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Telescopic view of the Moon. 
 
 Telescopic view of the Moon when five days old. 
 
COMPENDIUM OF ASTRONOMY; 
 
 CONTAINING THE 
 
 ELEMENTS OF THE SCIENCE, 
 
 FAMILIARLY EXPLAINED AND ILLUSTRATED, 
 
 WITH THE LATEST DISCOVERIES. 
 
 N. 
 
 ADAPTED TO THE USE OF 
 
 SCHOOLS AND ACADEMIES, 
 
 AND OF THB 
 
 GENERAL READER. 
 
 STEREOTYPE EDITION. 
 
 BY DENISON OLMSTED, A. M. 
 
 PROFESSOR OP NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE. 
 
 NEW YORK: 
 ROBERT B. COLLINS 
 
 254 PEARL STREET. 
 , 1852. 
 
 inr? 
 
 OF THE 
 
 UNIVERSITY 
 
Entered according to Act of Congress, in the year 1839, by 
 
 DENISON OLMSTED 
 
 in the Clerk's office, of the District Court of Connecticut. 
 
PREFACE. 
 
 THIS small volume is intended to afford to the General 
 Reader, and to the more advanced pupils of our Schools and 
 Academies, a comprehensive outline of Astronomy with its 
 latest discoveries. For its perusal, no further acquaintance 
 with mathematics is necessary, than a knowledge of common 
 arithmetic ; although some slight knowledge, at least, of ge- 
 ometry an4 trigonometry will prove very useful. 
 
 By omitting mathematical formulae, and employing much 
 familiar illustration, we have endeavored to bring the leading 
 facts and doctrines of this noble and interesting science, within 
 the comprehension of every attentive and intelligent reader. 
 In no science, more than in this, are greater advantages to be 
 derived from a lucid arrangement an order which brings out 
 every fact and doctrine of the science, just in the place where 
 the mind is ready to receive it. A certain maturity of mind, 
 and power of reflection, are, however, indispensable for under- 
 standing this science. Astronomy is no study for children. 
 Let them be employed on subjects more suited to the state of. 
 their capacities, until those faculties are more fully developed, 
 which will enable them to learn to conceive correctly of the 
 celestial motions. A work on Astronomy that is very easy, 
 must be very superficial, and will be found to enter little into 
 the arcana of the science. The riches of this mine lie deep ; 
 and no one can acquire them, who is either incompetent or 
 unwilling to penetrate beneath the surface. 
 
 Although -this treatise is based on the larger work of the 
 author, (" Introduction to Astronomy,") prepared for the stu- 
 dents of Yale College, yet it is not merely an abridgment of 
 that. It contains much original matter adapted to the pecu- 
 liar exigencies of the class of readers for whom it is intended. 
 The few passages taken verbatim from astronomical writers, 
 
 O f\ f\ 
 
IV PREFACE. 
 
 are not, as in the larger work, always accredited to their re- 
 spective authors, as this was deemed unimportant in a work 
 of this description. 
 
 It is strongly recommended to all who study this science, 
 even in its most elementary form, early to commence learning 
 the names of the constellations, and of the largest of the in- 
 dividual stars, in the order in which they are described in the 
 last part of the work. A celestial globe will be found a most 
 useful auxiliary in this as in every other part of Astronomy. 
 If it cannot supersede, it may greatly aid reflection. The 
 reader also should, if in his power, take frequent opportunities 
 of viewing the heavenly bodies through the telescope. This 
 will add much to his intelligence, and increase his interest in 
 the study. 
 
 ADVERTISEMENT. 
 
 SINCE the stereotype edition of this work was first pub- 
 lished, several new and interesting discoveries have been added 
 to Astronomy, an account of which will be found in the Sup- 
 plement. They make no change in the great facts and doc- 
 trines of the science, but these remain unaltered and immu- 
 table ; while the new discoveries extend still further our 
 knowledge of the Universe. We have, therefore, no occasion 
 to alter the text, except perhaps very slightly in one or two 
 statements, but by giving whatever is new and important in 
 the form of a supplement, (to which we may add as every 
 successive discovery is made,) we shall endeavor to secure to 
 this treatise the freshness and accuracy of the most recent 
 compilations, as well as furnish to the schools what has been 
 thoroughly tested and approved by the most able teachers of 
 the Union. 
 
CONTENTS. 
 
 Preliminary Observations, - - Page 
 
 Part I. OF THE EARTH. 
 
 Chapter I. Of the Figure and Dimensions of the Earth, 
 
 and the Doctrine of the Sphere, ... 5 
 Chapter II. Of the Diurnal Revolution Artificial 
 
 Globes, - i^l 
 
 Chapter III. Of Parallax, Refraction, and Twilight, 36 
 Chapter IV. Of Time, - - 45 
 
 Chapter V. Of Astronomical Instruments Figure 
 
 and Density of the Earth, - 51 
 
 Part II. OF THE SOLAR SYSTEM. 
 
 Chapter I. Of the Sun Solar Spots Zodiacal Light, 70 
 Chapter II. Of the Apparent Annual Motion of the 
 
 Sun Seasons Figure of the Earth's Orbit, - 79 
 Chapter III. Of Universal Gravitation Kepler's 
 
 Laws, Motion in an Elliptical Orbit Precession 
 
 of the Equinoxes, - - 91 
 
 Chapter IV. Of the Moon Phases, Revolutions, - 110 
 Chapter V. Of Eclipses, - - 137 
 
 Chapter VI. Of Longitude Tides, - 150 
 
 Chapter VII. Of the Planets the Inferior Planets, 
 
 Mercury and Venus, - 1 67 
 
 Chapter VIII. Of the Superior Planets Mars, Jupiter, 
 
 Saturn and Uranus Ceres, Pallas, Juno and Vesta, 183 
 
Vl OONTBNT8. 
 
 Page 
 
 Chapter IX. Of the Motions of the Planetary System 
 Quantity of Matter in the Sun and Planets 
 Stability of the Solar System, - - 205 
 
 Chapter X. Of Comets, - - - 218 
 
 Part III. OF THE FIXED STARS AND THE SYS- 
 TEM OF THE WORLD. 
 
 Chapter I. Of the Fixed Stars Constellations, - 235 
 
 Chapter II. Of Clusters of Stars Nebulae Variable 
 
 Stars Temporary Stars Double Stars, - - 247 
 
 Chapter III. Of the Motions of the Fixed Stars Dis- 
 tances Nature, - ... - 255 
 
 Chapter IV. Of the System of the World, - - 265 
 
COMPENDIUM OF ASTRONOMY, 
 
 PRELIMINARY OBSERVATIONS. 
 
 1. ASTRONOMY is that science which treats of the heav- 
 enly bodies. 
 
 More particularly, its object is to teach what is known 
 respecting the Sun, Moon, Planets, Comets, and Fixed 
 Stars ; and also to explain the methods by which this 
 knowledge is acquired. 
 
 Astronomy is sometimes divided into Descriptive, 
 Physical, and Practical. Descriptive Astronomy re- 
 spects facts ; Physical Astronomy, causes ; Practical As- 
 tronomy, the means of investigating the facts, whether 
 by instruments, or by calculation. It is the province of 
 Descriptive Astronomy to observe, classify, and record, 
 all the phenomena of the heavenly bodies, whether per- 
 taining to those bodies individually, or resulting from 
 their motions and mutual relations. It is the part of 
 Physical Astronomy to explain the causes of these phe- 
 nomena by investigating and applying the general laws 
 on which they depend ; especially by tracing out all the 
 consequences of the law of universal gravitation. Prac- 
 tical Astronomy lends its aid to both the other depart- 
 ments. 
 
 2. Astronomy is the most ancient of all the sciences. 
 At a period of very high antiquity, it was cultivated in 
 Egypt, in Chaldea, and in India. Such knowledge of 
 the heavenly bodies as could be acquired by close and 
 long continued observation, without the aid of instru- 
 
 1 - Define Astronomy. What does it teach ? Name the three 
 parta into which it is divided. What does Descriptive Astron- 
 omy respect ? What does Physical Astronomy ? What does 
 Practical Astronomy ? What is the peculiar province of each ? 
 
2 PRELIMINARY OBSERVATIONS. 
 
 ments, was diligently amassed ; and tables of the celes- 
 tial motions were constructed, which could be used in 
 predicting eclipses, and other astronomical phenomena. 
 
 About 500 years before the Christain era, Pythago- 
 ras, of Greece, taught astronomy at the celebrated school 
 at Crotona, (a Greek town on the southeastern coast of 
 Italy,) and exhibited more correct views of the nature 
 of the celestial motions, than were entertained by any 
 other astronomer of the ancient world. His views, how- 
 ever, were not generally adopted, but lay neglected for 
 nearly 2000 years, when they were revived and estab- 
 lished by Copernicus and Galileo. The most celebrated 
 astronomical school of antiquity, was at Alexandria in 
 Egypt, which was established and sustained by the Ptol- 
 emies, (Egyptian princes,) 300 years before the Chris- 
 tian era. The employment of instruments for measur- 
 ing angles, and bringing in trigonometrical calculations 
 to aid the naked powers of observation, gave to the Alex- 
 andrian astronomers great advantages over all their pre- 
 decessors. 
 
 The most able astronomer of the Alexandrian school 
 was Hipparchus, who was distinguished above all the 
 ancients for the accuracy of his astronomical measure- 
 ments and determinations. The knowledge of astron- 
 omy possessed by the Alexandrian school, and recorded 
 in the Almagest, or great work of Ptolemy, constituted 
 the chief of what was known of our science during the 
 middle ages, until the fifteenth and sixteenth centuries, 
 when the labors of Copernicus of Prussia, Tycho Brake 
 
 2. Trace the history of Astronomy. Among what ancient 
 nations was it cultivated ? What kind of knowledge of the 
 heavenly bodies was amassed ? Who was Pythagoras? When 
 and where did he live ? Where was his school ? How correct 
 were his views ? Were they generally adopted ? Give an ac- 
 count of the Alexandrian school. When was it established and 
 by whom ? What gave it great advantages over all its prede- 
 cessors ? Give some account of Hipparchus of Ptolemy of 
 Copernicus of Tycho Brahe of Kepler of Galileo of 
 Newton of La Place. Specify the respective labors of each 
 
PRELIMINARY OBSERVATIONS. 
 
 of Denmark, Kepler of Germany, and Galileo of Italy, 
 laid the solid foundations of modern astronomy. Coper- 
 nicus expounded the true system of the world, or the 
 arrangement and motions of the heavenly bodies ; Ty- 
 cho Brahe carried the use of instruments, and the art of 
 astronomical observation, to a far higher degree of accu- 
 racy than had ever been done before ; Kepler discovered 
 the great laws which regulate the movements of the 
 planets ; and Galileo, having first enjoyed the aid of the 
 telescope, made innumerable discoveries in the solar 
 system. Near the beginning of the eighteenth century, 
 Sir Isaac Newton discovered, in the law of universal 
 gravitation, tho great principle mat explains the causes 
 of all celestial phenomena ; and recently, La Place has 
 more fully completed what Newton begun, having fol- 
 lowed out all the consequences of the law of universal 
 gravitation, in his great work, the Mecanique Celeste. 
 
 3. Among the ancients, astronomy was studied chiefly 
 as subsidiary to astrology. Astrology was the art of di- 
 vining future events by the stars. It was of two kinds, 
 natural and judicial. Natural Astrology, aimed at pre- 
 dicting remarkable occurrences in the natural world, as 
 eathquakes, volcanoes, tempests, and pestilential dis- 
 eases. Judicial Astrology, aimed at foretelling the fates 
 of individuals, or of empires. 
 
 4. Astronomers of every age, have been distinguished 
 for their persevering industry, and their great love of ac- 
 curacy. They have uniformly aspired to an exactness 
 in their inquiries, far beyond what is aimed at in most 
 geographical investigations, satisfied with nothing short 
 of numerical accuracy wherever this is attainable ; and 
 years of toilsome observation, or laborious calculation, 
 have been spent with the hope of attaining a few se- 
 
 3. Define Astrology. What was Natural and what Judicial 
 Astrology ? 
 
 4. What is said of the industry and accuracy of astrono- 
 mers ? Can this science be taught by artificial aids alone ? 
 
4 PRELIMINARY OBSERVATIONS. 
 
 conds nearer to the truth. Moreover, a severe but de 
 lightful labor is imposed on all, who would arrive at a 
 clear and satisfactory knowledge of the subject of astron- 
 omy. Diagrams, artificial globes, orreries, and familiar 
 comparisons and illustrations, proposed by the author or 
 the instructor, may afford essential aid to the learner, 
 but nothing can convey to him a perfect comprehension 
 of the celestial motions, without much diligent study 
 and reflection. 
 
 5. In this treatise, we shall for the present assume the 
 Copernican system as the true system of the world, 
 postponing the discussion of the evidence on which it 
 rests to a late period, when the learner has been made ex- 
 tensively acquainted with astronomical facts. This sys- 
 tem maintains (1,) That, the apparent diurnal revolution 
 of the heavenly bodies, from east to west, is owing to 
 the real revolution of the earth dn its own axis from 
 west to east, in the same time ; and (2,) That the sun 
 is the center around which the earth and planets all re- 
 volve from west to east, contrary to the opinion that the 
 earth is the center of motion of the sun and planets. 
 
 5. What system is assumed as the true system of the world ? 
 Specify the two leading points in the Copernican system. , 
 
PART I. OF THE EARTH. 
 
 CHAPTER I. 
 
 OF THE FIGURE AND DIMENSIONS OF THE EARTH, AND THE 
 DOCTRINE OF THE SPHERE. 
 
 6. The figure of the earth is nearly globular. This 
 fact is known, first, by the circular form of its shadow 
 cast upon the moon in a lunar eclipse ; secondly, from 
 analogy, each of the other planets being seen to be 
 spherical ; thirdly, by our seeing the tops of distant ob- 
 jects while the other parts are invisible, as the topmast 
 of a ship, while either leaving or approaching the shore, 
 or the lantern of a light-house, which when first descried 
 at a distance at sea, appears to glimmer upon the very 
 surface of the water ; fourthly, by the testimony of nav- 
 igators who have sailed around it ; and, finally, by ac- 
 tual observations and measurements, made for the ex- 
 press purpose of ascertaining the figure of the earth, by 
 means of which astronomers are enabled to compute the 
 distances from the center of the earth of various places 
 on its surface, which distances are found to be nearly 
 equal. 
 
 The effect of the rotundity of the earth upon the ap- 
 pearance of a ship, when either leaving or approaching 
 the spectator, is illustrated by Fig. 1. 
 
 As light proceeds in straight lines, it is evident that, 
 if the earth is round, the top of the ship ought to come 
 into view before the lower parts, when the ship is ap- 
 proaching the spectator at A, and to remain longest iii 
 view when the ship is leaving^him. But, were the eartL 
 
 6. What is the figure of the earth"? Enumerate the various 
 proofs of its rotundity. 
 
a continued plane, then the spectator would see all parts 
 of the ship at the same time, as is represented in the an- 
 nexed figure. 
 
 Fig. 2. 
 
 7. The foregoing considerations show that the form 
 of the earth is spherical ; but more exact determinations 
 prove, that the earth, though nearly globular, is not ex- 
 actly so ; its diameter from the north to the south pole 
 is about 26 miles less than through the equator, giving 
 to the earth the form of an oblate spheroid, or a flattened 
 sphere resembling an orange. We shall reserve the ex- 
 
FIGURE AND DIMENSIONS. ; 7 
 
 planations of the methods by which this fact is estab- 
 lished, until the learner is better prepared than at present 
 to understand them. 
 
 The mean or average diameter of the earth, is 7912.4 
 miles, a measure which the learner should fix in his 
 memory as a standard of comparison in astronomy, and 
 of which he shoulc 1 endeavor to form the most adequate 
 conception in his power. The circumference of the 
 earth is about 25,000 miles. Although the surface of 
 the earth is uneven, sometimes rising in high mountains, 
 and sometimes descending in deep valleys, yet these ele- 
 vations and depressions are so small in comparison with 
 the immense volume of the globe, as hardly to occasion 
 any sensible deviation from a surface uniformly curvi- 
 linear. The irregularities of the earth's surface, in this 
 view, are no greater than the rough points on the rind 
 of an orange, which do not perceptibly interrupt its con- 
 tinuity ; for the highest mountain on the globe is only 
 about five miles above the general level ; and the deep- 
 est mine hitherto opened is only about half a mile.* 
 
 ~ T~W or a ^ out one sixteen hundredth part 
 
 of the whole diameter, an inequality which, in an arti- 
 ficial globe of eighteen inches diameter, amounts to only 
 the eighty eighth part of an inch. 
 
 8. The greatest difficulty in the way of acquiring 
 correct views in astronomy, arises from the erroneous 
 notions that pre-occuoy the mind. To divest himself 
 
 7. What is the exact figure of the earth ? How much greater 
 is its diameter through the equator than through the poles ?, 
 What is the mean average diameter of the earth ? What is its 
 circumference 1 Do the inequalities on the earth's surface af- 
 fect its rotundity ? To what may these be compared ? How 
 high is the highest mountain above the general level ? How 
 deep is the deepest mine ? To how much would this amount 
 on an artificial globe eighteen inches in diameter ? 
 
 * Sir John Herschel. 
 
8 THE EARTH. 
 
 of these, the learner should conceive of the earth as a 
 huge globe occupying a small portion of space, and en- 
 circled on all sides with the starry sphere. He should 
 free his mind from its habitual proneness to consider one 
 part of space as naturally up and another down, and 
 view himself as subject to a force which binds him to 
 the earth as truly as though he were fastened to it by 
 some invisible cords or wires, as the needle attaches it- 
 self to all sides of a spherical loadstone. He should 
 
 Fig. 3. 
 
 dwell on this point until it appears to him as truly up in 
 the direction of BB, CC, DD, (Fig. 3,) when he is at 
 B, C, and D, respectively, as in the direction *AA, when 
 he is at A. 
 
 DOCTRINE OF THE SPHERE. 
 
 9. The definitions of the different lines, points, and 
 circles, which are used in astronomy, and the proposi- 
 tions founded upon them, compose the Doctrine of the 
 Sphere. 
 
 8. Whence arises the greatest difficulty in acquiring correct 
 views in astronomy ? How should the learner conceive of 
 the earth ? Illustrate by figure 3. 
 
 9. Doctrine of the sphere define it. 
 
DOCTRINE OF THE SPHERE. 9 
 
 10. A section of a sphere by a plane cutting it in any 
 manner, is a circle. Great circles are those which pass 
 through the center of the sphere, and divide it into two 
 equal hemispheres : Small circles, are such as do not 
 pass through the center, but divide the sphere into two 
 unequal parts. Every circle, whether great or small, is 
 divided into 360 equal parts called degrees. A degree, 
 therefore, is not any fixed or definite quantity, but only 
 a certain aliquot part of any circle.* 
 
 The axis of a circle, is a straight line passing through 
 its center at right angles to its plane. 
 
 Fig. 4. 
 
 * As this work may be read by some who are unacquainted with 
 even the rudiments of geometry, we annex a few particulars respecting 
 angular measurements. 
 
 A line drawn from the center to the circumference of a circle is 
 called a radius, as CD, fig. 4. 
 
 Any part of the circumference of a circle is called an arc, as AB, 
 or BD. 
 
 An angle 'is measured by the 
 arc included between two radii. 
 Thus, in the annexed figure, the 
 angle contained between the two 
 radii CA and CB, that is, the an- 
 gle ACB, is measured by the arc 
 AB. But this arc is the same part 
 of the smaller circle that EF is of 
 the greater. The arc AB there- 
 fore contains the same number of 
 degrees as the arc EF, and either 
 may be taken for the measure of- 
 the angle ACB. As the whole 
 circle contains 360, it is evident 
 that the quarter of a circle, or'quad- 
 
 rant ABD, contains 90, and the 
 semicircle ABDG contains 180. 
 r The complement of an arc or an- 
 gle,^ what it wants of 90. Thus BD is the complement of AB, and 
 AB is the complement of BD. If AB denotes a certain number of de- 
 grees of latitude, BD will be the complement of the latitude or the co- 
 latitude, as it is commonly written. 
 
 The supplement of an arc or angle, is what it wants of 180. 
 Thus BA is the supplement of GDB, and GDB, is the supplement 
 of BA. If BA were 20 of longitude, GDB its supplement would 
 be 160. 
 
 An angle is said to be subtended by the side which is opposite to it. 
 Thus in the triangle ACK, the angle at C is subtended by the side AK, 
 the angle at A by CK, and the angle at K by CA. In like manner a 
 side is said to be subtended by an angle, as AK by the angle at C. 
 
10 
 
 THE EARTH. 
 
 The pole of a great circle, is the point on the sphere 
 where its axis cuts through the sphere. Every great 
 circle has two poles, each of which is every where 90 
 from the great circle. 
 
 All great circles of the sphere cut each other in two 
 points diametrically opposite, and consequently, their 
 points of section are 180 apart. 
 
 A great circle which passes through the pole of an- 
 other great circle, cuts the latter at right angles. 
 
 The great circle which passes through the pole of an- 
 other great circle and is at right angles to it, is called a 
 secondary to that circle. 
 
 The angle made by two great circles on the surface 
 of the sphere, is measured by the arc of another great 
 circle, of which the angular point is the pole, being the 
 arc of that great circle intercepted between those two 
 circles. 
 
 11. In order to fix the position of any plane, either on 
 the surface of the earth or in the heavens, both the earth 
 and the heavens are conceived to be divided into sepa- 
 rate portions by circles, which are imagined to cut 
 through them in various ways. The earth thus inter- 
 sected is called the terrestrial, and the heavens the ce- 
 lestial sphere. The learner will remark, that these cir- 
 cles have no existence in nature, but are mere land- 
 marks, artificially contrived for convenience of refer- 
 
 10. What figure is produced by the section of a sphere? 
 Define great circles. Define small circles. Into how many 
 degrees is every circle divided ? Is a degree any fixed or defi- 
 nite quantity ? What is the axis of a circle ? What is the pole 
 of a circle? How do all great circles cut each other? How 
 is a great circle cut by another great circle passing through its 
 pole ? What is the secondary of a circle ? How is the angle 
 made by two great circles on the surface of the sphere measured? 
 
 11. How are the earth and the heavens conceived to be di- 
 vided ? What constitutes the terrestrial sphere ? What the 
 celestial ? Have these circles any existence in nature ? In 
 what do the heavenly bodies appear to be fixed ? 
 
DOCTRINE OF THE SPHERE. 11 
 
 ence. On account of the immense distance of the heav- 
 enly bodies, they appear to us, wherever we are placed, 
 to be fixed in the same concave surface, or celestial 
 vault. The great circles of the globe, extended every 
 way to meet the concave surface of the heavens, become 
 circles of the celestial sphere. 
 
 12. The Horizon is the great circle which divides 
 the earth into upper and lower hemispheres, and sepa- 
 rates the visible heavens from the invisible. This is 
 the rational horizon. The sensible horizon, is a circle 
 touching the earth at the place of the spectator, and is 
 bounded by the line in which the earth and skies seem 
 to meet. The sensible horizon is parallel to the ra- 
 tional, but is distant from it by the semi-diameter of the 
 earth, or nearly 4,000 miles. Still, so vast is the dis- 
 tance of the starry sphere, that both these planes appear 
 to cut that sphere in the same line ; so that we see the 
 same hemisphere of stars that we should see if the up- 
 per half of the earth were removed, and we stood on the 
 rational horizon. 
 
 13. The poles of the horizon are the zenith and na- 
 dir. The Zenith is the point directly over bur head, 
 and the Nadir that directly under our feet. The plumb 
 line is in the axis of the horizon, and consequently di- 
 rected towards its poles. 
 
 Every place on the surface of the earth has its own 
 horizon ; and the traveller has a new horizon at every 
 step, always extending 90 degrees from him in all di- 
 rections. 
 
 12. Define the horizon. Distinguish between the rational 
 and the sensible horizon. What is the distance between the 
 sensible and rational horizons ? How do both appear to cut 
 the starry heavens ? 
 
 13. What are the poles of the horizon ? Define the zenith. 
 Define the nadir. How is the plumb line situated with respect 
 *o the horizon? How manv horizons are there on the earth 1 
 
12 THE EARTH. 
 
 14. Vertical circles are those which pass through the 
 ooles of the horizon, perpendicular to it. 
 
 The Meridian is that vertical circle which passes 
 through the north and south points. 
 
