where none had been before observed. These are called Temporary Stars. The most ancient is that given by Hipparchus, who flourished about 120 years before the Christian era. In 945, a new star appeared, and another in 1264 ; but the most remarkable was that observed by Tycho Brahe, in November, 1572. This star appeared suddenly in Cassiopeia, and shone with a brilliancy equal to that of Sirius. In three weeks after its first appearance, it commenced to diminish in bright- ness, and in 16 months entir'ely disappeared, not having since been seen. 181. Double' AND Binary Stars. When certain stars, which to the naked eye, and even when assisted by a telescope of moderate power, appear single, are examin- ed by telescopes of considerable power, they are resolved into two, sometimes three or more stars. These are called Double, or Multiple Stars. Previous to the time of the elder Herschel, but few stars were known to be double, but by the exertions of this great astronomer, and others of distinction, several hundred are now ascertain- ed to be of this kind. Some of these, no doubt, may appear double from the circumstance, that the two stars, though far remote from, and unconnected with each other, appear nearly in the same visual line. The stars Describe the changes in the star Algol. What are temporary stars When did new stars appear ? Describe the one obserred by Tycho Brahe. 181. What are double or multiple stars ? Are there many now ascer- tained to be of this kind ? From what cucumstance may some of them appear double ? 142 ASTRONOMY. composing a double star are generally of unequal magni- tade, and exhibit the singular phenomenon of shining with differently colored light. A most important and interesting discovery has been made by Sir W. Herschel, in relation to many of the double stars, namely, that they are physically connected by the laws of gravitation, and revolve round each other, or rather round their common centre of gravity. These, therefore, are called Binary Stars, sometimes Binary Systems. The following are some of the most prominent binary stars with their periods : v Coronae, 43 years ; Z Cancri, 55 years ; | Ursas Majoris, 58 years ; « Leonis, 83 years ; » Virginis, 145 years ; Castor, or « Geminorum, 232 years ; 61 Cygni, 540 years ; and o- Coronae, 608 years. 182. Annual Parallax and Distances op the Stars. When two straight lines are conceived to be drawn from a star, the one to the sun and the other to the extremity of the radius vector of the earth's orbit, at right angles to the first line, the angle contained by these lines is called the Annual Parallax of that star. Or the annual parallax is the greatest angle at the star subtended by the radius of the earth's orbit. Thus let the line « S be drawn from s the star to S the sun, and another line drawn to E the ex- tremity of the radius vector S E at right angles to the first line s S ; then the angle S « E will be the annual parallax of the star s. Pro- Wliat singular phenomenon do they generally exhibit ? What inter esting diacoTery has been made by Sir W. Herschel in relation to many of the double stars ? What are these called ? Name some of the most prominent binary stars and their periods ? 182. What is the annual parallax of a star ? Illustrate the annual ANNUAL PARALLAX. 143 duce E S to E' and join E' s ; now it is evident if the angle E 6' E', which is double the parallax, be sensible, it could be determined by finding the difference in position of the star s, as viewed from E and E', two opposite points of the earth's orbit. Hence the most eminent astronomers have, at opposite seasons of the year, determined within the nearest degree possible, the right ascensions and declinations (16) of some stars, which from their brilliancy and apparent magnitudes, were thought to be nearer the earth than the generality of others, with the view of finding their annual parallax. But the result of their observa- tions has led them to conclude that the angle in question is so small as not to be detected by this method, subject to small errors arising from the imperfections of the best instruments, and from the corrections for refraction, aberration and nutation. However, Professor Bessel, of Konigsberg, appears to have been successful in determining the parallax of the binary star 61 Cygni. This star, on account of its great proper motion, (63), which amounts to 5".3 in a year, and its large apparent orbit of 16", is thought to be nearer the earth than any other. Hence Bessel conceived the grand idea of finding the difference between the parallaxes of the middle point of the line joining the components of this star, and a small stationary star seen in nearly the same direction, and therefore supposed to be at a much greater distance. This difference in the parallaxes will nearly equal the absolute parallax of the star 61 Cygni. The method of obtaining this was by finding the semi-annual changes in the distance between the stars, and thereby having avoided the inevitable small errors in the corrections for refraction, aberration, &c., necessarily attending the method by finding the right ascensions and declinations. Bessel, for the sa!;e of great- er exactness, used two small stars, and taking the middle point between the two stars composing the double star, 61 Oygni, for the situation of the star, found its annual parallax to ba 0".3483. parallax by the diagram. "What have the most eminent astronomera done, with the view of ijading the annual parallax of some stars ! What haa the result of their observations led them to conclude ? "Vfiiy cannot the angle in question be detected by this method ? Who appears to have been successful in determining the parallax of the star 61 Cygni ? Why is this star tliouglit to be nearer the earth than any other ? What grand 144 ASTRONOMY. Knowing the parallax, we have in the right angled triangle E S s, sin E s S : Radius : : E S : E « ; taking E S, the dis- tance of the sun from the earth, equal to unity, and the length of radius expressed in seconds, {5l), E.^ Radius ^^6j64;;_^gQ,,oo^ sinE«S 0".3483 •which shows how many times the star 61 Oygni is farther from the earth than the sun. And 95000000m. X 592200 = 56259- 000000000 miles the distance of this star from the earth. The velocity of light is 192961 miles per second of time (142), and 192961OT. : 56259000000000m. : : Is. : 291556324s. = 9 years 87 days. Sothat if the star 61 Cygni were now just launched into existence hy the Almighty Creator, 9^ years, nearly, must elapse before its light would reach this our distant globe. 183. The Longitude of a Ship at Sea determined by THE Moon's distance from some of the principal Stars IN OR near her Orbit. When at the same instant the hours of the day at two places are determined, the longi- tude of the one from the other is easily obtained. The method of finding the longitude of a place by means of the eclipses of Jupiter's satellites, has already been given, (141), but it cannot be accurately employed at sea on ac- count of the motions of the vessel. Chronometers, which are well-regulated time pieces, are now, extensively used at sea for this purpose. The difference between the mean time at the ship, and that of a chronometer which can be depended upon, and which shows the mean time at the first meridian (9), converted into degrees at the rate of 15° to an hour, will give the longitude. If the time at the ship be later than that shown by the chronometer, the idea did Bessel conceive ! Explain hia method. When the parallax is known, how ia the distance found ? What is the distance of this star from the earth ? What time is required for the transmission of its light to our globe ? 183. What is the subject of this article ? Why cannot this be done by means of the eclipses of Jupiter's satellites ? What are chronometers ? Explain the method of iinding the longitude of a ship at sea by means of a chronometer. Can chronometers be depended upon ? LONGITUDE BY LUNARS. 145 longitude is east of the first meridian, but if earlier, it is west. However, as the best chronometers are subject to variations from change of temperature and other causes, it becomes important to the mariner to be possessed of a method not dependent on the motions produced by hu- man mechanism,.but on the sure and well established mo- tions of the heavenly bodies. This latter method, which depends on the moon's distance from any heavenly boav in or near, her path, and therefore called the Lunar Method, we will now briefly explain. In the'Nautical Almanac, the moon's true angular distances from tjie sun, Venus, Mars, Jupiter, Saturn and nine piincipal stars in or near her path, namely, » Arieds, Aldebaran, Castor, Pollux, Regulus, Spica Virginis, Antares, Altair and Fomal- haut, are given for every three hours, apparent Greenvfich time, of every day in the year. The time for any intermediate distance may easily be found by proportion sufficiently correct. These distances in the Almanac, are the distances between the centres of the bodies, calculated as if observed from the earth's centre ; the observed distance at the ship must therefore be reduced to this true distance. This reduction, which consists in corrections for parallax, refraction and semi-diameters, con- stitutes the chief difficulties of the problem. All the treatises on Navigation give formulas for this reduction. When the tnie angular distance of the moon at the ship has been found, and also the time at Greenwich found, when she has the same true angular distance ; the difference between this time, and that when the observation was made reduced to degrees, will give the longitude. What then becomes important to the mariner ? On what does this me- thod depend, and what tlierefore called ! What are given in the Nautical Almanac ' Name the principal stars from which the moon's distances are given. For what time are these distances computed! From what point 63 if observed are they calculated ? What constitutes the cliief difBcultiea of the problem! When tliis reduction is made, how is the longitude Immd ! 146 OBLIQUITY OF THE ECLIPTIC. CHAPTER XVIII. Obliquity or the Ecliptic, Equinoctial Points, Pee- CESSION OF THE EqUINOXES, NuTATION, AND ABERRA- TION OF Light. 184. Obliquity op the .Ecliptic The inclinatioa of the planes of the ecliptic and equinoctial, is the obli- quity of the ecliptic (10). By taking half the difference between the sun's greatest and least meridian altitudes at any place, the obliquity of the ecliptic, or the sun's greatest declination, will be obtained. Or the difference between the meridian altitude of the sun, found at the time of the summer or winter solstice, and the height of the equinoctial above the horizon, which is,e(iual to the complement of the latitude of the place, will give the obliquity. According to the most accurate observations of modem times, made at considerable intervals, the obliquity of the ecliptic is continually diminishing. This diminution is very small, and at the mean of about 51" in a eentuiy, called the secular diminution. It is the result of the action of the planets, particularly Venus and Jupiter, upon the earth. After the lapse of a very long period, according to La Place and others, the obliquity will begin to increase, the limit of variation being about 2° 42'. The present obliquity of the ecliptic, 1848, is 23° 27' 23". 185. Equinoctial Points. The equinoctial points may be determined by observing the sun's declination at noon for a few days before and after the equinoxes. Then on two consecutive days of these, it will be found that his declination will have changed from north to 184. Define the obliquity of the ecliptic. How is it obtained ? Is the obliquity diminishing S What is its amount ir. a century ? Of what is it the result ? What is said of it after the lapse of a very long period 1 What is the present obliquity ? 185. How may the equinoctial points be determined? PRECESSION OP THE EUUINOXES. 147 south, or from south to north; and hence the time when he crossed the equinoctial Hne can easily be found. Thus, on the 19th of March, 1848, the sun's declination at apparent noon, Greenwich, was 22' 52" south, and on the follow- ing day at noon 49" north ; then 22' 52'' + 49" : 49 : : 24A. : i9m. 39s. ; hence his declination was on the 20th of March at llh. lOm. 21s. A. M. apparent Greenwich time. Having found the precise instant when the declination is 0, and knowing the rate of the sun's apparent motion in the ecliptic, the point where the equinoctial and ecliptic intersect is easily ascertained. When one of these points is known, the other becomes known also, because they are directly opposite, or 180° distant. It is important that the equinoctial points should be accurately de- termined, because the natural or true year is computed from the instant on which the sun enters the vernal equinox until he returns to the same again. 186. Pkecession of the EauiNoxEs. The celebrated and ancient astronomer Hipparchus, from observations which he made at Alexandria about the year 130 before Christ, found that the autumnal equinox was about 6° east of the star Spica Virginis. He also, by much re- search, discovered the records of some observations made 150 years before, from which it appeared that the autumnal equinox was 8° east of the same star. Hence he concluded that the equinoctial points are not fixed in the heavens, but have a slow motion from east to west, or contrary to the order of the signs, which he called the Precession of the Equinoxes, because the time of the sun's return to one of these points, precedes that deter- mined by the usual calculation. This motion, according to Hipparchus, is about 1° in 75 years. Subsequent observations have confirmed the truth of this Give the example illustrating this subject. How is the point where the equinoctial and ecliptic inteisect, then ascertained ? Why is it important that the equinoctial points should be accurately determined ? 186. What did the ancient astronomer Hipparchus find ? What did he also dKcover? What did he conclude from tliese facts? What did ha imll this motion of the equinoctial points, and why ? 148 ASTEONOMY. motion of the equinoctial points. In the year IVSO, the autum- nal equinox was observed to be 20° 21' westward ofSpica Vir- ginis; hence I30y. + l750y. : ly. : : 6° + 20° 21' : 50".4, the annual precession. According to a series of accurate observa- tions made by M. de la Caille, the precession is 50".2 in a year. Henqe if the sun crosses the equinoctial in a certain point this year, he will cross it 50".2 to the west of the same point next year; and since the sun's daily motion in longitude is 59' 8" (96.) it follows that 59' 8" : 60".2 :■. 24h. : 20m. 23s. nearly, which shows how much the solar or tropical year is shorter than the siderial year (27.) The equinoctial points must have recede'd one sign in about 2150 years, and as the signs of ihe zodiac are reckoned from tlie point where the sun passes from the south to the north of the equinoctial, it follows that the longitudes of the stars since the infancy of astronomy, h^ve increased about one sign ; and hence the constellation Aries is now in Taurus, and Taurus in Gemini, &c. This may be seen by examining the celestial globe. 187. Retrograde Motion op the Pole of the Eaui- NOOTIAL, IN A SMALL CiRCLE, ROUND THE PoLE OF THE. Ecliptic. Since the latitudes of the fixed stars are their distances from the ecliptic (18), and since these latitudes have been found, by observations made at different periods of time, to continue nearly the same, it follows that the position of the ecliptic must remain fixed or nearly so, with respect to the stars. Hence it is evident, that the precession of the equinoxes is the consequence of a slow motion of the equinoctial in the same direction : and be- cause the equinoctial changes, its pole must also necessa- rily change. What was observed in the year 1750 ? Wliat is the amount of the pre- cession in a year, according to M. de la Caille ? From this, determine how much the solar year is shorter than the siderial year. How long doe ; it require the equinoctial points to recede one sign ! What is said of the longitudes of the stars, since the infancy of astronomy ! 1S7. How is it known that the position of the ecliptic must remain fixed or nearly so, with respect to the stars ? Of what therefore is tlie precession a consequence ! PRECESSION OF THE EaUINOXES. 149 Let A B V C represent the ecliptic, and p its pole, which is stationary ; also letAEVQrep- resent the equi- noctial, and P its pole. Because the distance be- tween the poles of two great cir- cles is equal to their inclination, and because the obliquity of the ecliptic, (10), or the inclination of the equinoctial to the ecliptic, remains very nearly tlie same, the pole P must always be in the small circle P P' P" described about the pole p, at a distance from it equal to the obliquity of the ecliptic. When the equinoctial is in the position A E V Q, V, tlie vernal equino.x, will be 90° distant from the poles P and p, and consequently will be the pole of the great circle P C jo' E ; hence this latter circle will be the position of the solstitial , colure (9) at that time. Also, when the equinoctial is in the position A' E' V Q' at any subsequent time, V, the vernal equi- nox, will still be the pole of the solstitial colure, which must now assume jthe position jo P' D p', consequently P', its inter- section with the small circle P P' P", will be the pole of the equinoctial. Hence while the vernal equinox has retrograded from V to V, the pole of the equinoctial, with an equal angular motion, has also retrograded from P to P' in the small circle P P' P". The south pole of the equinoctial will evidently have a corresponding motion round the south pole of the ecliptic. Since the precession of the equinoxes is 50".2 in a year, we have 50".2 : 360° : : ly : 25816 years, the time required foi the equinox and pole to make an entire revolution, which num- Draw the diagram and shoiv that the pole of the equinoctial moves in a small circle round the pole ->l the ecliptic. Calculate the time reqnirei for the pole of the equiaoctial to make an entire revohition. 150 ASTRONOMY. ber of years completes the GranA Celestial Period. That star to which the north pole of the heavens, in its motion, comes nearest, takes then the rank of the pole star. In 1550 A. M. a Draconis was the pole star. The precession of the equinoxes will cause a small annual variation in the right ascensions and declinations (16) of the stars. 188. Physical Cause of thk Precession of the Equinoxes. If we suppose the earth to have been ori- ginally in a fluid state, and rotating oh its axis with its present velocity, it is plain that the particles of matter about the equatorial regions, on account of their greater distance from the axis, would have a greater centrifugal force than those near the poles ; hence the parts about the equator would diminish in weight, and in order that the whole mass of the earth may be in equilihrio, its equa- torial diameter will increase, and, accordingly, its axis will decrease, causing it to assume the figure of an oblate spheroid. It has been proved by investigations in physical astron- omy, that the precession of the equinoxes depends on the action of the sun and moon, on that protuberant matter around the equatorial parts, bringing the equator sooner under them, in each revolution, than if the earth were a perfect sphere. Hence the effects of this action of the sun and moon will occasion a small deviation of the earth's axis from its parallelism, and consequently a cor- responding deviation in the position of the equinoctial and its pole, with respect to the fixed stars. The annual effects of these two bodies are respectively 15" and 35".2, that of the moon being greater, in consequence of her proximity to the earth. As there is no sensible change What is this period called j What star takes the rank of the pole star ? When was a Draconis the pole star ? 