 The Prime Vertical, is that vertical circle which 
 passes through the east and west points. 
 
 The Altitude of a body, is its elevation above the ho- 
 rizon, measured on a vertical circle. 
 
 The Azimuth of a body, is its distance measured on 
 the horizon from the meridian to a vertical circle passing 
 through the body. 
 
 'The Amplitude of a body, is its distance on the hori- 
 zon, from the prime vertical, to a vertical circle passing 
 through the body. 
 
 Azimuth is reckoned 90 from either the north or 
 south point ; and amplitude 90 from either the east or 
 west point. Azimuth and amplitude are mutually com- 
 plements of each other. When a point is on the hori- 
 zon, it is only necessary to count the 'number of degrees 
 of the horizon between that point and the meridian, in 
 order to find its azimuth ; but if the point is above the 
 horizon, then its azimuth is estimated by passing a ver- 
 tical circle through it, and reckoning the azimuth from 
 the point where this circle cuts the horizon. 
 
 The Zenith Distance of a body is measured on a ver- 
 tical circle, passing through that body. It is the com- 
 plement of the altitude. 
 
 1 5. The Axis of the Earth is the diameter, on which 
 the earth is conceived to turn in its diurnal revolution. 
 The same line continued until it meets the starry con- 
 cave, constitutes the axis of the celestial sphere. 
 
 14. Define vertical circles the meridian tlie prime verti- 
 cal altitude azimuth amplitude. How many degrees of 
 azimuth are reckoned ? from what points ? How are azimuth 
 and amplitude related to each other ? Define zenith distance 
 How is it related to the altitude ? 
 
 15. Define the axis of the earth the axis of the celestial 
 sphere the poles of the earth the poles of the heavens. 
 
DOCTRINE OF THE SPHERE. 13 
 
 The Poles of the Earth are the extremities of the 
 earth's axis : the Poles of the Heavens, the extremities 
 of the celestial axis. 
 
 16. The Equator is a great circle cutting the axis of 
 the earth at right angles. Hence the axis of the earth 
 is the axis of the equator, and its poles are the poles of 
 the equator. The intersection of the plane of the equa- 
 tor with the surface of the earth, constitutes the terres- 
 trial, and with the concave sphere of the heavens, the 
 celestial equator. The latter, by way of distinction, is 
 sometimes denominated the equinoctial. 
 
 17. The secondaries to the equator, that is, the great 
 circles passing through the poles of the equator, are 
 called Meridians, because that secondary which passes 
 through the zenith of any place is the meridian of that 
 place, and is at right angles both to the equator and the 
 ^orizon, passing as it does through the poles of both. 
 These secondaries are also called Hour Circles, because 
 the arcs of the equator intercepted between them are 
 used as measures of time. 
 
 18. The Latitude of a place on the earth, is its dis- 
 tance from the equator north or south. The Polar Dis- 
 tance, or angular distance from the nearest pole, is the 
 complement of the latitude. 
 
 19. The Longitude of a place is its distance from 
 some standard meridian, either east or west, measured 
 on the equator. The meridian usually taken as the 
 standard, is that of the Observatory of Greenwich, in 
 London. If a place is directly on the equator, we have 
 only to inquire how many degrees of the equator there 
 
 16. Define the equator. What constitutes the terrestrial 
 equator ? what the celestial equator ? What is this also called? 
 . 17. What are the secondaries of the equator called 7 
 
 18. Define the Latitude of a place the polar distance. 
 2 
 
14 THE EARTH. 
 
 are between that place and the point where the meridian 
 of Greenwich cuts the equator. If the place is north or 
 south of the equator, then its longitude is the arc of the 
 equator intercepted between the meridian which passes 
 through the place, and the meridian of Greenwich. 
 
 20. The Ecliptic is a great circle in which the earth 
 performs its annual revolution around the sun. It passes 
 through the center of the earth and the center of the 
 sun. It is found by observation that the earth does not 
 lie with its axis at right angles to the plane of the eclip- 
 tic, but that it is turned about 23J degrees out of a per- 
 pendicular direction, making an angle with the plane 
 itself of 66i. The equator, therefore, must be turned 
 the same distance out of a coincidence with the ecliptic, 
 the two circles making an angle with each other of 23J. 
 It is particularly important for the learner to form cor- 
 rect ideas of the ecliptic, and of its relations to the equa- 
 tor, since to these two circles a great number of astro- 
 nomical measurements and phenomena are referred. 
 
 21. The Equinoctial Points, or Equinoxes* are the 
 intersections of the ecliptic and equator. The time 
 when the sun crosses the equator in going northward 
 is called the vernal, and in returning southward, the au- 
 tumnal equinox. The vernal equinox occurs about 
 the 21st of March, and the autumnal the 22d of Sep- 
 tember. 
 
 19. Define the Longitude of a place. What is the standard 
 meridian ? When a place is on the equator, how is its longi- 
 tude measured ? how when it is north or south of the equator ? 
 
 20. Define the ecliptic. How does it pass with respect to 
 the earth and the sun ? How is it situated with respect to the 
 equator ? 
 
 21. Define the equinoctial points. When is the vernal equi- 
 nox, and when the autumnal ? 
 
 * The term Equinoxes strictly denotes the times when the sun ar- 
 rives at the equinoctial points, but it is frequently used to denote those 
 "*nts themselves. 
 
DOCTRINE OF THE SPHERE. 15 
 
 22. The Solstitial Points are the two points of the 
 ecliptic most distant from the equator. The times when 
 the sun comes to them are called solstices. The sum- 
 mer solstice occurs about the 22d of June, and the win- 
 ter solstice about the 22d of December. 
 
 The ecliptic is divided into twelve equal parts of 30 
 each, called signs, which, beginning at the vernal equi- 
 nox, succeed each other in the following order : 
 
 Northern. Southern. 
 
 1. Aries T 7. Libra 
 
 2. Taurus S 8. Scorpio fl\. 
 
 3. Gemini n 9. Sagittarius / 
 
 4. Cancer <s 10. Capricornus K? 
 
 5. Leo fl 11. Aquarius #? 
 
 6. Virgo TTJ? 12. Pisces ^ 
 
 The mocle of reckoning on the ecliptic, is by signs, de- 
 grees, minutes, and seconds. The sign is denoted either 
 by its name or its number. Thus 100 maybe express- 
 ed either as the 10th degree of Cancer, or as 3 s 10. 
 
 23. Of the various meridians, two are distinguished 
 by the name of Colures. The Equinoctial Colure, is 
 the meridian which passes through the equinoctial 
 points. From this meridian, right ascension and celes- 
 tial longitude are reckoned, as longitude on the earth is 
 reckoned from the meridian of Greenwich. The Sol- 
 stitial Colure, is the meridian which passes through the 
 solstitial points. 
 
 24. The position of a celestial body is referred to the 
 equator by its right ascension and declination. Right 
 
 22, Define the solstitial points, and solstices. When does 
 the summer solstice occur ? when does the winter solstice oc- 
 cur 1 Into how many signs is the ecliptic divided ? How 
 many degrees are there in each ? Name the signs. What is 
 the mode of reckoning on the ecliptic ? In what two wavs 
 may 100 be expressed ? 
 
 23, What is the equinoctial colure ? the solstitial colure 1 
 
16 THE EARTH. 
 
 Ascension, is the angular distance from the vernal equi- 
 nox measured on the equator. If a star is situated on 
 the equator, then its right ascension is the number of 
 degrees of the equator between the star and the vernal 
 equinox. But if the star is north or south of the equa- 
 tor, then its right ascension is the arc of the equator, in- 
 tercepted between the vernal equinox and that secon- 
 dary to the equator which passes through the star. De- 
 clination is the distance of a body from the equator, 
 measured on a secondary to the latter. Therefore, right 
 ascension and declination correspond to terrestrial longi- 
 tude and latitude, right ascension being reckoned from 
 the equinoctial colure, in the same manner as longitude 
 is reckoned from the meridian of Greenwich. On the 
 other hand, celestial longitude and latitude are referred, 
 not to the equator, but to the ecliptic. Celestial Longi- 
 tude, is the distance of a body from the vernal equinox 
 reckoned on the ecliptic. Celestial Latitude, is distance 
 from the ecliptic measured on a secondary to the latter. 
 Or, more briefly, Longitude is distance on the eclip- 
 tic ; Latitude, distance from the ecliptic. The North 
 Polar Distance of a star, is the complement of its de- 
 clination. 
 
 25. Parallels of Latitude are small circles parallel to 
 the equator. They constantly diminish in size as we go 
 from the equator to the pole. 
 
 The Tropics are the parallels of latitude that pass 
 through the solstices. The northern tropic is called the 
 tropic of Cancer ; the southern, the tropic of Capricorn. 
 
 The Polar Circles are the parallels of latitude that 
 pass through the poles of the ecliptic, at the distance of 
 23^ degrees from the pole of the earth. 
 
 24. Define right ascension and declination. To what do 
 they correspond on the terrestrial sphere ? Define celestia. 
 longitude and latitude. 
 
 25. What are parallels of latitude tropics polar circles ? 
 To what is the elevation of the pole always equal ? also that 
 of the equator ? 
 
DOCTRINE OF THE SPHERE. . 17 
 
 The elevation of the pole of the heavens above the 
 horizon of any place, is always equal to the latitude of 
 the place. Thus, in 40 of north latitude we see the 
 north star 40 above the northern horizon, whereas, if 
 we should travel southward its elevation would grow 
 less and less, until we reached the equator, where it 
 would appear in the horizon ; or, if we should travel 
 northward, the north star would rise constantly higher 
 and higher, until, if w r e could reach the pole of the earth, 
 that star would appear directly over head. The eleva- 
 tion of the equator above the horizon of any place, is 
 equal to the complement of the latitude. Thus, at the 
 latitude of 40 N. the equator is elevated 50 above the 
 southern horizon. 
 
 26. The earth is divided into five zones. That por- 
 tion of the earth which lies between the tropics, is called 
 the Torrid Zone ; that between the tropics and polar 
 circles, the Temperate Zones; and that between the 
 polar circles and the poles, the Frigid Zones. 
 
 27. The Zodiac is the part of the celestial sphere, 
 which lies about 8 degrees on each side of the ecliptic. 
 This portion of the heavens is thus marked off by itself, 
 because all the planets move within it. 
 
 28. After endeavoring to form, from the definitions, 
 as clear an idea as he can of the various circles of the 
 sphere, the learner may next resort to an artificial globe, 
 and see how they are severally represented there. Or if 
 he has not access to a globe, he may aid his conceptions 
 by the following easy device. To represent the earth, 
 select a large apple, (a melon when in season will be 
 found still better.) The shape of the apple, flattened as 
 
 26. Define each of the zones. 
 
 27. Define the zodiac. 
 
 28. Show how to represent the artificial sphere by any round 
 body, as an apple, and point out the various circles on it. 
 
 2* 
 
18 THE EARTH. 
 
 
 
 it usually is at the two ends, will not inaptly exhibit 
 the spheroidal figure of the earth, while the larger diam- 
 ter through the middle will indicate the excess of mat- 
 r about the equator ; although we should remark, thai 
 the disproportion between the polar and equatorial diam 
 eters of the earth is in fact so slight, that it would be 
 scarcely perceptible in a model. The eye and the stem 
 of the apple will indicate the position of the two poles 
 of the earth. Applying the thumb and finger of the 
 left hand to the poles, and holding the apple so that the 
 poles may be in a north and south line, turn the globe 
 from west to east, and its motion will correspond to the 
 diurnal movement of the globe. Pass a wire, as a knit- 
 ting needle, through the poles, and it will represent the 
 axis of the sphere. A circle cut around the apple half 
 way between the poles, will be the equator ; and several 
 other circles cut between the equator and the poles, par- 
 allel to the equator, will represent parallels of latitude, 
 of which, two drawn 23^ degrees from the equator, will 
 be the tropics, and two others at the same distance from 
 the poles, will be the polar circles. A great circle cut 
 through the poles in a north and south direction, will 
 form the meridian, and several other great circles drawn 
 through the poles, and of course perpendicularly to the 
 equator, will be secondaries to the equator, constituting 
 meridians or hour circles. A great circle cut through the 
 center of the earth from one tropic to the other, will rep- 
 resent the plane of the ecliptic, and consequently, a line 
 cut around the apple where such a section meets the sur- 
 face, is the terrestrial ecliptic. The points where this 
 circle meets the tropics, are the solstices, and its intersec- 
 tions with the equator are the equinoctial points. 
 
 29. The horizon is best represented by a circular 
 piece of pasteboard, cut so as to fit closely to the apple, 
 being movable upon it. When this horizon is slipped 
 
 29. How is the horizon represented in our model ? How ia 
 it placed to represent the horizon of the equator ? How for the 
 horizon of the poles ? How for our own horizon ? How shall 
 we represent the prime vertical ? 
 

 DOCTRINE OF THE SPHERE. 
 
 up to the poles, it becomes the horizon of the equator ; 
 when it is so placed as to coincide with the earth'? 
 equator, it becomes the horizon of the poles ; and in 
 every other situation it represents the horizon of a plac 
 on the globe 90 every way from it. Suppose we are 
 in latitude 40, then let us place our movable paper par 
 allel to our own horizon, and elevate the pole 40 above 
 it, as near as we can judge by the eye. If we cut a cir 
 cle around the apple, passing through its highest parts 
 and through the east and west points, it will represent 
 the prime vertical. 
 
 30. We cannot too strongly recommend to the young 
 learner to form for himself such a sphere as is here de 
 scribed, and to point out on it the various arcs of azimuth 
 and altitude, right ascension and declination, terrestrial 
 and celestial latitude and longitude, these last being re 
 ferred to the equator on the earth, and to the ecliptic ir? 
 the heavens. 
 
 31. When the circles of the sphere are well learned 
 we may advantageously employ projections of them ir* 
 various illustrations. By the projection of the sphere ifr 
 meant a representation of all its parts on a plane. The 
 plane itself is called the plane of projection. Let us take 
 any circular ring, as a wire bent into a circle, and hold 
 it in different positions before the eye. If we hold it 
 parallel to the face, or directly opposite to the eye, we 
 see it as an entire circle. If we turn it a little sideways 
 it appears oval, or as an ellipse ; and as we continue tt 
 turn it more and more round, the ellipse grows narrower 
 and narrower, until, when the edge is presented to the 
 eye, we see nothing but a line. Now imagine the rin 
 to be near a perpendicular wall, and the eye to be re 
 
 80. What is particularly recommended to the young learner 
 31 What is meant by the projection of trj.Q sphere 1 Wha 
 is the projection of a circle when seen directly before the face \ 
 what when seen obliquely 1 what when seen edgewise 1 
 

 20 
 
 THE EARTH. 
 
 moved at such a distance from it, as not to distinguish 
 any interval between the ring and the wall ; then the 
 several figures under which the ring is seen, will appear 
 to be inscribed on the wall, and we shall see the ring as 
 a circle when perpendicular to a straight line joining 
 the center of the ring and the eye, as an ellipse when 
 oblique to this line, or as a straight line when its edge is 
 towards us. 
 
 32. It is in this manner that the circles of the sphere 
 are projected, as represented in the following diagram 
 
 Here various circles are represented as projected on the 
 meridian, which is supposed to be situated directly be- 
 fore the eye, at some distance from it. The horizon HO 
 being perpendicular to the meridian is seen edgewise, and 
 consequently is projected into a straight line. The same 
 is the case with the prime vertical ZN, with the equator 
 EQ, and the several small circles parallel to the equator, 
 which represent the two tropics and the two polar cir- 
 
 32. In figure 5, what represents the plane of projection ? 
 Why are certain circles represented by straight lines ? why are 
 others represented by ellipses ? How is the eye supposed to 
 be situated ? 
 
DIURNAL REVOLUTION. 21 
 
 cles. In fact, all circles whatsoever, which are perpen- 
 dicular to the plane of projection, will be represented 
 by straight lines. But every circle which is perpendic- 
 ular to the horizon, except the prime vertical, being seen 
 obliquely as ZMN, will be projected into an ellipse. 
 In the same manner, PRP, an hour circle, being oblique 
 to the eye, is represented by an ellipse on the plane of 
 projection. 
 
 CHAPTER II. 
 
 DIURNAL REVOLUTION ARTIFICIAL GLOBES. 
 
 33. THE apparent diurnal revolution of the heavenly 
 bodies from east to west, is owing to the actual revolu- 
 tion of the earth on its own axis from west to east. If 
 we conceive of a radius of the earth's equator extended 
 until it meets the concave sphere of the heavens, then 
 as the earth revolves, the extremity of this line would 
 trace out a curve on the face of the sky, namely, the ce- 
 lestial equator. In curves parallel to this, called the cir- 
 cles of diurnal revolution, the heavenly bodies actually 
 appear to move, every star having its own peculiar cir- 
 cle. After the learner has first rendered familiar the 
 real motions of the earth from west to east, he may 
 then, without danger of misconception, adopt the com- 
 mon language, that all the heavenly bodies revolve 
 around the earth once a day from east to west, in circles 
 parallel to the equator and to each other. 
 
 34. The time occupied by a star in passing from any 
 point in the meridian until it comes round to the same 
 
 33. To what is the apparent diurnal revolution of the heav- 
 enly bo.dies from east to west owing ? If a radius of the earth's 
 equator were extended to meet the concave sphere of the heav- 
 ens, what would it trace out as the earth revolves ? WhaJ 
 are circles of diurnal revolution ? 
 
 
22 THE EARTH. 
 
 point again, is called a sidereal day, and measures the 
 period of the earth's revolution on its axis. If we watch 
 the returns of the same star from day to day, we shall 
 find the intervals exactly equal to one another ; that is, 
 the sidereal days are all equal. Whatever star we se- 
 lect for the observation, the same result will be obtained. 
 The stars, therefore, always keep the same relative posi- 
 tion, and have a common movement round the earth 
 a consequence that naturally flows from the hypothesis, 
 that their apparent motion is ajl produced by a single 
 real motion, namely, that of the earth. The sun, moon, 
 and planets, as well the fixed stars, revolve in like man- 
 ner, but their returns to the meridian are not, like those 
 of the fixed stars, at exactly equal intervals. 
 
 35. The appearances of the diurnal motions of the 
 heavenly bodies are different in different parts of the 
 earth, since every place has its own horizon, (Art. 8,) 
 and different horizons are variously inclined to each 
 other. Let us suppose the spectator viewing the diurnal 
 revolutions from several different positions on the earth. 
 
 On the equator, his horizon would pass through both 
 poles ; for the horizon cuts the celestial vault at 90 de- 
 grees in every direction from the zenith of the spectator ; 
 but the pole is likewise 90 degrees from his zenith, and 
 consequently, the pole must be in the horizon. The ce- 
 lestial equator would coincide with the Prime Vertical, 
 
 34. Define a sidereal day. Are the sidereal days equal or 
 unequal ? Are the returns of the sun, moon, and planets to 
 the meridian, likewise at equal intervals ? 
 
 35. How are the appearances of the diurnal motions in dif- 
 ferent parts of the earth ? When the spectator is on the equa- 
 tor, where would his horizon pass with respect to the poles of 
 the earth ? With what great circle would the celestial equator 
 coincide ? How would all the circles of diurnal revolution be 
 situated with respect to the horizon ? Define a right sphere. 
 In a right sphere, how would a'star situated in *he celestial 
 equator perform its circuit ? how would stars nearer the poles 
 appear to move 1 
 
DIURNAL 
 
 being a great circle passing through the east and west 
 points. Since all the diurnal circles are parallel to the 
 equator, consequently, they would all, like the equator, 
 be perpendicular to the horizon. Such a view of the 
 heavenly bodies, is called a right sphere ; or, 
 
 A RIGHT SPHERE is one in which all the daily revolu- 
 tions of the stars, are in circles perpendicular to the horizon. 
 
 A right sphere is seen only at the equator. Any star 
 situated in the celestial equator, would appear to rise di- 
 rectly in the east, when on the meridian to be in the 
 zenith of the spectator, and to set directly in the west ; 
 in proportion as stars are at a greater distance from the 
 equator towards the pole, they describe smaller and 
 smaller circles, until, near the pole, their motion is hardly 
 perceptible. 
 
 36. If the spectator advances one degree towards the 
 north pole, his horizon reaches one degree beyond the 
 pole of the earth, and cuts the starry sphere one degree 
 below the pole of the heavens, or below the north star, 
 if that be taken as the place of the pole. As he moves 
 onward towards the pole, his horizon continually reaches 
 farther and farther beyond it, until when he comes to 
 the pole of the earth, and under the pole of the heavens, 
 his horizon reaches on all sides to the equator and coin- 
 cides with it. Moreover, since all the circles of daily 
 motion are parallel to the equator, they become, to the 
 spectator at the pole, parallel to the horizon. This is 
 what constitutes a parallel sphere. Or, 
 
 A PARALLEL SPHERE is that in which all the cwcles of 
 daily motion are parallel to the horizon. 
 
 To render this view of the heavens familiar, the 
 learner should follow round in his mind a number of 
 
 36. What changes take place in one's horizon as he moves 
 from the equator towards the pole ? How would it be situated 
 when he reached the pole ? Define a parallel sphere. Explain 
 the appearances of the stars and of the sun in a parallel sphere. 
 Where only can such a sphere be seen ? Has the pole of the 
 earth ever been reached by man ? 
 
 
24 THE EARTH. 
 
 separate stars, one near the horizon, one a few degrees 
 above it, and a third near the zenith. To one who 
 stood upon the north pole, the stars of the northern hemi- 
 sphere would all be perpetually in view when not ob- 
 scured by clouds or lost in the sun's light, and none of 
 those of the southern hemisphere would ever be seen. 
 The sun would be constantly above the horizon for six 
 months in the year, and the remaining six constantly 
 out of sight. That is, at the pole the days and nights 
 are each six months long. The phenomena at the south 
 pole are similar to those at the north. 
 
 A perfect parallel sphere can never be seen except at 
 one of the poles a point which has never been actually 
 reached by man ; yet the British discovery ships pene- 
 trated within a few degrees of the north pole, and of 
 course enjoyed the view of a sphere nearly parallel. 
 
 37. As the circles of daily motion are parallel to the 
 lorizon of the pole, and perpendicular to that of the 
 equator, so at all places between the two, the diurnal 
 motions are oblique to the horizon. This aspect of the 
 neavens constitutes an oblique sphere, which is thus de- 
 nned : 
 
 An OBLIQUE SPHERE is that in which the circles of 
 iaily motion are oblique to the horizon. 
 
 Suppose, for example, the spectator is at the latitude of 
 <ifty degrees. His horizon reaches 50 beyond the pole 
 :>f the earth, and gives the same apparent elevation to 
 die pole of the heavens. It cuts the equator, and all 
 che circles of daily motion, at an angle of 40, being al- 
 ways equal to the co-altitude of the pole. Thus, let HO 
 ' v Fig. 6,) represent the horizon, EQ the equator, and 
 PP' the axis of the earth. Also, //, mm, &c., parallels 
 of latitude. Then the horizon of a spectator at Z, in 
 'atitude 50 reaches to 50 beyond the pole ; and the 
 ingle ECH, is 40. As we advance still farther north 
 
 37. Define an oblique sphere. Where is it seen ? At the 
 latitude of 50 how is the horizon situated ? Illustrate by fig. 6 
 
DIURNAL REVOLUTION. 
 
 Fig. 6. 
 
 25 
 
 the e.evation of the diurnal circles grows less and less, 
 and consequently the motions of the heavenly bodies 
 more and more oblique, until finally, at the pole, where 
 the latitude is 90, the angle of elevation of the equator 
 vanishes, and the horizon and equator coincide with 
 each other, as Before stated. 
 
 38. The CIRCLE OP PERPETUAL APPARITION, is the 
 boundary of that space around the elevated pole, where 
 the stars never set. Its distance from the pole is equal 
 to the latitude of the place. For, since the altitude of 
 the pole is equal to the latitude, a star whose polar dis- 
 tance is just equal to the latitude, will when at its low- 
 est point only just reach the horizon ; and all the stars 
 nearer the pole than this will evidently not descend so 
 far as the horizon. 
 