188. Supposing the earth originally in a fluid state, explain, particular- ly, the cause of its assuming the figure of an oblate spheroid. On what does the precession of the equinoxes depend ? What will the effects of the action of the sun and moon occasion ! What will be the consequence of this ? What aie the respective aunual effects of the sun and moon ! NUTATION AND ABERRATION. 151 in the latitudes of places, it follows that there is no sensible change in the terrestrial axis with respect to the matter of the earth. 189. Nutation. It has been stated that the preces- sion of the equinoxes is caused by the attractive force of the sun and moon on the protuberance of the equatorial regions of the earth. Now, when either of these bodies is in the plane of the equator, its attractive force will draw the earth towards it without changing the position of the axis, it keeping still parallel to itself; but the farther the body recedes from this plane, the more will the equatorial parts be drawn than the rest of the earth. Hence the sun and moon, on account of their various and contin- ually changing positions with regard to the plane of the equator, will cause a small tremulous or oscillatory mo- tion of the axis, called Nutation. The nutation was dis- covered by Dr. Bradley. 190. Aberration op Light. Dr. Bradley, towards the middle of the last century, made a series of careful observations with the view of finding the annual parallax of the fixed stars. But the result, instead of indicating a parallax, was the contrary to what had been expected. From this incident he discovered the fact that there is a small apparent change in the positions of the heavenly bodies, caused by the progressive motion of light, and the orbitual motion of the earth. This apparent motion, which is common to all the heavenly bodies, but more striking in the case of the fixed stars, is called the Aberra- tion of Light, or simply Aberration. The theory may be thus explained. Suppose E E", regarded as a straight line, to represent Is there any change in the terrestrial axis with respect to the matter of the earth ! Why ? 189. What is nutation, and by what caused ? Who discovered it ? 190. What incident led to the discovery that there is an apparent change in the position of the heavenly bodies ? By what caused % What IS this apparent change called ? 152 ASTRONOMY. T i JB' 4- tlie distance through which the earth is car- ried in one second of time, and a E" the dis- tance through which a particle of light, coming from the sun or star S, moves in the same time. When the earth is at E, the par- ticle of light entering the axis of a telescope at a, will descend in this axis while it keeps parallel to itself, and moves from E to E" ; hence at E, E' and E", the star will ap- pear successively at s, / and s". Now when the earth is at E", the true position of the star is in the direction E** S, and the ap- parent position in the direction E"s". Therefore the angle S E"s", or its equal, E''aiE, expressing the apparent change of the star S from its true place, caused by the combined motions of light and the earth, is the aberration of the star. The motion occa- sioned by the rotation of the earth on its axis is disregarded, because it is so small, compared with the annual motion, as to produce no sensible effect. 191. Amount of Abekration. Since the mean rate of the earth's motion in its orbit per hour is 68189 miles (84), we have \h. : 1«. : : 6S186??i. : 19 miles nearly, the orbitual velocity of the earth per second. The velocity of light per second is 1&2961 miles (142); hence the triangle E a E" (see last fig.) gives a E" : E E" : : «» a E E" : «m E a E" = dn S E" «" ; but a E" : E E» : : velocity of light : velocity of the earth : : 102961 : 19. Hence 192961 : 19 : : dn a E E" : sin S E" s". Therefore, But since the length of radius is 206264", and also since the Draw the diagram, and explain the theory. 191. What is the orbitual velocity of the earth per secor>d ? Knowing this and the velocity of light per second, how is the aberration found ? SOLAR AND LUNAR SCLIPSES. 153 angle S E" s" is very stuall, and may be taken for its sine, it follcjws that, r. ^.. . 19 X 206264" S E" s" = f^9^f sill a E E" = 20".3 sin a E E". Tlie aberration increases as the angle a E E" increases, and evidently takes place in a direction parallel to, and in the same ■way as, that of tire earth's motion. When the angle a E E" is 90°, the aberration is a maximum, or 20".3, which is nearly the constant aberration in longitude with i-egai'd to the sun ; but for a planet, the aberration will be affected by the planet's motion during the time that the light is passing from it to the earth. As the directions of the earth's motion are opposite at opposite seasons of the year, the amount of aberration of a star may be 20".3 X 2 = 40".6. The aberrations of the stars found by observations made at opposite seasons of the year, correspond with the computed deviations, and hence we have not only a proof of the uniform transmission of light, but that the orbitual motion of the earth is a truth susceptible of the strictest demonstration. CHAPTER XIX. ECLIPSES OF THE SUN AND MOON. OCCULTATIONS OF THE FIXED STARS. 192. Causes of Solar and Lunar Eclipses. An eclipse of the sun is occasioned by the moon coming be- tween the earth and the sun, so as to intercept his light, that to any place on the earth the sun may appear partly What is the constant aberration in longitude with regard to the sun ? Wh.at will affect the aberration of a planet ? What may be the amount of aberration of a star ? Do the observed aberrations and computed deviations of the stars agree ! What does this fact prove ? 192. What occasions an eclip'^e of the sun ? 7* 154 ASTRONOMY. or wholly covered. This privation of the sun's light is nothing more than the moon's shadow falling on the earth at the place of observation ; hence, all solar eclip- ses happen at the time of new moon. An eclipse of the moon is occasioned by the earth coming between the sun and the moon, so as to deprive her of the sun's light, or by the moon entering into the earth's shadow ; hence all lunar eclipses must happen when the moon is in oppo- sition to the sun, or at the time of full moon. Solar Eclipses. The phenomenon of a solar may be better understood as to its nature and 193. eclipse cause, by reference to the following figure, where S re presents the sun, E the earth, and M the moon, at the change, or in conjunction. Having drawn the common tangents on the same and different sides of the sun and moon, and therefore limit- ing the real and partial shadows of the latter body, it is evident that the dark shadow of the moon will be of a conical form because she is globular and much smaller than the sun whose rays of light she obstructs. The When do all solar eclipses happen ? What occasions an eclipse of the moon ? When must all lunar eclipses happen ! 193. Show by drawing the diagram, how the real and partial shadows of the moon are limited. Whv will the dark shadow be of a conical form? LENGTH OF THE MOOn's SHADOW. 155 dark conical shadow a b c of the moon is called the um- bra, and at c on the earth's surface where it falls, the eclipse of the sun will be total. The bright or partial shadow at a d b e, which surrounds the umbra, is called the penumbra, and at d e, where it fails, there will be a partial eclipse ; but, at all other places of that hemisphere of the earth turned towards the sun on which the penum- bra does not fall, there will be no eclipse. 194. Length of the Moon's Shadow. Let AB, a b, and a' b' be sections of the sun, moon, and earth, made by a plane passing through their centres S, M, and E in the same straight line. Also, le"t the common tangents be drawn to the same and different sides of the sections of the sun and moon, and therefore limiting the sections of the umbra and penumbra. The sun and moon will have the same apparent semi-diame- ter as seen from C, the vertex of the shadow, and this semi- diameter of the sun, namely, the angle S C A, or M C a, will be very nearly the same as that seen from E the centre of the earth, because the distance C E, even when it is the greatest, is small when compared* with the great distance of the sun. Put d = angle M o =: the sun and moon's ap. semi-diam. as seen from C, d' = angle M E a = the moon's ap. semi-diam. as seen from E, L = M C ^ the length of the shadow, and D := M E = the moon's distance in radii of the earth. What is the dark shadow called ? "WTiat the partial shadow ? Show where there will be a total eclipse, and where a partial one ? 194. Draw the diagram, and fully explain how the length of the moon's shadow is found. When is the length of the shadow greatest i 156 ASTRONOMY. N(jw since the apparent semi-diameters of the moon as seen from Mild E, namely, the angles M C a and M E a, are in- versely proportional to the distances M C and M E, we have, MCa: MEa:: ME: MC, or, d:d' :: D : L, d' whence L ^ D -j- By using the proper values for D, d' and d (97, IQl, 85), the shadow will be found, when the sun is in apogee and the moon in perigee, to extend about 3.5 radii of the earth beyond its centre. But when the sun is in perigee and the moon in apo- gee, the shadow will want 6.3 radii of reaching the earth's centre. 195. Greatkst Breadth of the Moon's Shadow at THE Earth. When the shadow would ext^d to the greatest distance be- yond the earth's centre, its breadth at the surface will evident- ly be the greatest. From c, (see the last fig.) the point where the tangent A C would cut the earth's surface, draw c E ; then we have in the triangle c E C, the side EC = MC — ME = D -^— D = f-^— 1 ] D, c E = 1, the radius, and the d U J angle E C c = (£ the sun's least semi-diameter, to find the angle EcC. Thus, E c : E C : : «m E C c : «m E c C, or 1 : — \ \ J) : : mi d : sin EcC. id \ By using the small angles d and E c Q, instead of their sines, we have. (!-■]» d:'EcG = {d' — d)J). The value of {d' — d)!) will give for the angle EcC 56' 22". But the exterior angle eEc = EcC-f-ECc = 56 What is its extent then ? When is the length of the shadow least ? TIow far does it want then of readiing the earth's centre ? 195. Wlien will the breadth of the shadow at the earth's surface be the greatest i Explaiu by the diagram, the method of finding its breadth I BREADTH OF THE MOON 3 SHADOW. 157 22" + 15' 45" = 1° 12"7" = tliearc ec ; and 2 ec = C(^ = 2° 24' 1--4"= 166 miles, the greatest breadth or diameter of the circular portion of the earth's surface ever covered by the moon's umbra. If the moon is at some distance from the node, the shadow will fall obliquely on the earth's surface, and will therefore cover an extent exceeding the above distance. 196. Greatest Bbeadth of the Penumbral Shadow AT THE Earth. 1'he breadth of the moon's penumbra will evidently be the greatest, when the sun is in perigee, and the moon in apogee. From a! (see the last fig.) where the common tangent B/ would cut the earth's surface, draw E a' and produce it to Z, also draw a'Sanda'M. Theanglea'M E==Sa'M + a'S M ; butSa'M = S a' B + / a' M = c? + c^', the sun and moon's apparent semi-diameters as seen from a', and a' S M, the sun's parallax in altitude at a' being so small, may be disregarded ; therefore o' M E = c^ + rf' = 16' 1'7".3 + 14' 41" = 31' nearly. Now the angle a' M E is the moon's parallax in altitude at a', and M a! Z is the zenith distance at the same place ; hence (54), we have, sin H 53' 51" (55) ar. co. - 1.8051059 : Radius 10.0000000 ::OT)ip, 31' - '7.9550819 : mi M w Z 35° 9' - 9.7601878 The angle a' E M = M a' Z — a' M E = 35° 9' — 31' =. 34° 38' = the arc a! e, and 2 a' e = a' 5* = 69° 16' == 4800 miles, nearly, the greatest breadth of the portion of the earth's- surfaoe ever covered by the penumbra. 197. Greatest Breadth of the part of the Earth's Surface, at which the Eclipse can be Annular. Let A S B, a m 6, and a' E &', be sections of the sun, moon. What is the greatest breadth of the earth's sm-face that can erer be covered by the umbra ? 196. When will the breadth of the moon's penumbral shadow at the earth be the greatest ? Explain by the diagram the method of finding its breadth. What is the greatest bi-eadth of the earth's sm-face that can ever be covered by the penumbra ? 158 ASTRONOMY. and earth, also A a and B b common tangents to the sun and moon, intersecting at C before meeting the earth at a' and h'. From c, where the axis of the shadow produced meets the earth's surface, draw c d and c e, tangents to the moon. It is evident that to an observer at c, or any other point of the earth's surface between a' and b', the moon will cover the central part of the sun, leaving a luminous ring, s.s d ef, unob- scured. In the triangle o' C E, we have the angle a' C E = S C B, the sun's apparent semi-diameter, as seen from C, which may be regarded the same as seen from the earth, C E = 6.3 radii of the earth, or the distance of the apex of the conical shadow from the centre (194), and a' E = 1, or the earth's ra- dius, to find the angle a' E C. Tiius : a' E, 1 - .0000000 : E C, 6.3 - - .8000294 : : sin a' C E, 16' 11" - • 7.6754678 : sin ^ a' E, 1° 42' 46" - 8.4754972 But c E a' = ^ a' E — a' C E = 1° 42' 46" — 16' 17" == 1° 26' 29" = the arc a' a, and 2 a' e = a' V = 2° 52' 58" =. 199 miles, the greatest breadth of the part of the earth's sur. face at which the eclipse can be annular. 198. Ecliptic Limits op the Sun. Let A B and a b represent sections of the sun and earth, made by a plane passing through their centres S and E. Draw the tangents A a and B b limiting the section, made by this plane, of the frustum of a cone formed by rays tangent to the sun and earth ; and describe m m' & portion of the moon's or- 197. Draw the diagram and calculate the greatest breadth of the part of the earth's surface at which the eclipse can tie annular. ECLIPTIC LIMITS OF THE SON. 159 bit about the centre E, with a radius equal to her distance from the earth at the time of conjunction. It is evident that whenever the moon comes within the frus- tum A a 5 B, there will be an eclipse of the sun somewhere on the earth's surface. From m, where the moon's orbit intersects A a, draw m E, and the angle m E S will be the apparent semi- diameter of the frustum at the distance of the moon as seen from E, the earth's centre. Now the angle otES = AES + mEA = AES4-E»ia — mAE; butAES = ci, the sun's apparent serai-diameter, E m a == H, the moon's horizon- tal parallax, and m A E == ^, the sun's parallax ; therefore, ffiES = £?+ H— ^. If the moon's orbit were in the plane of the ecliptic, there would be an eclipse of the sun at every new moon ; but since it is inclined to it, an e.clipse cannot occur, unless the moon's latitude (18) be less than the sum of her apparent semi-diame- ter d' , at the time of conjunction, and the apparent semi-diame- ter of the luminous frustum at her orbit. Let N S, N TO, repre- sent portions of the eclip- tic and moon's orbit re- ferred to the celestial sphere, N the descending node, S,S' transverse sec- tions of the luminous frus- tum corresponding to the direction of the sun from E, the earth, and m, the place of the moon in con- junction, when her lati- tude, which call l=^d-\- H — 'p ■\- d'. It is evi- 198. Draw the diagram, and demonstrate that the apparent semi-diam- 160 ASTRONOMY. dent the moor, will not obscure any portion of the sun iit the time of conjunction, unless she is in a position as m' nearer tlio node than m, and consequently her latitude less than m S. In the right angled spheiical triangle m N 8, we have the angle TO N S, equal to the inclination of the moon's orbit, which has its greatest value at the time of syzygies, namely, 5° 17' (102), and m S = i!, to find S N, the difference between the longitude of the node and that of the sun or moon. Thus. Radius : co- tang. OT N S : : tang. Z : sin S N. Taking, therefore, 5° 17' for m N S, and the greatest and least values of I, the above pro- portion will give for the greatest value of 8 N, 17° 17', and for the least, 15° 21'. Hence at the time of new moon, if the differenfe between the longitude of the nearest node and that of the sun or moon, ex- ceeds 17° 17' there cannot be an eclipse of the sun; but if the difference is less than 15° 21', there must be an eclipse. These are the solar ecliptic limits. Should the difference in longitude fall between these numbers, farther calculations become neces- sary to determine whether there will or will not be an eclipse. 199. Different kinds op Solar Eclipses. When the moon changes in perigee, and within the solar ecliptic limits, she appears large enough to cover the whole of the sun's disc, from those places of the earth on which her dark shadow falls ; and, consequently, there the eclipse of the sun will be total. But when the moon changes in apogee, and within the solas ecliptic limits, she appears less than the sun, and therefore cannot cover his whole eter of the luminous frustum formed by the raya tangent to the sun and eartli, at the distance of the moon as seen from the earth's centre, is equal to the sum of the sun's apparent semi-diameter, and the difference of the Bun and moon's horizontal parallaxes. If the moon's orbit were in the plane of the ecliptic, how often would there be an eclipse of the sun ! In order that an eclipse may occur, what must the moon's latitude be less than ? Draw the diagram and calculate the ecliptic limits of the sun. When can there not be an eclipse of the sun ! When must there be one I When does it become necessary to make farther calculations whether there will or will not be an eclipse ! 199. When and at what places can the eclipse of the sun lie total ! VISIBILITY OF SOLAR ECLIPSES. 161 disc from any part of the eaj'th ; and at that place of the earth which is in a straight line with the centres of the sun and moon, a person would see the edge of the sun round the dark body of the moon, appearing like a lumi- nous ring, called an annular eclipse. If a part only of the sun's disc is obscured, the eclipse is a partial one. At all those places of the earth, over which the axis of the shadow, or the straight line connecting the centres of the sun and moon produced, passes, the eclipse will be central. When an eclipse of the sun is considered with respect to the whole earth_, and not with respect to any particular place, it is called a general eclipse. 200. Visibility of Solar Eclipses. As the moon moves in her orbit from west to east, her shadow will also move over the earth's surface in the same direction ; hence the eclipse must begin earlier at the western parts than at the eastern ; hence also the eclipse begins on the western edge of the sun, and ends on the eastern. Since the moon's penumbra is tangent to the earth, where the eclipse begins and ends, (the eclipse begins at f and ends at g, see fig. page 154), it follows that at the place where the eclipse is first seen, the sun will be just rising ; and where it is last seen, he will be setting. At all those places over which the axis of the shadow passes, or those contiguous to them, the eclipse will be either total or an- nular, according as the moon's apparent diameter is greater or less than that of the sun ; but if the axis of the shadow does not meet the earth, which is the case when the moon changes far from the node, and yet within the ecliptic limit, there will be no central eclipse at any place, When and where can it he annular ? What is a partial eclipse ? When ■will the eclipse be central ? What does a general eclipse respect ? 200. Why does the eclipse begin earlier at the ■western parts of the earth than at the eastern ? On what edge of the sun does the eclipse be- gin, and on ■what edge end ? Where wUl the sun appear at the place where the eclipse is first seen ! Where at the place it is last seen ? Where will the eclipse be either total or annuln?