 Thus, mm (Fig. 6,) is the circle of perpetual appari- 
 tion, between which and the north pole, the stars never 
 set, and its distance from the pole OP is evidently equal 
 to the elevation of the pole, and of course to the lati- 
 tude. 
 
 38. What is the circle of perpetual apparition ? 
 by fig. 6. 
 
 3 
 
 I.lustrate 
 
26 THE EARTH. 
 
 39. In the opposite hemisphere, a similar part of the 
 sphere adjacent to the depressed pole never rises. Hence 
 
 The CIRCLE OF PERPETUAL OCCULTATION, IS the boUH* 
 
 dary of that space around the depressed pole, within 
 which the stars never rise. Thus, m'm (Fig. 6,) is the 
 circle of perpetual occultation, between which and the 
 south pole, the stars never rise. 
 
 40. In an oblique sphere, the horizon cuts the circles 
 of daily motion unequally. Towards the elevated pole, 
 more than half the circle is above the horizon, and a 
 greater and greater portion as the distance from the 
 equator is increased, until finally, within the circle of 
 perpetual apparition, the whole circle is above the hori- 
 zon. Just the opposite takes place in the hemisphere 
 next the depressed pole. Accordingly, when the sun is 
 in the equator, as the equator and horizon, like all other 
 great circles of the sphere, bisect each other, the days 
 and nights are equal all over the globe. But when the 
 sun is north of the equator, the days become longer than 
 the nights, but shorter when the sun 4s south of the 
 equator. Moreover, the higher the latitude, the greater 
 is the inequality in the lengths of the days and nights. 
 All these ooints will be readily understood by inspecting 
 figure 6 
 
 41. Most of the appearances of the diurnal i evolution 
 can be explained, either on the supposition that the ce- 
 lestial sphere actually all turns around the earth once in 
 24 hours, or that this motion of the heavens is merely 
 apparent, arising from the revolution of the earth on its 
 
 39. What is the circle of perpetual occultation ? Illustrate 
 by fig. 6. 
 
 40. How does the horizon of an oblique sphere cut the cir- 
 cles of daily motion ? Towards the elevated pole what rortion 
 of the circles is above the horizon ? Towards the depressed 
 pole, how is the fact? When are the days and nights equal 
 all over the world ? When are the days longer, and when 
 shorter than the nights ? 
 
DIURNAL REVOLUTION. 27 
 
 axis in the opposite direction a motion of which we 
 are insensible, as we sometimes lose the consciousness 
 of our own motion in a ship or a steamboat, and observe 
 all external objects to be receding from us with a com- 
 mon motion. Proofs entirely conclusive and satisfac- 
 tory, establish the fact, that it is the earth and not the 
 celestial sphere that turns ; but these proofs are drawn 
 from various sources, and the student is not prepared to 
 appreciate* their value, or even to understand some of 
 them, until he has made considerable proficiency in the 
 study of astronomy, and become familiar with a great 
 variety of astronomical phenomena. To such a period 
 of our course of instruction, we therefore postpone the 
 discussion of the hypothesis of the earth's rotation on 
 its axis. 
 
 42. While we retain the same place on the earth, the 
 diurnal revolution occasions no change in our horizon, 
 but our horizon goes round as well as ourselves. Let 
 us first take our station on the equator at sunrise ; our 
 horizon now passes through both the poles, and through 
 the sun, which we are to conceive of as at a great dis- 
 tance from the earth, and therefore as cut, not by the 
 terrestrial but by the celestial horizon. As the earth 
 turns, the horizon dips more and more below the sun, at 
 the rate of 15 degrees for every hour, and, as in the case 
 of the polar star, the sun appears to rise at the same rate. 
 In six hours, therefore, it is depressed 90 degrees below 
 the sun, which brings us directly under the sun, which, 
 for our present purpose, we may consider as having all 
 the while maintained the same fixed position in space 
 
 4 1 . On what suppositions can the appearances of the diurna. 
 revolution be explained ? Is it the earth or the heavens tha 
 really move ? Why is the discussion of this subject postponed ? 
 
 42. Explain the true cause of the sun's appearing to rise and 
 set, as observed at the equator. What is the position of the ho- 
 rizon at sunrise ? What at six hours afterwards ? What a 
 the end of twelve hours ? What at the end of eighteen hours' 
 
28 THE EARTH. 
 
 The earth continues to turn, and in six hours more, it 
 completely reverses the position of our horizon, so that 
 the western part of the horizon which at sunrise was 
 diametrically opposite to the sun now cuts the sun, and 
 soon afterwards it rises above the level of t-he sun, anci 
 the sun sets. During the next twelve hours, the sun 
 continues on the invisible side of the sphere, until the 
 horizon returns to the position from which it started, and 
 a new day begins. 
 
 43. Let us next contemplate the similar phenomena 
 at the poles. Here the horizon, coinciding as it does 
 with the equator, would cut the sun through its center, 
 and the sun would appear to revolve along the surface 
 of the sea, one-half above and the other half below the 
 horizon. This supposes the sun in its annual revolution 
 to be at one of the equinoxes. When the sun is north 
 of the equator, it revolves continually round in a circle, 
 which, during a single revolution, appears parallel to the 
 equator, and it is constantly day ; and when the sun 
 is south of the equator, it is, for the same reason, contin- 
 ual night. 
 
 We have endeavored to conceive of the manner in 
 which the apparent diurnal movements of the sun are 
 really produced at two stations, namely, in the right 
 sphere, and in the parallel sphere. These two cases 
 being clearly understood, there will be little difficulty in 
 applying a similar explanation to an oblique sphere. 
 
 ARTIFICIAL GLOBES. 
 
 44. Artificial globes are of two kinds, terrestrial and 
 celestial. The first exhibits a miniature representation 
 of the earth ; the second, of the visible heavens ; and 
 both show the various circles by which the two spheres 
 
 43. Explain the similar phenomena at the poles, first, when 
 the sun is at the equinoxes, and secondly, when it is north and 
 when it is south of the equator. 
 
ARTIFICIAL GLOBES. 29 
 
 are respectively traversed Since all globes are similar 
 solid figures, a small globe, imagined to be situated at 
 the center of the earth or of the celestial vault, may rep- 
 resent all the visible objects and artificial divisions of 
 either sphere, and with great accuracy and just propor- 
 tions, though on a scale greatly reduced. The study of 
 artificial globes, therefore, cannot be too strongly recom- 
 mended to the student of astronomy.* 
 
 45. An artificial globe is encompassed from north to 
 south by a strong brass ring to represent the meridian of 
 the place. This ring is made fast to the two poles and 
 thus supports the globe, while it is itself supported in a 
 vertical position by means of a frame, the ring being 
 usually let into a socket in which it may be easily slid, 
 so as to give any required elevation to the pole. The 
 brass meridian is graduated each way from the equator 
 to the pole 90, to measure degrees of latitude or decli- 
 nation, according as the distance from the equator refers 
 to a point on the earth or in the heavens. The horizon 
 is represented by a broad zone, made broad for the con- 
 venience of carrying on it a circle of azimuth, another of 
 amplitude, and a wide space on which are delineated 
 the signs of the ecliptic, and the sun's place for every 
 day in the year ; not because these points have any spe- 
 cial connexion with the horizon, but because this broad 
 surface furnishes a convenient place for recording them. 
 
 44. What does the terrestrial globe exhibit ? What does 
 the celestial globe ? What do both show ? 
 
 45. How is the meridian of the place represented ? To what 
 points is the brass meridian fastened ? What supports the ring ? 
 How is it graduated ? How is the horizon represented ? Why 
 is it made broad ? What circles are inscribed on it ? 
 
 * Tt were Desirable, indeed, that every student of the science should 
 have a celestial globe, at least, constantly before him. One of a 
 small size, as eight or nine inches, will answer the purpose, although 
 globes of these dimensions cannot usually be relied on for nice meas- 
 urements 
 
 3* 
 
SO THE EARTH. 
 
 46. Hour Circles are represented on the terrestrial 
 globe by great circles drawn through the pole of the 
 equator ; but, on the celestial globe, corresponding cir- 
 cles pass through the poles of the ecliptic, constituting 
 circles of latitude, while the brass meridian, being a se- 
 condary to the equinoctial, becomes an hour circle of 
 any star which, by turning the globe, is brought under it. 
 
 47. The Hour Index is a small circle described around 
 the pole of the equator, on which are marked the hours 
 of the day. As this circle turns along with the globe, it 
 makes a complete revolution in the same time with the 
 equator ; or, for any less period, the same number of de- 
 grees of this circle and of the equator pass under the 
 meridian. Hence the hour index measures arcs of right 
 ascension, 15 passing under the meridian every hour. 
 
 48. The Quadrant of Altitude is a flexible strip of 
 brass, graduated into ninety equal parts, corresponding 
 in length to degrees on the globe, so that when applied to 
 the globe *nd bent so as closely to fit its surface, it meas- 
 ures the angular distance between any two points. 
 When the zero, or the point where the graduation be- 
 gins, is laid on the pole of any great circle, the 90th de- 
 gree will reach to the circumference of that circle, and 
 being therefore a great circle passing through the pole 
 of another great circle, it becomes a secondary to the 
 latter. Thus the quadrant of altitude may be used as a 
 secondary to any great circle on the sphere ; but it is 
 used chiefly as a secondary to the horizon, the point 
 
 46. How are hour circles represented on the terrestrial 
 globe ? How are circles of latitude represented on the celes- 
 tial globe ? 
 
 47. Describe the hour index. What does it measure ? 
 
 48. What is the quadrant of altitude? How is it gradua 
 ted ? When the zero point is laid on the pole of any great cir- 
 cle, to what will the 90th degree reach ? How may it be used 
 as a secondary to any great circle ? When screwed on the 
 zenith what does it become ? What arcs does it then measure ? 
 
TERRESTRIAL GLOBE. 31 
 
 marked 90 being screwed fast to the pole of the hori- 
 zon, that is, the zenith, and the other end, marked 0. 
 being slid along between the surface of the sphere and 
 the wooden horizon. It thus becomes a vertical circle, 
 on which to measure the altitude of any star through 
 which it passes, or from which to measure the azimuth 
 of the star, which is the arc of the horizon intercepted 
 between the meridian and the quadrant of altitude pass- 
 ing through the star. 
 
 49. To rectify the. globe for any place, the north pole 
 must be elevated to the latitude of the place ; then the 
 equator and all the diurnal circles will have their due in- 
 clination in respect to the horizon ; and, on turning the 
 globe, every point on either globe will revolve as the 
 same point does in nature ; and the relative situations of 
 all places will be the same as on^the native spheres. 
 
 PROBLEMS ON THE TERRESTRIAL GLOBE. 
 
 50. To find the Latitude and Longitude of a place : 
 Turn the globe so as to bring the place to the brass me- 
 ridian ; then the degree and minute on the meridian di- 
 rectly over the place will indicate its latitude, and the 
 point of the equator under the meridian, will show its 
 longitude. 
 
 Ex. What is the Latitude and Longitude of the city 
 of New York? 
 
 51. To find a place having its Latitude and Longitude 
 given : Bring to the brass meridian the point of the equa- 
 tor corresponding to the longitude, and then at the de- 
 gree of the meridian denoting the latitude, the place will 
 be found. 
 
 Ex. What place on the globe is in Latitude 39 N. and 
 Longitude 77 W. ? 
 
 49. How do we rectify the globe for any place ? 
 
 50. Find the latitude and longitude of Washington City. 
 
 51. What place lies in latitude 39 N. and longitude 77 W.? 
 
32 THE EARTH. 
 
 52. To find the bearing and distance of two places : 
 Rectify the globe for one of the places ; screw the quad- 
 rant of altitude to the zenith,* and let it pass through 
 the other place. Then the azimuth will give the bear- 
 ing of the second place from the first, and the number 
 of degrees on the quadrant of altitude, multiplied by 69, 
 (the number of miles in a degree,) will give the distance 
 between the two places. 
 
 Ex. What is the bearing of New Orleans from New 
 York, and what is the distance between these places ? 
 
 53. To determine the difference of time in different 
 places : Bring the place that lies eastward of the other 
 to the meridian, and set the hour index at XII. Turn 
 the globe eastward until the other place comes to the 
 meridian, then the index will point to the hour required. 
 
 Ex. When it is noon at New York, what time is it at 
 London ? 
 
 54. The hour being given at any place, to tell what 
 hour it is in any other part of the world : Bring the 
 given place to the meridian, and set the hour index to 
 the given time ; then turn the globe, until the other 
 place comes under the meridian, and the index will 
 point to the required hour. 
 
 Ex. What time is it at Canton, in China, when it is 
 9 o'clock A. M. at New York ? 
 
 55. To find what people on the earth live under us, 
 having their noon at the time of our midnight : Bring 
 the place where we dwell to the meridian, and set the 
 
 52. What is the bearing and distance of New Orleans from 
 New York ? 
 
 53. When it is noon at New York, what time is it at Pekin ? 
 54 What time is it at London when it is noon at Boston ? 
 
 * The zenith will of course be the point of the meridian over the 
 place. 
 
TERRESTRIAL GLOBE. 33 
 
 hour index to XII ; then turn the globe until the other 
 XII comes under the meridian; the point under the 
 same part of the meridian where we were before, will 
 be the place sought. 
 
 Ex. Find what place is directly under New York. 
 
 56. To find what people of the southern hemisphere 
 are directly opposite to us : Bring our place to the me- 
 ridian ; the place in the same latitude south, then un- 
 der the meridian, will be the place in question. 
 
 Ex. What place in the southern hemisphere corres- 
 ponds to New Haven ? 
 
 57. To find the antipodes of a place, or the people 
 whose feet are exactly opposite to ours : Bring our place 
 to the^meridian ; set the hour index to XII, and turn the 
 globe until J;he other XII comes under the meridian; 
 then the point of the southern hemisphere under the me- 
 ridian and having the same latitude with ours, will be 
 the place of our antipodes. 
 
 Ex. Who are antipodes to the people of Philadelphia ? 
 
 58. To rectify the globe for the sun 9 s place : On the 
 wooden horizon, find the day of the month, and against 
 it is given the sun's place in the ecliptic, expressed by 
 signs and degrees.* Look for the same sign and degree 
 on the ecliptic, bring that point to the meridian and set 
 the hour index to XII. To all places under the merid- 
 ian it will then be noon, 
 
 Ex. Rectify the globe for the sun's place on the 1st 
 of September. 
 
 55. Find what place is directly under Philadelphia. 
 
 56. What place in south latitude corresponds to Boston ? 
 
 57. Who are the antipodes of the people of London ? 
 
 58. Rectify the globe for the sun's place for the first of June 
 
 * The larger globes have the day of the month marked against the 
 corresponding sign on the ecliptic itself. 
 
34 THE EARTH. 
 
 59. Tne latitude of the place being given, to find the 
 time of the sun's rising and setting on a.ny given day 
 at that place : Having rectified the globe for the lati- 
 tude, bring the sun's place in the ecliptic to the gradua- 
 ted edge of the meridian, and set the hour index to XII ; 
 then turn the globe so as to bring the sun to the eastern 
 and then to the western horizon, and the hour index 
 will show the times of rising and setting respectively. 
 
 Ex. At what time will the sun rise and set at New 
 Haven, Lat. 41 18', on the 10th of July ? 
 
 PROBLEMS ON THE CELESTIAL GLOBE. 
 
 60. To find the Declination and Right Ascension oj 
 a heavenly body : Bring the place of the body (whether 
 sun or star) to the meridian. Then the degree and 
 minute standing over it will show its declination, and 
 the point of the equinoctial under the meridian will give 
 its right ascension. It will be remarked, that the decli- 
 nation and right ascension are found in the same man- 
 ner as latitude and longitude on the terrestrial globe. 
 Right ascension, is expressed either in degrees or in 
 hours ; both being reckoned from the vernal equinox. 
 
 Ex. What is the declination and right ascension of the 
 bright star Lyra? also of the sun on the 5th of June? 
 
 61. To represent the appearance of the heavens at any 
 time : Rectify the globe for the latitude, bring the sun's 
 place in the ecliptic to the meridian, and set the hour 
 index to XII ; then turn the globe westward until the 
 index points to the given hour, and the constellations 
 would then have the same appearance to an eye situated 
 
 59. Find the time of the sun's rising and setting at Boston 
 (Lat, 42, Lon. 71) on the first day of December. 
 
 60. On the celestial globe, What is the right ascension and 
 declination of any star taken at pleasure ? 
 
 61. Represent the appearanceof the heavens at Tuscaloosa 
 (Lat. 33, Lon. 87) at 8 o'clock in the evening of Nov. 13th, 
 
CELESTIAL GLOBE. 35 
 
 at the center of the globe, as they have at that moment 
 in the sky. 
 
 Ex. Required the aspect of the stars at New Haven, 
 Lat. 41 18', at 10 o'clock, on the evening of Decem- 
 ber 5th. 
 
 62. To find the altitude and azimuth of any star . 
 Rectify the globe for the latitude, and let the quadrant 
 of altitude be screwed to the zenith, and be made to pass 
 through the star. The arc on the quadrant, from the 
 horizon to the star, will denote its altitude, and the arc 
 of the horizon from the meridian to the quadrant, will be 
 its azimuth. 
 
 Ex. What is the altitude and azimuth of Sirius (the 
 brightest of the fixed stars) on the 25th of December at 
 10 o'clock in the evening, in Lat. 41 ? 
 
 63. To find the angular distance of two stars from 
 each other : Apply the zero mark of the quadrant of alti- 
 tude to one of the stars, and the point of the quadrant 
 which falls on the other star, will show the angular dis- 
 tance between the two. 
 
 Ex. What is the distance between the two largest 
 stars of the Great Bear.* 
 
 64. To find the sun's meridian altitude, the latitude 
 and day of the month being given : Having rectified 
 the globe for the latitude, bring the sun's place in the 
 ecliptic to the meridian, and count the number of de- 
 
 62. Find the altitude and azimuth of Lyra at 10 o'clock in 
 the evening of June 1 8th, in Lat. 42. 
 
 63. Find the angular distance between any two stars taken 
 at pleasure. 
 
 * These two stars are sometimes called "the Pointers," from the line 
 which passes through them being always nearly in the direction of the 
 north star. The angular distance between them is about 5, and may 
 be learned as a standard of reference in estimating by the eye, the dis- 
 tance between any two points on the celestial vault. 
 
36 
 
 THE EARTH. 
 
 grees and minutes between that point of the meridian 
 and the zenith. The complement of this arc will be 
 the sun's meridian altitude. 
 
 Ex. What is the sun's meridian altitude at noon on 
 the 1st of August, in Lat. 41 18 / ? 
 
 CHAPTER III. 
 
 OP PARALLAX, REFRACTION, AND TWILIGHT. 
 
 65. PARALLAX is the apparent change of place which 
 bodies undergo by being viewed from different points. 
 
 Fig. 7. 
 
 Thus in figure 7, let A represent the earth, CH the ho- 
 rizon. HZ a quadrant of a great circle of the heavens, 
 
 64. What is the sun's meridian altitude at noon on the 18th 
 of June, in latitude 35 ? 
 
 65. Define parallax. Illustrate by the figure. What angle 
 measures the parallax? Why do astronomers consider the 
 heavenly bodies as viewed from the center of the earth ? 
 
PARALLAX. 37 
 
 extending from the horizon to the zenith ; and let E, F, 
 G, O, be successive positions of the moon at different 
 elevations, from the horizon to the meridian. Now a 
 spectator on the surface of the earth at A, would refer 
 the place of E to h, whereas, if seen from the center of 
 the earth, it would appear at H. The arc H/i is called 
 the parallactic arc, and the angle HE/i, or its equal AEC, 
 is the angle of parallax. The same is true of the angles 
 at F, G, and O, respectively. 
 
 Since then a heavenly body is liable to be referred to 
 different points on the celestial vault, when seen from 
 differe-nt parts of the earth, and thus some confusion 
 occasioned in the determination of points on the celes- 
 tial sphere, astronomers have agreed to consider the true 
 place of a celestial object to be that, where it would 
 appear if seen from the center of the earth. The doc- 
 trine of parallax teaches how to reduce observations 
 made at any place on the surface of the earth, to such as 
 hey would be if made from the center. 
 
 66. The angle AEC is called the horizonta parallax, 
 which may be thus defined. Horizontal Parallax, is 
 the change of position which a celestial body, appearing 
 in the horizon as seen from the surface of the earth, 
 would assume if viewed from the earth's center. It is 
 the angle subtended by the semi-diameter of the earth, 
 as viewed from the body itself. 
 
 It is evident from the figure/that the effect of parallax 
 upon the place of a celestial body is to depress it. Thus, 
 in consequence of parallax, E is depressed by the arc 
 Hh ; F by the arc Pp ; G by the arc Rr ; while O sus- 
 tains no change. Hence, in all observations on the al- 
 titude of the sun, moon, or planets, the amount of par- 
 allax is to be added : the stars, as we shall see here- 
 after, have no sensible parallax. 
 
 66. Define horizontal parallax By what is it subtended? 
 (See Art. 10. Note.) What is the effect of parallax upon the 
 place of a heavenly body? 
 
 4 
 
38 
 
 THE EARTH. 
 
 67. The determination of the horizontal parallax of a 
 celestial body is an element of great importance, since it 
 furnishes the means of estimating the distance of the 
 body from the center of the earth. Thus, if the angle 
 AEC (Fig 7,) be found, the radius of the earth AC be- 
 ing known, we have in the right angled triangle AEC, 
 the side AC and all the angles, to find the side CE, 
 which is the distance of the moon from the center ot 
 the earth.* 
 
 REFRACTION. 
 
 68. While parallax depresses the celestial bodies sub* 
 ject to it, refraction elevates them; and it affects alike 
 the most distant as well as nearer bodies, being occa- 
 sioned by the change of direction which light undergoes 
 
 Fig. 8. 
 
 67. Why is the determination of the parallax of a heavenly 
 body an element of great importance ? Illustrate by figure 7. 
 
 * Should the reader be unacquainted with the principles of trigonom- 
 etry, yet he ought to know the fact that these principles enable us, 
 when we have ascertained certain parts in a triangle, to find the un- 
 known parts. Thus, in the above case, when we have found the an- 
 gle of parallax, AEB, (which is determined by certain astronomical ob- 
 servations,) knowing also the semi-diameter of the earth AC, we can 
 find by trigonometry, the length of the side CE, which is the distance 
 of the body from the center of the earth. 
 
REFRACTION. 39 
 
 in passing through the atmosphere. Let us conceive of 
 the atmosphere as made up of a great number of concen- 
 tric strata, as AA, BB, CC, and DD, (Fig. 8,) increasing 
 rapidly in density (as is known to be the fact) in ap- 
 proaching near to the surface of the earth. Let S be a 
 star, from which a ray of light Sa enters the atmosphere 
 at a, where, being much turned towards the radius of 
 the convex surface,* it would change its direction into 
 the line &, and again into 6c, and cO, reaching the 
 eye at O. Now, since an object always appears in the 
 direction in which the light finally strikes the eye, the 
 star would be seen in the direction of the ray Oc, and 
 therefore, the star would apparently change its place, 
 in consequence of refraction, from S to S', being ele- 
 vated out of its true position. Moreover, since on ac- 
 count of the continual increase of density in descending 
 through the atmosphere, the light would be continually 
 turned out of its course more and more, it would there- 
 fore move, not in the polygon represented in the figure, 
 but in a corresponding curve, whose curvature is rapidly 
 increased near the surface of the earth. 
 
 68. What effect has refraction upon the place of a heavenly 
 body? By what is it occasioned ? Illustrate by figure 8. How 
 is a ray of light affected by passing out of a rarer into a denser 
 medium? Why is an oar bent in the water ? In what line 
 does the light move as it goes through the atmosphere ? 
 
 * The operation of this principle is seen when an oar, or any stick, 
 is thrust into water. As the rays of light by which the oar is seen, have 
 their direction changed as they pass out of water into air, the apparent 
 direction in which the body is seen is changed in the same degree, 
 giving it a bent appearance. Thus, in the figure, if Sax represents, the 
 oar, Sab will be the bent appearance as affected by refraction. The 
 transparent substance through which any ray of light passes, is called 
 a medium. It is a general fact in optics, that when light passes out of 
 a rarer into a denser medium,*s out of air into water, or out of space 
 into air, it is turned towards a perpendicular to the surface of the me- 
 dium, and when it passes out of a denser into a rarer medium, as out 
 of water into air, it is turned from the perpendicular. In the above 
 ease the light, passing out of space into air, is turned towards the ra- 
 dius of the earth, this being perpendicular to the surface of the atmos- 
 phere; and it is turned more and more towards that radius the nearer 
 it approaches to the earth, because the density of the air rapidly in- 
 creases. 
 