-? When will there be no cen- tral eclipse p.t any place, and where will tht re be but a partial one ! 162 ASTRONOMY. and the partial eclipse will be visible only in a portion of the northern or southern hemisphere, according as the moon's latitude is north or south. To a great portion of the enlightened hemisphere of the earth, the eclipse will be invisible, because the breadth of the penumbra, even when greatest, (196), is less than half the semi-circum- ference of the earth. 201. Duration of Solar Eclipses. The general eclipse will commence the instant that the moon's eastern edge touches the luminous frustum A a B &, (see fig. page 159), and will continue until her western edge leaves it ; hence the general eclipse of longest continuance will last during the period of time required for the moon to make an advance in longitude over the sun equal to the sum of the diameters of the frustum and moon, or equal to 2 (vill be at a distance from the nodes greater than the lunar ecliptic limits. The sun's ecliptic limits are greater than the moon's, consequently there will be more solar than lunar eclipses ; yet there are more visible eclipses of the moon than of the sun, because every lunar eclipse is visible to every part of that hemisphere of the earth which is turned next When there are eeven, prove that five are of the sun, and two of the moon. When but two, that both are of the sun. Why are there more solar than lunar eclipses? Why, then, are there more visible eclipses of the moon than of the sun ? OCCULTA. IONS. 174 her, at the same time ; but a solar eclipse is only visible to that part of the earth on which the moon's shadow falls. 213. OccuLTATiONS. When the moon passes directly between the earth and a star or planet, and thereby ren- ders it invisible somewhere upon the earth, the star or planet is said to suffer an occultation from the moon. Since the stars have neither sensible parallaxes nor apparent diameters, it follows that an occultation for the earth in gene- ral will begin and end when the true distance of the moon's centre from the star, before and after conjunction, is equal to H + d', as expressed in the articles on solar eclipses. The greatest value of H + rf' = 61' 29" + 16' 45" = 1° 18' 14"; hence if -the distance between the moon's centre and the star, at the time of conjunction, exceeds this quantity, the star can- not be eclipsed. And as the greatest inclination of the moon's orbit or her maximum latitude, is 5° 17'; we find that those stars only, whose latitude is less than 5° \T + 1° 18' 14" == 6° 35' 14", can be occulted. By allowing for the inequalities of the moon's motions, and taking the greatest and least values of H -{- d', it has been found, that if the difference between the latitude of the star and mean latitude of the moon, at the time of their mean conjunc- tion, exceeds 1° 3 '7', there cannot be an occultation ; but if this difference is less than 51', there must be one. Should the dif- ference fall between these limits, the true place of the moon must be calculated in order to determine whether there will or will not be an obscuration of the star. The calculation of an occultation for a given place, is nearly the same as that of a solar eclipse. The star takes the place of the sun's centre, but has neither parallax, semi-diameter, nor 213. When is a star or planet said to suffer an occultation ? What ex- presses the distance of the moon's centre from a star at the beginning and end of an occultation ? What is the greatest value of this expression ? Hence what ? What of tlie latitude of those stars which can be occulted f 'RTiat is farther said on this subject, when allowance is made for the me- qualitiea of the moon's motion ? How may an occultation be calculated for a given place ? 176 ASTKONOJiy. hourly motion. Instead of the moon's latitude, the difference between the latitude of the star and that of the moon, must be used ; and in the place of the apparent difference in the longi- tudes of the two bodies, we have this difference reduced to an arc between their circles of latitude, and passing through the star parallel to the ecliptic. This reduction is made by multi- plying the difference by the cosine of the latitude of the s-tar. From what has been advanced in relation to the stars on this subject, it will not be difficult to apply a similar process in the case of the occultations of the planets. OHAPTEE XX. THE CALENDAR. JULIAN AND GREGORIAN GAL-ENDAKS, ETC. 214. Calendar. A register, fixing tbe dates of im- portant occurrences, and noting the lapse of time by periods, yearsy months, weeks, days, hours, minutes, and seconds, is called the Calendar. The true solar or tropi- cal year contains 365d. 5A. 48m. 48s. (26), and since it is most convenient for the common purposes of life, that the civil year should contain a certain nuraber of whole days, it has been an object of the greatest importance to invent a scheme by which in all future time, these years may keep pace together. The nations of ancient times had different calendars, none of which was well arranged for fixing the seasons of the year with any degree of precision. Julius Caesar, having attained considerable accuracy on this subject, reformed the calendar, by establishing one more simple and less erroneous, than any which had obtained previous to his time. 214. What ia a calendar ? What is an otgeet of great importance t What is Baid of the calendars of ancient times ? Who established one more simple and less erroneous, than any previous to his time ? CtlEGORIAN CALENDAR. 177 215. Julian Cat.endar. Julius Csesar supposed the year to consist of 365a!. 6h., and according to this assump- tion, made the civil year to contain 365 days for three years in succession, and to allow for the 6 hours, every fourth 366 days. In every fourth year he reckoned the 23d of February twice, which was called Bis sextusdies, because the sixth of the calends of March, and thence this year was called Bissextile, and the day added, the Intercalary day. This year is now frequently called Leap year, and we add the intercalary day to the end of February. According to this method of reckoning, call- ed the Julian Calendar, and dating from the epoch of the Christian era, every year that is divisible by 4 without a remainder, is a leap year, and the others common years. Now since the Julian year exceeds the true or astro- nomical year by Hot. 12s., it would follow that the times of the equinoxes or solstices would occur this much earlier every year, and for ins.tance, the vernal equinox instead of happening on the 20th of March, would hap- pen, after a sufficient lapse of years, on a day previous to that date. Hence, in order hereafter to preserve the commencement of the same seasons, on the same months and the same days of the months, the Julian correction itself needs correction. 216. Gregorian Calendar. The error of the Julian calendar amounts to one day in about 129 years, or 10 days in 1290 years. Pope Gregory XIII., was the first to correct this error. At the time of the Council of Nice, which was held A. D. 325, the vernal equinox hap- pened on the 21st of March, and Gregory, in the year 215. Explain the Julian calendar. In every fourth year, what day did he reckon twice ? What was that year called ? What the day added ? What is this year now frequently called ? What day do we add in leap year ? How is it ascertained what years are, and what are not leap years ! How much does the Julian year exceed the true year ! What follows from this ? Why does the Julian correction itself need correction ! 216. Who first corrected the Julian error, and in what year ? On what day did the vernal equinox liappen, at the timp of the Council of Nice ! 8* 178 ASTRONOMY. 1582, or 1257 years after the Council of Nice, being de- sirous that it should occur on or near the same day, ordered 10 days, nearly the accumulation of error at this time, to be suppressed in that year, by reckoning the day following the 4th of October, to be called instead of the 5th, the 15th. Thus the calendar was reformed, and in order to correct it for the time to come, it was agreed that three intercalary days should be omitted every 400 years ; or, that those centurial years as 1700, 1800, 1900, not divisible by 400, though according to the Julian cal- endar bissextiles, are to be counted common years, but the centurial year 2000, and others divisible by 400, are still to be considered leap years. The degree of accuracy according to this mode of reckoning, called the Gregorian Calendar, is easily found. The Julian error in one year is 11m. 12s., and ll?n. 12s. X 400 = 3rf. 2h. 40m. in 400 years ; hence, by omitting 3 days, 2h. 40m. -.Id. : : 400y. : 3600 years, the time requir- ed to produce an error of one day. 217. Adoption of the Gregorian Calendar. In England and her colonies, the Gregorian calendar was not adopted till the year 1752, when the error amounted to 11 days. It was thei-efore enacted by"Parliament, that the day following the 2d of September of that year, should be called the 14th, instead of the 3d. This brought the English dates and the Gregorian calendar to agree, in consequence of the intercalary day in the latter, in the year 1700, having been omitted. The same act of Par- liament also changed the beginning of the year from the 25th of March to the 1st of January. In consequence of the suppression of the intercalary day in the year Of what was Pope Gregory desirous ? "What was the error at this time, and how did he correct it ? What was agreed, in order to correct it for the time to come ? What will result according to the Gregorian mode of reckoning ? Show this by the calculation ! 21'7. When was the Gregorian calendar adopted in England and her colonies ? What was the error tlien ? What was enacted by Parliament I THE TIDES. 170 1800, there is now 12 days of difference between the Julian and Gregorian calendars, or the Old and New Styles, as they are now more frequently termed. All Christian countries, except Russia, have adopted the New Style. CHAPTER XXI. THE TIDES. 218. Remarks. The alternate rise and fall of the waters of the ocean, seas, &c., are called the Tides, or jlux and rejlux of the sea. When the waters approach the shore or are rising, it is called food tide ; and when again they recede, it is called ebh tide. The determinate limits of the elevation and subsequent depression of the waters at any place, are those of high water and low water at that place. If the motion of the water is against the wind, it is called a windward tide, but if with the wind, it is called a leeward tide. The swell in the ocean, called the primitive tide-wave, produces tides in the contiguous bays and rivers, called derivatite tide- waves. 219. Causes of the Tides. The action of the' sun and moon occasions the tides, particularly that of the What is noTV the difference between the Julian and Gregorian calen- dars, or the Old and New Styles ? "What countries have adopted the New Style ? 218. What are called the tides ? What the flood tide and ebb tide ? What is understood by high and low water at any place ? What are windward and leeward tides ? Describe the primitive and derivative tide-waves f 219. What occasions the tides ? 180 ASTRONOMY. latter body. This power of attraction in a remote body is not the same upon the several particles of the earth, but according to the well established theory of universal gravitation, decreases as the squares of the distances of the particles from the centre of that body, increase ; hence the parts of the earth nearest the moon, for example, are more attracted than the lateral and central parts, and these again more than the parts diametrically opposite *the former. The parts immediately under the moon are drawn from the earth's centre, and therefore rendered specifically lighter than the lateral parts, which are less drawn and nearly in a horizontal direction : and, the parts opposite to the moon, though they are drawn towards the earth's centre, are also specifically lighter than the lateral parts, which are more drawn and in a direction somewhat towards the earth. Now if the earth were entirely solid, this inequality of the moon's action in attracting the different particles would make no sensible impression on these particles, however situated ; but, since a large portion of the external surface is composed of water, which yields to these unequally impressed forces, it is obvious that the waters of the fluid mass nearest and opposite to the moon, must rise, according to the principles of Hydrostatics, and be protnided till by their greater height they balance the waters of the other lateral parts less altered by the inequalities of the moon's action. The greatest depression will evidently be in a great circle 90° distant from the parts nearest and oppo- site the moon, and if the earth were entirely covered with water, it would assume the figure of an oblong spheroid, having the longest diameter directed towards the moon. How does this power of attraction . in a remote body vary ? Hence what ! How are the parta immediately under the moon, the lateral, and opposite parts, affected aa to their specific gravity, by the inequalities of the moon's action ? If the earth were entnely solid, what impression would her unequal action make on the different particles ? But since a large portion of the external surface is composed of water, which yields THE TIDES. 181 Thus let M represent the moon, and E the earth, surrounded with water. The waters on the several parts of the hemis- phere CAD, nearest the moon, will be darwn from the earth. by the attractive force which is inversely as the squares of the distances of those parts ; hence, the specific gravity of the waters from C and D, where the moon appears in the horizon, to A where she is vertical, will diminish. Again, the waters on the several parts of the opposite hemisphere C B D, will be drawn towards the earth by the moon's attractive force, which to these unequally impressed forces, what raust follow ? Where will there be the greatest depression ? Fully explain these principles by 182 ASTRONOMY. diminishes as the squares of her distances from those parts in- crease ; hence, also the specific gravity of the waters from C and D to B, the point opposite the moon, will diminish. There- fore it if evident, the fluid mass will form itself into an oblong spheroid, causing high water both at A and B, and low water in the vicinity of the great circle C D, 90° distant from A and B. The elevation of the waters at A and B, or on the sides of the earth nearest and opposite to the moon is nearly equal, because there is nearly an equal diminution of gravity in these positions, on account that the length of the earth's radius is small in comparison to the moon's distance. The time of high or low water at any place is about 50 minutes later than on the preceding day, because this is the daily variation in the time of the moon's corning to the meridian of any place, and therefore according to the above illustration, it is obviflus that in the course of a lunar day, or 24A. 50m., there will be two floods and two ebbs, which we find to agree with observation. Similar effects are produced in the waters of the ocean by the action of the sun, but in a less degree ; for although his whole attractive force upon the earth is about 1-66 times that of the moon, yet, as his distance is 400 times as great, the inequality of his action at the different parts is therefore less. The attractive force of the sun in raising the tides, is about one-third that of the moon. 220. Spring and Neap Tides. At the change, the attraction of the sun and moon is nearly in the same line of direction, and therefore united in raising the tides ; the force of both bodies is also conjoint, and the effect is very nearly the same at the full, for each raises a tide on the nearest and opposite side of the earth. Hence, at referring to the figure. Why is the elevation on the nearest and opposite sides nearly equal ! What is the variation in the time of high or low water each day ? How many floods and ebbs occur in a lunar day ? How many times greater is the whole attractive force of the sun upon the earth, than that of the moon ? How then is the inequality of his action at the different pavts less ! What is the ratio of these forces in raising the tides i PERIGEAN AND APOOEAN TIDES. 183 the times of syzygies, the tides run strongei and higher than at other times, and are therefore called Sj. 'ing Tides. But when the sun and moon differ in longitude 90° or 270°, the influence of the one body counteracts that of the other (see the fig.) ; for the sun then produces low water where the moon produces high water, and the con- trary. Hence, at the times of the quadratures, the tides do not rise to their average height, and are therefore call- ed Neap Tides. The greatest effects of the sun and moon's action, do not immediately follow that action, but some time after ; hence, the most marked spring and neap tides generally occur about 36 hours after the time^s of syzygies and quadratures. Since the attractive forces of the sun and moon in raising the tides, are as 1 to 3, it follows that the effect of these forces, when they act conjointly, is to the effect when they counteract each other, as 4 to 2 ; hence the spring tides rise to a height above the medium surface about double that of the neap tides. 221. Perigban and Apogean Tides. The influence of the moon on the waters of the ocean, is, as already stated, in the inverse ratio of the quare of her distance ; therefore the greatest tides will occur when she is in peri- gee, and the least when in apogee. Hence the spring tides that occur soon after the moon passes the perigean point, are unusually high ; and on the contrary, the neap tides that occur soon after she passes the apogean point, ai'e unusually low. These are therefore called the Pe?-i- gean and Apogean tides. 220. When do the tides run stronger and higher, and what then called I Fully expl.iin the cause of these high tides. Refer to the figure. When is it, the tides do not rise to their average height, and what then called ? Explain the cause of these low tides. When do the most marked spring and neap tides occur ? Why do the spring tides rise to a height double that of the neap tides ? 221. Why are the spring tides unusually high soon after the moon passes the perigean point ? And why are the neap tides unusually low, after she passes the apogean point ? What are these tides called i 184 ASTRONOMY. A slight change in the tides will also result, on ae !ount of the variation of the sun's distance from the earth. 222. Effect of the Moon's Declination on the Tides. When the moon is in the equinoctial, the highest tides will evidently occur -along the equator. But when the moon declines from the equinoctial, the opposite ele- vations will describe opposite -parallels, one of which will correspond to her declination. From these parallels the height of the tides will gradually diminish towards the north and south, arid therefore, in considerable high lati- tudes, any two consecutive tides will be of unequal height. At places 90° distant from the greatest elevation, on the opposite side of the equator, the less tide will vanish ; and hence, in the polar seas there will be but one small flood and ebb in the course of a lunar day. In north latitude, when the moon's declination is north, the tide will be higher when she is above the horizon, than when she is below it ; but when the declination is south, the reverse will be the case. This irregularity in the tides will be the greatest when the sun and moon have the same and the great- est declination. 223. Motion and Lagging of the Tides. The prim- itive tide- wave follows the moon in her apparent westerly course round the earth. This is not the continued forward motion of the same portion of water, but the effect of the attractive force on successive portions. Though the moon's action is the greatest on the waters of any place, when she is on the meridian of that place, yet in the open ocean, where the waters flow freely, it will not be high water generally untih about two hours after she has pass- 222. When the moon is in the equinoctial, where will the highest tides occur ? When the moon declines from tlie equinoctial, why will two con- secutive tides in considerable high latitudes, be of unequal height ! And why, in the polar seas, will there be but one small flood and ebb in the course of a lunar day ? When will the irregularity in the tides be the greatest, and why ? 223. How long, generally, in the open ocean, after the moon has passed ESTABLISHMENT OF A PORT. 185 cd either the superior or inferior meridian. A want of time in the waters to yield to the impulse given by the action of the moon, is the cause of this delay or Lagging of the tide-wave. The tide- wave does not always answer to the same distance of the moon from the meridian, but is slightly affected in its motion, caused by the relative positions of the sun and moon. Although the great tide- wave in the open ocean follows the moon at the distance of about 30o from her, yet the time of high water at places situated on bays, rivers, eater's sailing. TilE TEEEESTEIAL, GLOBK. 195 5. What is the direct distance between Cape Horn and the Cape of Good Hope ? 6. What is the extent of Europe in statute miles from the North Cape to Cape Matapan ? 7. What is the shortest distance between Cape Cod and the Island Bermuda ? 8. What is the extent of the Atlantic Ocean from Cape Look- out to Cape Finisterre ? 9. How many miles is Africa broader than South America, where crossed by the equator ? PROBLEM VIII. A place being given, to find all those places which ai-e situated at the same distance from it as any other given place. RULE. Place the division marked of the quadrant of altitude on the first given place, and the graduated edge over the other, then observe the degree on the quadrant over the other place ; move the quadrant entirely round, keeping the division marked in its first situation, and all places which pass under the same degree which was observed to stand over the other place, are those required. Or, take the distance between the two places in a pair of compasses, and with the first place as a centre, describe a circle ; then all places situated in the circumference of this circle, are those required. When the distance between the two places exceeds the length of the quadrant, or the extent of the compasses, stretch a thread between them, and mark their distance, with Vv'hich proceed as with the quadrant. EXAMPLES. 1. What places are situated at the same distance from Lon- don as Warsaw is ? Ans. Alicant, Buda, Koningsburg, 62950 THE TRRRESTRIAL GLOBE. •SLTu brass meridian and each of the points of intersection; the hour arcs will respectively contain these degree^i. The dial must be numbered 12 at the brass meridian, thence, 11, 10, 9, 8, 7, 6, towards the' west for morning hours ; and 1, 2, 3, 4, 5, 6, towards the east, for evening hours. It is unnecessary to draw any more houis on such a dial, than these, because the sun cannot ;jhine longer upon it than 12 hours in the course of one day The style or gnomon must be parallel to the earth's axis, and elevated as many degrees above the plane (»i' the dial-plate, as are equal to the complement of the lautude het it be required to make a vertical dial, facing the south, for the latitude of Baltimore. Elevate the south pole 50° 43' above the horizon, and bring the point Aries to the brass meridian ; then, you will find the degrees on the eastern part of the horizon, between the south point and the meridians on the globe, to be as follows, namely, 11° 43', 24° 5', 37° 44', 53° 17', 70° 54', and 90°, for the hours 1, 2, 3, 4, 5, and 6, in the afternoon ; and on the western part of the horizon, the hour arcs will contain the same degrees, for the hours, 11, 10, 9, 8, 7, and 6, in the morning. , The following table is calculated precisely in the same manner as the table in the preceding problem by using the complement of the latitude inbtead of the latitude. Houi-s. Hour Angles. Hour Arcs. Hours. Hour Angles. Hour Arcs. 12i 3° 45' 2° 54' H 48° 45' 41° 26' 12i 7 30 5 49 H 52 30 45 15 12i 11 15 8 45 H 56 15 ■ 49 12 1 15 11 43 4 60 53.17 H 18 45 14 43 H 63 45 57 30 H 22 30 17 47 H 67 30 61 51 If 26 15 20 54 4f 71 15 66 19 2 30 24 5 5 75 70 54 2i 33 45 27 21 H 78 45 75 35 n 37 30 30 42 H 82 30 80 21 2f 41 15 34 10 5f 86 15 85 10 3 45 37 44 6 90 90 12* 274 PROBLEMS PERFORMED BY It may be observed, that the time shown by a sun-dial is the apparent time, and not the true or mean time of the day, as shown by a well regulated clock. (26.) The fol- lowing table of the equation of time will show how much a clock should be faster or slower than a sun-dial. Every> sun-dial should have such a table engraven upon it. Days and Months. Minutes. Days and Months. Minutes. Days and Months. Minutes. Jan. 1 4 19 1 24 8 3 5 23 2 o 27 9 5 6 30 3 t 30 10 1 7 May 13 4 ^ Oct. 3 11 ' 9 8 29 3 %■ 6 12 12 9 June 5 2 i 10 13 15 10 10 1 ? 14 14 18 11 15 19 15 g 21 25 12 13 9 * 27 Nov. 15 16 § 15 r 20 1 31 14 § 25 2 20 14 o" Feb. 10 15 s: 29 3 24 13 i 21 14 1 July 5 4 o 27 12 a 27 _ 13 ES 11 5 ? 30 11 s March 4 12 ^ 28 6 ^ Dec. 2 10 I 8 11 g Aug. 9 5 ^ 5 9 g- 12 10 s^ 16 4 S- 7 8 a 15 9 » 20 3 ^ 9 7 g: 19 8 5 24 2 11 6 ■ 22 7 P 28 1 13 5 25 6 31 16 4 28 April 1 5 4 * 18 20 3 2 Sept. 3 1 4 • 3 6 2 ? 22 1 1 2 9 3 1- 24 11 15 1 12 15 4 «, 6 » * 26 1 9 18 28 2 ^ 21 7 ■ 30 3 S. THE CELESTIAL GLOBE. 875 CHAPTER II. PEOBLEMS PERFORMED BY THE CELESTIAL GLOBE. PROBLEM I. To find the right ascension and declination of any star, RULE.* Bring the given star to that part of the brass meridian which is numbered from the equinoctial towards the poles ; the degree on the brass meridian above the star is the declination, and the degree on the equinoctial cut by the brass meridian, reckoning from the point Aries eastward, is the right ascension. EXAMPLES. 1 . Required the right ascension and declination of «, Arctu- rus, in the right thiffh of Bootes. Ans. Right ascension 211° 55 , decimation 20° 8' N. 2. Required the right ascension and declinations of the fol- lowing stars : /3, Arided, in Cygnus, /, Algorah, in the Crow, at,, Oanopas, in Argo Navis, /3, Rigel, in Orion, », Spica Virginis, in Virgo, £, Mirach, in Bootes, a, Arietis, in Aries, <*, Oastor, in Gemini, /3, Algol, in Perseus, a, Altair, in the Eagle, «, Antares, in the Scorpion, «, Schedar, in Cassiopeia. * This rule will answer for finding the sun's right ascension and decli- nation, by using the sun's place in the ecliptic, instead of the given star. The right ascension and declination of the moon and planets must be ound from the Nautical Almanac. 276 PROBLEMS PERFOEMED BY PROBLEM II. To find the latitude and longitude of any star.* RULE. Bring the north or south pole of the ecliptic, according as the star is on the north or south side of the ecliptic, to the brass meridian, and 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 ; then, the degree on the quadrant over the star is its latitude, and the number of degrees on the ecliptic, reckoning from the point Aries eastward to the quadrant, is its longitude. EXAMPLES. 1. Required the latitude and longitude of a, Marhab, in Pe-. g.asus. Ans. Latitude 19° 25' K, and longitude 11 signs 20° 54'. 2. Required the latitudes and longitudes of the following stars : a, Altair, in the Eagle, /S, Mirach, in Andromeda, «, Arcturus, in Bootes, «, Aldebaran, in Taurus, 7, Vega, in Lyra, 08, Fomalhaut, in the S. Fish «, Sirius, in Canis Major, «, Begulus, in Leo, /3, Rigel, in Orion, y, Bcllatrix, in Orion, «, Capella, in Auriga, «, Procyon, in Canis Minor, a, JRastabcn, in Di-aco, /3, Pollux, in Gemini, /3, Algol, in Perseus, Y, Algenib, in Pegasus. * The latitudes and longitudes of the moon and planets must be found from the Ifautical Almanac, or an Ephemeris ; because, tbey cannot be placed on the globe, as the stars are placed, on account of their continual motion. THE CELESTIAL GLOBE. 277 PROBLEM III. The right ascension and declination of the moon, a star, or a planet, being given, to find its place on the globe. Bring the given degree of right ascension to that part of the brass meridian, which is numbered from the equi- noctial towards the poles ; then, under the given declina- tion on the brass meridian, you will find the star, or the place of the moon or planet. EXAMPLES. 1. What star has 163° 6' of right ascension, and 62° 44' K declination ? Ans. «, Dtibke, in the back of the Great Bear. 2. On the 10th of September, 1848, the moon's right ascen- sion was 20 hours 54 minutes, and her declination 13° 58', S. find her place on the globe at that time. Ans. About 4° in Pisces, nearly in the plane of the ecliptic. 3. What stars have the following right ascensions and decli- nations ? R7GHT ASCENT. DKCLIN. RIGHT ASCEN. DECLIN. 29° 14' 22° 36' K 22A. 41m. 20° 35' S. 86 20 7 22 N. 20 35 44 38 ISr. 176 3 54 42 N. 4 27 16 12 N. 4. On the 13th of December, 1848, the declination of Mars was 21° 3' S. and his right ascension 16 hours 8 minutes ; find bis place on the globe at that time. 5. On the 25th of December, 1848, the right ascension of Jupiter was 9 hours 38 minutes 53 seconds, and his declination 14° 59' 34" N. ; find his place on the globe. 6. On the 31st of December, 1848, the right ascension of Saturn was 23 hours 26 minutes 18 seconds, and his declina- tion 5° 58' 58" S. ; find his place on the globe. 278 PROBLEMS PERFORMED BV PROBLEM IV. The latitude and longitude of the moon, a star, or a planet, being given, to find its place on the globe. RULE. Bring the north or south pole of the ecliptic, according as the latitude is north or south, to the brass meridian, and screw the quadrant of altitude upon the brass meri- dian over the pole of the ecliptic ; keep the globe from revolving on its axis, and move the quadrant till its gradu- ated edge cuts the given degree of longitude on the eclip- tic ; then under the given latitude, on the quadrant, you will find the star, or the place of the moon or planet. EXAMPLES. 1. What star has 2 signs 1° 12' of longitude, and 5° 28' S. latitude ? Am. «, Aldeharan, in Taurus. 2. What stars have the following latitudes and longitudes ? LAT. LON. LAT. LON. 6° 40' N. 3s 20° 40' 19° 25' K lis 20° 54' 9 58 N. 1 5 5 4 33 S. 8 7 11 21 n S. 11 1 15 29 19 N. 9 29 10 le 3 S. 2 25 51 39 33 S. 3 11 13 22 52 IST. 2 18 57 10 4 N. 3 17 21 12 35 S. 1 11 25 44 20 N. 7 9 22 3. On the 9th of December, 1848, at midnight, the moon's, longitude was 2 signs 11° 9', and her latitude 4° 69' S. ; re- quired her place on the globe? 4. On the 15th of May, 1848, the longitude of Venus was 36° 15', and latitude 1° 24' S. ; required her place on the globe? THE CELESTIAL GLOBE. 279 PROBLEM V. The month, day, and hour of the day at any place being given, to place the globe in such a manner as to repre- sent the heavens at that time and place ; in order to find the relative situations and names of the constellations and principal stars. Place the globe, on a clear star-light night, due north and south by the compass, upon a horizontal plane, where the surrounding horizon is uninterrupted by different ob- jects, and elevate the pole for the latitude of the place ; find the sun's place in the ecliptic for the given day, 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 ; keep the glftbe in this position, then the flat end of a pen- cil being placed on any star on the globe, so as to point towards the centre, the other end will point to that par- ticular star in the heavens. PROBLEM VL The month, day, and hour of the day at a place being given, to find what stars are rising, setting, culmina- ting, (19,) 6fC. RULE. Elevate the pole for the latitude of the place, bring the sun's place in the ecliptic 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 280 PROBLEMS PERFORMED BY index has passed over as many hours as the time is past noon ; but, if the time be before noon, turn the globe east- ward till the index has passed over as many hours as the time w^ants of noon ; keep the globe in this position ; then, all the stars along the eastern edge of the horizon will be rising at the given place, those along the western edge will be setting, those under the brass meridian above the horizon will be culminating, those above the horizon will be visible, and those below the horizon will be invisible. If the globe be turned on its axis from east to west, those stars which do not descend below the horizon, never set at the given place; and those which do not ascend above the horizon, never rise. EXAMPLES. 1. On the 21st of October, when it is 1 o'clock in the even- ing at Philadelphia, what stars are rising, what stars are set- ting, and what stars are culminating ? Ans. Menkar in Cetus, is rising ; Capella, a little above the eastern edge of the horizon, Deneb, on the meridian, Arcturus, a little east of the western edge of the horizon ; Antares, in the Scorpion, setting, &c. 2. On the 16 th of January, when it is three o'clock in the morning at Baltimore, what stars are rising, what stars are set- ting, and what stars are culminating ? Ans. Deneb is rising, Dubhe culminating, Alamak in Andro- meda, setting, &c. 3. On the 10th of November, when it is ten o'clock in the evening, at Washington, what stars are rising, what stars are setting, and what stars are culminating ? 4. What stars never set at Paris, and what stars never rise at the same place ? 5. How far northward must a person travel from New- York, to lose sight of Antares ? 6. How far southward must a person travel from Mexico, to lose sight of Dubhe ? 1. In what latitude do those reside, to whom Sirius is never visible, but when in their horizon ? 8. In what latitude is Aldebaran always vertical, when on the meridian ? THE CELESTIAL GLOBE. 281 PROBLEM VII. The month and day being given, to find at what hour of the day any star, or planet, will rise, culminate, and set at any given place. RULE. Elevate the pole for the latitude of the given place, bring the sun'g place in the ecliptic for the given day to the brass meridian, and set the index of the hour circle to 12 ; then if the star or planet* be below the horizon, turn the globe westward on its axis till the star, &c., comes to the eastern edge of the horizon, the brass meri- dian, and the western edge of the horizon successively ; the hours passed over by the index in each case, will show the time from noon, that the star or planet rises, culminates, and sets. If the star, &c., be above the horizon and east of the brass meridian, find the time of culminating, setting, and rising, in a similar manner ; but, if it be west of the brass meridian, then you will find the time of setting, rising and culminating. EXAMPLES. 1. At what time will Arcturus rise, culminate, and set at Washington, on the 21st of August ? Ans. It will rise 45 minutes past 8 o'clock in the morning', culminate at 4 in the afternoon, and set at 15 minutes past 11 o'clock at night. 2. On the 14th of December, 1848, the right ascension of Venus was 301° 13', and her declination 22° 23' S., at what time did she rise, culminate, and set, at Baltimore, and was she a morning or an evening star ? Ans. Venus culminated" at 32 minutes past 2 o'clock in the * The planet's plaoe on the globs must be determined by Prob. III. at IV 282 PROBLEMS PERFORMED BY afternoon, sot at 16 minutes past 7, and rose at 6 minutes before 10. Venus was ad evening star, because she set after the sun. 3. At what time will Sirius rise, culminate, and set at New- York, on the 25th of December? 4. On the 8th of September, 1848, the right ascension of Jupiter was 8 hours 57 minutes 12 seconds, and his declination 17° 47' N., at what time did he rise, culminate, and set, at Washington, and was he a morning or an evening star ? 5. On the 3d of October, 1848, the right ascension of Saturn was 23 hours 28 minutes 45 seconds, and his declination 6° 69' 6" S., at what time did he rise, culminate, and set, at Boston ? PROBLEM VIII. RULE. The month and day being given, to find all those stars that rise and set achronically , cosmically, and heliacally (24), at any given place. ve. Elevate the pole for the latitude of the given place. Then, 1. For the achronical rising and setting. Bring the sun's place in the ecliptic to the western edge of the horizon, and all the stars along the eastern edge of the horizon will rise achronically, while those along the west- ern edge will set achronically. 2. For the cosmical rising and setting. Bring the sun's place to the eastern edge of the horizon ; and all the stars along that edge of the horizon will rise cosmically, while those along the western edge will set cosmically. 3. For the heliacal rising and setting. Screw the quadrant of altitude on the brass meridian over the de- gree of latitude, turn the globe eastward on its axis till the sun's place cuts the quadrant 12° below* the eastern * The brighter a star is when above the horizon, the leas will the sun be depressed below the horizon, when that star first becomes visible THE CELESTIAL GLOBE. 283 edge of the horizon ; then, all stars of the first magnitude, along the same edge of the horizon, will rise heliacally ; continue the motion of the globe till the sun's place in- tersects the quadrant in 13", 14°, 15°, &c., below the horizon, and you will find the stars of the second, third, fourth, &c., magnitudes, which rise heliacally, at the given place on the given day. Bring the quadrant to the western edge of the horizon, turn the globe westward on its axis, till the sun's place intersects the quadrant in a similar manner as before, and you will find all the stars that set heliacally. EXAMPLES. 1. What stars rise and set aohronically at Washington, on the 1st of January? Ans. Castor in Gemini, Betelguese in Orion, (fee, rise achroni- cally ; and S' in Bootes, y in Hercules, &c., set achronically. 2. What stars rise and set cosmically at Philadelphia, on the 2d of June ? Ans. Aldeharan, and ^ in Taurus, (fee, rise cosmically, and Arcturus, (fee, in Bootes, set cosmically. 3. What star of the first magnitude rises heliacally at New- York, on the 25th of June ? Ans. Aldeharan in Taurus. 4. What star of the first magnitude sets heliacally at Balti- more, on the 22d of January 1 Ans. Altair in the Eagle. 5. What stars rise and set cosmically at Dublin, on the 14th. of November ? 6. What stars rise and set achronically at London, on the 2Tth of April ? hence, the heliacal rising and setting of the stars will vary according to their different degrees of magnitude and brilliancy. According to Ptol- emy, stars of the first magnitude are seen rising and setting when the sun is 12° below the horizon, stars of the second magnitude when the sun is 13° below the horizon, stars of the third magnitude 14°, and so on, reck- oning one degree for each magnitude. 284 PROBLEMS PERFOKMED BY PROBLEM IX. To find the time of the year at which any given star rises or sets achronically, at a given place. RULE. Elevate the pole for the- latitude of the given place, bring the given star to the eastern edge of the horizon, observe what degree of the ecliptic is cut by the western edge of the horizon; and, the day of the month answer- ing to that degree will show the time when the star rises achronically, or when it begins to be visible in the even- ing. Bring the given star to the' western edge of the horizon, observe what degree of the ecliptic is cut by the same edge of the horizon ; and the day of the month an- swering to that degree will show the time when the star sets achronically, or when it ceases to appear in the evening. EXAMPLES. 1. At what time does Arided rise achronically at Baltimore, and on what day of the year does it set achronically ? Ans. Arided rises achronically on the 21st of May, and it sets achronically on the 22d of March. 