40 
 
 THE EARTH. 
 
 69. When a body is in the zenith, since a ray of light 
 from it enters the atmosphere at right angles to the re- 
 fracting medium, it suffers no refraction. Consequently, 
 the position of the heavenly bodies, when in the zenith, 
 is not changed by refraction, while, near the horizon, 
 where a ray of light strikes the medium very obliquely, 
 and traverses the atmosphere through its densest part, 
 the refraction is greatest. The following numbers, ta- 
 ken at different altitudes, will show how rapidly refrac- 
 tion diminishes from the horizorrrrpwards. The amount 
 of refraction at the horizon is 34' GO 7 '. At different ele- 
 vations it is as follows : 
 
 Elevation. 
 
 Refraction. 
 
 Elevation. 
 
 Refraction. 
 
 10' 
 
 32' 00" 
 
 30 
 
 1' 40" 
 
 20' 
 
 30' 00" 
 
 40 
 
 i' 09" 
 
 1 00' 
 
 24' 25" 
 
 45 
 
 0' 58" 
 
 5 00' 
 
 10' 00" 
 
 60 
 
 0' 33'' 
 
 10 00' 
 
 5' 20" 
 
 80 
 
 0' 10'" 
 
 20 00' 
 
 2' 39" 
 
 90 
 
 0' 00" 
 
 From this table it appears, that while refraction at the 
 horizon is 34 minutes, at so small an elevation as only 
 10' above the horizon it loses 2 minutes, more than the 
 entire change from the elevation of 30 to the zenith. 
 From the horizon to 1 above, the refraction is dimin- 
 ished nearly 10 minutes. The amount at the horizon, 
 at 45, and at 90, respectively, is 34', 58", and 0. In 
 finding the altitude of a heavenly body, the effect of pa- 
 rallax must be added, but that of refraction subtracted. 
 
 70. Since the whole amount of refraction near the 
 horizon exceeds 33', and the diameters of the sun and 
 moon are severally less than this, these luminaries are in 
 
 69. Has refraction any effect on aflbody in the zenith ? Why 
 not. ? When is the refraction greatest ? What is the amount 
 of refraction at the horizon ? Ho\C much does it lose within 
 10' of the horizon 1 What is the amount of refraction at an 
 elevation of 45 ? 
 
REFRACTION. 41 
 
 view both before they have actually risen and after they 
 have set. 
 
 The rapid increase of refraction near the horizon, is 
 strikingly evinced by the oval figure which the sun as- 
 sumes when near the horizon, and which is seen to the 
 greatest advantage when light clouds enable us to view 
 the solar disk. Were all parts of the sun equally raised 
 by refraction, there would be no change of figure ; but 
 since the lower side is more refracted than the upper, 
 the effect is to shorten the vertical diameter and thus to 
 give the disk an oval form. This effect is particularly 
 remarkable when the sun, at his rising or setting, is ob- 
 served from the top of a mountain, or at an elevation 
 near the sea shore ; for in such situations the rays of 
 light make a greater angle than ordinary, with a perpen- 
 dicular to the refracting medium, and the amount of re- 
 fraction is proportionally greater. In some cases of this 
 kind, the shortening of the vertical diameter of the sun 
 has been observed to amount to 6', or about one fifth of 
 the whole. 
 
 71. The apparent enlargement of the sun and moon 
 in the horizon, arises from an optical illusion. These 
 bodies in fact are not seen under so great an angle when 
 in the horizon, as when on the meridian, for they are 
 nearer to us in the latter case than in the former. The 
 distance of the sun is indeed so great that it makes very 
 little difference in his apparent diameter, whether he is 
 viewed in the horizon or on the meridian ; but with the 
 moon the case is otherwise ; its angular diameter, when 
 measured with instruments, is perceptibly larger at the 
 time of its culmination. Why then do the sun and 
 moon appear so much larger when near the horizon? It 
 
 70. What effect has refraction upon the appearances of the 
 sun and moon when near rising or setting 1 Explain the oval 
 figure of the sun when near the horizon. In what position of 
 the spectator does this phenomenon appear most conspicuous? 
 How much has the vertical diameter of the sun ever appeared 
 to be shortened ? 
 
 4* 
 
42 THE EARTH. 
 
 is owing to that general law, explained in optics, by 
 which we judge of the magnitudes of distant objects, 
 not merely by the angle they subtend at the eye, but 
 also by our impressions respecting their distance, allow- 
 ing, under a given angle, a greater magnitude as we im- 
 agine the distance of a body to be greater. Now, on ac- 
 count of the numerous objects usually in sight between 
 us and the sun, when on the horizon, he appears much 
 farther removed from us than when on the meridian, and 
 ve assign to him a proportionally greater magnitude. If 
 we view the sun, in the two positions, through smoked 
 glass, no such difference of size is observed, for here no 
 objects are seen but the sun himself. 
 
 The extraordinary enlargement of the sun or moon, 
 particularly the latter, when seen at its rising through a 
 grove of trees, depends on a different principle. Through 
 the various openings between the trees, we see differ- 
 ent images of* the sun or moon, a great number of which 
 overlapping each other, swell the dimensions of the 
 body under the most favourable circumstances, to a very 
 unusual size. 
 
 TWILIGHT. 
 
 72. Twilight also is another phenomenon depending 
 upon the agency of the earth's atmosphere. It is that 
 illumination of the sky which takes place just before 
 sunrise, and which continues after sunset. It is due 
 partly to refraction and partly to reflexion, but mostly to 
 the latter. While the sun is within 18 of the horizon, 
 before it rises or after it sets, some portion of its light is 
 conveyed to us by means of numerous reflections from 
 
 71. To what is the apparent enlargement of the sun and 
 moon when near the horizon owing ? Are these bodies seen 
 under a greater angle when in the horizon than in the zenith ? 
 To what general law of optics is the enlargement to be ascri- 
 bed ? How is it when we view the sun through smoked glass ? 
 To what is the extraordinary enlargement of these luminaries 
 owing, when seen through a grove of trees ? 
 
the atmosphere. Let AB (Fig. 9,) be the horizon of 
 the spectator at A, and let SS be a ray of light from the 
 sun when it is two or three degrees below the horizon. 
 Then to the observer at A, the segment of the atmos- 
 phere ABS would be illuminated. To a spectator at C, 
 whose horizon was CD, the small segment SDx w r ould 
 be the twilight ; while, at E, the twilight would disap- 
 pear altogether. 
 
 73. At the equator, where the circles of daily motion 
 aie perpendicular to the horizon, the sun descends 
 through 18 in an hour and twelve minutes (r|-=ljh.), 
 and the light of day therefore declines rapidly, and as 
 rapidly advances after day break in the morning. At the 
 pole, a constant twilight is enjoyed while the sun is 
 within 18 of the horizon, occupying nearly two- thirds 
 of the half year when the direct light of the sun is with- 
 drawn, so that the progress from continual day to con- 
 
 72. Define twilight How many degrees below the horizon 
 is the sun when it begins and ends ? How is the light of the 
 sun conveyed to us ? Explain by the figure. 
 
 73. What is the length of twilight at the equator? How 
 long does it last at the poles ? How is the progress from con- 
 tinual day to Constant night? To the inhabitants of an oblique 
 sphere, in what latitudes is twilight longest ? 
 
_ 44 THE EARTH. 
 
 stant night is exceedingly gradual. To the inhabitants 
 of an oblique sphere, the twilight is longer in proportion 
 as the place is nearer the elevated pole. 
 
 74. Were it not for the power the atmosphere has of 
 dispersing the solar light, and scattering it in various di- 
 rections, no objects would be visible to us out of direct 
 sunshine ; every shadow of a passing cloud would be 
 pitchy darkness ; the stars would be visible all day, and 
 every apartment into which the sun had not direct ad- 
 mission, would be involved in the obscurity of night. 
 This scattering action of the atmosphere on the solar 
 light, is greatly increased by the irregularity of tempera- 
 ture caused by the sun, which throws the atmosphere 
 into a constant state of undulation, and by thus bringing 
 together masses of air of different temperatures, produces 
 partial reflections and refractions at their common boun- 
 daries, by which means much light is turned aside from 
 the direct course, and diverted to the purposes of general 
 illumination. In the upper regions of the atmosphere, 
 as on the tops of very high mountains, where the air is 
 too much rarefied to reflect much light, the sky assumes 
 a black appearance, and stars become visible in the dav 
 time. 
 
 CHAPTER IV. 
 
 OF TIME. 
 
 75. TIME is a measured portion of indefinite duration.* 
 The great standard of time is the period of the revo- 
 lution of the earth on its axis, which, by the most exact 
 
 74. What would happen were it not for the power the at- 
 mosphere has of dispersing the solar light ? What would every 
 shadow of a cloud produce ? How is the scattering action of 
 the atmosphere increased ? What is the aspect of the sky in 
 the upper regions of the atmosphere-? 
 
 * From old Eternity's mysterious orb, 
 
 Was Time cut off and cast beneath the skies. Young- 
 
TIME. 45 
 
 observations, is found to be always the same. The time 
 of the earth's revolution on its axis is called a sidereal 
 day, and is determined by the revolution of a star from 
 the instant it crosses the meridian, until it comes round 
 to the meridian again. ' This interval being called a si- 
 dereal day, it is divided into 24 sidereal hours. Obser- 
 vations taken upon numerous stars, in different ages of 
 the world, show that they all perform their diurnal rev- 
 olutions in the same time, and that their motion during 
 any part of the revolution is perfectly uniform. 
 
 76. Solar time is reckoned by the apparent revolution 
 of the sun, from the meridian round to the same meridian 
 again. Were the sun stationary in the heavens, like a 
 fixed star, the time of its apparent revolution would be 
 equal to the revolution of the earth on its axis, and the 
 solar and the sidereal days would be equal. But since 
 the sun passes from west to east, through 360 in 365J 
 days, it moves eastward nearly 1 a day, (59' 8".3). 
 While, therefore, the earth is turning round on its axis, 
 the sun is moving in the same direction, so that when 
 we have come round under the same celestial meridian 
 from which we started, we do not find the sun there, 
 but he has moved eastward nearly a degree, and the 
 earth must perform so much more than one complete 
 revolution, in order to come under the sun again. Now 
 since a place on the earth gains 359 in 24 hours, how 
 long will it take to gain 1 ? 
 
 24 
 359 : 24 : : 1 : =^ nearly. 
 
 75. Define time What is the standard of time ? What is 
 a sidereal day ? Do the stars all perform their revolutions in 
 the same time ? Is their motion uniform 1^ 
 
 76. How is the solar time reckoned? How far does the sun 
 move eastward in a day ? How much longer is the solar than the 
 sidereal day ? If we reckoned the sidereal day 24 hours, how 
 should we reckon the solar? Reckoning the solar day at 24 
 hours, how long is the sidereal ? 
 
46 THE EARTH. 
 
 Hence the solar day is about 4 minutes longer than 
 the sidereal ; and if we were to reckon the sidereal day 
 24 hours, we should -reckon the solar day 24h. 4m. To 
 suit the purposes of society at large, however, it is found 
 most convenient to reckon the solar day 24 hours, and to 
 throw the fraction into the sidereal day. Then, 
 
 24h 4m. : 24 : : 24 : 23h. 56m. nearly (23h. 56 m 4*.09) 
 rrthe length of a sidereal day. 
 
 77. The solar days, however, do not always differ from 
 the sidereal by precisely the same fraction, since the in- 
 crements of right ascension, which measure the differ- 
 ence between a sidereal and a solar day, are not equal to 
 each other. Apparent time, is time reckoned by the 
 revolutions of the sun from the meridian to the meridian 
 again. These intervals being unequal, of course the 
 apparent solar days are unequal to each other. 
 
 78. Mean time, is time reckoned by the average 
 length of all the solar days throughout the year. This 
 is the period which constitutes the civil day of 24 hours, 
 beginning when the sun is on the lower meridian, name- 
 ly, at 12 o'clock at night, and counted by 12 hours from 
 the lower to the upper culmination, and from the upper 
 to the lower. The astronomical day is the apparent so- 
 lar day counted through the whole 24 hours, instead of 
 by periods of 12 hours each, and begins at noon. Thus 
 
 10 days and 14 hours of astronomical time, would be 
 
 1 1 days and 2 hours of apparent time ; for when the 10th 
 astronomical day begins, it is 10 days and 12 hours of 
 civil time. 
 
 79. Clocks are usually regulated so as to indicate mean 
 solar time ; yet as this is an artificial period, not marked 
 
 77. Do the solar days always differ from the sidereal by the 
 same quantity ? Define apparent time. 
 
 78. Define mean time. What constitutes the civil day ? 
 What makes an astronomical day ? When does the civil day 
 begin ? When does the astronomical day begin ? 
 
THE CALENDAR. 47 
 
 off, like the sidereal day, by any natural event, it is ne- 
 cessary to know how much is to be added to or sub- 
 tracted from the apparent solar time, in order to give the 
 corresponding mean time. The interval by which ap- 
 parent time differs from mean time, is called the equation 
 of time. If a clock were constructed (as it may be) so 
 as to keep exactly with the sun, going faster or slower 
 according as the increments of right ascension were 
 greater or smaller, and another clock were regulated to 
 mean time, then the difference of the two clocks, at any 
 period, would be the equation of time for that moment. 
 If the apparent clock were faster than the mean, then 
 the equation of time must be subtracted ; but if the ap- 
 parent clock were slower than the mean, then the equa- 
 tion of time must be added, to give the mean time. 
 The two clocks would differ most about the 3d of No- 
 vember, when the apparent time is 16 T m greater than the 
 mean (16 m 16 S .7). But, since apparent time is some- 
 times greater and sometimes less than mean time, the 
 two must obviously be sometimes equal to each other. 
 This is in fact the case four times a year, namely, April 
 15th, June 15th, September 1st, and December 24th. 
 
 THE CALENDAR. 
 
 80. The astronomical year is the time in which the 
 sun makes one revolution in the ecliptic, and consists of 
 365d. 5h. 48m. 51 s 60. The civil year consists of 365 
 days. The difference is nearly 6 hours, making one day 
 in four years. 
 
 The most ancient nations determined the number of 
 days in the year by means of the stylus, a perpendicular 
 
 79 What time do clocks commonly keep j Define the equa- 
 tion of time. How might two clocks be regulated so that their 
 difference would indicate the equation of time 1 How must 
 the equation of time be applied when the apparent clock is 
 faster than the mean 1 How when it is slower ? When would 
 the two clocks differ most ? How much would they then differ 7 
 When would they come together ? 
 
48 THE EARTH. 
 
 rod which casts its shadow on a smooth plane, bearing a 
 meridian line. The time when the shadow was shortest, 
 would indicate the day of the summer solstice ; and the 
 number of days which elapsed until the shadow returned 
 to the same length again, would show the number of 
 days in the year. This was found to be 365 wnc ie 
 days, and accordingly this period was adopted for trie 
 civil year. Such a difference, however, between the 
 civil and astronomical years, at length threw all dates 
 into confusion. For, if at first the summer solstice hap- 
 pened on the 21st of June, at the end of four years, the 
 sun would not have reached the solstice until the 22d of 
 June, that is, it would have been behind its time. At 
 the end of the next four years the solstice would fall on 
 the 23d ; and in process of time it would fall succes- 
 sively on every day of the year. The same would be 
 true of any other fixed date. Julius Caesar made the 
 first correction of the calendar, by introducing an inter- 
 calary day every fourth year, making February to con- 
 sist of 29 instead of 28 days, and of course the whole 
 year to consist of 366 days. This fourth year was de- 
 nominated Bissextile. It is also called Leap Year. 
 
 8], But the true correction was not 6 hours, but 5h 
 49m. ; hence the intercalation was too great by 1 1 min- 
 utes. This small fraction would amount in 100 years 
 to f of a day, and in 1000 years to more than 7 days. 
 From the year 325 to 1582, it had in fact amounted to 
 about 10 days ; for it was known that in 325, the vernal 
 equinox fell on the 21st of March, whereas, in 1582 it 
 fell on the llth. In order to restore the equinox to the 
 same date, Pope Gregory XIII, decreed, that the year 
 
 80. Define the astronomical year What is its exact period? 
 Of how many days does the civil year consist? How much 
 shorter is the civil than the astronomical year ? How didthe most 
 ancient nations determine the number of days in the year ? 
 When would the stylus mark the shortest day and when the 
 longest ? Explain the confusion which arose by reckoning the 
 year only 365 days. How did Julius Csesar reform the calendar ? 
 
THE CALENDAR 49 
 
 should be brought forward 10 days, by reckoning the 
 5th of October the 15th. In order to prevent the cal- 
 endar from falling into confusion afterwards, the follow- 
 ing rule was adopted : 
 
 Every year whose' number is not divisible by 4 with' 
 cut a remainder, consists of 365 days ; every*year which 
 is so divisible, but is not divisible by 100, of 366; every 
 year divisible by 100 but not by 400, again of 365; and 
 every year divisible by 400, of 366. 
 
 Thus the year 1838, not being divisible by 4, contains 
 365 days, while 1836 and 1840 are leap years. Yet to 
 make every fourth year consist of 366 days would in- 
 crease it too much by about f of a day in 100 years ; 
 therefore every hundredth year has only 365 days. 
 Thus 1800, although divisible by 4 was not a leap year, 
 but a common year. But we have allowed a whole day 
 in a hundred years, whereas we ought to have allowed 
 only three fourths of a day. Hence, in 400 years we 
 should allow a day too much, and therefore we let the 
 400th year remain a leap year. This rule involves an 
 error of less than a day in 4237 years. If the rule were 
 extended by making every year divisible by 4000 (which 
 would now consist of 366 days) to consist of 365 days, 
 the error would not be more than one day in 100,000 
 years. 
 
 82. This reformation of the calendar was not adopted 
 in England until 1752, by which time the error in the 
 Julian calendar amounted to about 11 days. The year 
 was brought forward, by reckoning the 3d of September 
 the 14th. Previous to that time the year began the 25th 
 
 81. By how many minutes was the allowance made by the 
 Julian calendar too great ? To how much would the error 
 amount in one hundred years ? To how much in a thousand 
 years ? To how much had it amounted from the year 325 to 
 1582 ? What changes did Pope Gregory make in the year? 
 State the rule for the calendar. Of the three years 1836, 
 1 838, and 1 840, which are leap years ? Was 1 800 a leap year ? 
 How is every 400th year ? 
 
 5 
 
50 THE EARTH. 
 
 of March ; but it was now made to begin on the 1st of 
 January, thus shortening the preceding year, 1751, one 
 quarter.* 
 
 As in the year. 1582, the error in the Julian calendar 
 amounted^to 10 days, and increased by f of a day in a 
 century, a*t present the correction is 12 days ; and the 
 number of the year w ;1 l differ by one with respect to 
 dates between the 1st of January and the 25th of March, 
 
 Examples. General Washington was born Feb. 11 
 1781, old style ; to what date does this correspond in 
 new style ? 
 
 As the date is the earlier part of the 18th century, the 
 correction is 1 1 days, which makes the birth day fall on 
 the 22d of February ; and since the year 1731 closed 
 the 25th of March, while according to new style 1732 
 would have commenced on the preceding 1st of Janu- 
 ary ; therefore, the time required is Feb. 22, 1732. It 
 is usual, in such cases, to write both years, thus : Feb. 
 11, 1731-2, O. S. 
 
 2. A great eclipse of the sun happened May 15th, 
 1836 ; to what date would this time correspond in old 
 style ? Ans. May 3d. 
 
 83. The common year begins and ends on the same 
 day of the week ; but leap year ends one day later in the 
 week than it began. 
 
 For 52x7=364 days; if therefore the year begins 
 on Tuesday, for example, 364 days would complete 52 
 weeks, and one day would be left to begin another week, 
 
 82. When was this reformation first adopted in England ? 
 How was the year brought forward ? When did the year be- 
 gin before that time ? To how many days did the error amount 
 in 1752 ? How many days are allowed at present between 
 old and new style ? 
 
 * Russia, and the Greek Church generally, adhere to the old style. 
 [n order to make the Russian dates correspond to ours, we must add to 
 them 12 days. France and other Catholic countries, adopted the Gre- 
 gorian calendar soon after it was promulgated 
 
ASTRONOMICAL INSTRUMENTS 51 
 
 and the following year would begin on Wednesday. 
 Hence, any day of the month is one day later in the 
 week than the corresponding day of the preceding year. 
 Thus, if the 16th of November, 1838, falls on Friday, 
 the Itith of November, 1837, fell on Thursday, and in 
 1839 will fall on Saturday. But if leap year begins on 
 Sunday, it ends on Monday, and the following year be- 
 gins on Tuesday ; while any given day of the month is 
 two days latei in the week than the corresponding date 
 of the preceding year. 
 
 CHAPTER V. 
 
 OF ASTRONOMICAL INSTRUMENTS FIGURE AND DENSITY OP 
 
 THE EARTH. 
 
 84. THE most ancient astronomers employed no in- 
 struments of observation, but acquired their knowledge 
 of the heavenly bodies by long continued and most at- 
 tentive inspection with the naked eye. Instruments for 
 measuring angles were first used in the Alexandrian 
 school, about 300 years before the Christian era, 
 
 85. Wherever we are situated on the earth we appear 
 to be in. the center of a vast sphere, on the concave sur- 
 face of which all celestial objects are inscribed. If we 
 take any two points on the surface of the sphere, as two 
 stars for example, and imagine straight lines to be drawn 
 to them from the eye, the angle included between these 
 
 w 
 
 83. If the common year begins on a certain day of the week, 
 how will it end ? How is it with leap year 1 How does any 
 day of the month compare in the preceding and following year 
 with respect to the day of the week ? How is this in leap 
 year? 
 
 84. How did the most ancient nations acquire their knowl- 
 edge of the heavenly bodies ? When were astronomical in- 
 struments first introduced ? 
 
52 THE EARTH. 
 
 lines will be measured by the arc of the sky contained 
 between the two points. Thus if HBD, (Fig. 10,) rep- 
 Fig. 10. 
 
 resents the concave surface of the sphere, A, B, two 
 points on it, as two stars, and CA, CB, straight lines 
 drawn from the spectator to those points, then the angu- 
 lar distance between them is measured by the arc AB, 
 or the angle ACB. But this angle may be measured on 
 a much smaller circle, having the same center, as EFG, 
 since the arc EF will have the same number of degrees 
 as the arc AB. The simplest mode of taking an angle 
 between two stars, is by means of an arm opening at a 
 joint like the blade of a penknife, the end of the arm 
 moving like CE upon the graduated circle KEG. 
 
 The common surveyor's compass affords a simple ex- 
 ample of angular measurement. Here the needle lies in 
 a north and south line, while the circular rim of the 
 compass., when the instrument is level, corresponds to 
 the horizon. Hence the compass shows how many de- 
 grees any object to which we direct the eye, lies east or 
 \vest of the meridian. 
 
 85. How is the angular distance between two points on the 
 celestial sphere measured ? Explain figure 10, Show how the 
 circles of the sphere may be truly represented by the smaller 
 circles of the instrument, as the horizon by the surveyor's com- 
 pass. Explain the simplest mode of taking angles by figure 10 
 
ASTRONOMICAL INSTRUMENTS. 53 
 
 86. It is obvious that the larger the graduated circle 
 is, the more minutely its limb may be divided. If the 
 circle is one foot in diameter, each degree will occupy 
 jL of an inch. If the circle is 20 feet in (diameter, a 
 degree will occupy the space of two inches and could 
 be easily divided to minutes, since each minute would 
 cover a space of ^ of an inch. Refined astronomical 
 circles are now divided with very great skill and accu-- 
 racy, the spaces between the divisions being, when read 
 off, magnified by a microscope ; but in former times, 
 astronomers had no mode of measuring small angles 
 but by employing very large circles. But the telescope 
 and microscope enable us at present to measure celestial 
 arcs much more accurately than was done by the older 
 astronomers. * t 
 
 The principal instruments employed in astronomy, 
 are the Telescope, the Transit Instrument, the Altitude 
 and Azimuth Instrument, and the Sextant. 
 