2. On what day of the year does Arcturus rise achronically at Washington, and at what time does it set achronically ? 3. On what day of the year does Aldeharan begin to be vis- ible in the evening at Grlasgow, and on what day does it cease to appear in the evening ? 4. At what time does Procyon in Canis Minor rise achroni- cally at New- York, and on what day of the year does it set achronically ? 5. On what day of the year does Spica Virginis set achron- ically, or cease to appear in the evenings at Baltimore ? THE CELESTIAL GLOBE. 285 PROBLEM X. RULE. To find the time of the year at which any given star rises or sets cosmically, at a given place. Elevate the pole for the latitude of the given place, bring the given star to the eastern edge of the horizon, and observe what degree of the ecliptic is cut by the same edge of the horizon ; the month and day of the month answering to that degree, will show the time when the star rises cosmically, or when it rises with the sun. Bring the given star to the western edge of the horizon, and observe what degree of the ecliptic is cut by the eastern edge ; the month and day of the month answer- ing to that degree, will show the time when the star sets cosmically, or when it sets at sun-rising. EXAMPLES. 1. At what time of the year does Procyon in Oanis Minor, rise cosmically at Washington ; and, at what time does the same star set cosmically at the same place ? Ans. Procyon rises cosmically on the 24th of July, or rises with the sun on that day, and sets cosmically on the 25th of December, or sets at sun-rising on that day. 2. At what time of the year does Regulus rise cosmically at New- York, and at what time does it set cosmically ? 3. At what time of the year does Bellatrix in Orion rise vs'ith the sun at London, and at what time does it set at sun- rising ? 4. At what tjlme of the year does Arcturus rise with the sun at Philadelphia ; and at what time of the year will it set, when the sun rises at the same place ? 5. At what time of the year do the Pleiades rise cosmically at Baltimore ; and at what time do they set cosmically at the same place ? 286 PROBLEMS PERFORMED BY PROBLEM XI. To find the time of the year at which any given star rises or sets heliacally, at a given place. RULE. Elevate the pole for the latitude of the given place, and screw the quadrant of altitude on the brass meridian over the degree of latitude ; bring the given star to the eastern edge of the horizon, and move the quadrant till it cuts the ecliptic 12° below* the eastern edge of the horizon, if the star be of the first magnitude ; 13° if it be of the second magnitude ; 14° if it be of the third mag- nitude, and so on ; the degrees of the ecliptic cut by the quadrant will show, on the horizon, the day of the month, when the star rises heliacally. Bring the given star to the western edge of the horizon, and move the quadrant of altitude till it cuts the ecliptic below the western edge of the horizon, in a similar manner as before ; the degree of the ecliptic cut by the quadrant will show, on the horizon, when the star sets heliacally. EXAMPLES. 1. At what time of the year does Arcturus rise heliacally at Jerusalem, and at what time does it set heliacally at the same place ? Ans. Arcturus will rise heliacally on the 23d of October, that is, when it first becomes visible in the morning, after having been so near the sun as to be hid by the splendor of his rays ; and, Arcturus will set heliacally on the Yth of November, that is, when it first becomes invisible in the evening, on account of its nearness to the sun. 2. At what time of the year does Sirius, or the Dog Star, rise heliacally at Rome, and at what time does it set beli-acally at the same place ? * See the note to Prob. VIII THE CELESTIAL GLOBE. 287 3. What time of the year does Procyon rise heliacally at New-York, and at -what time does it set hehacally at the same place ? 4. At what time of the year does Spica Virginis rise heli- acally at London, and at what time does it set heliacally at the same place ? PROBLEM XII. To find the diurnal arc (25,) of any star, or its contin- uance above the horizon for any day at a given place. Elevate the pole for the latitude of the given place, bring the given star to the eastern edge of the horizon, and set the index of the hour circle to 12 ; turn the globe westward on its axis till the given star comes to the western edge of the horizon ; the hours passed over by the index will be the star's diurnal arc, or its continuance above the horizon for any day, at the given place. EXAMPLES. 1. What is the diurnal arc of Regulus, or its continuance above the horizon for one day at New- York ? Ans. 13 hours 35 minutes. 2. What is the diurnal arc of Sirius, at London? 3. Aldebaran in Taurus, rises cosmically at Philadelphia, on the 2d of June, does that star set before or after t'.ie sun on the same day, and how long ? 4. What is the diurnal arc of Arcturus at Washin;^ton ? 5. How long does Procyon continue above thd horizon, during one revolution of the earth on its axis, at Baldmore ? 6. What is the diurnal •re of Capella at Eome ? 7. Arietis sets cosmically at Baltimore on the 31st of Octo- ber, how long does that star rise before the sun sets on the same day ? 8. What is the diurnal arc of Pollux at Quebec ? 288 PROBLKMS PERFORMED BY PROBLEM XIII. To find the oblique ascension and descension of any star, and its rising and setting amplitude, at a given place Elevate the pole for the latitude of the given place, and bring the given star to the eastern edge of the hori- zon, then the degree of the equinoctial cut by the same edge of the horizon, will be the oblique ascension, and the number of degrees between the star and the eastern point of the horizon will be its rising amplitude : turn* the globe westward on its axis till the given star comes to the western edge of the horizon, then the degree of the equinoctial cut by .the same edge of the horizon, will be the oblique descension, and the number of degrees between the star and the western point of the horizon, will be its setting amplitude. EXAMPLES. 1. Required the oblique ascension and descension of Castor, and its rising and setting amplitude, at Philadelphia. Ans. The oblique ascension is 78°, oblique descension 144° ; rising amplitude 45° to the north of the east, and setting am- plitude 45° to the north of the west. 2. Required the oblique ascension and descension of Regulus, and its rising and setting amplitude at New- York ? 3. Required the oblique ascension, oblique descension, and its rising and setting amplitude of y in Leo, at Washington ? 4. Required the rising and setting amplitude of Arcturus, its oblique ascension, and oblique descension, at London ? 5. Required the rising and setting amplitude of a Aquilse, its oblique ascension, and oblique dm cension, at Baltimore ? * The star's diurnal arc may here be found, by observing the number of hours passed over by the index, during this motion of the globe on its THE CELESTIAL GLOBE. : 289 PROBLEM XIV. To find the distance in degrees between any two Stars, or the angle which they subtend, as seen by a spectator on the earth. RULE. Lay the graduated edge of the quadrant of altitude over the two given stars, so that the division marlted may be on one of the stars ; the degrees on the quadrant comprehended between the two stars will be their dis- tance, or the angle which they subtend, as seen by a. spectator on the earth. EXAMPLES. 1. What is the difference between Arcturus and Duhhei Ans. 54°. 2. What is the distance between a in Serpentarius, and yiii Cygnus ? 3. What is the distance between Lyra and Mirach? 4. What is the distance between Gemma and Antares ? 5. What is the distance between Alioth in the tail of the Great Bear, and ^ in the tail of Leo ? - 6. What is the distance between Deneb and MenJcar ? PROBLEM XV. To find the meridian altitude of a star c planet, on any day,* at a given place. RULE. Elevate the pole for the latitude of the given place, * It is not requisite to give the day of the month, in finding the m»n iiaa altitude of the stars, because it is iuTariable at the same place 13 290 PROBLEMS PERFORMED BY and bring the given star or planet's* place on the globe to the brass meridian ; then the number of degrees on the meridian, contained between the star or planet's place and the horizon, will be the altitude required. EXAMPLES. 1. What is the meridian altitude of Aldeharan in Taurus, at "Washington ? Ans. 67^° 2. What is the meridian altitude of Arcturus at Paris ? 3. What is the meridian altitude of Capella at Baltimore ? 4. On the 1st of January, 1848, the right ascension of Mars •was 2 hours 12 minutes 7 seconds, and declination 14° 43' 44" N.; what was his meridian altitude at New- York ? 5. On the 6th of December, 1848 the moDU passed the meridian of Baltimore at 8 hours 42 minutes,f when her right * The moon or planet's place on the globe must be determined by Erob. III. or IV. f The longitude of Baltimore is 76° 39' = 5A. Hm. west of Greenwich. On the 6th and 7th of December, 1 848, the moon's meridian passages ' were at 8A. 30m. and 9A. 25m. Greenwich mean time, the difference is 55m.; therefore, 24/t. : 557W. :: 5A. tm. : 12/n., which added to the Green- wicli mean time of transit on the 6th, gives 8/i. ilm. for the mean time of transit at Baltimore. On the 6th of December, by the Ifautical ilmanac, the Eight ascension at midnight was lA. 40m. 48s., declination 7° 5' 34" N noon, " 1 12 56 " 4 53 36 N. Increase in 12 hours from noon 27 52 2 11 58 Then, 12A. : 27m. 52«. : : 8A. 42m. : 20m. 12s., which added to the right ascension at noon gives \h. 337n. 8s., the moon's right ascension at 8A. 42m. when she passed the meridian of Baltimore^ And 12A. : 2° 11' 58" : : 8/1. 42m. ; 1° 35' 40", which added to 4° 53' 36" K the declination at uoon, because increasing, gives 6° 29' 16" N., the declination when she passed the meridian. Hence, 90° — 39° 17' + 6° 29' 16" = 57° 12' 16", the meridian altitude at the time proposed. The places of the planets may be taken from the Nautical Almanac for noon, without material error, because they vary Ibs.« than that of the moou. THE CELESTIAL GLOBE. 291 ascension was 1 hour 33 minutes 8 seconds, and declination 6° 29' 16" N,; required her meridian altitude at Baltimore ? 6. On the 1st of November, 1848, the right ascension of Venus was 16 hours 15 minutes, and declination 22° 4' south ; required her meridian altitude at Baltimore. PROBLEM XVI. The month, day, and hour of the day at any place being given, to find the altitude of any star, and its azimuth. RULE. Elevate the pole for the latitude of the given place, and screw the quadrant of altitude on the brass meridian over the degree of latitude ; bring the sun's place in the ecliptic for the given day 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 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 axii till the index has passed over as many hours as the time is past noon ; keep the globe from revolving on its axis, anJl move the quadrant of altitude, till its graduated edge comes over the given star ; the degrees on the quadrant, comprehended between the horizon and the star, will be the altitude ; and the degrees on the horizon, between the north or south point thereof and the quadrant, will be the azi- muth. EXAMPLES. 1. Required the altitude and azimuth of jS in Leo, at Phila- delphia, on the 20th of March at 10 o'clock in the evening ? Ans. The altitude is 59°, and azimuth 49|-° fiom the south towards the east. 2. On what point of the compass does Altair bear at Wash- ington, on tlie i9th of April, at 3 o'clock in tlie morning ; and what is its altitude ? 292 PROBLEMS PERFORMED BV 3. Required the altitude and azimuth of Arcturus at Dublin, on the 5th of September, at 8 o'clock in the evening ? 4. Required the altitude and azimuth of Markab in Pegasus, at Paris, on the 30th of August, at 9 o'clock in the evening ? PROBLEM XVII. The manth and day of the month being given, and the altitude of a xtar at any place, to find the hour of the night,* and the star's azimuth. Elevate the pole for the latitude of the given place, and screw the quadrant of altitude on the brass meridian over the degree of latitude ; bring the sun's place in the ecliptic for the given day to the brass meridian, and set the index of the hour circle to 12 ; bring the quadrant to that side of the meridianf on which the star was situated when observed ; turn the globe westward on its axis, till the centre of the star cuts the given altitude on the quadrant ; then the houi's passed over by the index will show the time from noon, when the star has the given altitude, and the degree on the horizon intersected by the quadrant, will be the azimuth. EXAMPLES. 1. At Philadelphia, on the 20th of March, the star ;3 in Leo, was observed to be 59° above the horizon, and east of the me- ridian, what hour was it, and what was the star's azimuth ? * If the observation be made in the morning, the hour can be as easily found by turning the globe eastward on its axis, and the number of linurs passed over by the index will show the time from noon, in the morning, when the star has the given 'altitude. f A star will have the same altitude on both sides of the meridian ; therefore, it is necessary to mention on which side of the meridian the star was situj ted at the time of observation. THE CELESTIAL GLOBE. 293 Ans. It was. ten o'clock in the evening, and the star's azi- Lcath was 49-|-° from the south towards the east. 2. At Washington, on the 23d of October, the star Lyra was observed to be 52° above the horizon, and west of the meridian, what hour was it, and what was the star's azimuth ? 3. At Dublin, on the 11th of December, Mirach in Andro- meda was observed to be 65° above the horizon, and east of the meridian- what hour was it, and what was the star's azi- muth ? 4. At Baltimore, on the 1st of January, in the morning, the altitude of Arcturus was observed to be 44^°, and it was east of the meridian, what hour was it, and what was the star's azimuth ? PROBLEM XVIII. The month and day of the month being given, and the azimuth of a star at any place, to find the hour of the night, and the star's altitude. RULE. Elevate the pole for the latitude of the given place ; and screw the quadrant of altitude on the brass meridian over the degree of latitude ; bring the sun's place in the ecliptic for the given day to the brass meridian, and set the index of the hour circle to 12 ; bring the graduated edge of the quadrant to coincide with the given azimuth on the horizon, and keep it in that position ; then, turn the globe westward on its axis till the centre of the given star comes to the graduated edge of the quadrant, the hours passed over by the index will show the time from noon when the star has the given azimuth, and the de- grees on the quadrant, comprehended between the hori- zon and the star, will be the altitude. EXAMPLES. 1. At Philadelphia, on the 20th of March, the azimuth of S in Leo, was observed to be 49^° from the south towards the east, what hour was it, and what was the star's altitude ? 294 PROBLEMS PERFORMED BY Ans. It was 10 o'clock in the evening, and the star's alti- tude was 59°. 2. At Washington, on the 23d of October, the azimuth of Lyra was 73° from the north towards the west, what hour was it, and what was the star's altitude ? 3. At Dublin, on the 5th of September, the azimuth of Arc- turus was 89° from the south towards the west, what hour was it, and what was the star's altitude ? 4. At Paris, on the 30th of August, the azimuth of MarJcab in Pegasus was 66° from the south towards the east, what hour was it, and what was the star's altitude ? PROBLEM XIX. The month and day of the month being given, and the hour when any known star rises or sets, to find the lat- itude of the place. RULE. Bring the sun's place in the ecliptic for the given day 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 as many hours as the time wants of noon ; but, if the given time be past noon, turn the globe westward on its axis as many hours as the time is past noon ; keep the globe from revolving on its axis, elevate or depress the pole till the centre of the given star coincides with the edge of the horizon, and the elevation of the pole will show the latitude required. EXAMPLES. 1. In what latitude does Menkar in Cetus rise at Y o'clock in the evening of the 21st of October? Am. 40° N. 2. In what latitude does Arcturus rise at 45 minutes past 8 o'clock in the morning, on the 21st of August ? 3. In what latitude does Alamak. in Andromeda, set at 3 o'clock in the morning, on the 16 th of January ? 4. In what latitude does Alph^cca, in the Northern Crown, rise at 9 o'clock in the evening, on the 9th of February ? THE CELESTIAL GLOBE. 21)5 PROBLEM XX. The meridian altitude of a known star bcMg given, to find the latitude of the place of observation. RULE. Bring the centre of the given star to that part of the brass meridian which is numbered from the equinoctial towards the poles ; count as many degrees on the brass meiidian, from the star, either towards the north or south point of the horizon, according as the star was north or south of you when observed, as are equal to the given altitude, and mark where the reckoning ends ; then ele- vate or depress the pole till this mark coincides with the north or south point of the horizon, and the elevation of the pole will show the latitude. EXAMPLES. 1. In what latitude is the meridian altitude of Aldebaran in Taurus, &1\° above the south point of the horizon ? Ans. 38° 53' N. 2. In what latitude is the meridian altitude of Arcturus, 6\\° above the south point of the horizon ? 3. Being at sea on the 22d of August, 1848, I took the me- ridian altitude of Altair, and found it to be 56:|-° above the south point of the horizon ; required the latitude of the ship ? 4. In what latitude is the meridian altitude of Lyra 80° above the north point of the horizon ? PROBLEM XXL The altitude of two known stars being given, to find the latitude of the place. RULE. Take the complement of the altitude of the first given star from the equinoctial in a pair of compasses, and, witli one foot in the centre of that star, and a fine pencil 296 PROBLEMS PEEFORMED BY in the Other foot, describe an arc ; take the complement of the altitude of the second star from the equinoctial as before, and, with one foot in the centre of this star, describe an arc to cross the former arc ; bring the point of intersection to that part of the brass meridian which is numbered from the equinoctial towards the poles, and the degree above it will be the latitude sought. EXAMPLES. 1. In north latitude, I observed the altitude of Capella tohe 30°, and that of Castor 48° ; what latitude was I in ? Ans. 40" N. 2. At sea in north latitude, I observed the altitude of Lyra to be 35°, and that of Altair 25° ; required the latitude in? 3. In north latitude, I observed the altitude of Menkar in Cetus to be 60°, and that of Algenih in Pegasus 35° ; what was the latitude of the place of observation ? 4. In north latitude, the altitude of Procyon was observed to be 40°, and that of Bellatrix in Orion, at the same time, was 64° ; required the latitude of the place of observation ? PROBLEM XXII. Two stars being given, the one on the meridian and the other on the eastern or western edge of the horizon, to find the latitude of the place. RULE. Bring the star which was observed to be on the meri- dian, to the brass meridian ; keep the globe from revolv- ing on its axis, and elevate or depress the pole till the entre of the other given star coincides with the eastern or western edge of the horizon ; then the elevation of the pole will show the latitude. EXAMPLES. 1. When Lyra was on the meridian, j8 in Leo was settino- ; required the latitude ? Ans. 35° N. THE CELESTIAL GLOBE. 297 2. When Markah in Pegasus was on the meridian, Gastor was rising ; required tlie lalitLide ? 3. Wlien Arcturus was on tlie meridian, Procyon was set- ting ; required the latitude ? 4. In wliat latitude is /3 in Leo rising, when Aldebaran is on the meridian ? PROBLEM XXIII. The latitude of a place, the day of the month, and two stars that have the same azimuth, being given, to find the hour of the night, and the common azimuth. Elevate the pole for 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 for the given day to the brass meridian, and set the index of the hour circle to 12 ; turn the globe westward on its axis, till the two given stars coincide with the graduated edge of the quadrant of altitude ; the hours passed over by the index will show the time from noon, and the degree of the ho- rizon, intersected by the quadrant, will show the common azimuth. EXAMPLES. 1. At what hour at Philadelphia, on the 10th of May, will Arcturus, and /3 in Libra, have the same azimuth, and what will that azimuth be ? Ans. At 10 o'clock in the evening, and the azimuth will be 36° from the south towards the east. 2. At what hour at Paris, on the 16th of August, willZyra and Altair Ixave the same azimuth, and what will that azi- muth be ? 3. On the Vth of September, what is the hour at "Washing- ton, when Deneh in Cygnus, and Oem.ma have the same azi- muth, and what is the azimuth ? 4. On the 19th of May, what is the hour at London, when Buhhe and Capella have the same azimuth, and what is the azimuth ? 13* 298 PROBLEMS PERFORMED BY PROBLEM XXIV. The latitude of a place, the day of the month, and two stars that have the same altitude, being given, to find the hour of the night. RULE. Elevate the pole for 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 for the given day to the brass meridian, and set the index of the hour circle to 12; turn the globe westward on its axis till the two given stars coincide with the given altitude on the fraduated edge of the quadrant ; the hours passed over y the index will show the time from noon when the two stars have that altitude. EXAMPLES. *. 1. At what hour at New- York, on the 22d of August, will Duhhe and Arcturus have each 24° of altitude ? Ans. At 9 o'clock in the evening. 2. At what hour at Washington, on the 17th of February, will Aldeharan in Taurus, and Betelguese in Orion, have each 58° of altitude? 3. At what hour at Dublin, on the 22d of December, will Procyon and Alioth have each 28° of altitude ? 4. At what hour at London, on the 16th of November, will Algenih in Pegasus, and Algol in Perseus, have each 5li° of al- titude ? PROBLEM XXV. To find on what day of the year, any given star passes the meridian of any place, at any given hour. RULE. Bring the given star to the brass meridian, and set the index of the hour circle to 12 ; then, if the given time he THE CELESTIAL GLOBE. 299 before noon, turn the globe westward on its axis, 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 eastward on its axis, till the index has passed over as many hours as the time is past noon ; then, the degree of the ecliptic cut by the brass meridian, will show on the horizon the day of the month required. EXAMPLES. 1. On what day of the month does Arcturus come to the meridian of Philadelphia, at 9 o'clock in the evening ? Ans. On the Ith of June. 2. On what day of the month, and in what month, does Altair come to the meridian of Washington, at 3 o'clock in the morning ? 3. On what day of the month, and in what month does Sirius come to the meridian of Baltimore, at midnight ? 4. On what day of the month, and in what month does Procycm come to the meridian of Greenwich, at noon ?* PROBLEM XXVI. The day of the month and hour of the night or morn- ing at any place being given, to find what planets will he visible at that hour. KULE. Elevate the pole for the latitude of the place, bring the sun's place in the ecliptic for the given day 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 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 * When the given star comes to the meridian at noon, the sun's placo will be found under the brass meridian, without turning the globe. 300 PROBLEMS PERFORMED BY has passed. over as many hours as the time is past noon ; keep the globe from revolving on its axis, find the planets' places on the globe (by Prob. III. or IV.) and if any of their places be above the horizon, such planets will be visible at the given time and place. EXAMPLES. 1. On the 28th of October, 18t8, the right ascension of Venus, by the Nautical'Almanac, was 15 hours 54 minutes, H seconds, and declination 20° 56' 33" S., was she visible at Washington at 6 o'clock in the evening ? Ans. Venus was a little above the western edge of the hori- zon, nearly in conjunction with j8 Scorpii. 2. On the 31st of December, 1848, the right ascensions and declinations of the planets were as follows ; were any of them visible at New- York, at 9 o'clock in the evening ? RIGHT ASCBN. DECLIN. RIGHT ASCEN. DECIIN. S 18h. 22m.24s. 24° 45' 30" S. ? 21 29 10 16 46 43 S. J 17 17 23 41 S. D's 23 39 29 3 9 52 S. at midnight. PROBLEM XXVII. V Qh. 37to. 24s. 15° 8'23"K '?23 26 18 5 58 58 S. VI 8 40 6 37 49 N. 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, on any given day, at any given place. RULE. Elevate the pole for the latitude of the place ; then, if Venus be a morning star, bring the sun's place in the * When Venus' longitude is less than the sun's longitude, she rises before him in the morning, and is then called a morning star ; but when her longitude is greater than the sun's longitude, she shines in the evening after liim, and is then called an evening star. THE CELESTIAL GLOBE. 301 ecliptic for the given day to the eastern edge of the hori- zon, and set the index of the hour circle to 12 ; turn the globe eastward on its axis till the place of Venus on the globe for the given day (found by Prob. III. orlV.) comes to the eastern edge of the horizon, and the hours passed over by the index will show how long Venus rises before the sun. But, if Venus be an evening star, bring the sun's place to the western edge of the horizon, and set the index to 12 ; turn the globe westward on its axis till the place of Venus on the globe, comes to the western edge of the horizon, and the hours passed over by the index will show how long Venus sets after the sun. Note. — The same rule will serve for Jupiter or Saturn, by finding his place on the globe instead of that of Venus. EXAMPLES. On the 11th of December, 1848, the right ascension of Venus was 19 hours 49 minutes 17 seconds, and declination 23° 4' 55" S. ; was she an evening star, and if so, how long did she shine after the sun set at Washington ? Ans. Venus shone 2 hours and 30 minutes after the sun set. 2. On the 15th of May, 1848, the longitude of Venus was 36° 15', and latitude 1° 24' S., and of course a morning star ; how long did she rise before the sun at Paris ? 3. On the 1st of October, 1848, -the right ascension of Jupi- ter was 9 hours 14 minutes 31 seconds, and dechnation 16° 36' N., was he a morning star, and if so, how long did he rise before the sun at Philadelphia ? 4. On the 18th of April, 1848, the right ascension of Jupi- ter was 6 hours 58 minutes 3 seconds, and declination 23° 1' 1" N., was he an evening star, and if so, how long did he shine after the sun set at Baltimore ? 5. On the 1st of May, 1848, the right ascension of Saturn was 23 hours 33 minutes 25 seconds, and declination 4° 57' 42" S. ; was he a morning or an evening star ? If a morning star, how long did he rise before the sun at New- York ; but if an evening star, how long did he shine after the sun set ? 302 PROBLEMS PERFORMED BY PROBLEM XXVIII. To find what stars the moon can eclipse, or make a near approach to, or what stars lie in or near her path. RULE. Find the moon's longitude and latitude, or her right ascension and declination, for several days together, in the Nautical Almanac, and mark her places on the globe ; (by Prob. III. or IV.) then lay the quadrant of altitude over these places, and you will see the moon's orbit, con- sequently, what stars lie in or near her path. EXAMPLES. 1. What stars were in or near the moon's path on the 21st, 22d, 23d, 24th, 25th, and 26th of August, 1848? her right ascensions and declinations, at midnight, on these days, being as follows : EIGHT ASCEN. DECLINATION. 21st, 4A.9m. \s. 15° 56' 22" N. 22d, 5 7 16 17 38 53 N. 23d, 6 5 42 18 16 35 N. EIGHT ASCEN. DECLINATION. 24th, Ih. 3m. 32s. 17° 48' 34" N. 25th, 8 1 16 19 13 N. 26th, 8 54 37 13 57 17 N. Ans. The stars will he found to be « Tauri, y Geminorum, X Geminorum, &c. 2. On the 16th, l'7th, 18th, 19th, 20th, and 21st of Decem- ber, 1848, what stars lay in or near the moon's path? her right ascensions and declinations at midnight, on these days being as follows : BIGHT ASCEN. BECLINATION, 16th, 11A.23ot.22s. 4° 19' 25" N. 17th, 12 10 39 23 31 N. 18lh, 12 56 49 3 28 10 S. EIGHT ASCEN. DECLINATION. 19th, 13A.42ot.37s. 7° 7' 68'' S 20th, 14 28 38 10 28 54 S 21st, 15 15 24 13 24 7 S THE CELESTIAL GLOBE. 303 PROBLEM XXIX. The day of the month being given, to find all those places on the earth to which the moon will be nearly vertical on that day. Find the moon's declination in the Nautical Almanac for the given day, and observe whether it be north or south ; then, (by the terrestrial globe,) mark the moon's declination on that part of the brass meridian which is numbered from the equator towards the poles ; turn the globe eastward on its axis, and all places that come under the above mark, will have the moon nearly* verti- cal on the given day. EXAMPLES. 1. On the 10th of December, 1848, the moon's declination at midnight was 18° 291 N., over what places on the earth did she pass nearly vertical ? Arts. The moon was nearly vertical at Port au Prince, Tim- buctoo, Bombay, &c. 2. On the 27th of October, 1848, the moon's declination at midnight, was 12° 12' S., over what places did she pass nearly vertical ? 3. To what places of the earth will the moon be vertical, when she has the greatestf north declination ? 4. To what places of the earth will the moon be vertical, when she has the greatest south declination ? * On account of the swift naotion of the moon in her orbit, and conse- quently, a considerable increase or decrease of declination in the course of 24 hours, the solution will differ materially from the truth. ] When the moons ascending node is in Aries, she will have the great- est north and south declination ; for her orbit making an angle of about 6i° with the ecliptic, her greatest declination will be 5^° more than the greatest declination of the sun. 304 PROBLEMS PERFORMED BY PROBLEM XXX. To find the time of the moon's southing, or coming to the meridian of any place, on any gfven day. RULE. Elevate the pole for the latitude of the place, find the moon's longitude and latitude, or her right ascension and declination, in the Nautical Almanac, for the given day, and mark her place on the globe ; bring the sun's place in the ecliptic for the given day to the brass meridian, and set the index of the hour circle to 12 ; turn the globe westward oil its axis 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 comes to the meridian of the place. Or, correctly, without the globe. Take the difference between the sun and moon's increase of right ascension in 24 hours ; then, as 24 hours less this difference, are to 24 hours, so is the moon's right ascension at noon less* the sun's right ascension at the same instant, to the time of the moon's passage over the meridian. EXAMPLES. 1. At what hour on the 14th of June, 1848, did the moon pass over the meridian of Greenwich, her right ascension at noon being 15 hours 42 minutes 4 seconds, and her declination 15° 13' S. Ans. By the globe the moon came to the meridian at 10 minutes past 10 o'clock in the evening. , By Calculation. Sun's right ascension at noon, 14th June, 5 A. 31 to. S3s. " 16th " 5 35 42 ' Increase in 24 hours, - - 4m. 9s. * If the eun'8 right ascension be greater than the moon's, 24 hours must be added to the moon's right ascension before you subtract. THE CKLKSTIAL GLOBE. 305 Moon's right ascension at noon, 14tli June, I5h. 42m. 4s. " 15th " 16 31 40 Increase in 24 hours, ... 49m. 3Qs. Hence 49m. 36s. — 4m. 9s. = 45m. 27s., the excess of the moon's motion in right ascension above the sun's in 24 hours. Then 24/i. — 45m. 27s. : 24h. : : ISA. 42m. 4s. — 5/t. 31ot. 33s. : lOA. 30m., the true time of the moon's passage over the meridian, agreeing with the Nautical Almanac. 2. At vfhat hour, on the 16th of October, 1848, did the moon pass over the meridian of Greenwich ; her right ascen- sion at midnight being 5 hours 36 minutes, and her declination 18° 8' N.? 3. At what hour on the 1st of September, 1848, did the moon pass over the meridian of Greenwich ; her right ascen- sion at noon, being 13 hours 23 minutes 10 seconds, and decli- nation 5° 55' S? 4. At xhat hour, on the 6th of December, 1848, did the moon pass over the meridian of Greenwich ; her right ascen- sion at noon being 1 hour 12 minutes 56 seconds, and declina- tion 4° 54' N. ? 306 MISCELLAXFOUS EXAMFLBI). CHAPTER III. MISCELLANEOUS EXAMPLES EXERCISING THE PROBLEMS ON THE GLOBES. 1. Whbn it is 8 o'clock in the morning ai Paris, what is the hour at Washington ? 2. What is the sun's longitude and declination on the l^th of January? 3. How many miles make a degree of longitude in the lati- tude of Philadelphia ? 4. When the sun is on the meridian of Philadelphia, what places have midnight ? 5. What is the angle of position between London and Rome ? 6. On what point of a compass must a ship steer from Cape Henry to Cape Clear ? 7. What places of the earth have the sun vertical on the 13th of April?, 8. What places of the earth are in perpetual darkness on the 18th of December ? and how far does the sun shine over the south pole ? 9. Where does the sun begin to shine constantly without setting on the 9 th of May, and in what latitude is he beginning to be totally absent ? 10. On what two days of the year will the sun be vertical at Bencoolen ? 11. What is the length of the longest day at Washington ? 12. What day of the year is of the same length as the 12th of May ? 13. In what latitude does the sun set at 11 o'clock on the 1st of June ? 14. How many days in the year does the sun rise and set in latitude 78° N. ? 15. On what two days of the year at Philadelphia, is the time of the sun's rising to the time of his setting in the direct ratio of 4 to 3 ? MISCELLANEOUS EXAMP1E3. 307 16. What day following the 4th of July is one hour shorter than it, at Baltimore ? 17. What is the equation of time! dependent on the obliquity of the ecliptic on the 1st of August? 18. On what day of the year is the meridian altitude of the Bun at Washington equal to 45° ? 1 9. At what hour will the sun be due east at Philadelphia on the 25th of May ? 20. Being at sea on the 14th of June, I found the sun's set- ting amplitude to be 29° from the west tovrards the north ; re- quired the latitude the ship was in ? 21. At what hour in the afternoon on the 2d of August, is the length of the shadow of any object at Washington equal to its heigiit ? 22. What is the sun's azimuth at New- York on the 30th of April, at 8 o'clock in the morning ? 23. Required the duration of twilight at the north pole ? 24. When the sun is setting to the inhabitants of Baltimore, to what inhabitants of the earth is he then rising ? 25. What inhabitants of the earth have the greatest portion of moon light ? 26. Required the latitude and longitude of Dubhe, in the back of the Great Bear ? 27. What is the altitude of the north polar star at Mexico ? 28. What is the hour at Paris, when a cane placed perpen- dicular to the horizon of Philadelphia on the 10th of June in the afternoon, casts a shadow equal to the length of the cane ? 29. On the 1st of May, 1848, the geocentric longitude of Venus was 19° 10', and latitude 1° 35' S. ; was she a morning or an evening star ? If a morning star, how long did she rise before the sun at Washington ; but if an evening star, how long did she shine after the sun set ? 30. What inhabitants of the earth have no shadow on the I7th of May, when it is 40 minutes past 1 o'clock in the after- noon, at Philadelphia ? 31. In what latitude is the meridian altitude of Procycn 57° above the south point of the horizon ? 32. Being at sea in north latitude on the 5th of June, I ob- served the altitude of Lyra to be 49°, and that of Altair 21° ; required the latitude in, and the hour of the night ? 33. What stars never set at Washington, and what stars never rise at the same place ? 308 MISCELLANEOUS EXAMPL-ES. 34. How far northward must a person travel from Baltimore to lose sight of Sirius ? 35. On what day of the month, and in what month, will the pointers* of the Great Bear be on the meridian of Washington at 10 o'clock in the evening ? 36. When Lyra was on the meridian, I observed that Spica in Virgo was setting ; required the latitude of the place of ob- servation ? 37. What is the sun's greatest meridian altitude at Paris ? ^ 38. What stars rise achronically at Washington, on the 11th of February ? 39. What stars rise cosmically at Dublin, on the 2nd of May? 40. What stars set heliacally at London, on the 4th of July ? 41. What stars set cosmically at Baltimore, on the 9th of October ? 42. On what day of the year does Aldeharan rise achroni- cally at Washington ? 43. On what day of the year does Procyon begin to be visi- ble in the evening at Washington ? 44. On what day of the year does Sirius cease to appear in the evening at Baltimore ? 45. At what time of the year does Bellatrix rise with the sun at New- York ? 46. At what time of the year does Sirius become visible in the morning at Washington, after having been so near the sun as to be hid by the splendor of his rays ? 47. At what time of the year does Arcturus first become invisible in the evening at Washington, on account of its near- ness to the sun ? 48. How long does /3 in Leo continue above the horizon, during one revolution of the earth on its axis, at Baltimore ? 49. What is the distance in degrees between Regulus and Dubhe ? 50. What are the sun's right ascension, oblique ascension, oblique descension, ascensional or descensional difference, rising * The two stars, marked « and /3 in the Great Bear, are called the pointers, because a line drawn through them, points to the polar star in the Little Boar ; consequently they will both be on the meridian at the eaUiC time. MISCELLANEOUS EXAMPLES. 309 amplitude, setting amplitude, and the time of his rising and setting at Washington, on the 21st of June? 51. Hequired the Antoeci of New- York ? 62. Required the Perioeci of Washington ? 53. Required the Antipodes of 0-why-hee ? 54. Required the time of the moon's passage over the meri- dian of Greenwich, on the 31st of August, 1848; her right ascension being 12 hours 36 minutes 61 seconds, and declina- tion 2° 13' S. ? 65. There is a place in latitude 19° 26' N. which is 1110 geographical miles from Philadelphia, and -west of it; required that place ? 66. At what rate per hour are the inhabitants of Baltimore carried by the revolution of the earth on its axis from west to east ? 57. What inhabitants of the earth have the days and nights always of equal length ? 58. What is the length of the longest day in latitude 15° N. ? 59. In what latitude north, is the length of the longest day 100 days? 60. On what day of the year does the sun set without rising for several revolutions of the earth on its axis, in latitude '73° N.? 61. How manv days in the year does the sun rise and set in latitude 81° N. ?' 62. At what time does day break at Dubhn, on the morning of the 1st of May ? 63. What star has 11 signs 1° 15' of longitude, and 21° 6' S. latitude ? 64. Being at sea in north latitude, I observed the altitudo of Capella to be 37° 20', and that of Castor at the same time, t>S° 30' ; required the latitude in ? 65. Describe a horizontal dial for the latitude of New- York ? 