 87. The Telescope has greatly enlarged our knowl- 
 edge of astronomy, both by revealing to us many things 
 invisible to the naked eye, and also by enabling us to 
 attain a much higher degree of accuracy than we could 
 otherwise reach, in angular measurements. It was in- 
 vented by Galileo about the year 1600. The powers of 
 the telescope were improved and enlarged by successive 
 efforts, and finally, about 50 years ago, telescopes were 
 constructed in England by Dr. Herschel, of a size and 
 power that have not since been surpassed. 
 
 A complete knowledge of the telescope cannot be ac- 
 quired without an acquaintance with the science of op- 
 tics ; but we may perhaps convey to one unacquainted 
 with that science, some idea of the leading principles of 
 
 86. What is the advantage of having large circles for angu- 
 lar measurements ? When the circle is one foot in diameter, 
 what space will 1 occupy on the limb ? What space when 
 the circle is twenty feet in diameter ? What are the princi- 
 pal instruments used in astronomical observations ? 
 
54 THE EARTH. 
 
 this noble instrument. By means of the telescope, we 
 first form an image of a distant object as the moon for 
 example, and then magnify that image by a microscope. 
 Let us first see how the image is formed. This may be 
 done either by a convex lens, or by a concave mirror. A 
 convex lens is a flat piece of glass, having its two faces 
 convex, or spherical, as is seen in a common sun glass. 
 Every one who has seen a sun glass, knows that when 
 held towards the sun it collects the solar rays into a 
 small bright circle in the focus. This is in fact a small 
 image of the sun. In the same manner the image of 
 any distant object, as a star, may be formed as is repre- 
 sented in the following diagram. Let ABCD represent 
 Fig. 11. 
 
 the tube of a telescope. At the front end, or at the end 
 which is directed towards the object, (which we will 
 suppose to be the moon,) is inserted a convex lens, 
 L, which receives the rays of light from the moon, and 
 collects them into the focus at a, forming an image of 
 the moon. This image is viewed by a magnifier attach- 
 ed to the end BC. The lens L is called the object-glass, 
 and the microscope in BC the eye-glass. We apply a 
 magnifier to this image just as we would to any object ; 
 
 87. Who invented the telescope ? Who constructed tele- 
 scopes of great size and power? Explain the leading prin- 
 ciple of the telescope. How is the image formed 1 What is 
 a convex lens ? How does it affect parallel rays of light ? 
 How do we view the image formed by the lens ? How is the 
 image magnified ? How is it rendered brighter ? 
 
ASTRONOMICAL INSTRUMENTS. 5^ 
 
 ncTby greatly enlarging its dimensions, we may render 
 us various parts far more distinct than they would other- 
 wise be, while at the same time the object lens collects 
 and conveys to the^eye a much greater quantity of light 
 than would proceed directly from the body under exam- 
 ination. A very small beam of light only from a distant 
 object, as a star, can enter the eye directly ; but a lens 
 one foot in diameter will collect a beam of light of the 
 same dimensions, and convey it to the eye. By these 
 means many obscure celestial objects become distinctly 
 visible, which would otherwise be either too minute, or 
 not sufficiently luminous to be seen by us. 
 
 88. But the image may also be formed by means of a 
 concave mirror, which, as well as the convex lens, has 
 the property of collecting the rays of light which pro- 
 ceed from any luminous body, and of forming an image 
 of that body. The image formed by the concave mir- 
 ror is magnified by a microscope in the same manner as 
 when formed by the convex lens. When the lens is 
 used to form an image, the instrument is called a Re- 
 fracting telescope ; when a concave mirror is used, it is 
 called a Reflecting telescope. 
 
 The telescope in its simplest form is employed not so 
 much for angular measurements, as for aiding the pow- 
 ers of vision in viewing the celestial bodies. When di- 
 rected to the sun, it reveals to us various irregularities on 
 his disk not discernible by naked vision ; when turned 
 upon the moon or the planets, it affords us new and in- 
 teresting views, and enables us to see in them the linea- 
 ments of other worlds ; and when brought to bear upon 
 the fixed stars, it vastly increases their number and re- 
 veals to us many surprising facts respecting them. 
 
 88. How is an image formed by a concave mirror? How is 
 this image magnified? *When-is the instrument called a re- 
 fracting and when a reflecting telescope ? For what pur- 
 poses are telescopes chiefly employed ? 
 
56 
 
 THE EARTH. 
 
 89. The Transit Instrument is a telescope, which is 
 fixed permanently in the meridian, and moves only in 
 that plane. It rests on a horizontal axis, which consists 
 gf two hollow cones applied base tobase, a form uniting 
 lightness and strength. The two ends of the axis rest 
 Fig. 12. 
 
 on two firm supports, as pillars of stone, for example, so 
 connected with the building as to be as free as possible 
 from all agitation. In figure 12, AD represents the tele- 
 
 89. What is a Transit Instrument ? On what supports does 
 it rest as represented in figure 12. Whv are they made so firm? 
 Describe all parts of the instrument, what is its use ? How 
 used to regulate clocks and watches ? What kind of time is 
 shown when the sun is on the meridian ? How is this 
 verted into mean t'me ? Give an example. 
 
 cori- 
 
ASTRONOMICAL INSTRUMENTS. 57 
 
 scope, E, W, massive stone pillars supporting the hori 
 zontal axis, beneath which is seen a spirit level, (which 
 is used to bring the axis to a horizontal position,) and n 
 a vertical circle graduated N into degrees and minutes. 
 This circle serves the purpose of placing the instrument 
 at any required altitude, or distance from the zenith, and 
 of course for determining altitudes and zenith distances. 
 The use of the transit instrument is to show the pre- 
 cise moment when a heavenly body is on the meridian. 
 One of its uses is to enable us to obtain the true time, 
 and thus to regulate our clocks and watches. We find 
 when the sun's center is on the meridian, and this gives 
 us the time of noon or apparent time. (Art. 78.) But 
 watches and clocks usually keep mean time, and there- 
 fore in order to set our time piece by the transit instru- 
 ment, we must apply the equation of time. 
 
 90. A TiooTi mark may easily be made by the aid of 
 the Transit Instrument. A window sill is frequently 
 selected as a suitable place for the mark, advantage be- 
 ing taken of the shadow projected upon it by the per- 
 pendicular casing of the window. Let an assistant stand 
 with a rule laid on the line of shadow and with a knife 
 ready to make the mark, the instant when the observer 
 at the Transit Instrument announces that the center of 
 the sun is on the meridian. By a concerted signal, as 
 the stroke of a bell, the inhabitants of a town may all 
 fix a noon mark from the same observation. It must be 
 borne in mind, however, that the noon mark gives the 
 apparent time, and that the equation of time must be 
 allowed for in setting the clock or watch. Suppose we 
 wish to set our clock right on the first of January. We 
 find by a table of the equation of time, that mean time 
 then precedes apparent time 3m. 43s. ; we must there- 
 fore set the clock at 3m. 43s. the instant tfte center of 
 the sun is on the meridian. If the time had been the 
 first of May instead of the first of January, then we 
 find by the table that 3m. is to be subtracted from the 
 apparent time, and consequently, when the center of the 
 
 90 Describe the mode of making a noon mark. 
 
58 THE EARTH. 
 
 sun was on the meridian, we should set our clock at llh. 
 57m. or 3m. before twelve. 
 
 91. The equation of time varies a little with different 
 years, but the following table will always be found 
 \vithin a few seconds of the truth. The equation for 
 the current year is given -exactly in the American Al- 
 manac. 
 
 Equation of Time for Apparent Noon. 
 
 
 
 1 
 
 JAN. 
 
 FEB. 
 
 MAR.JArR. 
 
 MAY 
 Sub. 
 
 JUN. 
 
 SnbT 
 
 M. S 
 
 JUL. 
 
 AUG 
 
 SEPT 
 
 OCT. 
 
 Nov. 
 
 D 1 
 
 Sub. 
 
 Add. 
 
 Add. 
 
 Add. 
 
 Add. 
 
 Add. 
 
 M. S. 
 
 Add. 
 
 M. S. 
 
 Add. 
 
 Sub. 
 
 Sub. 
 
 M. S. 
 
 M. S. 
 
 
 
 
 M. S. 
 
 M. S. 
 
 M. S. 
 
 M. S. 
 
 C 3 
 ?> 
 4 
 5 
 (5 
 
 8 
 9 
 10 
 
 3.43;13.53 
 4.1114. 1 
 4.3914. 8 
 5. 714.14 
 5.3414.19 
 
 12.42 
 12.30 
 12.18 
 12. 5 
 11.51 
 
 4. 6 
 3.48 
 3.30 
 3.12 
 2.54 
 
 3. 
 3. 7 
 3.15 
 3.21 
 3.27 
 
 2.38 
 2.29 
 2.19 
 2.10 
 2. 
 1.49 
 1.39 
 1.28 
 1.17 
 1. 5 
 
 3.19 
 3.31 
 3.4-2 
 3.53 
 4. 4 
 4.15 
 4.25 
 4.34 
 4.44 
 4.53 
 
 5^59 
 555 
 5.50 
 5.45 
 5.39 
 5.33 
 5.25 
 5.18 
 5.. 9 
 
 aO. I 
 
 sO.17 
 0.36 
 0.56 
 1.15 
 
 10. 9 
 10.28 
 10.47 
 11. 6 
 11.24 
 
 16.15 
 16.16 
 16.17 
 16.17 
 16.16 
 
 10.54 
 10.32 
 10. 8 
 9.45 
 9.20 
 
 6. 1 
 6.27 
 6.53 
 
 7.18 
 7.43 
 
 14.24 
 14.27 
 14.30 
 14.32 
 14.33 
 
 11.38 
 11.23 
 11. 8 
 10.53 
 10.38 
 
 2.37 
 2.19 
 2. 2 
 1.45 
 
 1.28 
 
 3.32 
 3.37 
 3.42 
 3.46 
 3.49 
 
 1.35 
 1.55 
 2.15 
 2.36 
 2.56 
 
 11.4216.14 
 11.59116.11 
 12.1616. 7 
 12.33116. 3 
 12.49 15.58 
 
 8.55 
 8.30 
 8. 4 
 7.37 
 7.10 
 
 LI 
 1-3 
 
 13 
 11 
 
 if) 
 
 16 
 
 17 
 IS 
 19 
 :30 
 -31 
 :2 
 
 2:! 
 
 -21 
 85 
 
 8. 7 
 8.31 
 8.54 
 9.16 
 9.37 
 
 14.34 
 14.33 
 14.32 
 14.30 
 14.28 
 
 10.22 
 10. 6 
 9.49 
 9.32 
 9.15 
 
 1.11 
 0.55 
 0.39 
 0.23 
 0. 8 
 
 3.51 
 3.53 
 3.55 
 3.56 
 3.56 
 
 0.53 
 0.41 
 0.29 
 0.17 
 0. 4 
 
 5. 1 
 5. 9 
 5.17 
 5.24 
 5.30 
 
 5. 1 
 4.51 
 4.41 
 4.31 
 4.20 
 
 3.17 
 3.38 
 3.59 
 4.20 
 4.41 
 
 13. 515.51 
 13.20 15.44 
 13.34 15.37 
 I3.49jl5.28 
 14. 215.18 
 
 6.43 
 6.15 
 5.47 
 5.18 
 4.49 
 
 9.58 
 10.19 
 10.38 
 10.57 
 11.15 
 11.33 
 11.49 
 12. 5 
 12.20 
 1235 
 12.48 
 13. 1 
 13.13 
 13.24 
 13.35 
 1344 
 
 14.25 
 14.20 
 14.16 
 14.10 
 14. 4 
 
 8.58 
 8.41 
 
 8.23 
 8. 5 
 
 7.47 
 
 Sub. 
 
 0. 7 
 0.22 
 0.36 
 0.50 
 1. 3 
 1.16 
 1.29 
 1.41 
 152 
 2. 4 
 2.14 
 2.24 
 2.34 
 2.43 
 2.52 
 
 3.56 
 3.55 
 3.54 
 3.52 
 3.49 
 3~46 
 3.42 
 3.38 
 3.33 
 3.28 
 3^22 
 3.16 
 3. 9 
 3. 2 
 254 
 2~46 
 
 Add. 
 0/8 
 0.21 
 0.34 
 0,17 
 1.0 
 1.13 
 1.26 
 1.39 
 1.52 
 2. 5 
 2.18 
 2.30 
 2.43 
 2.55 
 3. 8j 
 "1 
 
 5.37 
 5.42 
 
 5.48 
 5.52 
 557 
 
 
 6. 3 
 6. (i 
 6. 8 
 6. 9 
 
 4. 8 
 3.56 
 3.44 
 3.31 
 3.17 
 3. 3 
 2.19 
 2.34 
 2.19 
 2. 3 
 
 L47 
 1.30 
 1.13 
 0.56 
 
 0.38 
 0.20 
 
 5. 2 
 N 5.23 
 5.44 
 6. 5 
 6.26 
 
 ... 
 
 14.28 
 14.39 
 14.51 
 15. 1 
 
 15. 8 
 14.56 
 14.44 
 14.31 
 14.17 
 1473 
 13.47 
 13.31 
 13.14 
 12.56 
 
 4.20 
 3.50 
 3.21 
 2.51 
 2.21 
 
 13.58 
 13.50 
 13.42 
 13.34 
 13.25 
 
 7.29 
 7.11 
 6.52 
 6.34 
 615 
 
 6.4715.11 
 7. 815.21 
 "7.29^15.29 
 7.49 15.37 
 8.1015.44: 
 
 1.51 
 1.21 
 0.51 
 0.21 
 aO. 9 
 
 -2C, 
 37 
 28 
 29 
 30 
 ffl 
 
 13.15 
 13. 4 
 12.54 
 
 5.57 
 5.38 
 5.20 
 
 5. ^ 
 
 4.43 
 
 6.10 
 6.10 
 6.10 
 6. 9 
 
 6. 8 
 6. 5| 
 
 8.3015.51 12.38 
 8.5015.5712.18 
 9.11 16. 2fll.58 
 9.3016. 611.38 
 9.5016.1011.16 
 
 0.39 
 1. 9 
 1.39 
 2. 8 
 2.37 
 
 
 4.25 
 
 116.13! 
 
 3. 6 
 
 91. Is the equation of time the same or different in different 
 years ? In what book mav it he found exactly for the cur- 
 rent year ? 
 
 
ASTRONOMICAL INSTRUMENTS. 59 
 
 92. The Astronomical Clock is the constant compan- 
 ion of the Transit Instrument. This clock is so regu- 
 lated as to keep exact pace with the stars, and of course 
 with the revolution of the earth on its axis ; that is, it 
 is regulated to sidereal time. It measures the progress 
 of a star, indicating an hour for every 15, and 24 hours 
 for the whole period of the revolution of the star. Si- 
 dereal time, it will be recollected, commences when the 
 vernal equinox is on the meridian, just as solar time com- 
 mences when the sun is on the meridian. Hence, the 
 hour by the sidereal clock has no correspondence with 
 the hour of the day, but simply indicates how long it is 
 since the equinoctial point crossed the meridian. For 
 example, the clock of an observatory points to 3h 20m. ; 
 this may be jn the morning, at noon, or any other time 
 of the day, since it merely shows that it is 3h. 20m. 
 since the equinox was on the meridian. Hence, when 
 a star is on the meridian, the clock itself shows its right 
 ascension ; (Art. 24,) and the interval of time between 
 the arrival of any two stars upon the meridian, is the 
 measure of their difference of right ascension. 
 
 93. Astronomical clocks are made of the best work- 
 manship, with a compensation pendulum, and every 
 other advantage which can promote their regularity. 
 The Transit Instrument itself, when once accurately 
 placed in the meridian, affords the means of testing the 
 correctness of the clock, since one revolution of a star 
 from the meridian to the meridian again, ought to cor- 
 respond to exactly 24 hours by the clock, and to con- 
 
 92. How is the astronomical clock regulated ? What does 
 it measure ? How inany^ degrees does a star pass over in an 
 hour ? When does sidereal time commence ? What is de- 
 noted by the hour and minute of a sidereal clock ? How do 
 we determine the right ascension of a star ? 
 
 93. How is the workmanship of astronomical clocks? How 
 is the correctness of a clock tested ? To what degree of 
 perfection are clocks brought ? By what instrument are 
 clocks regulated? 
 
60 THE EARTH. 
 
 tinue the same from day to day; and the right asce-j 
 sion of \arious stars as they cross the meridian, ought 
 to be such by the clock as they are given in the tables, 
 where they are stated according to the accurate determi- 
 nations of astronomers. Or by taking ^the difference of 
 right ascension of any two stars on successive days, it 
 will be seen whether the going of the clock is uniform 
 for that part of the day ; and by taking the right ascen- 
 sion of different pairs of stars, we may learn the rate of 
 the clock at various parts of the day. We thus learn, 
 not only whether the clock accurately measures the 
 length of the sidereal day, but also whether it goes uni- 
 formly from hour to hour. 
 
 Although astronomical clocks have been brought to a 
 great degree of perfection, so as to vary hardly a second 
 for many months, yet none are absolutely perfect, and 
 most are so far from it as to require to be corrected by 
 means of the Transit Instrument every few days. In- 
 deed, for the nicest observations, it is usual not to at- 
 tempt to bring the clock to an absolute state of correct- 
 ness, but after bringing it as near to such a state as can 
 conveniently be done, to ascertain how much it gains or 
 loses in a day ; that is, to ascertain its rate of going, and 
 to make allowance accordingly. 
 
 94. The Transit Instrument is adapted to taking obser- 
 vations on the meridian only ; but we sometimes require 
 to know the altitude of a celestial body when it is not 
 on the meridian, and its azimuth, or distance from the 
 meridian measured on the horizon. An instrument es- 
 pecially designed to measure altitudes and azimuths, is 
 called an Altitude and Azimuth Instrument, whatever 
 may be its particular form. When a point is on the hor- 
 izon its distance from the meridkm, or its azimuth, may 
 be taken by the common surveyor's compass, the direc- 
 
 94. To what kind of observations only is the transit instru- 
 ment adapted ? What instrument is employed for finding alti- 
 tude and azimuth? Describe the Altitude and Azimuth In- 
 stuiment from figure 13 
 
ASTRONOMICAL INSTRUMENTS. 
 
 61 
 
 tion of the meridian being determined by the needle ; 
 but when the object, as a star, is not on the horizon, its 
 azimuth, it must be remembered, is the arc of the hori- 
 zon from the meridian to a vertical circle passing through 
 the star ; at whatever different altitudes, therefore, two 
 stars may be, and however the plane which passes 
 through them may be inclined to the horizon, still it is 
 their angular distance measured on the horizon which 
 determines their difference of azimuth. Figure 13 rep- 
 resents an Altitude and Azimuth Instrument, several of 
 the usual appendages and subordinate contrivances being 
 omitted for the sake of distinctness and simplicity. Here 
 abc is the vertical or altitude circle, and EFG the hori- 
 zontal or azimuth circle ; AB is a telescope mounted on 
 
 Fig. 13. 
 
 a horizontal axis and capable of two motions, one in al- 
 titude parallel to the circle abc, and the other in azimuth 
 parallel to EFG. Hence it can be easily brought to 
 
 6 
 
 
62 THE EARTH. 
 
 bear upon any object. At m, under the eye glass of the 
 telescope, is a small mirror placed at an angle of 45 
 with the axis of the telescope, by means of which the 
 image of the object is reflected upwards, so as to be 
 conveniently presented to the eye of the observer. At d 
 is represented a tangent screw, by which a slow motion 
 is given to the telescope at c. At h and g are seen two 
 spirit levels, at right angles to each other, which show 
 when the azimuth circle is truly horizontal. The in- 
 strument is supported on a tripod, for the sake of greater 
 steadiness, each foot being furnished with a screw for 
 levelling. 
 
 95. The SEXTANT is an instrument used for taking the 
 angular distance between any two bodies on the surface 
 of the celestial sphere, by reflecting the image of one of 
 the bodies so as to coincide with the other body as seen 
 directly. It is particularly valuable for measuring celes- 
 tial arcs at sea, because it is not, like most astronomical 
 instruments, affected by the motion of the ship. 
 
 This instrument (Fig 14,) is of a triangular shape, 
 and is made strong and firm by metallic crossbars. It 
 has two reflectors, I and H, called, respectively, the Index 
 Glass, and the Horizon Glass, both of which are firmly 
 fixed perpendicular to the plane of the instrument. The 
 Index Glass is attached to the movable arm ID and 
 turns as this is moved along the graduated limb EF. 
 This arm also carries a Vernier at D, which enables us to 
 take off minute parts of the spaces into which the limb 
 is divided. The Horizon Glass, H, consists of two 
 parts ; the upper being transparent or open, so that the 
 eye, looking through the telescope T, can see through 
 it a distant i>ody as a star at S, while the lower part is 
 a reflector. 
 
 95. Define the Sextant For what is it particularly valu- 
 able ? Describe it from figure. 14. Where is the Vernier and 
 what is its use ? Specify the manner in which the light comes 
 from the object to the eye. How can we measure the angulai 
 distance between the moon and a star ? 
 
ASTRONOMICAL INSTRUMENTS. 
 
 63 
 
 Suppose it were required to measure the angular dis- 
 tance between the moon and a certain star, the moon 
 
 Fig. 14. 
 
 being at M , and the star at S. The instrument is held 
 firmly in the hand, so that the eye, looking through the 
 telescope, sees the star S through the transparent part of 
 the Horizon Glass. Then the movable arm ID is moved 
 from F towards E, until the image of M is carried down 
 to S, when the number of degrees and parts of a degree 
 reckoned on the x limb from F to the index at D, will 
 show the angular distance between the two bodies. 
 
 FIGURE AND DENSITY OF THE EARTH. 
 
 96. We have already shown, that the figure of the 
 earth is nearly globular ; but since the semi-diameter of 
 the earth is taken as the base line in determining the 
 parallax of the heavenly bodies, and lies therefore at the 
 foundation of all astronomical measurements, it is very 
 
64 THE EARTH. 
 
 important that it should be ascertained with the greatest 
 possible exactness. Having now learned the use of as- 
 tronomical instruments, and the method of measuring 
 arcs on the celestial sphere, we are prepared to under- 
 stand the methods employed to determine the exact fig- 
 ure of the earth. This element is indeed ascertained 
 in different ways, each of which is independent of all 
 the rest, namely, by investigating the effects of the cen- 
 trifugal force arising from the revolution of the earth 
 on its axis by measuring arcs of the meridian and by 
 experiments with the pendulum. 
 
 97. First, the known effects of the centrifugal force, 
 would give to the earth a spheroidal figure, elevated in 
 the equatorial, and flattened in the polar regions. 
 
 By the centrifugal force is meant, the tendency which 
 revolving bodies exhibit to recede from the 
 Fig. 15. center. Thus when a grindstone is turn- 
 ed swiftly, water is thrown off from it in 
 .straight lines. The same effect is notic- 
 ed when a carriage wheel is driven rapidly 
 through the water. If a pail, containing 
 a little water, is whirled, the water rises 
 on the sides of the pail in consequence of 
 the centrifugal force. The same principle 
 is more strikingly illustrated by the annex- 
 ed cut, (Fig. 15,) which represents an 
 open glass vessel suspended by a cord at- 
 tached to its opposite sides, and passed 
 through a staple in the ceiling of the room. 
 A little water is introduced into the ves- 
 sel which is made to whirl rapidly by ap- 
 plying the hand to the opposite sides. As 
 it turns, the water rises on the sides of the 
 vessel, receding as far as possible from the 
 
 96. Why is it so necessary to ascertain accurately the semi- 
 diameter of the earth ? In how many different ways is this 
 element ascertained ? Specify them. What is meant by the 
 centrifugal force ? Give an illustration. Describe figure 15. 
 
ASTRONOMICAL INSTRUMENTS. 65 
 
 center. The same effect is produced by suffering the 
 cord to untwist freely, which gives a swift revolution 
 to the vessel. In like manner, a ball of soft clay when 
 made to turn rapidly on its axis, swells out in the central 
 parts and becomes flattened at the ends, forming the fig- 
 ure called an oblate spheroid. 
 
 Had the earth been originally constituted (as geolo- 
 gists suppose) of yielding materials, either fluid or semi- 
 fluid, so that its particles could obey their mutual at- 
 traction, while the body remained at rest it would spon- 
 taneously assume the figure of a perfect sphere ; as soon, 
 however, as it began to revolve on its axis, the greater 
 velocity of the equatorial regions would give to them a 
 greater centrifugal force", and cause the body to swell 
 out into the form of an oblate spheroid. Even had the 
 solid part of the earth consisted of unyielding materials 
 and been created a perfect sphere, still the waters that 
 covered it would have receded from the polar and have 
 been accumulated in the equatorial regions, leaving bare 
 extensive regions on the one side, and ascending to a 
 mountainous elevation on the other. 
 
 On estimating, from the known dimensions of the 
 earth and the velocity of its rotation, the amount of the 
 centrifugal force in different latitudes, and the figure of 
 equilibrium which would result, Newton inferred that 
 the earth must have the form of an oblate spheroid be- 
 fore the fact had been established by observation ; and 
 he assigned nearly the true ratio of the polar and equa- 
 torial diameters. 
 
 \ 97. What would be the figure of the earth derived from the 
 centrifugal force ? What figure would the earth have assumed 
 
 : if at rest ? How would this figure be changed when it began to 
 revolve ? Had the earth been originally a solid sphere covered 
 with water, how would the water have disposed itself when the 
 earth was made to turn on its axis ? How was the spheroidal 
 figure of the earth inferred before the fact was established by 
 observation ? 
 
 6* 
 
66 
 
 THE EARTH. 
 
 98. Secondly, the. spheroidal figure of the earth is 
 proved, by actually measuring the length of a degree on 
 the meridian in different latitudes. 
 
 Were the earth a perfect sphere, the section of it made 
 by a plane passing through its center in any direction 
 would be a perfect circle, whose curvature would be 
 equal in all parts ; but if we find by actual observation, 
 that the curvature of the section is not uniform, we in- 
 fer a corresponding departure in the earth from the figure 
 of a perfect sphere. The task of measuring portions of 
 the meridian, has been executed in different countries. 
 We may know, in each case, how far we advance on 
 the meridian, because every step we take northward, 
 produces a corresponding increase in the altitude of the 
 north star. That an increase of the length of the de- 
 grees of the meridian, as we advance from the equator 
 towards the pole, really proves that the earth is flattened 
 at the poles, will be readily seen on a little reflection. 
 We must bear in mind that a degree is not any certain 
 length, but only the three hundred and sixtieth part of a 
 circle, whether great or small. If, therefore, a degree is 
 longer in one case than in another, we infer that it is the 
 three hundred and sixtieth part of a larger circle ; and 
 since we find that a degree towards the pole is longer 
 than a degree towards the equator, we infer that the cur- 
 vature is less in the former case than in the latter. 
 
 The result of all the measurements is, that the length 
 of a degree increases as we proceed from the equator 
 towards the pole, as may be seen from the following 
 table : 
 
 98. By what measurements is the spheroidal figure of the 
 earth proved ? What would be the curvature in all parts were 
 the earth a perfect sphere ? How may we know when we have 
 advanced one degree northward in the meridian ? Explain how 
 an increase of the length of a degree proves that the earth is 
 flattened towards the poles ? In what places hive arcs of the me- 
 ridian been measured 7 What is the mean diameter of the 
 earth ? What is 'the difference between the two diameters ? 
 What fraction expresses the ellipticity of the earth ? 
 
ASTRONOMICAL INSTRUMENTS. 
 
 67 
 
 Places of observation. 
 
 Latitude. 
 
 Length of a degree in miles 
 
 Peru, 
 Pennsylvania, 
 Italy, 
 France, 
 England, 
 Sweden, 
 
 00 00' 00" 
 30 12 00 
 43 01 00 
 46 12 00 
 51 29 541 
 66 20 10 
 
 68.732 
 68.896 
 68.998 
 69.054 
 69.164 
 69.292 
 
 Combining the results of various estimates, the di- 
 mensions of the terrestrial spheroid are found to be as 
 follows : 
 
 Equatorial diameter, . . . 7925.648 
 Polar diameter, .... 7899.170 
 Mean diameter, , 7912.409 
 
 The difference between the greatest and the least, is 
 26.478 = ^ 9 of the greatest. This fraction (^Q) is de- 
 nominated the ellipticity of the earth, being the excess 
 of the longest over the shortest diameter. 
 
 99. Thirdly, the figure of the earth is shown to be 
 spheroidal, by observations with the pendulum. 
 
 If a pendulum, like that of a clock, be "suspended 
 and the number of its vibrations per hour be counted, 
 they will be found to be different in different latitudes. 
 A pendulum that vibrates 3600 times per hour at the 
 equator, will vibrate 3605J times at London, and a still 
 greater number of times nearer the north pole. Now the 
 vibrations of the pendulum are produced by the force of 
 
 96. Explain how we may ascertain the figure of the earth by 
 means of a pendulum How will the number of vibrations be 
 in different latitudes ? How many times will a pendulum vi- 
 brate in an hour at London, which vibrates 3600 times per hour 
 at the equator ? How are the vibrations of the pendulum pro- 
 duced ? Why are these comparative numbers at different 
 places measures of the relative distances from the center of the 
 earth ? What could we infer from two observations with the 
 pendulum, one at the equator and the other at the north pole ? 
 To what conclusions have pendulum observations, made in va- 
 rious parts of .he earth, led ? 
 
THE EARTH. 
 
 gravity. Hence their comparative number at different 
 places is a measure of the relative forces of gravity at 
 those places. But when we know the relative forces of 
 gravity at different places, we know their relative dis- 
 tances from the center of the earth, because the nearer a 
 place is to the center of the earth, the greater is the force 
 of gravity. Suppose, for example, we should count the 
 number of vibrations of a pendulum at the equator, and 
 then carry it to the north pole and count the number of 
 .vibrations made there in the same time ; we should be 
 able from these two observations to estimate the relative 
 forces of gravity at these two points ; and having the rel- 
 ative forces of gravity, we can thence deduce their rela- 
 tive distances from the center of the earth, and thus ob- 
 tain the polar and equatorial diameters. Observations 
 of this kind have been taken with the greatest accuracy 
 in many places on the surface of the earth, at various 
 distances from each other, and they lead to the same 
 conclusions respecting the figure of the earth, as those 
 derived from measuring arcs of the meridian. 
 
 100. The density of the earth compared with water, 
 that is, its specific gravity, is 5^ The density was first 
 estimated by Dr. Hutton, from observations made by Dr. 
 Maskelyne, Astronomer Royal, on Schehallien, a moun- 
 tain of Scotland, in the year 1774. Thus, let M (Fig. 
 16,) represent the mountain, D, B, two stations on op- 
 posite sides of the mountain, and I a star ; and let IE 
 and IG be the zenith distances as determined by the 
 difference of latitude of the two stations. But the ap- 
 parent zenith distances as determined by the plumb line 
 are IE' and IG'. The deviation towards the mountain 
 on each side exceeded 7". The attraction of the moun- 
 tain being observed on both sides of it, and its mass be- 
 ing computed from a number of sections taken in all di 
 
 100 What is the specific gravity of the earth ? How was it 
 ascertained? "Explain figure 16. Why is the density of the 
 earth so important an element ? 
 
DENSITY OF THE EARTH. 
 
 69 
 
 rections, tnese data, when compared with the known 
 attraction and magnitude of the earth, led to a knowl- 
 edge of its mean density. According to Dr. Hutton, 
 this is to that of water as 9 to 2 ; but later and more ac- 
 curate estimates have made the specific gravity of the 
 earth as stated above. But this density is nearly double 
 the average density of the materials that compose the 
 exterior crust of the earth, showing a great increase of 
 density towards the center. 
 
 The density of the earth is an important element, as 
 we shall find that it helps us to a knowledge of the den- 
 sity of each of the other members of the solar system. 
 
 OF 
 
PART II. OF THE SOLAR SYSTEM. 
 
 101. HAVING considered the Earth, in its astronomical 
 relations, and the Doctrine of the Sphere, we proceed 
 now to a survey of the Solar System, and shall treat suc- 
 cessively of the Sun, Moon, Planets, and Comets. 
 
 CHAPTER I. 
 
 OF THE SUN SOLAR SPOTS ZODIACAL LIGHT. 
 
 102. THE figure which the sun presents to us is that 
 \f a perfect circle, whereas most of the planets exhibit a 
 jisk more or less elliptical, indicating that the true shape 
 of the body is an oblate spheroid. So great, however, 
 is the distance of the sun, that a line 400 miles long 
 would subtend an angle of only I" at the eye, and would 
 therefore be the least space that could be measured. 
 Hence, were the difference between two conjugate di- 
 ameters of the sun any quantity less than this, we could 
 not determine by actual measurement that it existed at 
 all. Still we learn from theoretical considerations, 
 founded upon the known effects of centrifugal force, 
 arising 'from the sun's revolution on his axis, that his 
 figure is not a perfect sphere, but is slightly spheroidal. 
 
 103. The distance of the sun from the earth, is nearly 
 95,000,000 miles. In order to form some faint concep- 
 
 101. What subjects are treated of in Part II 
 
 102. What figure does the sun present to us ? What angle 
 would a line of 400 miles on the sun's disk subtend ? How is 
 it inferred that the figure of the sun is spheroidal 1 
 
DENSITY. 71 
 
 tion at least of this vast distance, let us reflect that a rail- 
 way car, moving at the rate of 20 miles per hour, would 
 require more than 500 years to reach the sun. 
 
 The apparent diameter of the sun is a little more than 
 half a degree, (32' 3 X/ .) Its linear diameter is about 
 885,000 miles ; and since the diameter of the earth is 
 only 7912 miles, the latter number is contained in the 
 former nearly 112 times ; so that it would require one 
 hundred and twelve bodies like the earth, if laid side by 
 side, to reach across the diameter of the sun ; and a ship 
 sailing at the rate of ten miles an hour, would require 
 more than ten years to sail across the solar disk. 
 
 The sun is about 1,400,000 times as large as the earth. 
 The distance of the moon from the earth being 238,000 
 miles, were the center of the sun made to coincide with 
 the center of the earth, the sun would extend every way 
 from the earth nearly twice as far as the moon. 
 
 104. In density, the sun is only one-fourth that of the 
 earth, being but a little heavier than water-; and the 
 quantity of matter in the sun is three hundred and fifty 
 thousand times as great as in the earth. A body would 
 weigh nearly 28 times as much at the sun as at the 
 earth. A man weighing 200 Ibs. would, if transported 
 to the surface of the sun, weigh 5,580 Ibs., or nearly 2 \ 
 tons. To lift one's limb, would, in such a case, be be- 
 yond the ordinary power of the muscles. At the surface 
 of the earth, a body falls through 16 r ^feet in a second 
 
 103. What is the distance of the sun from the earth ? How 
 long would a railway car, moving at the rate of 20 miles per 
 hour, require to reach the sun ? How many bodies equal to 
 the earth could lie side by side across tho sun ? How long 
 would a ship be in sailing across it at 10 miles an hour ? If 
 the sun's center were made to coincide with the center of the 
 earth, how much farther would it reach than the moon ? What 
 is the sun's apparent diameter ? What is its linear diameter ? 
 
 104. In density how does the sun compare with the earth? 
 How in quantity of matter ? How much more would a body 
 weigh at the sun than at the earth ? How far would a body 
 fall in one second at the surface of the sun ? 
 
72 THE SUN. 
 
 but a body would fall at the sun in one second through 
 448.7 feet. 
 
 SOLAR SPOTS. 
 
 105. The surface of the sun, when viewed with a 
 telescope, usually exhibits dark spots, which vary much, 
 at different tinmss, in number, figure, and extent. One 
 hundred or more, assembled in several distinct groups, 
 are sometimes visible at once on the solar disk. Tl?e 
 greatest part of the solar spots are commonly very small, 
 but occasionally a spot of enormous size is seen occupy- 
 ing an extent of 50,000 miles in diameter. They are 
 sometimes even visible to the naked eye. when the sun 
 is viewed through colored glass, or, when near the hori- 
 zon, it is seen through light clouds or vapours. When it 
 is recollected that I" of the solar disk implies an extent 
 of 400 miles, it is evident that a space large enough to be 
 seen by the naked eye, must cover a very large extent. 
 
 A solar spot usually consists of two parts, the nucleus 
 and the umbra, (Fig. 17.) The nucleus is black, of a 
 
 rig. n: 
 
 105. Solar spots. Are they constant or variable in number 
 and appearance ? How many are sometimes seen on the sun's 
 disk at once 1 Are they usually large or small ? How many 
 miles in diameter are the largest ? Describe a spot. What 
 changes occur in the nucleus ? What is the umbra ? In what 
 part of the sun do the spots mostly appear ? What apparent 
 motions have they ? What is the period of their revolution ? 
 
SOLAR SPOTS. 
 
 73 
 
 very irregular shape, and is subject to great and sudden 
 changes, both in form and size. Spots have sometimes 
 seemed to burst asunder, and to project fragments in dif- 
 ferent directions. The umbra is a wide margin of 
 lighter shade, and is often of greater extent than the 
 nucleus. The spots are usually confined to a zone ex- 
 tending across the central regions of the sun, not exceed- 
 ing 60 in breadth. When the spots are observed from 
 day to day, they are seen to move across the disk of the 
 sun, occupying about two weeks in passing from one 
 limb to the other. After an absence of about the same 
 period, the spot returns, having taken 27d. 7h. 37m. in 
 the entire revolution. 
 
 106. The spots must be nearly 
 or quite in contact with the body 
 of the sun. Were they at any 
 considerable distance from it, the 
 time during which they would 
 be seen on the solar disk, would 
 be less than that occupied in 
 the remainder of the revolution. 
 Thus, let S, (Fig. 18,) be the 
 sun, E the earth, and abc the path 
 of the body, revolving about 
 the sun. Unless the spot were 
 nearly or quite in contact with 
 the body of the sun, being pro- 
 jected upon his disk only while 
 passing from b to c, and being 
 invisible while describing the 
 arc cab, it would of course be 
 out of sight longer than in sight, 
 whereas the two periods are 
 found to be equal. Moreover, 
 
 Fig. 18 
 
 106. How are the spots known to be nearly or quite in con- 
 tact with the body of the sun ? Illustrate by figure 18. What 
 causes the motion of the spots ? What is the period of the sun's 
 revolution on his axis * Explain by figure 19. 
 
 7 
 
74 
 
 THE SUN. 
 
 the lines which all the solar spots describe on the disk 
 of the sun, are found to be parallel to each other, like 
 the circles of diurnal revolution around the earth, and 
 hence it is inferred that they arise from a similar cause, 
 namely, the revolution of the sun on its axis, a fact which 
 is thus made known to us. 
 
 But although the spots occupy about 27-J- days in pass- 
 ing from one limb of the sun around to the same limb 
 again, yet this is not the period of the sun's revolution 
 on his axis, but exceeds it by nearly two days. For, 
 let AA'B (Fig. 19,) represent the sun, and EE'M the 
 orbit of the earth. Thus, when the earth is at E, the 
 visible disk of the sun will be 
 AA'B ; and if the earth remain- 
 ed stationary at E, the time oc- 
 cupied by a spot after leaving A 
 until it returned to A, would be 
 just equal -to the time of the 
 sun's revolution on his axis. 
 But during the 27J days in 
 which the spot has been per- 
 forming its apparent revolution, 
 the earth has been advancing 
 in his orbit from E to E', where 
 the visible disk of the sun is 
 
 A'B'. Consequently, before the spot can appear again 
 on the limb from which it set out, it must describe so 
 much more than an entire revolution as equals the arc 
 AA X , and this occupies nearly two days, which sub- 
 tracted from 27^ days, makes the sun's revolution on 
 its axis about 25J days ; or more accurately, it is 25d. 
 9h. 56m. 
 
 107. A telescope of moderate powers is sufficient to 
 show the spots on the sun, and it is earnestly recom- 
 mended to the learner to avail himself of the first oppor- 
 
 107. How large a telescope is sufficient to view the spots on 
 the sun ? How is the eye protected from the glare of the sun's 
 light ? How may these shades be made ? 
 
 
SOLAR SPOTS. 75 
 
 tunity he may have, to view them for himself. For ob- 
 servations on the sun, telescopes are usually furnished 
 with colored glass shades, which are screwed upon the 
 end of the instrument to which the eye is applied, foi 
 the purpose of protecting the eye from the glare of the 
 sun's light. Such screens may be easily made by hold- 
 ing a small piece of window glass over the flame of a 
 lamp, the wick being raised higher than usual so as to 
 smoke freely. 
 
 108. The cause of the solar spots is unknown. It is 
 not easy to determine what it is that occasions such 
 changes on the surface of the sun ; but various conjec- 
 tures have been proposed by different astronomers. Ga- 
 lileo supposed that the dark part of a spot is owing to 
 black cinders which rise from the interior of the sun, 
 where they are formed by the action of heat, constitu- 
 ting a kind of volcanic lava that floats upon the surface 
 of the fiery flood, which he supposed to constitute the 
 outer portion of the sun. But the vast extent which 
 these spots occasionally assume is unfavourable to such a 
 supposition. It is incredible that a quantity of volcanic 
 lava should suddenly rise to the surface of the sun, suffi- 
 cient to occupy (as a spot is sometimes found to do) 
 2000,000,000 s'quare miles. 
 
 Dr. Herschel proposed a theory respecting the nature 
 * nd constitution of the sun, which, more from respect 
 ;,o his authority than on account of any evidence by 
 which it is supported, has been generally received. Ac- 
 cording to him, the sun is itself an opake body like the 
 earth, but is envelpped at a considerable distance from 
 his body by two different strata of clouds, the exterior 
 
 108. Is the cause of solar spots well known ? What was 
 Galileo's hypothesis ? What objections are there against it 1 
 What is Herschel's theory of the nature and constitution of 
 ihe sun ? What sort of a body does he consider the sun itself? 
 By what is it encompassed ? Where is the repository of the 
 sun's light and heat ? How does he explain the spots ? What 
 objections are there to this theory ? What are faculeB ? 
 
76 THE SUN. 
 
 stratum being the fountain from which emanates the 
 sun's light and heat. The solar spots arise from the oc- 
 casional displacement of portions of this envelope of 
 clouds, disclosing to view tracts of the solid body of tl 
 sun. 
 
 We regard this view of the origin of the sun's light ar, 
 heat as unsubstantiated by any satisfactory proofs, ar 
 as in itself highly improbable. Such a medium wou] 
 be a very unsuitable repository for the intense heat < 
 the sun, which can arise only from fixed matter in a stai 
 of high ignition. The most probable supposition is, thi 
 the surface of the sun consists of melted matter in sue 
 a state. We must confess our ignorance of any know 
 cause which is adequate to explain the sudden extinc- 
 tion and removal of so large portions of this fiery flood, 
 as is occupied by some of the solar spots. 
 
 Besides the dark spots on the sun, there are also seen, 
 in different parts, places that are brighter than the neigh- 
 boring portions of the disk. These are called faculce. 
 Other inequalities are observable in powerful telescopes, 
 all indicating that the surface of the sun is in a state of 
 constant and powerful agitation. 
 
 ZODIACAL LIGHT. 
 
 109. The Zodiacal Light is a faint light resembling 
 the tail of a comet, and is seen at certain seasons of the 
 year following the course of the sun after evening twi- 
 light, or preceding his approach in the morning sky. 
 Figure 20 represents its appearance as seen in the even- 
 ing in March, 1836. The following are the leading facts 
 respecting it. 
 
 1. Its form is that of a luminpus pyramid, having its 
 base towards the sun. It reaches to an immense dis- 
 tance from the sun, sometimes even beyond the orbit of 
 the earth. It is brighter in the parts nearer the sun than 
 in those that are more remote, and terminates in an ob- 
 tuse apex, its light fading away by insensible gradations, 
 until it becomes too feeble for distinct vision. Hence 
 its limits are at the same time fixed at different dis- 
 
ZODIACAL LIGHT. 77 , 
 
 Fig. 2,). 
 
 lances from the sun by different observers, according to 
 their respective powers of vision. 
 
 2. Its aspects vary very much with the different seasons 
 of the year. About the first of October, in our climate 
 (Lat. 41 18') it becomes visible before the dawn of day. 
 rising along north of the ecliptic, and terminating above 
 the nebula of Cancer. About the middle of November, 
 its vertex is in the constellation Leo. At this time no 
 traces of it are seen in the west after sunset, but about 
 the first of December it becomes faintly visible in the 
 west, crossing the Milky Way near the horizon, and 
 reaching from the sun to the head of Capricornus, form- 
 ing, as its brightness increases, a counterpart to the Milky 
 
 109. Zodiacal Light. -Describe it. When and where 
 seen ? What is its form 1 How far does it reach ? Where 
 brightest ? How do its aspects vary at different seasons of 
 the year ? What, motions has it ? Is it equally conspicuous 
 every year ? What was it formerly held to be ? With what 
 phenomenon has it been supposed to be connected ? 
 
 7* 
 
78 THE SUN. 
 
 Way, between which on the right, and the Zodiacal 
 Light on the left, lies a triangular space embracing the 
 Dolphin. Through the month of December, the Zo- 
 diacal Light is seen on both sides of the sun, namely, 
 before the morning and after the evening twilight, some- 
 times extending 50 westward, and 70 eastward of the 
 sun at the same time. After it begins to appear in the 
 western sky, it increases rapidly from night to night, 
 both in length and brightness, and withdraws itself from 
 the morning sky, where it is scarcely seen after the 
 month of December, until the next October. 
 
 3. The Zodiacal Light moves through the heavens in 
 the order of the signs. It moves with unequal velocity, 
 being sometimes stationary and sometimes retrogade, 
 while at other times it advances much faster than the 
 sun. In February and March, it is very conspicuous in 
 the west, reaching to the Pleiades and beyond ; but in 
 April it becomes more faint, and nearly or quite disap- 
 pears during the month of May. It is scarcely seen in 
 this latitude during the summer months. 
 
 4. It is remarkably conspicuous at certain periods of 
 a few years, and then for a long interval almost disap- 
 pears. 
 
 5. The Zodiacal Light was formerly held to be the 
 atmosphere of the sun. But La Place has shown that 
 the solar atmosphere could never reach so far from the 
 sun as this light is seen to extend. It has been supposed 
 by others to be a nebulous body revolving around the 
 sun. The author of this work has ventured to suggest 
 the idea, that the extraordinary Meteoric Showers, which 
 at different periods visit the earth, especially in the 
 month of November, may be derived from this body. 
 See American Journal of Science, Vol. 29, p. 378. 
 
79 
 
 CHAPTER II 
 
 OF THE APPARENT ANNUAL MOTION OF THE SUN SEASONS 
 FIGURE OF THE EARTH'S ORBIT. 
 
 110. THE revolution of the earth around the sun once 
 a year, produces an apparent motion of the sun around 
 the earth in the same period. When bodies are at such 
 a distance from each other as the earth and the sun, a 
 spectator on either would project the other body upon 
 the concave sphere of the heavens, always seeing it on 
 the opposite side of a great circle, 180 from himself. 
 Thus when the earth arrives at Libra (Fig. 21,) we see 
 
 Fig. 21. 
 
 
 the sun in the opposite sign Aries. When the earth 
 moves from Libra to Scorpio, as we are unconscious of 
 our own motion, the sun it is that appears to move from 
 Aries to Taurus, being always seen in the heavens, where 
 
80 THE SUN. 
 
 a line drawn from the eye of the spectator through the 
 body meets the concave sphere of the heavens. Hence 
 the line of projection carries the sun forward on one 
 side of the ecliptic, at the same rate as the earth moves 
 on the opposite side ; and therefore, although we are un- 
 conscious of our own motion, we can read it from day to 
 day in the motions of the sun. If we could see the stars 
 at the same time with the sun, we could actually observe 
 from day to day the sun's progress through them, as we 
 observe the progress of the moon at night ; only the 
 sun's rate of motion would be nearly fourteen times 
 slower than that of the moon. Although we do not see 
 the .stars when the sun is present, yet after the sun is set, 
 we can observe that it makes daily progress eastward, 
 as is apparent from the constellations of the Zodiac oc- 
 cupying, successively, the western sky after sunset, pro- 
 ving that either all the stars have a common motion east- 
 ward independent of their diurnal motion, or that the 
 sun has a motion -past them, from west to east. We' 
 shall see hereafter abundant evidence to prove, that this 
 change in the relative position of the sun and stars, is 
 owing to a change in the apparent place of the sun, 
 and not to any change in the stars. 
 