66. In what climate is Edinburg, and what other places are situated in the same climate ? 67. What is the sun's altitude at Washington on the 31st of August, when the sun is setting at London ? 63. Desciibe a vertical dial, facing the south, for the latitude of Washington. 69. In what latitude is the meridian altitude of Cor Hydra; 55° above the south point of the horizon ? 70. Required the oblique ascension and de.'icension of /3 in Leo, and its rising and setting amplitude, at Washington ? 310 MISCELLANEOUS EXAMPLES. 71.- What is the breadth of the 10 th north climate, and wliat places are situated within it ? 72. What is the breadth of the 27th climate, or the 3d within the polar circles ? i 7-3. On the 7th of June, 1848, the sun's meridian altitude was observed to be 81° 20' north of the observer ; required the latitude ? 74. On the 24th of April, in the afternoon, the sun's altitude was observed to be 58° 25', and after 2f hours had elapsed, his altitude was 29° 10' ; required the latitude, supposing it to be north ? 75. Required the right ascension and declination of /3 in Le- pus ? 76. On the 25th of November, when it is 9 o'clock in the evening at Washington, what stars are culminating ? 77. On the 1st of May, 1848, the right ascension of Jupiter was 7 hours 5 minutes 55 seconds, and his declination 22° 56' N., was he a morning or an evening star ? If a morning star, how long did he rise before the sun at Washington ; but, if an evening star, how long did he shine after the sun set ? 78. What is the meridian altitude of Bigel in the left foot of Orion, at Washington ? 79. On what point of the compass does Arcturus bear at Washington, on the 21st of March, at 9 o'clock in the evening; and what is its altitude ? 80. At London, on the 18th of October, the star Capella was observed to be 31° above the horizon, and east of the me- ridian ; what was the hour at Washington at that time ? 81. At what hour of the night at Washington, on the 15th of March, did Regulus bear S. E. by E. ? 82. At what hour at Washington, on the 7th of December, will Castor and Capella have the same azimuth ? 83. What inhabitants of the earth have noon, when day breaks at Washington, on the I7th of January? 84. At what hour at Washington, on the 8th of January, will Rigcl and Pollux, have each 38° of altitude ? 85. On the 10th of March, 1848, the moon's declination at midnight was 16° 28' N., over what places on the earth did she pass nearly vertical ? 86. In what latitude does the sun begin to shine constantly without setting, when the inhabitants of Mexico have no shadow at noon ? MISCELLANEOUS EXAMPLES. 3l 1 87. When the inhabitants of London begin to have constant day or twilight, what stars rise heliacally at Washington ? 88. When the sun is on the meridian at Washington, at the time of the vernal equinox, what stars are rising at Canton ? 89. When the sun sets without rising for several revolutions of the earth on its axis, at the North Cape, at what time does day break at Washington ? 90. Are the clocks of Paris faster or slower than those at Washington, and how much ? 91. What inhabitants of the earth have the sun vertical, when the Pleiades come to the meridian of Ispahan, at 8 o'clock in the evening ? 92. What is the moon's longitude when new moon happens on the 24th of November ? 93. What is the moon's longitude, when full moon happens on the 11th of September? 94. In what latitude is the length of the Ipngest day, to the length of the shortest, in the ratio of two to one ? 95. What is the length of the longest night, where the sun's least meridian altitude is 10° ? I 96. What is the length of the longest day, where the sun's greatest meridian altitude is' 62° ? 97. What is the altitude of the sun at Washington, when he is due west on the 10th of June ? 98. At what hour does the sun rise at Washington, when constant day or twilight begins at Edinburg ? 99. When Aldeharan rises with the sun at Washington, at what hour will Altair culminate at London ? 100. Calculate the true time of the moon's passage over the mei'idian of Greenwich, on the 6th of December, IS '8. The moon's right ascension at noon on the 6th of Decomber was 1 hour 12 minutes 56 seconds, and on the 7th, at noon, it was 2 hours 9 minutes 18 seconds. The sun's right ascension at noon, on the 6th of December, was 16 hours 62 minutes 59 seconds, and on the 7 th, at noon, it was 16 hours 7 minutes 22 seconds. 101. What is the length of the longest day at all ]:laces situ- ated on the Arctic circle ? 102. How many degrees must a person travel southward from Baltimore, that the north polar star may decrease 10° in allitude ? 81» THE LATITtTDES AND CHAPTER IV. A TABLE OP THE LATITUDES AND LONGITUDES 01' SOME OF THE PRINCIPAL PLACES IN THE WORLD. The Longitudes are reckoned from the meridian of Greenwich Observatory. Names of Placet. Aberdeen, Abo, Acapulco, Achen, Adrianople, Albany, Aleppo, Alexandretta, Alexandria, Alexandria, Algiers, Alicant, Amboy, Amiens, Amsterdam, Annapolis, Antigua I., Antiooh, Archangel, Ascension I., Athens, St. Augustine, Babylon, (anc.) Bagdad, Baltimore, Barcelona, Basil or Basle, Batavia, Bavonne, Belfast, Belgrade, Bencoolen, Bergen, Beriid, Cmmtry or Sea. Latitudes. Zongitudes. Scotland, 57° 9'N. 2° s'W. Sweden, 60 27 K 22 13 E. Mexico, 17 10 N. 101 26 W. Sumatra 1, 5 22 N. 96 86 E. Turkey, 41 10 N. 26 28 E. New-York, 42 89 N. 73 46 W. Syria, 86 11 N. 87 10 E. Syria, 86 35 W. 86 15 E. Egypt, 81 12 N. 29 56 E. Virginia, 88 45 N. 77 16 W. Africa, 36 49 N. 2 12 E. Spain, 88 21 N. 80 "W. New-Jersey, 40 33 W. 74 20 "W. France, 49 54 N. 2 18 E. Holland, 52 22 N. 4 53 E. Maryland, 39 2 N. 76 45 "W Caribbean Sea, 17 4 N. 62 9 W. Syria, 85 56 N. 86 15 E. Eussia, 64 84 N. 88 55 E. South Atlantic,- 7 66 S. 14 21 W. Turkey, Europe, 38 5 K 23 52 E East Florida, 29 58 N. 61 40 "W. Syria, S3 W. 42 46 E. Syria, 83 20 N. 44 23 E. Maryland, 39 17 N. 76 39 W. Spain, 41 26 N. 2 12 E. Switzerland, 47 34 N. 7 86 E. Java 1, 6 11 S. 106 52 E. France, 43 29 N. 1 29 W. Ireland, 54 48 N. 5 51 W. Turkey, E., 45 N. 21 20 B. Sumatra, 3 49 S. 102 3 E. Norway, 60 24 N. 5 18 B. Germany, 52 32" N. 13 23 £. LONGITUDES OF PLACES. 313 Names of Places. Country or Sea. Latitudes. Longitudei. Bsrmudas I. N. Atlantic, 32' ' 36' N. 640 28' W. Berne, Switzerland, ' 46 57 N. 7 26 K Bilboa, Spain, 43 26 N. 2 47 W. Bologna, Italy, 44 30 N. 11 21 E. Bologne, France, 50 43 N. 1 36 E. Bombay I., India, E. 18 66 N. 72 54 E. Boston, Massachusetts, 42 23 N. 71 OW. Botany Bay, New-HoUand, 84 S. 151 20 E. Bourbon, I. K., Indian Ocean, 20 51 S. 56 30 E. Bordeaux, France, 44 50 N. 86 W. Bremen, Germany, 63 6 N. 8 49 E. Brest, France, 48 28 N. 4 80 E. Bristol, England, 51 28 N. 2 35 W. Brunswick, Germany, 62 25 N. 10 81 E. Brunswick, Maine, 43 62 N. 69 59 W. Brunswick, New-Jersey, Netherlands, 89 39 N. 74 18 W. Brussels, 50 61 N. 4 21 E. Buenos Ayres, South America, 84 36 S. 68 22 W. Cadiz, Spain, 36 81 N. 6 17 "W. Cagliari, Sardinia I., 39 26 N. 9 88 E. Cairo, Egypt, 30 8 N. 81 17 E. Calais, France, 60 67 N. 1 50 E. Calcutta, Bengal, 22 36 N. 88 28 E. Cambridge, England, 52 13 N. 5 K Cambridge, Massachusetts, 42 28 N. 71 1W. Canary L, Canary Islands, 28 13 N. 15 89 W. Candi, Ceylon, 1 46 N. 80 46 E. Candia, Candy L, 86 19 N. 25 18 E. Canton, China, 23 7 N. 113 16 K Oape Clear, Ireland, 61 18 N. 9 80 W. " Finisterre, Spain, 42 53 N. 9 18 W. " St. Vincent, Portugal, 87 2 N. 9 2 W. " Blanco, Africa, 20 66 N. 17 low. " Verd, " 14 47 N. 17 83 W, " Siera Leon, " 8 80 N. 13 9 W. " Good Hope, " 34 29 S. 18 28 £. " Comorin, Hindoostan, 8 4 N. 77 34 E. « Cod,(Ught,) Massachusetts, 42 5 N. 70 14 W. " Charles, Virginia, 37 12 N. 76 9 W. " Hatteras, North Carolina, 85 12 N. 75 6W. " Horn, South America, 55 68 S. 67 26 W. " Blanco, Peru, 3 45 8. 83 OW. " Farewell, Greenland, 69 88 N. 42 42 W. " Henry, Virginia, 36 57 N. 76 19 W. " May, New-Jersey, 39 4 N. 74 64 W Carthagena, Spain, 37 37 N. 1 1 W. Carthagena, Terra Firma, 10 26 N. 76 21 TV. Charleston, South Carolina, 32 60 N. 80 1 W. Christiana, Norway, 69 56 N. 10 48 K Conception, South America, U 36 43 S. 7S 6 W. 314 THE LATITUDES AND Names of Places. Country or Sea. Zatitudes. lonffitudei. CoDstaatinople, Turkey, 41° I'N. 28° 55' E. Copenhagen, Denmark, 65 41 K 12 35 B. Corinth, Turkey, 37 64 N. 22 54 E. Cork, Ireland, 61 54 N. 8 28 W. Cracow, Poland, 60 11 N. 19 60 E. Cusco, Peru, 12 25 N. 73 86 W. Damascus, Syria, 83 16 N. 86 20 E. Dardanelles, Turkey, 30 10 N. 26 26 E. St. Domingo, Hispaniola, 18 20 N. 69 46 W. Douglas, Isle of Man, 64 'ZN. 4 38 W. Dover, England, 61 8N. 1 19 E. Dresden, Germany, 61 8N. 13 41 E. Drontheim, Norway, 63 23 N. 10 22 E. Dublin, Ireland, 68 22 N. 6 17 W. East Cape, Xew-Zealand, 37 44 S. 178 68 E. Eddystone light, England, BO 7K 4 25 W. Edinburg, Scotland, 65 67 N. 3 12 W. Exeter, England, 60 44 N. 3 84 W. False Cape, Delaware, 38 38 N. 76 9 W. Fayetteville, Korth Carolina, 86 11 N. 78 50 W. Pez, Africa, 33 81 N. 5 W. Florence, Italy, 48 46 N. 11 2 E. France, I. Indian Ocean, 20 27 N. 57 16 E. Francford on the Main 1, Germany, 60 8N-. 8 35 E. Funchal, Madeira, 32 88 N. 16 66 W. Galway, Ireland, 63 10 N. 10 1 W. Geneva, Switzerland, 46 12 BT. 6 8 E. Genoa, Italy, 44 25 N. . 8 50 E. Georgetown, , St. George's towD^ Columbia District, 38 65 N. 77 14 W. Bermudas I., 32 22 N. 64 83 W. Ghent, Netherlands, 61 3 N. 8 48 E Gibraltar, Spain, 86 6 N. 6 4 W. Glasgow, Scotland, 55 52 N. 4 16 W. Goa, Malabar, 15 28 N. 78 59 E. Gottenburg, Sweden, 57 42 N. 11 67 E. Gottingen, (obs.) Germany, 61 82 N. 9 54 E. Greenwich, " England, 51 28m. Guadaloupe, West-Indies, 15 69 N. 61 59 W. Hague, HoUand, 62 4 N. 4 17 E. HaUfax, Nova Scotia, 44 44 N. 63 36 W. Hamburg, Germany, 53 84 N. 9 54 E. Hanghoo, China, 30 26 N. 120 12 E. Hanover, Germany, 62 22 N. 5 49 K Hartford, Connecticut, 41 60 N. 72 85 W. Havana, Cuba I., 28 12 N. 82 22 W. Havre de Grace, France, 49 29 N. 6 K StHelena, Jamestown, Atlantic, 16 66 S. 6 49 W. Herve/s L, Society Isles, 19 17 S. 158 56 W. Holvhead, Wales, 68 28 N. 4 45 W. FiPgland, 63 48 N. 88 W. LONGITUDES OF PLACES. 315 jVanws of Placet. Country or Sea. Zatitudea. Longitudei. Jackson, (Port) New-Holland, 8S°52' S. 161° 14' E. Jaffa, Syria, 32 5 N. 85 10 E. StJago, Cuba L, 19 66 N. 75 85 W. Ice Cape, Nova Zembla, 76 SO N. 67 30 K Jeddo, Japan I., 86 SO N. 140 K Jersey I, St Aubina, English Channel, 49 13 N. 2 12 W. Jerusalem, Syria, 31 46 N. 85 20 E. St. John's, Newfoundland, 41 32 N. 52 26 "W. Ispahan, Persia, 82 25 N. 62 60 E. Isthmus of Darien joins North and South America, , " Suez joinj 1 Africa to Asia, , Kamtschatka, Siberia, 66 SO N. 161 E. Kilkenny, Ireland, 52 87 N. 7 15 W. Kingston, Jamaica L, 18 15 N. 76 44 W. Kinsale, Ireland, 61 82 N. 8 88 W. Koningsberg, Prussia, 64 43 N. 21 36 E. Lancaster, England, 64 4 N. 2 60 E. Lancaster, Pennsylvania, 40 8 N. 76 20 W. Lands End, TJngland, 50 6 N. 5 54 W. Leghorn, Italy, 43 33 N. 10 16 K Lexington, Kentucky, 87 69 N. 84 46 W. Leyden, United Provincea, 62 8 N. 4 28 E. Lima, ' Peru, 12 2 S. -76 SOW. Limerick, Ireland, 52 33 N. 8 42 W. Lisbon, Portugal, 38 42 N. 9 gw. Liverpool, England, 63 22 N. 2 67 "W. Lizard, « 49 57 N. 6 13 W. London, IC 61 SI N. 6 W. Londonderry, Ireland, 54 69 N. 7 15 "W. Lyons, France, 45 46 N. 4 49 E. Madeira L, Funchal, Atlantic, 82 88 N. 16 56 W. Hadras, India, 13 - 6 N. 80 25 E. Madrid, Spain, 40 25 N. 8 38 W. Majorca I, Mediterranean, 89 86 N. 2 30 E. Malacca, East India, 2 12 N. 102 9 K Malta I, Mediterranean, 85 54 N. 14 28 E. Marietta, Ohio, 89 8 N. 81 saw. Marseilles, France, 43 18 N. 6 22 E. Martinico L, Ft Royal, West Indies, 14 36 N. 61 low. Mecca, Arabia, 21 46 N. 40 16 E. Mexico, North America, 19 26 N. 100 7 W. Milan, Italy, 45 28 N. 9 14 E. Minorca, Port Mahoa Mediterranean, 39 61 N. 3 54 E. Montpelier, France, 43 37 N. 3 52 E. Montreal, Canada, 45 83 N. 73 18 W. Morocco, Barbary, 81 N. 7 4W. Moscow, Russia, 65 45 N. 37 46 K Nankin, China, 32 6 N. 118 46 E. Nantes, Franc% 47 IS N. 1 84 W. Nantucket, Nantucket L, 41 18 N. 70 10 W 316 THE LATITUDES AND Names 6f Plouies. Country or Sea. JiatHudet. Zonffitndet. Naples, Italy, 40°60'N. 14° 17' E. Newcastle, England, 55 3N. 1 SOW. New-Orleans, Louisiana, 29 68 N. 90 6 W. New-York, New-York, 40 42 N. 74 1 W. Niagara, H 43 16 N. 79 W. Norfolk, Virginia, 86 66 N. 76 22 W. North Cape, Lapland, 71 SON. 26 49 E. ■Oporto, Portugal, 41 ION. 8 27 W. L'Orient, (Port) Prance, 47 45 N. 3 22 E. Olaheite, South Fm^c Ocean, 17 20 S. 149 80 W. O why-hee, North « " 18 54 N. 165 48 W. Palermo, SicUy L, 38 7N. 13 36 E. Palmyra, Arabia, 88 58 N. 88 42 E. Panama, Mexico, 8 58 N. 80 16 W. Paris, (obsv.) France, 48 60 N. 2 20 E. Pekin, China, 39 64 N. 116 27 K Pensacola, West Florida, 80 SON. .87 10 W. Petersburg, Rnssia, 69 66 N. 30 18 E. Philadelphia, Pennsylvania, 89 67 N. 75 11 W. Pico I, Azores, 88 27 N. 28 28 W. Pittsburg, Pennsylvania, 40 26 N. 80 W. Pondicherry, East India, 11 56 N. 79 52 E. Portland, - Maine, 48 89 N. 70 28 W. Porto Bello, Terra Firma, 9 8SN. 79 60 W. Port Royal, Jamaica, 18 ON. 76 45 W. Portsmouth, England, 60 47 N. 1 6 W. Potosi, Peru, 20 s. 66 16 W. Prague, Bohemia, 50 6N. 14 24 E. Presburg, Hungary, 48 8N. 17 10 E. Quebec, Canada, 46 48 N. 71 6W. Quito, Peru, 13 S. 78 low. Rhodes, Rhodes I., 85 27 N. 28 45 E. Richmond, Virginia, 87 35 N. 77 43 W. Riga, Russia, 66 65 N. 24 E. Rio Janeiro, BrazU, 22 64 S. 42 44 W. Rochelle, France, 46 9N. ^ 1 low. Rochester, England, 51 26 N. 30 E. Rome, (St. Peters,) Italy, 41 54 N. 12 28 E. Rotterdam, XJnited Provinces, 61 56 N. 4 28 E. Rouen, France, 49 27 N. 1 6 W. Salonica, Turkey, 40 41- N. 28 7 K Samarcand, West Tartary, 89 85 N. 64 20 E. Santa Cruz, Teneriffe I., 28 89 N. 16 22 W. Santa Fe, Ne-w-Mexico, 86 64 N. 104 30 W Savannah, Georgia, 82 4N. 81 11 W. Siam, East India, 14 18 N. 100 49 E. Smyrna, Natolia, 88 28 N. 27 7 E. Stockholm, Sweden, 69 21 N. 18 4 E. Suez, Egypt, South America, 29 50 N. 83 27 E. Surinam, 6 SON. 65 SOW LONGITUDES OF PLACES. 317 Names of Places. Country or Sea. Jjatitudes. Longjtudea. Syracuse, Sicily I., 86'^ '53'N. 15° 17' E. Teneriffe Peak, Canary I, 28 15 N. 16 46 W. Tobolsk, Siberia, 58 12 N. 68 19 K Tornca, Lapland, 65 51 N. 24 14 E. Toulon, France, 43 7N. 5 65 E. Toulouse, " 43 46 If. 1 26 E. Trent, Germany, 46 5N. 11 6 E. Trenton, New-Jersey, 40 13 N. 74 50 W. Trincomale, Ceylon I., 8 33 K 81 21 K Tripoli, Barbary, 32 54 N. 13 20 E. Tunis, " 36 16 N. 10 40 E. Turin, Italy, 45 5N. 7 39 E. TJpsal, Sweden, 59 52 W. 17 43 E. Utretcht, United Provinces, 52 5N. 6 9 P* Venice, Italy, 45 27 N. 12 4 E. Vera Cruz, Mexico, 19 ION. 97 20 W. Versailles, France, 48 48 N. 2 7 E. Vienna, (obs.) Austria, 48 12 N. ' 16 22 E. Warsaw, Poland, 62 16 N. 21 3 E. Washington, (obs.) Korth America, 88 53 N. 77 2 W. Waterford, Ireland, 52 12 N. 7 6 W. Wexford, " 52 22 N. 6 SO W. Wjburg, Russia, 60 55 N. 30 20 E. Tork, England, 58 69 N. 1 7 W. Torktown, Virginia, 37 14 N. 76 86 W. Zurich, Switzerland, 47 22 N. 8 S3 E, Zutphen, United Provinces, 52 12 N. C 16 E. INDEX. Abeeeation of light 110-151 Theory of 161, 152 Amount of 152, 163 Achronical rising and setting of the stars 30 Prob. Till, and IX., relating to the 282-284 Almacanters 27 Alphabet, the Greek 138 Altitude 27 of the sun at any hour, Pr.XLI. 253 of the eun, by placing the globe in the sunshhie, Prob. LVII. 269 of a star, Prob. XVI 291 of a star, determined bv its azimuth, Prob. XVIIlI ... 293 Amplitude 28 of the sun, Prob. XLTV 257 of the stars, Prob. XIII 288 Angle of position 28 between two places, Pr. XII. 199 Angular velocity 41 Annular eclipses 157 greatest breadth of, at the earth's surface 3 58 Antarctic circle 23 Antipodes 34 of places, Prob. XIII 201 Antoeci 34 of places, Prob. XIII 201 Aphelion point 40 Apogean point 41 tides 183 Apparent place of a celestial body 62 Arctic circle 23 Ascensional difiference . , 25 to find, Prob. L 26S Artificial globes 14 Aspect of the sun, moon, and planets 29 Asteroids 100 Astrcea 102 astronomical sign of 102 Astronomy, descriptive, physi- cal and practical 34 Atmosphere, height of ...... . 61 Attraction of gravitation 42 Axis of the heavens 15 of the earth 16 Azimuth circles 21 of a heavenly body 27 found by Prob. XVL 291 determined by its altitude, Prob.XVn. 292 of the sun, found by Prob. XLV. and XLVI. 258, 259 found by placing the globe in the sunshine, Prob. LVIIl 270 Bayer's characters 137 Bearing, to find, Prob. XI. 198 Biela's comet 130 Binary stars 142 systems 142 Bissextile 177 Bode's law of the planetary dis- tances 122 Brass meridian 19 Calendar 176 Julian 177 Gregorian, and its adoption, 177, 178 Cardinal points of the ecliptic . . 23 320 INDEX. Page Cardinal points of the heaTens 21 of the horizon 21 Celestial globe 15 placed 80 as to represent the heavens, Prob. V 279 Celestial meridians 18 Centrifugal forces 44 Centripetal forces 44 Ceres 101 atronomical sign of 101 Circles of celestial latitude 21 Circumpolar stars 14 Oivil day 32 Climates 33 found for different places, by Prob. XXXVIII 247 breadths of, fomid by Prob. XXXIX 248 Colures 18 Comets 124 parts of 125 distances and dimensions of. . 127 orbits of 126 physical constitution ■of 126 number of 131 Comparative lengths of the days and nights at the different seasons of the year, Pr.XIX. 215 Compass 17 Constant day or twilight, found by Prob. XXXVII 245 Constant day or night, where, by Prob. XXIV 225 when begins and ends, by Prob.XXV 225 Constellations 133 northern 134 southern 136 zodiacal 134 Conic sections 38 Conjugate axis 40 Conjunction 30 Cosmical rising and setting of the stars 30 Prob; VIII. and X., relating to the....- 282-285 CrepuscuKim 50 Culminate 27 Culminating of the stars, Pr. VI. and VII. relating to.. 279-281 Day, apparent solar ' 31 Piig» Day, artificial 32 astronomical 31 civil 32 mean solar 31 of the month, found from its length, Prob. XXXL 236 of the year, found when any given star passes the me- ridian at a given hour, Prob. XXV. 298 following a given day, an hour longer or shorter, Prob.XXXV 242 Days on which the sun rises and sets in the north frigid zone, Prob. XXXIV. 240 Declination circles 18 Declination of a heavenly body 24 Declination of the sun, found by Prob.XVni. 211 found from the length of the day, Prob. XXXI 236 found by placing the globe in the sunshine, Prob. LVIII. 270 Declination of a star, found by Prob. 1 275 given to find the star, Pr. III. 277 Densities of the sun, moon, and planets 46 Descensional difference 25 found by Prob. L 263 Difference of latitude 26 of longitude 26 Dip of tlie horizon 46 Direct motion of the interior planets 73 fiiscs of the heavenly bodies . . 29 Distance between two places, found by Prob. VII 193 between two stars, found by . Prob. XIV. 289' Diurnal arc 80 found by Prob. XII 287 Diurnal motion of the he.ivenly bodies 14 Double stars 141 Earth 76 period and distance of the. . 76 figure of the , 77 diameter of the 78 an oblate spheroid 78 1 M U E X . 321 Page Earth, oblater.esa of the 79 eccentricity of the 79 seasons of the 80 astronomical sign of the. ... 83 as seen from the inoon 89 Earth's inchnation of the axis. . 80 rotation on tlie axis 80 East, the part of the heavens called 13 East point 21 Eccentricity of the ellipse .... 40 of the earth 79 of the earth's orbit 77 of the moon's orbit 92 of Mercury's orbit 65 of the orbit, of Venus 68. of tlie orbit of Mars 98 of the orbits of the .Asteroids, Jupiter, Saturn, Uranus, and Neptune 123 Eclipses of the sun and moon. . 153 causes of 153 periiid of 173 number of 173, 174 Ecliptic 19 limits of the sun 158, 159 limits of the moon 170, 171 Elongation 30 of Mercury 74 of Venus 75 Encke's comet 129 Equation of time 31 found by Prob. LI 264 table of the 274 Equator 16 Equinoctial 16 Equinoctial points 20 how found 146, 147 precession of the 33, 147, 148 Establishment of a port 186 Extenor planets 37 Faculje 58 First meridian 19 Fixed stars 14, 131 why so called 132 number of 132 classification of 1 32 three principal regions of the 133 groups of 139 clusfers of 140 annual parallax of the 142 1 Page Fixed stars, distances of the . . 144 Flora , 102 Foci of the ellipse 40 Force of attraction, varies di- rectly as the mass 43 varies inversely as the square of the distance 43 Frigid zones 33 Gambart's comet 130 Geocentric latitudes 27 longitudes 27 Grand celestial period 150 Gravity 42 Great circles 16 Greek alphabet 138 Gregorian calendar 177 adoption of the 178 Halley's comet 128 Harvest moon 94 difference in the time of rising, found by Prob. LIV 267 Heavenly bodies 13 Hebe 102 Heliacal rising and setting of the stars 30 Prob. VIII. and XI. relating to the 282-286 Heliocentiic latitudes and lon- gitudes 27 Higher apsis 41 Horary angles 18 Horizon 16 sensibl e, rational, and wooden 1 7 Hour circle 19 Hour circles 18 Hour of tlie day, found at a given place, from tl)e hour at any other place, Pr.XVI. 206 found by placing the globe in the sunshine, Pr. LVI. . . 269 found when any star or planet rises, culminat(>, or sets, Prob. VII. 281 Hour of the night, found by the altitude of a star, Pr.XVIJ. 292 found bv the azimuth of a star, Prob. XVIII 293 determined when two stars have the same azimuth, Prob. XXlir 297 determined when two stars * 322 INDEX. fagt haye the eame altitude, Prob. XXIV. 298 Inferior meridian 18 Intensity of light, at Mercury . . 65 at Venu3 67 at Mars 98 at Jupiter 104 at Saturn Ill at Uranus 118 Intercalary day. . ; 177 luterior planets 37 Iris 102 Julian calendar 177 Juno 101 astronomical sign of 101 Jupiter 103 period and distance of 103 diameter and magnitude of. . I(i4 inclination of the orbit of . . . 1U4 oblateness of 104 rotation on tlie axis of 104 seasons and days of 105 belts of 105 astronomical sign of 105 satellites of 106 Kepler's laws 37 first law 39 second law 41 thirdlaw 42 Latitude of a heaienly body . . 26 found by Prob. II. 276 Latitude of a place 25 found by Pr. I. and III.. .187, 189 Latitude and longitude of a place given, to find it, Prob. IV. 190 of a star given, to find its place, Prob IV. 278 Latitude, differeace of, Prob. V. 191 of a place and distance from a given place, given, to find it, Prob IX 196 given, to find how many miles make a degree of longitude in it, Prob XIV. 202 found f''om the sun's meridian altitude and dav of the month, Prob. XLIII 265 found from the sun's ampli- tude and day of the month, PiobXLVII 260 found from two observed al- Pagt titudes of the sun, Frob. XLVIII 261 found where the longest day is a certain length, Prob. XXXII. and XXXIIL 237, 239 determined by the hour when a star rises or sets, Pr. XIX. 294 determined by the meridian altitude of a star, Pr. XX. 295 determined by the altitude of two stars, Prob. XXL. . 295 determined by two stars, one on the meridian, and the other in the horizon, Prob. XXII 296 Leap year 177 Least altitude of the sun, Frob. XLII 254 Length of day and night, Prob. XXVII 228 Light, -velocity of, determined by the eclipses of Jupiter's satellites 108 Line of the Apsides 41 Longest day and night in the north frigid zone, Prob. XXIX. and XXX 283, 234 Longitude of a place 26 found by Pr. If. and III, 188, 189 Longitude, difference of, Pr. VI. 192 of a place and distance from another place given, to find it, Pro'o. X 197 determined by the eclipses of Jupiter's satellites 107 at sea, determined by chro- nometers 144 at sea, determined by the lunar method 145 of a heavenly body 28 of the sun, Prob. XVIII 211 of a star, Prob. II 276 of a star or plaaet given, to find its place, Prob. IV. . . 278 Lower apsis 41 Luculi 58 Lunar eclipses 168 computation of 171, 172 quantity of 172 Prob. LIII. relating to 266 Lunar month 85 INDEX. 323 Page Lunation 85 Macuias 58 Major axis 40 Muis 97 period and distance of 97 diameter and magnitude of. . 98 inclination of the orbit of . . . 98 telescopic appearances of . . . 99 astronomical sign of 99 Mercury 62 period and distance of ... . 63 diameter and magnitude of. . 63 inchnation of the orbit and transit of 64 rotation on tlie axis and sea- sons of 65 velocity per hour in the or- bit of 63 astronomical sign of 65 Meridians 18 Meridian altitude of the sun, found by Prob. XL 251 of a star or planet, found by Prob. XV 289 Metis 102 Milky way 138 Minor axis 40 Miscellaneous examples, exer- ci'iing the problems on the globiM 306 Moon 83 siderial and synodic revolu-. tions of ihe 81 distance of the 86 daily motion in lonffilude of tlw ." 86 diameter and magnitude of the 87 phages of tlie 87 new, first quarter, full, last quarter 88 dark part visible of the .... 89 inclination of tlie orbit and nodes of the 90 retrograde motion of the nodes of the 91 same hemisphere always seen of the 91 inclination of the axis, seasons, and days of the 91 librations of the 92 Paga Moon, surface and mountains of the 93 atmosphere of the 94 astronomical sign of the. ... 96 vertical, at what place, Prob. XXIX 303 Moon's distance from some of the principal stars, a means of determining the longi- tude of a ship at sea 145 Moon's southing 27 determined by Prob. XXX.. 304 Multiple _,star3 141 Nadir . . ' . : 20 Natural day 32 Neap tides 183 Nebulae 139 Neptune 120 period and distance of 121 Newtonian theory of gravitation 44 Nocturnal arc 81 Nodes 29 of the orbit of Mercury .... 64 of the orbit of Venus 69 of the orbit of Mars 99 of the orbit of Jupiter 104 of the orbit of Saturn 112 of the orbit of Uranus 118 Northern signs of the zodiac . . 20 North pole of the heavens 14 Nutation 151 Oblique ascension and descen- sion 25 of the sun, found by Prob. L. 263 of a star, found by Pr. Xllf. 288 Oblique sphere 23 position of the, Prob. XX. . . 218 Obliquity of the ecliptic 20 how found 145 Occultations 176 Opposition SO Orbits of the primary and sec- ondary planets 29 Order of the planets 37 Pallas 101 astronomical sign of 102 Parallels of latitude and dech- nation 22 of celesti.al latitude 23 of altitude 27 Parallel sphere 23 324 INDEX. Parallel sphere, position of, Prob. XX 218 Paraltax 52 in aitiiude 63 borizonlal 53, 54 equatorial 53 of the aun and moon 56 of the sun, determined by means of a transit of Venus 72 Penumbra 165 Perigean tides 183 Perii^ee 41 Perihelion point 40 PerioBci 34 of places, found by Pr. XIII. 201 Phenomena of the heavenly bodies 13 Places found at -which the day is a certain length, Prob. XXXIL 237 Planets 14, 28 order of the... 37 visible at a given day and hour, Prob. XXVI 299 Poetical rising and setting' of the stars SO Polar chcles 23 Polar distance 24 Poles 14 Pole star 15 Positions of the sphere. ...... 23 iUustrated by Prob. XX. ... 218 Precession of the equinoxes. . . 33 physical causes of the 150 Primary planets 29 Prime meridian 19 vertical .- 21 Projectile forces 44 Proportional magnitudes of the planets represented to the eye 124 Quadrant of altitude 21 Quadrature 30 Quantities of matter in the feun and planets 44 Quantity of a lunar eclipse ... . 172 of a solar eclipse 167 Radios vector 40 national horizon 17 Kefraction 47 ajnouut and effects of 49 Pagt Relative vav,>i?, of the eun and planeti) 44 Retrogrs.i'.i Motion of the inte- riov nl vjcts 73 Retrogf/,pc oiotion of the pole of fae equinoctial .... 148, 149 Rhumb lines 18 Right ascension 24 of the sun, found by Prob. L. 263 of a star, found by Prob. I-. ■ 275 and declination given, to find the star, Prob. IIL 271 Right sphere 2S il)H.strated by Prob. XX 218 Rings of Saturn US dimensions of the 114 jnclinatio-.) and rotation of the 114 apparent 'brrab of the 114 disappea .anoj of tlie 116 Rising alio i.jUing of the stars, Piob.VI 279 Rotation of the earth on its axLi 80 Prob. XV. relating to the . . 206 of Mercury on its axis 65 of Venus on the axis 68 of the moon on her axi^. ... 91 of Mars on his axis 99 of Jupiter on his axis 104 of Saluni on his axis 112 of the sun on his axis 68 Satellites 29 Satellites of Jupiter 106 period and distance of the. . 106 uiagnitiide.s of the 105 eclipi«es of the 107 Satelli:es of Saturn 11? revolutions and magnitudes of the 113 Satellites of Uranus 118 periods and distances 119 Saturn 110 period and distance of Ill diameter and magnitude ... Ill inclination of the orbit of . . . 112 astronomical sign of. 112 riug^ of 113 Secondary planets 29 Sensible horizon 17 Setting of the stars, Prob. VI. relating U) 279 INDEX. 825 Page Shadow of the earth, length of the 169 semi-diameter of the 170 Shadow of the moon 155 greatest breadth at the earth, 156, \m Siderial day 32 year 32 Signs of the zodiac 20 Small circles 16, 22 Spring tides 182, 183 Solar attraction 43 Solar eclipses 154 different kinds of 160, 161 visibility of 161 duration of 162 computation of 163-167 quantity of 1 67 Prob. LIL relating to 265 Solar spots 57 theory of the 58 Solar year 32 Snistitial points 22 Souih, part of the heavens called 13 South pole of the heavens. ... 15 Soutliern signs 20 Stars, eclipsed by the moon, Pr. XXVUI. relating to 302 proper mdtion of 61 Summer solstice 22 Sun 55 distance of the 56 diameter and magnitude of the 57 rotation on the axis of the . . 58 inclination of the axis of the 60 motion in absolute space of the — astronomical sign of the. ... 62 -daily motion in longitude of the 85 Sun's longitude and declination, foimd by Prob.XVlII.. . . 211 rising and setting, found bv Pr. XXVII. and L.. . .228, 263 declination, found from the length of the day, Prob. XXXI.... 236 meridian al.itude, fcjund by Prob. XL 251 altitude, found at any hour, Prob.XLI 263 Paga Sun's least altitude in the frigid zone, Prob. XLIL 254 ampUtude, found by Prob. XLIV 257 azimuth, found by Pr. XLV. 258 right ascension, oblique ascen- sion, (fee, Prob. L 263 altitude, found by placing the globe in the sunshine, Prob. LVII 269 declination, found by placing the globe in the sunshine, Prob. LVIIl 270 Sun-dials, Prob. LIX. and LX. relating to 271, 272 Superior meridian 18 Superior planets 37 System, Pythagorean 35 Ptolemean 25 Copernican 35 Tychonic 36 Solar 36 Tables, relative to the sun, moon, and planets . . .-; 123 of the constellations 134, 137 showing how many miles make a degree of longitude in every degree of latitude 204 of the sun's declination. .213, 214 of climates 250 of the hour arcs of a horizon- tal and vertical sun-dial, 272, 273 of the equation of time 274 of latitude and longitude of places 312 Telescopic stars 132 Temporary stars 141 Temperate zone 33 Terrestrial globe 14 natural position of the, Pr.LV. 268 Terrestrial equator 16 Terrestrial meridian 18 an ellipse 79 Tides 179 causes of the 179-182 effect of the moon's declina- tion on the 184 motion and lugging of the. 184, 186 height of the 186 326 INDEX. Page Time at which the sun is due east or west, Prob. XLfX. relating to the 262 Torrid zone 33 Transits of Mercury and Venus, their frequency 10 Transverse axis 40 Tropics of Cancer and Capricorn 23 True place of a celestial body . . 52 Twilight 50 Prob. XXXVI. relating to. . 244 Ultra-zodiacal planets 102 Umbra 155 Universal gravitation 43 Uranus -. 117 period and distance of 117 inclination of the orbit of . . . 118 astronomical sign of 118 Variable stars 140 Variation of the compass 18 Venus 66 period and distance of 66 velocity per hour in the orbit 67 diameter and magnitude of. . 67 Pagt Venus, when a morning and an evening star 68 inclination of the orbit and transit of 69 astronomical sign of 76 how long she shines before the sun, when an evening star, and how long she sets after him, when an evening star, Prob. XXVII SOO Vertical circles 21 Vertical sun, Pr.XXL, XXII., and XXVI., relating to, 221, 222, 227 West part of the heavens "1.3 West point 22 Winter solstice 22 Wooden horizon 17 Zenith 21 distance 27 Zodiac 20 Zodiacal light 61 Zones 88 HATIONAL SERIES OF STAKDAED SCHOOL-BOOKa D AVI E S' Complete Course of Mathematics. IBUmmtaxs (ftourse. DAVIES' PRIMARY ARITHMETIC ANT) TABLE-BOOK DATIES' FIRST LESSONS IN ARITHMETIC DaVIKS' INTELLECTUAL ARITHMETIC DAVIES' NEW SCHOOL ARITHMETIC KEY TO DAVIES' NEW SCHOOL ARITHMETIC DAVIES' NEW UNIVERSITY ARITHMETIC KEY TO DAVIES' NEW UNIVERSITY AKITHMETIO DAVIES' GRAMMA=K OF ARITHMETIC DAVIES' NEW ELEMENTARY ALGEBRA KEY TO DAVIES' NEW ELEMENTARY ALGEBRA i>AVIES' ELEMENTARY GEOMETRY AND TRIGONOMETET .... DAVIES' PRACTICAL MATHEMATICS _ 0Dbanc8D Coutse DAVIES' UNIVERSITY ALGEBRA KEY TO DAVIES' UNIVERSITY ALGEBRA DAVIES' BOURDON'S ALGEBRA KEY TO DAVIES' BOURDON'S ALGEBRA DAVIES' LEGEMDBES GEOMETRY DAVIES' ELEMENTS OF SURVEYING.... 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It complete in itself, and contains all that is ncceesary for the general student Also ruceutly issued — ^EvV IStEMSNTA'^Y ALGEBKA, UNlVEE'ilTY AIGEBRA, Formiug, vrl'h the Author's Bourdon's Algebra, a complete and ocoMWUtiT* eoariB. A. S, BARNES & BHRR, Publisher, 51 and Sit John Street. New York. NATIONAL 8EKIES Oj* STANDAED SCHOOL-BOOKS. mOIWTJGlTIl AND IWcNAL.LY'S MONTBITH'S FIRST LESSONS IN QEOGRAPHY MONTEITH'S INTRODUCTION TO MANUAL OF GBOaRAPHY. MONTEITH'S NEW MANUAL OF GEOGRAPHY MaNALLY'S COMPLETE SCHOOL GEOGRAPHY Monteith'8 First Lessons in Geo^aphy— Introduction to Man* aal of GeoRraphy— ftnd New Manual of Geograt>hy, are arranged on the cateclietical plan, which has been proven to be the best and most Rucccasfal method of trnching this branch of study. The quefltJons and answers are models ol brev'ty and adaptation, and the maps are simple, but Accurate and beautiful. McNally's Geography completes the Series, and follows the name geneia) plan. The maps are splendidly eneraved, beautifully colored, and perfectly accurate; and a profile of the country, showing the elevations and depressions of land, is given St the hottoui of the maps. The order and arrangement of map questions is also peculiarly happy and systematic, and the descriptive matter just what is needed, and nothing more. No Series heretofore published has been so extensively introduced in so short a time, or gained such a wide-spread popularity. These Geogrfli)hies are used more extensively in the Public Schools of New York, Brooklyn, and Newark, than all ottiers. ^^ A. B. Clark, Principal of one of the largest Public Schools in Brooklyn, says ** T have used over a thousand copies of Monteith's Manual of Geography since its adoption by the Board of Edii<^ation, and am prepared to say it is the beat wo i ht ,««rH' Aaaootations and Institutes throughout the country, ami are in succeasiW ■mU UQUltituc'a of Public and Private Schools throughout the United Statoa. A. S BAHNES & BbuK, Publishers. 61 & 5? John Stteet, New To RATJONAL SERIES OF STANDARD SCHOOL-BOOKS. rillKEH & WATSON'S RKADING SKKIES. niE NATIONAL ELEMENTARY SPELLER. THE NATIONAL PRONOUNCING SPELLER. 188 pa^es. A full treatise, with words ftrranged and classified accordtnff lo their tow«| sounds, and reading and dictation exercises. rHE NATIONAL SCHOOL PRIMER; or, *' PRIMARY WORD-BinLDER* (Beauti/iillj' Illustrated) THE NATIONAL FIRST READER; or, '"WORD-BUILDER." (Beautifully Illustrated) 118 pages. fHE NATIONAL SECOND READER 224 pages. Ccntaiiilng Primary Exercises in Articulation, Pronunciation, and Punctnation. (Splendidly Illustrated.) THE NATIONAL THIRD READER 288 pages. Containing Exercises in Accent, EmphasiR, Punctuation, &C (Illustrated.) IHE NATIONAL FOURTH READER 405 pages. Ountaining a Course of Instruction in Elocution, Exerciser) in Beading, Declama- tion, &c. THE NATIONAL FIFTH READER 600 pages. With cnpioua JlJotes, and Biographical Sketches of each Writer. These Rbaukbs have been prepared witl^ the greatest care and labor, by Bichabp S Parker, A.M., of Boston, and J. Madison Watson, an experienced Teacher o( New York. No amount of ^abor or expense has been spared to render them as neoi perfect as po^Ible. The Illustrations, which are from original designs, and ch* Ty|)ograpliy. are unrivalled by any similar works. The First Keader, or ** "Word-13uilder," being the first issued, is alrend} In esiiensive nee. It is on a plan entirely new and original, ccnnmencing wich word, of one letter, and building up letter by letter, until sentences are formed The Second, Third, and Fourth Headers follow the same inductiv* plan, with a pi^rfecl and systematic gradation, and a strict classification of snbjects The pronunciHtion and definition of difficult words are given in notes at the botU>ni yf each page. Mnch attention has been paid to ArtiaulaUim and Orthoepy ; am Exercises on the Elementary Sounds and their combinations have been so introdnceo Bs to teach but one element at a time, and to apply this knowledge to immediate use^ nntil the whole is accurately and thoroughly acquired. The Fifth Reader is a full work upon Reading and Elocution loe works a mnny authors, ancient and modern, have bften consulted, and more than a hnndie* Btanilard writers of the English language, on both sides the Atlantic, laid under con bibution to enable the authors to present a collection rich in all that can inform tbi understanding, improve the taste, and cultivate the heart, and whicli, at the sam» time, shall Furnish every variety of style and subject to exemplify the principl*'S • Rhetorical delivery, and form a linished reader and elocutionist^ Classical and liia t*)rlcal allusions, so cr mmon among the best writers, have in all cases been explained «nd concise Biographica*. Sketches of authors from whose works extracts have teftL (elected, have also been introduced, together with Alphabetical and Chroncdogiea L'sts of the Names of Authors; thus rundering this a convenient text-book tbi Stu tents ii! English and Anierican Literature. A. S. BAKNES & BUER, Publishers, 51 & 53 Joim Btreet, New Fork BATIOHAL SERIES OF STAKDAS,D SCHOOL-BOOKS ENGLISH GEAMMAE, BY S. W. CLARK and A. S. WELCH, CONSISTING OF CLAKS'S FIEST LESSONS IN ENGLISH GBAMUAB CLAEK*S NEW ENGLISH GBAMMAE CLARK'S GRAMMATICAL CHART CTJ^K'S ANALYSTS 0? THE ENGLISH LANGUAGE WELCH'S ANALYSIS OF THE ENGLISH SENTENCE A mora Advanced 'Work, designed P,r Higher Glasses in Academies and ]7orm^ SchoolB. By A. 8. Welch, A. M., Principal of tlie State Normal Schoo. Michigan, at Ypsilanti. The ^'irst Xjessons in Grammar are prepared for young pupils, and as «, appropriate introduction to the larger work. The elements of Grammar are her« presented lu a series of gradual oral exercises, and, as far as possible, in plain Baxo» words. Clark's H"ew Gram.mar, it is confidently believed, presents the only truo and successful method of tencliing the science of the English Language. The work i« thoTonghly progressive and practical ; the relations of elements happily iilustratef" wid their analysis thorough and simple. This Grammar has been oflBcially recommended by the Superintendents of Publfo [nstruction of Illinois, Wisconsin, Michigan, and Missouri, and is the Text-boo^ •tdopted in the State Normal Scliools of New York, and other States. Its extenslvi -circulation and universal success is good evidence of its practical worth and super* ority. Fiofeasor F. S. Jbwbi,!*, ofths New York State Normal School, says: "Clark's System of Grammar is worthy of the marked attention of the friends cl Kducation. Its points of excellence are of the most decided character, and will qc4 soon be surpassed." '' " Let any clear-headed, independent-minded teacher master the system, and theu give it a fair trial, and there will be no doubt as to his testimony/' _ "Welcli's Analysis of the llnglish Sentence.— The prominent featnret of this work have been presented by Lectures to numerous Teachers' Institutes, and ananiinously approved. The classification, founded upon the fact that there are hui three elements In the language, i» very simple, and. in many respects, new. T!i* method of disposing of connectives is entirely so. The author has endeavored -» study the language Oi it is, and to analyze it without the aid of antiquated rules. This work is high'y recommended by the Superintendents of Public Instruetitui o Michigan, Wisconsin, and uther States, and Is being used in many of the best school* Usroiighoul the Union. It was introduced soon after publication into Oberlin Col lAffe, a«id h w met with desorvd wuccefls, A. S BARNES & BT7IIE. Publishers, 61 & S3 John St^-eet, New Tork