 111. Although the apparent revolution of the sun is 
 in a direction opposite to the real motion of the earth, as 
 regards absolute space, yet both are nevertheless from 
 west to east, since these terms do not refer to any direc- 
 tions in absolute space, but to the order in which certain 
 constellations (the constellations of the Zodiac) succeed 
 one another. The earth itself, on opposite sides of its 
 orbit, does in fact move towards directly opposite points 
 
 110. What produces the apparent motion of the sun around 
 the earth once a year ? How would a spectator on either body 
 see the other ? When the earth is at Libra, where does the 
 sun appear to be ? Explain figure 21. If the stars were visi- 
 ble in the day time, how could we determine the sun's path ? 
 What change do the constellations of the Zodiac undergo with 
 respect to the sun ? 
 
ANNUAL MOTION. 81 
 
 of space ; but it is all the while pursuing its course in 
 the order of the signs. In the same manner, although 
 the earth turns on its axis from west to east, yet any 
 place on the surface of the earth is moving in a direc- 
 tion in space exactly opposite to its direction twelve 
 hours before. If the sun left a visible trace on the face 
 of the sky, the ecliptic would of course be distinctly 
 marked on the celestial sphere as it is on an artificial 
 globe ; and were the equator delineated in a similar man- 
 ner, (by any method like that supposed in Art. 33,) we 
 should 'then see at a glance the relative position of these 
 two circles, the points where they intersect one another 
 constituting the equinoxes, the points where they are at 
 the greatest distance asunder, or the solstices, and vari- 
 ous other particulars, which for want of such visible 
 traces, we are now obliged to search for by indirect and 
 circuitous methods. It will even aid the learner to have 
 constantly before his mental vision, an imaginary delin- 
 eation of these two important circles on the face of the 
 sky. 
 
 112. The equator makes an angle with the ecliptic oj 
 23 28'. This is called the obliquity of the ecliptic. 
 As the sun and earth are both always in the ecliptic, and 
 as the motion of the earth in one part of it makes the 
 sun appear to move in the opposite part at the same rate, 
 the sun apparently descends in the winter 23 28' to the 
 south of the equator, and ascends in the summer the 
 same number of degrees to the north of it. We must 
 keep in mind that the celestial equator and the celestial 
 ecliptic are here understood, and we may imagine them 
 
 111. In what sense are the motions of the sun and earth 
 opposite, and in what sense in the same direction ? If the 
 ecliptic and equator were distinctly delineated on the face of 
 the sky, what points in them could be easily observed ? 
 
 112. What angle does the equator make with the ecliptic? 
 In what circle do the sun and earth always appear ? How far 
 do they recede from the equator ? How does the obliquity oi 
 the ecliptic vary ? 
 
82 THE SUN. 
 
 to be two great circles distinctly delineated on the face 
 of the sky. On comparing observations made at differ- 
 ent periods for more than two thousand years, it is found, 
 that the obliquity of the ecliptic is not constant, but 
 that it undergoes a slight diminution from age to age, 
 amounting to 52" in a century, or about half a second 
 annually. We might apprehend that by successive ap- 
 proaches to each other the equator and ecliptic would 
 finally coincide ; but astronomers have found by a most 
 profound investigation, founded on the principles of 
 universal gravitation, that this variation is confined with- 
 in certain narrow limits, and that the obliquity, after di- 
 minishing for some thousands of years, will then in- 
 crease for a similar period, and will thus vibrate for ever 
 about a mean value. 
 
 113. Let us conceive of the sun as at that point of the 
 ecliptic where it crosses the equator, that is, at one of the 
 equinoxes, as the vernal equinox. Suppose he stands 
 still then for twenty four hours. The revolution of the 
 earth on its axis from east to west during this twenty 
 four hours, will make the sun appear to describe a great 
 circle from east to west, coinciding with the equaton 
 At the end of this period, suppose the sun to move 
 northward one degree and to remain there for the next 
 twenty-four hours, in which time the revolution of the 
 earth will make the sun appear to describe another cir- 
 cle from east to west, parallel to the equator, but one 
 degree north of it. Thus we may conceive of the sun 
 as moving one degree every day for about three months, 
 when it will reach the point of the ecliptic farthest 
 from the equator, which is called the tropic from a Greek 
 
 113. Suppose the sun to start from the equator and to ad- 
 vance one degree north daily, explain its apparent diurnal rev- 
 olutions. When is the sun at the northern tropic ? When is 
 he at the southern tropic ? How are the respective meridian 
 altitudes of the sun at these periods ? How do we find from 
 *hese observations, the obliquity of the ecliptic ? 
 
THE SEASONS. 83 
 
 word (i^errw) which signifies to turn, because when the 
 sun arrives at this point, his motion in his orbit carries 
 him continually towards the equator, and therefore he 
 seems to turn about. 
 
 When the sun is at the northern tropic, which hap- 
 pens about the 21st of June, his elevation above the 
 southern horizon at noon, is the greatest of the year ; 
 and when he is at the southern tropic, about the 21st 
 of December, his elevation at noon is the least in the 
 year. The difference between these two meridian alti- 
 tudes, will give the whole distance from one tropic to 
 the other, and consequently twice the distance from each 
 tropic to the equator. By this means we find how far 
 the tropic is from the equator, and that gives us the in- 
 clination of the two circles to one another ; for the great- 
 est distance between any two great circles on the sphere, 
 is always equal to the angle which they make with each 
 other. 
 
 114. The dimensions of the earth's orbit, when com- 
 pared with its own magnitude, are immense. 
 
 Since the distance of the earth from the sun is 
 95,000,000 miles, and the length of the entire orbit nearly 
 000,000,000 miles, it will be found, on calculation, that 
 the earth moves 1,640,000 miles per day, 68,000 miles 
 per hour, 1,100 miles per minute, and nearly 19 miles 
 every second, a velocity nearly sixty times as great as 
 the maximum velocity of a cannon ball. A place on 
 the earth's equator turns, in the diurnal revolution, at the 
 rate of about 1,000 miles an hour and ^ of a mile per 
 second. The motion around the sun, therefore, is nearly 
 seventy times as swift as the greatest motion around the 
 axis. 
 
 114. What is said of the dimensions of the earth's orbit ? 
 At what rate does the earth move in its orbit per day, hour, 
 minute, and second ? How far does a place on the earth's 
 equator move per hour and second ? How much swifter is 
 the motion in the orbit than on its axis ? 
 
84 THE SUN. 
 
 THE SEASONS. 
 
 115. The change of seasons depends on two causes, 
 (1) the obliquity of the ecliptic, and (2) the earth's axis 
 always remaining parallel to itself. Had the earth's 
 axis been perpendicular to the plane of its orbit, the 
 equator would have coincided with the ecliptic, and the 
 sun would have constantly appeared in the equator 
 To the inhabitants of the equatorial regions, the sun 
 would always have appeared to move in the prime ver- 
 tical ; and to the inhabitants of either pole, he would 
 always have been in the horizon. But the axis being 
 turned out of a perpendicular direction 23 28', the 
 equator is turned the same distance out of the ecliptic ; 
 and since the equator and ecliptic are two great circles 
 which cut each other in two opposite points, the sun, 
 while performing his circuit in the ecliptic, must evi- 
 dently be once a year in each of those points, and must 
 depart from the equator of the heavens to a distance on 
 either side equal to the inclination of the two circles, 
 that is, 23 28'. 
 
 116. The earth being a globe, the sun constantly en- 
 Kghtens the half next to him,* while the other half is in 
 darkness. The boundary between the enlightened and 
 unenlightened part, is called the circle of illumination. 
 When the earth is at one of the equinoxes, the sun is at 
 the other, and the circle of illumination passes through 
 both the Doles. When the earth reaches one of the 
 
 115. The Seasons. On what two causes does the change 
 of seasons depend ? Had the earth's axis been perpendicu- 
 lar to the plane of its orbit, in what great circle would the sun 
 always have appeared to move ? 
 
 * In fact, the sun enlightens a little more than half the earth, since 
 on account of his vast magnitude the tangents drawn from opposite 
 sides of the suit to opposite sides of the earth, converge to a point 
 behind the earth, as will be seen by and by in the representation of 
 eclipses 
 
THE SEASONS. 
 
 65 
 
 tropics, the sun being at the other, the circle of illumin- 
 ation cuts the earth, so as to pass 23 28' beyond the 
 nearer, and the same distance short of the remoter pole. 
 These results would not be uniform, were not the earth's 
 axis always to remain parallel to itself. The following 
 figure will illustrate the foregoing statements. 
 Fig. 22. - 
 
 ^ 
 
 Let ABCD represent the earth's place in different 
 parts of its orbit, having the sun in the center. Let A, 
 
 116. How much of the earth does the sun enlighten at once ? 
 Define the circle of illumination. How does it cut the earth at 
 the equinoxes ? How at the solstices ? Explain figure 22. 
 When the earth is at one of the tropics and the sun at the 
 other, where is it continual day and where continual night? 
 
86 THE SUN. 
 
 C, be the positions of the earth at the equinoxes, and B, 
 
 D, its positions at the tropics, the axis ns being always 
 parallel to itself.* At A and C the sun shines on both 
 7i and s ; and now let the globe be turned round on its 
 axis, and the learner will easily conceive that the sun 
 will appear to describe the equator, which being bisected 
 by the horizon of every place, of course the day and 
 night will be equal in all parts of the globe.f Again, 
 at B when the earth is at the southern tropic, the sun 
 shines 23J beyond the north pole n, and falls the same 
 distance short of the south pole s. The case is exactly 
 reversed when the earth is at the northern tropic and 
 the sun at the southern. While the earth is at one of 
 the tropics, at B for example, let us conceive of it as turn- 
 ing on its axis, and we shall readily see that all that part 
 of the earth which lies within the north polar circle will 
 enjoy continual day, while that within the south polar 
 circle will have continual night, and that all other places 
 will have their days longer as they are nearer to the en- 
 lightened pole, and shorter as they are nearer to the un- 
 enlightened pole. This figure likewise shows the suc- 
 cessive positions of the earth at different periods of the 
 year, with respect to the signs, and what months corres- 
 pond to particular signs. Thus the earth enters Libra 
 and the sun Aries on the 21st of March, and on the 21st 
 of June the earth is just entering Capricorn and the sun 
 Cancer. 
 
 117. Had the axis of the earth been perpendicular 
 to the plane of the ecliptic, then the sun would always 
 have appeared to move in the equator, the days would 
 every where have been equal to the nights, and there 
 could have been no change of seasons. On the other 
 hand, had the inclination of the ecliptic to the equator 
 
 * The learner will remark that the hemisphere towards n is above, 
 and that towards 5 is below the plane of the paper. It is important to 
 form a just conception of the position of the axis with respect to the 
 plane of its orbit. 
 
 t At the pole, the solar disk, at the time of the equinox, appears bis- 
 ected by the horizon. 
 
THE SEASONS. 87 
 
 been much greater than it is, the vicissitudes of the yea- 
 sons would have been proportionally greater than at pres- 
 ent. Suppose, for instance, the equator had been at 
 right angles to the ecliptic, in which case the poles of 
 the earth would have been situated in the ecliptic itself; 
 then in different parts of the earth the appearances 
 would have been as follows. To a spectator on the 
 equator, the sun as he left the vernal equinox would 
 every day perform his diurnal revolution in a smaller 
 and smaller circle, until he reached the north pole, when 
 he would halt for a moment, and then wheel about and 
 return to the equator in the reverse order. The pro- 
 gress of the sun through the southern signs, to the south 
 pole, would be similar to that already described. Such 
 would be the appearances to an inhabitant of the equa- 
 torial regions. To a spectator living in an oblique 
 sphere, in our own latitude for example, the sun while 
 north of the equator would advance continually north- 
 ward, making his diurnal circuits in parallels farther and 
 farther distant from the equator, until he reached the 
 circle of perpetual apparition, after which he would 
 climb by a spiral course to the north star, and then as 
 rapidly return to the equator. By a similar progress 
 southward, the sun would at length pass the circle of 
 perpetual occultation, and for some time (which would 
 be longer or shorter according to the latitude of the place 
 of observation) there would be continual night. 
 
 The great vicissitudes of heat and cold which would 
 attend such a motion of the sun, would be wholly in- 
 compatible with the existence of either the animal or 
 the vegetable kingdoms, and all terrestrial nature would 
 
 117. Had the earth's axis been perpendicular to the plane 
 of the ecliptic, would there have been any change of seasons ? 
 What would have been the consequence had the equator been 
 at right angles to the ecliptic ? How would the sun appear to 
 move to a person on the equator ? How to one situated at the 
 pole ? How to an inhabitant of an oblique sphere ? How 
 would have been the vicissitudes of heat and cold ? 
 
88 
 
 THE SUN. 
 
 be doomed to perpetual sterility and desolation. The 
 happy provision which the Creator has made against 
 such extreme vicissitudes, by confining the changes of 
 the seasons within such narrow bounds, conspires with 
 many other express arrangements in the economy of 
 nature to secure the safety and comfort of the human 
 race. 
 
 FIGURE OF THE EARTH'S ORBIT. 
 
 118. Thus far we have taken the earth's orbit as a 
 great circle, such being the projection of it on the celes- 
 tial sphere ; but we now proceed to .investigate its actual 
 figure. 
 
 Fig. 23. 
 
 Were the earth's path a cii^le, having the sun in the 
 center, the sun would always appear to be at the same 
 
 118. Were the earth's path a circle, how would the distance 
 of the sun from us always appear 1 Define the radius vector. 
 What do we infer from the fact that the radius vector is con- 
 stantly varying ? How do we learn the relative distances ol 
 the earth ? How do we construct a figure representing the 
 earth's orbit ? Explain figure 23. 
 
89 
 
 distance from us ; that is, the radius of its orbit, or ra- 
 dius vector, the name given to a line drawn from the 
 center of the sun to the orbit of any planet, would al- 
 ways be of the same length. But the earth's distance 
 from the sun is constantly varying, which shows that 
 its orbit is not a circle. We learn the true figure of the 
 orbit, by ascertaining the relative distances of the earth 
 from the sun at various periods of the year. These all 
 being laid down in a diagram, according to their respec- 
 tive lengths, the extremities, on being connected, give 
 us our first idea of the shape of the orbit, which appears 
 of an oval form, and at least resembles an ellipse ; and, 
 on further trial, we find that it has the properties of an 
 ellipse. Thus, let E (Fig. 23,) be the place of the 
 earth, and a, b, c, &c. successive positions of the sun ; 
 the relative lengths of the lines Ea, Eft, &c. being 
 known : on connecting the points, a, b, c, &c. the result- 
 ing figure indicates the true shape of the earth's orbit. 
 
 119. These relative distances are found in two differ- 
 ent ways ; first, by changes in the sun's apparent diam- 
 eter, and, secondly, by variations in his angular velo- 
 city. The same object appears to us smaller in propor- 
 tion as it is more distant ; and if we see a heavenly body 
 varying in size at different times, we infer that it is at 
 different distances from us ; that when largest, it is near- 
 est to us, and when smallest, farthest off. Now when 
 the sun's diameter is measured accurately by instru- 
 ments, it is found to vary from day to day, being when 
 greatest more than thirty-two minutes and a half, and 
 when smallest only thirty-one minutes and a half, differ- 
 ing in all, about seventy-five seconds. When the diam- 
 eter is greatest, which happens in January, we know 
 
 119. How does the same body appear when at different dis- 
 tances ? What inferences do we make from its variations of 
 size ? How much does the apparent diameter of the sun vary 
 in different parts of the year ? When is it greatest, and 
 when smallest ? Define the terms perihelion and aphelum. 
 
 8* 
 
90 THE SUN. 
 
 that the sun is nearest to us ; and when the diameter is 
 least, which occurs in July, we infer that the sun is at 
 the greatest distance from us. 
 
 The point where the earth or any planet, in its revo- 
 lution, is nearest the sun, is called its perihelion ; the 
 point where it is farthest from the sun, its aphelion, 
 
 120. Similar conclusions may be drawn from obser- 
 vations on the sun's angular velocity. A body appears 
 to move most rapidly when nearest to us. Indeed the 
 apparent velocity of the sun increases rapidly as it ap- 
 proaches us, and as rapidly diminishes when it recedes 
 from us. If it were to come twice as near as before it 
 would appear, to move not merely twice as swift, but 
 four times as swift ; if it came ten times nearer, its appa- 
 rent velocity would be one hundred times as great as 
 before. We say, therefore, that the velocity varies 
 inversely as the square of the distance, for as the dis- 
 tance is diminished ten times, the velocity is increased 
 the square of ten, that is, one hundred times. Now by 
 noting the time it takes the sun, from day to day, to re- 
 turn to the meridian, we learn the comparative veloci- 
 ties with which it moves at different times, and from 
 these we derive the comparative distances of the sun 
 at the corresponding times. 
 
 When by either of the foregoing methods, we have 
 learned the relative distances of the sun from the earth 
 at various periods of the year, we may lay down, or plot 
 in a diagram like figure 23, a representation of the orbit 
 which the sun apparently describes about the earth, and 
 it will give us the figure of the orbit which the earth 
 really 'describes about the sun, in its annual revolution. 
 
 120. What conclusions are drawn from the variations in 
 the sun's angular velocity ? According to what law does the 
 velocity vary 1 How may we ascertain tlic sun's daily rate ? 
 What great doctrine is it necessary to be acquainted with, in 
 order to understand the celestial motions ? 
 
UNIVERSAL GRAVITATION. 91 
 
 But neither the revolution of the earth about the sun, 
 nor indeed that of any of the planets, can be well and 
 clearly understood, until we are acquainted with the 
 forces by which their motions are produced, especially 
 with the doctrine of Universal Gravitation. To this 
 subject, therefore, let us next apply our attention. 
 
 CHAPTER III. 
 
 OF UNIVERSAL GRAVITATION KEPLER's LAWS MOTION 
 
 IN AN ELLIPTICAL ORBIT PRECESSION OF THE EQUI- 
 NOXES. 
 
 121. WE discover in nature a tendency of every por- 
 tion of matter towards every other. This tendency is 
 called gravitation. In obedience to this power, a stone 
 falls to the ground and a planet revolves around the sun. 
 
 It was once supposed that we could not reason from 
 the phenomena of the earth to those of the heavens ; 
 since it was held that the laws of motion might be 
 very different among the heavenly bodies from what 
 we find them to be on this globe ; but Galileo and New- 
 ton in their researches into nature, proceeded on the 
 idea that nature is uniform in all her works, and that 
 every where the same causes produces the same effects, 
 and that the same effects result from the same causes. 
 That this is a sound principle of philosophy, is proved 
 by the fact, that all the conclusions derived from it in 
 the interpretation of nature are found to be true. Hence 
 by studying the laws of motion as exhibited constantly 
 before our eyes in all terrestrial motions, we are learning 
 
 121. What force do we observe in nature ? What is this 
 force called ? Can we reason from terrestrial to celestial phe- 
 nomena ? On what idea did Galileo and Newton proceed ? 
 How is this proved to be a sound principle of philosophy I 
 
92 UNIVERSAL GRAVITATION. 
 
 the laws that govern the movements of the heavenly 
 bodies. 
 
 122. On the earth all bodies are seen to fall towards 
 its center. A stone let fall in any part of the earth, de- 
 scends immediately to the ground. This may seem to 
 the young learner as so much a matter of course as to 
 require no explanation. But stones fall in exactly op- 
 posite directions on opposite sides of the earth, always 
 falling towards the center of the earth from every part 
 exterior to its surface ; as when Fi S- 24 - 
 
 we hold a small needle towards 
 a magnetic ball or load stone, the 
 needle will fly towards the ball, 
 and cling to its surface, to which- 
 ever side of the ball it is present- 
 ed. (Fig. 24.) From this uni- 
 versal descent of bodies near the 
 earth, we infer the existence of 
 some force which draws or impels them, and this invisi- 
 ble force we call the attraction of gravitation, or simply 
 gravity. 
 
 123. By the laws of gravity we mean the manner in 
 which it always acts. They are three in number, and 
 are comprehended in the following proposition : 
 
 Gravity acts on all matter alike, with a force propor- 
 tioned to the quantity of matter, and inversely as the 
 square of the distance. 
 
 First, gravity acts on all matter alike. Every body 
 in nature, whether great or small, whether solid, liquid, 
 or aeriform, exhibits the same tendency to fall towards 
 the center of the earth. Some bodies, indeed, seem less 
 prone to fall than others, and some even appear to rise, 
 as smoke and light vapors. But this is because they are 
 supported by the air ; when that is removed, they de- 
 
 1 22. In what directions do bodies fall in all parts of the 
 earth ? Illustrate by figure 24. What is gravity ? 
 
LAWS OF GRAVITY. 93 
 
 scend alike towards the earth ; a guinea and a feather, 
 the lightest vapor and the heaviest rocks, fall with equal 
 velocities. 
 
 Secondly, the force of gravity is proportioned to the 
 quantity of matter. A mass of lead contains perhaps 
 fifty times as much matter as an equal bulk of cotton ; 
 yet, if carried beyond the atmosphere, and let fall in ab- 
 solute space, they would both descend towards the earth 
 with equal speed, until they entered the atmosphere, 
 and were the atmosphere removed they would continue 
 to fall side by side until they reached the earth. Now 
 if the lead contains fifty times as much matter as the 
 cotton, it must take fifty times the force to make it move 
 with equal velocity. If we double the load we must 
 double the team, If we would continue to travel at the 
 same speed as before. Hence, from the fact that bodies 
 of various degrees of density descend alike towards the 
 center of the earth by the force of gravity, we infer 
 that that force is always exerted upon bodies in exact 
 proportion to their quantity of matter. 
 
 Thirdly, the force with which gravity acts upon bod- 
 ies at different distances from the earth, is inversely as 
 the square of the distarmz from the center of the earth. 
 If a pound of lead were carried as far above the earth as 
 from the center to the surface of the earth, it would 
 weigh only one-fourth of a pound ; for being twice as 
 far as before from the center of the earth, its weight 
 would be diminished in the proportion of the square of 
 two, that is, four times. 
 
 123. What do we mean by the law of gravity ? State the 
 general proposition. Show that gravity acts on all matter alike. 
 How is this consistent with the fact, that some bodies appear to 
 rise ? How would all bodies fall in a vacuum ? Explain how 
 gravity is proportioned to the quantity of matter. How would 
 equal masses of lead and cotton fall^if carried beyond the at- 
 mosphere ? What do we infer from the fact, that all bodies fall 
 towards the earth with equal velocities ? To what is gravity 
 acting at different distances proportioned ? How much would 
 a pound of lead weigh, if carried as far above the earth as from 
 
94 UNIVERSAL GRAVITATION. 
 
 124. Bodies falling to the earth by gravity have their 
 velocity continually increased. For since they retain 
 what motion they have and constantly receive more 
 by the continued action of gravity, they must move 
 faster and faster, as a wheel has its velocity constantly 
 accelerated when we continue to apply successive im 
 pulses to it. 
 
 The spaces which bodies describe, when falling freely 
 by gravity, are as the squares of the times. It is found 
 by experiment, that a body will fall from a state of 
 rest 16 j 1 ^ feet in one second. In two seconds it w r ill not 
 fall merely through double this space, but through four 
 times this space, that is, through a distance expressed 
 by the square of the time multiplied into 16-^. Conse- 
 quently, in two seconds the fall will be 64i, in three se- 
 conds 144 J, and in ten seconds 1608i feet, that is, 
 through one hundred times 16^ feet. 
 
 The weight of a body is nothing more than the ac- 
 tion of gravity upon it tending to carry it towards the 
 center of the earth. The counterpoise which is placed 
 in the opposite scale by which its weight is estimated, is 
 the force it takes to hold the body back, which must be 
 just equal to that by which it endeavors to descend. 
 
 125. There is another principle which it is necessary 
 clearly to comprehend before we can understand the mo- 
 tions of the heavenly bodies. It is commonly called the 
 First Law of Motion and is as follows : 
 
 Every body perseveres in a state of rest, or of uniform 
 motion in a straight line, unless compelled by some force 
 to change its state. This law has been fully established 
 by experiment, and is conformable to all experience. 
 It embraces several particulars. First, A body when at 
 
 124. When a body is falling towards the earth, how is its 
 velocity affected ? To what are the spaces described by fall- 
 ing bodies proportioned ? How far will a body fall from a state 
 of rest in one second ? How far in two seconds ? What is 
 the weight of a body ? 
 

 LAWS OF MOTION. 95 
 
 rest remains so unless some force puts it in motion ; 
 and hence it is inferred, when a body is found in mo- 
 tion, that some force must have been applied to it suffi- 
 cient to have caused its motion. Thus, the fact that 
 the earth is in motion around the sun and around its own 
 axis, is to be accounted for by assigning to each of these 
 motions a force adequate, both in quantity and direction, 
 to produce these motions respectively. 
 
 Secondly, When a body is once in motion it will con- 
 tinue to move forever, unless something stops it. When 
 a ball is struck on the surface of the earth, the friction 
 of the earth and the resistance of the air soon stop its 
 motion ; when struck on smooth ice it will go much 
 farther before it comes to a state of rest, because the ice 
 opposes much less resistance than the ground ; and were 
 there no impediment to its motion it would, when once 
 set in motion, continue to move without end. The 
 heavenly bodies are actually in this condition : they 
 continue to move, not because any new forces are ap- 
 plied to them, but, having been once set in motion, they 
 continue in motion because there is nothing to stop them. 
 
 Thirdly, The motion to which a body naturally tends 
 is uniform ; that is, the body moves just as far the se- 
 cond minute as it did the first, and as far the third as 
 the second, passing over equal spaces in equal times. 
 
 Fourthly, A body in motion will move in a straight 
 line, unless diverted out of that line by some external 
 force ; and the body will resume its straight forward mo- 
 tion, when ever the force that turns it aside is with- 
 drawn. Every body that is revolving in an orbit, like 
 the moon around the earth, or the earth around the sun, 
 
 125. Recite the first law of motion. How has this law been 
 established ? What does the fact, that the earth is in motion 
 around the sun imply? How would a ball when once struck 
 continue to move, if it rnet with no resistance ? Why do the 
 heavenly bodies continue to move ? What is meant by saying 
 that motion is naturally uniform ? In what direction does 
 every revolving body tend to move. 
 
96 UNIVERSAL GRAVITATION. 
 
 tends to move in a straight line which is a tangent* to 
 its orbit. 
 
 Let us now see how the foregoing principles, which 
 operate upon bodies on the earth, are extended so as to 
 embrace all bodies in the universe, as in the doctrine of 
 Universal Gravitation. This important principle is thus 
 defined : 
 
 126. UNIVERSAL GRAVITATION, is that influence by 
 which every body in the universe, whether great or small, 
 tends towards every other, with a force which is directly 
 as the quantity of matter, and inversely as the square of 
 the distance. 
 
 As this force acts as though bodies were drawn to- 
 wards each other by a mutual attraction, the force is de- 
 nominated attraction ; but ^ it must be " borne in mind, 
 that this term is figurative, and implies nothing respect- 
 ing the nature of the force. 
 
 The existence of such a force in nature was distinctly 
 asserted by several astronomers previous to the time of 
 Sir Isaac Newton, but its laws were first promulgated 
 by this wonderful man in his Principia, in the year 1687. 
 It is related, that while sitting in a garden, and musing 
 on the cause of the falling of an apple, he reasoned 
 thus :f that, since bodies far removed from the earth fall 
 towards it, as from the tops of towers, and the highest 
 mountains, why may not the same influence extend 
 even to the moon ; and if so, may not this be the reason 
 why the moon is made to revolve around the earth, as 
 would be the case with a cannon ball were it projected 
 horizontally near the earth with a certain velocity. Ac- 
 cording to the first law of motion, the moon, if not con- 
 tinually drawn or impelled towards the earth by some 
 force, would not revolve around it, but would proceed 
 on in a straight line. But going around the earth as she 
 does, in an orbit that is nearly circular, she must be 
 
 * A tangent is a straight line which touches a curve. Thus AB (Fig 
 25,) is a tangent to the circle at A. 
 
 t Pemberton's View of Newton's Philosophy. 
 
UNIVERSAL BRAVITATION. 
 
 97 
 
 urged towards the earth by some force, which diverts 
 her from a straight course. For let the earth (Fig. 25,) 
 be at E, and let the arc described by the moon in one 
 second of time be Ab. Were the moon influenced by 
 no extraneous force, to turn aside, she would have de- 
 scribed, not the arc Ab, but the straight line AB, and 
 would have been found at the end of the given time at 
 B instead of b. She therefore departs from the line in 
 which she tends naturally to move, by the line B&, 
 which in small angles may be taken as equal to Aa. 
 Fig. 25. 
 
 This deviation from the tangent must be owing to some 
 extraneous force. Does this force correspond to what , 
 the force of gravity exerted by the earth, would be at 
 the distance of the moon ? The question resolves itself 
 into this : Would the force of gravity exerted by the 
 earth upon the moon, cause the moon to deviate from 
 her straight forward course towards the earth just as 
 much as she is actually found to deviate ? Now we 
 
 126. Universal Gravitation. Define it. Why called at- 
 traction ? State the historical facts connected with its discov- 
 ery. How did Sir Isaac Newton reason from the falling of an 
 apple ? Explain by figure 25. How is it proved that gravity 
 and no other force causes the moon to revolve about the earth ? 
 
 9 
 
98 UNIVERSAL GRAVITATION. 
 
 know how far the moon is from the earth, namely, sixty 
 times as far as it is from the center to the surface of the 
 earth ; and since the force of gravity decreases in pro- 
 portion to the square of the distance, this force must be 
 3600 times (which equals the square of 60,) less than at 
 the surface of the earth. This is found, on computa- 
 tion, to be exactly the force required to make the moon 
 deviate to the amount she does from the straight line in 
 which she constantly tends to move ; and hence it is 
 inferred that gravity, and no other force than gravity, 
 causes the moon to circulate around the earth. 
 
 By this process it was discovered that the law of grav- 
 itation extends to the moon. By subsequent inquiries 
 it was found to extend in like manner to all the planets, 
 and to every member of the solar system ; and, finally, 
 recent investigations have shown that it extends to the 
 fixed stars. The law of gravitation, therefore, is now 
 established as the grand principle which governs all the 
 motions of the heavenly bodies. 
 
 127. There are three great principles, according to 
 which the motions of the earth and all the planets 
 around the sun are regulated, called Kepler's Laws, hav- 
 ing been first discovered by the great astronomer whose 
 name they bear. They may appear to the young learner, 
 when he first reads them, dry and obscure ; yet they 
 will be easily understood from the explanations that fol- 
 low ; and so important have they proved in astronomical 
 inquiries, that they have acquired for their renowned 
 discoverer the exalted appellation of the legislator of the 
 skies. 
 
 We will consider each of these laws separately. 
 
 127. Kepler's Laws. Why so called ? What appellation 
 has been given to Kepler ? 
 
KEPLER S LAWS. 
 
 99 
 
 128. FIRST LAW. The orbits of the earth and all the 
 ^planets are ellipses, having the sun in the common 
 focus. 
 
 In a circle all the diameters are equal to each other ; 
 but if we take a metallic wire or hoop and draw it out on 
 opposite sides, we elongate it into an ellipse, of which the 
 different diameters are very unequal. That which con- 
 nects the two points most distant from each other is called 
 the transverse, and that which is at right angles to this 
 is called the conjugate axis. Thus AB (Fig. 26) is the 
 
 transverse axis and CD the conjugate of the ellipse AB. 
 By such a process of elongating the circle into an el- 
 lipse, the center of the circle may be conceived of as 
 drawn opposite ways to E and F, each of which be- 
 comes a focus, and both together are called the foci of the 
 ellipse. The distance GE or GF of the focus from the 
 
 128. Recite the first law. In a circle, how are all the diam- 
 eters ? How are they in an ellipse ? What is the longest di- 
 ameter called ? What is the shortest called ? Explain by figure 
 26. What is the eccentricity of the ellipse ? How many el- 
 lipses may there be having a common focus ? Explain figure 
 2 How eccentric is the earth's orbit ? 
 
100 
 
 UNIVERSAL GRAVITATION. 
 
 center is called the eccentricity of the ellipse ; and the 
 ellipse is said to be more or less eccentric, as the distance" 
 of 'the focus from the center is greater or less. 
 
 Now there may be an indefinite number of ellipses 
 having one common focus, but varying greatly in ec- 
 centricity. Figure 27 represents such a collection of 
 
 ellipses around the common focus F, the innermost AGD 
 having a small eccentricity or varying little from a cir- 
 cle; while the outermost ACB is a very eccentric ellipse. 
 The orbits of all the bodies that revolve about the sun, 
 both planets and comets, have, in like manner, a com- 
 mon focus in which the sun is situated, but they differ 
 in eccentricity. 
 
 Most of the planets have orbits of very little eccen- 
 tricity, differing little from circles, but comets move in 
 very eccentric ellipses. 
 
 The earth's path around the sun varies so little from 
 a circle, that a diagram representing it truly would 
 scarcely be distinguished from a perfect circle ; yet 
 when the comparative distances of the sun from the 
 earth are taken at different seasons of the year, as is ex- 
 plained in Art. 118, we find that the difference between 
 
KEPLER'S LAWS. 101 
 
 the greatest and least distances is no less than 3,000,000 
 miles. 
 
 129. SECOND LAW. The radius vector of the earth, 
 or of any planet, describes equal areas in equal times. 
 
 ft will be recollected that the radius vector is a line 
 drawn from the center of the sun to a planet revolving 
 about the sun, (Art. 118.) Thus Ea, Eb, EC, (Fig. 23,) 
 &c. are successive representations of the radius vector. 
 Now if a planet sets out from a and travels round the sun 
 in the direction ofabc, it will move faster when nearer the 
 sun, as at a, than when more remote from it, as at m ; 
 yet if ab and mn be arcs described in equal times, then, 
 according to the foregoing law, the space Eab will be 
 equal to the space Emn ; and the same is true of all the 
 other spaces described in equal times. Although the 
 figure Eab is much shorter than Emn, yet its greater 
 breadth exactly counterbalances the greater length oi 
 those figures which are described by the radius vector 
 where it is longer. 
 
 130. THIRD LAW. The squares of the periodical times 
 are as the cubes of the mean distances from the sun. 
 
 The periodical time of a body is the time it takes to 
 complete its orbit in its revolution about the sun. Thus 
 the earth's periodic time is one year, and that of the 
 planet Jupiter is about twelve years. As Jupiter takes 
 so much longer time to travel round the sun than the 
 earth does, we might suspect that his orbit was larger 
 than that of the earth, and of course that he was at 
 a greater distance from the sun, and our first thought 
 might be that he was probably twelve times as far off; 
 but Kepler discovered that the distances did not increase 
 as fast as the times increased, but that the planets which 
 
 129. State Kepler's second law. Explain by figure 23, p. 88. 
 
 130. State Kepler's third law. What is meant by the peri- 
 odical time of a body ? Do planets jnove faster or slower as 
 they are more distant from the sun ? Explain the law. 
 
 9* 
 
102 UNIVERSAL GRAVITATION. 
 
 are more distant from the sun actually move slower than 
 those which are nearer. After trying a great many pro- 
 portions, he at length found that if we take the squares 
 of the periodic times of two planets, the greater square 
 contains the less, just as often as the cube of the dis 
 tance of the greater contains that of the less. This fact 
 is expressed by saying, that the squares of the periodic 
 times are to one another as the cubes of the distances. 
 This law is of great use in determining the distances 
 of all the planets from the sun, as we shall see more fully 
 hereafter. 
 
 MOTION IN AN ELLIPTICAL ORBIT. 
 
 131. Let us now endeavor to gain a just conception 
 of the forces by which the earth and all the planets are 
 made to revolve about the sun. 
 
 In obedience to the first law of motion, every moving 
 body tends to move in a straight line ; and were not the 
 planets deflected continually towards the* sun by the 
 force of attraction, these bodies as well as others would 
 move forward in a rectilineal direction. We call the force 
 by which they tend to such a direction the projectile 
 force, because its effects are the same as though the body 
 were originally projected from a certain point in a certain 
 direction. It is an interesting problem for mechanics to 
 solve, what was the nature of the impulse originally 
 given to the earth, in order to impress upon it its two 
 motions, the one around its own axis, the other around 
 the sun. If struck in the direction of its center of 
 gravity it might receive a forward motion, but no rota- 
 tion on its axis. It must, therefore, have been impelled 
 by a force, whose direction did not pass through its 
 
 131. Explain how a body is made to revolve in an orbit, 
 under the action of two forces. What is meant by the projec- 
 tile force ? How must the earth have been impelled in order 
 to receive its present motions ? How illustrated by the mo- 
 tions of a top 7 
 
MOTION IN AN ELLIPTICAL ORBIT. 103 
 
 center of gravity. Bernoulli!, a celebrated mathemati- 
 cian, has calculated that the impulse must have been 
 given very nearly in the direction of the center, the 
 point of projection being only the 165th part of the 
 earth's radius from the center. This impulse alone 
 would cause the earth to move in a right line : gravita- 
 tion towards the sun causes it to describe an orbit. 
 Thus a top spinning on a smooth plane, as that of glass 
 or ice, impelled in a direction not coinciding with that 
 of the center of gravity, may be made to imitate the two 
 motions of the earth, especially if the experiment is tried 
 in a concave surface like that of a large bowl. The re- 
 sistance occasioned by the surface on which the top 
 moves, and that of the air, will gradually destroy the 
 force of projection and cause the top to revolve in a 
 smaller and smaller orbit ; but the earth meets with no 
 such resistance, and therefore makes both her days and 
 years of the same length from age to age. A body, 
 therefore, revolving in an orbit about a center of attrac- 
 tion, is constantly under the influence of two forces, 
 the projectile force, which tends to carry it forward in a 
 straight line which is a tangent to its orbit, and the cen- 
 tripetal force, by which it tends towards the center. 
 
 132. As an example of a body revolving in an orbit 
 under the influence of two forces, suppose a body pla- 
 ced at any point P (Fig. 28,) above the surface of the 
 earth, and let PA be the direction of the earth's center. 
 If the body were allowed to move without receiving 
 any impulse, it would descend to the earth in the direc- 
 tion PA with an accelerated motion. But suppose that 
 at the moment of its departure from P, it receives an 
 impulse in the direction PB, which would carry it to B 
 in the time the body would fall from P to A ; then un- 
 der the influence of both forces it would descend along 
 the curve PD. If a stronger impulse were given it in 
 
 132. Explain figure 28. How might a body be made to 
 circulate quite around the earth ? 
 
104 
 
 UNIVERSAL GRAVITATION. 
 
 the direction PB, it would describe a larger curve PE, 
 or PF, or finally, it would go quite round the earth and 
 return again to P. 
 
 133. The most simple example we have of the com- 
 bined action of these two forces, is the motion of a mis- 
 sile thrown from the hand, or of a ball fired from a can- 
 non. It is well known that the particular form of the 
 curve described by the projectile, in either case, will de- 
 pend upon the velocity with which it is thrown. In 
 each case the body will begin to move in the line of di- 
 rection in which it is projected, but it will soon be de- 
 flected from that line towards the earth. It will how- 
 ever continue nearer to the line of projection as the ve- 
 
 Fig. 29. 
 
 locity of projection is greater. Thus let AB (Fig. 29,) 
 
 133. When a cannon ball is fired with different velocities, 
 when is its motion nearest to the line of projection ? 
 
MOTION IN AN ELLIPTICAL ORBIT. 
 
 105 
 
 perpendicular to AC represent the line of projection. 
 The body will, in every case, commence its motion in 
 the line AB, which will therefore be the tangent to the 
 curve it describes ; but if it be thrown with a small ve- 
 'ocity, it will soon depart from the tangent, describing 
 the line AD ; with a greater velocity it will describe a 
 
 curve nearer to the tangent, as AE ; and with 
 greater velocity it will describe the curve AF. 
 
 still 
 
 134. In figure 30, suppose the planet to have passed 
 the point C with so small a velocity, that the attraction 
 of the sun bends its path very much, and causes it im- 
 mediately to begin to approach towards the sun ; the 
 sun's attraction will increase its velocity as it moves 
 through D, E, and F. For the sun's attractive force on 
 
 the planet, when at D, is acting in the direction DS, 
 and, on account of the small inclination of DE to DS, 
 the force acting in the line DS helps the planet forward 
 in the path DE, and thus increases its velocity. In like 
 manner, the velocity of the planet will be continually 
 increasing as it passes through E, and F ; and though 
 
 134. Explain the motion of a planet in an elliptical orbit, 
 from figure 30. 
 
UNIVERSAL GRAVITATION. 
 
 the attractive force, on account of the planet's nearness, 
 is much increased, and tends therefore to make the 
 orbit more curved, yet the velocity is also so much in- 
 creased that the orbit is not more curved than before. 
 The same increase of velocity occasioned by the planet' s 
 approach to the sun, produces a greater increase of cen- 
 trifugal force which carries it off again. We may see 
 also why, when the planet has reached the most distant 
 parts of its orbit, it does not entirely fly off, and never 
 return to the sun. For when the planet passes along 
 H, K, A, the sun's attraction retards the planet, just as 
 gravity retards a ball rolled up hill ; and when it has 
 reached C, its velocity is very small, and the attraction 
 at the center of force causes a great deflection from the 
 tangent, sufficient to give its orbit a great curvature, 
 and the planet turns about, returns to the sun, and goes 
 over the same orbit again. As the planet recedes from 
 the sun, its centrifugal force diminishes faster than the 
 force of gravity, so that the latter finally preponderates. 
 
 135. We may imitate the motion of a body in its orbit 
 by suspending a small ball from the ceiling by a long string. 
 The ball being drawn out of its place of rest, (which is 
 directly under the point of suspension,) it will tend con- 
 stantly towards the same place by a force which corres- 
 ponds to the force of attraction of a central body. If 
 an assistant stands under the point of suspension, his 
 head occupying the place of the ball when at rest, the 
 ball may be made to revolve about his head as the earth 
 or any planet revolves about the sun. By projecting the 
 ball in different directions, and with different degrees of 
 velocity, we may make it describe different orbits, ex- 
 emplifying principles which have been explained in the 
 foregoing articles. 
 
 135. How may we imitate the motion of a body in its or- 
 bit ? How may we make the ball describe different orbits ? 
 
- 
 
 PRECESSION OF THE EQUINOXES. 107 
 
 PRECESSION OF THE EQUINOXES. 
 
 136 THE PRECESSION OF THE EQUINOXES, is a slow 
 but continual shifting of the equinoctial points from east 
 to west. 
 
 Suppose that we mark the exact place in the heavens 
 where, during the present year, the sun crosses the equa- 
 tor, and that this point is close to a certain star ; next 
 year the sun will cross the equator a little way west- 
 ward of that star, and thus every year a little farther west- 
 ward, so that in a long course of ages, the place of the 
 equinox will occupy successively every part of the eclip- 
 tic, until we come round to the same star again. As, 
 therefore, the sun, revolving from west to east in his ap- 
 parent orbit, comes round towards the point where it 
 left the equinox, it meets the equinox before it reaches 
 that point. The appearance is as though the equinox 
 goes forward to meet the sun, and hence the phenome- 
 non is called the Precession of the Equinoxes, and the 
 fact is expressed by saying that the equinoxes retrograde 
 on the ecliptic, until the line of the equinoxes makes a 
 complete revolution from east to west. The equator is 
 conceived as sliding westward on the ecliptic, always 
 preserving the same inclination to it, as a ring placed at 
 a small angle with another of nearly the same size, 
 which remains fixed, may be slid quite around it, giving 
 a corresponding motion to the two points of intersec- 
 tion. It must be observed, however, that this mode of 
 conceiving of the precession of the equinoxes is purely 
 imaginary, and is employed merely for the convenience 
 of representation. 
 
 137. The amount of precession annually is 50. "1 ; 
 whence, since there are 3600" in a degree, and 360 in 
 
 136. Precession of the Equinoxes. Define it. If the sun 
 crosses the equator near a certain star this year, where will it 
 cross it next year ? Why is the fact called the precession of 
 the equinoxes 1 How is the equator conceived as moving 
 with regard to the ecliptic ? 
 
108 UNIVERSAL GRAVITATION. 
 
 the whole circumference, and consequently, 1296000", 
 this sum divided by 50.1 gives 25868 years for the pe- 
 riod of a complete revolution of the equinoxes. 
 
 138. Suppose now we fix to the center of each of the 
 two rings, (Art. 136,) a wire representing its axis, one 
 corresponding to the axis of the ecliptic, the other to 
 that of the equator, the extremity of each being the pole 
 of its circle. As the ring denoting the equator turns 
 round on the ecliptic, which with its axis remains fixed, 
 it is easy to conceive that the axis of the equator re- 
 volves around that of the ecliptic, and the pole of the 
 equator around the pole of the ecliptic, and constantly at 
 a distance equal to the inclination of the two circles. To 
 transfer our conceptions to the celestial sphere, we may 
 easily see that the axis of the diurnal sphere, (that of 
 the earth produced, Art. 15,) would not have its pole 
 constantly in the same place among the stars, but that 
 this pole would perform a slow revolution around the 
 pole of the ecliptic from east to west, completing the cir- 
 cuit in about 26,000 years. Hence the star which we 
 now call the pole star, has not always enjoyed that dis- 
 tinction, nor will it always enjoy it hereafter. When 
 the earliest catalogues of the stars were made, this star 
 was 12 from the pole. It is now 1 33', and will ap- 
 proach still nearer ; or to speak more accurately, the pole 
 will come still nearer to this star, after which it will 
 leave it, and successively pass by others. In about 
 13,000 years, the bright star Lyrse, which lies on the 
 circle of revolution opposite to the present pole star, 
 
 137. What is the amount of precession annually? In what 
 time will the equinoxes perform a complete revolution ? 
 
 138. Illustrate the precession of the equinoxes by an appa- 
 ratus of wires. How is the pole of the earth situated with 
 respect to the stars at different times? Has the present pole 
 star always been such ? What will be the pole star 13,000 
 years hence ? Will this cause affect the elevation of tho 
 north pole above the horizon ? 
 
PRECESSION OF THE EQUINOXES. 109 
 
 will be within 5 of the pole, and will constitute the 
 Pole Star. As a Lyrae now passes near our zenith, the 
 learner might suppose that the change of position of the 
 pole among the stars, would be attended with a change 
 of altitude of the north pole above the horizon. This 
 mistaken idea is one of the many misapprehensions 
 which result from the habit of considering the horizon 
 as a fixed circle in space. However the pole might 
 shift its position in space, we should still be at the 
 same distance from it, and our horizon would always 
 reach the same distance beyond it. 
 
 139. The time occupied by the sun in passing from 
 the equinoctial point round to the same point again, is 
 called the TROPICAL YEAR. As the sun does not perform 
 a complete revolution in this interval but falls short of it 
 50." 1, the tropical year is shorter than the sidereal by 
 20m. 20s. in mean solar time, this being the time of de- 
 scribing an arc of 50."1 in the annual revolution.* The 
 changes produced by the precession of the equinoxes in 
 the apparent places of the circumpolar stars, have led to 
 some interesting results in chronology. In consequence 
 of the retrograde motion of the equinoctial points, the 
 signs of the ecliptic, do not correspond at present to 
 the constellations which bear the same names, but lie 
 about one whole sign or 30 westward of them. Thus, 
 that division of the ecliptic which is called the sign 
 Taurus, lies in the constellation Aries, and the sign 
 Gemini in the constellation Taurus. Undoubtedly how- 
 ever when the ecliptic was thus first divided, and the 
 divisions named, the several constellations lay in the re- 
 spective divisions which bear their names. How long 
 is it, then, since our zodiac was formed ? 
 
 139. Define the tropical year. How much shorter is the 
 tropical than the sidereal year ? How has the precessioof the 
 equinoxes been applied in Chronology ? 
 
 * 59' 8."3 : 24h. : : 50."1 : 20m. 20s. 
 10 
 
110 THE MOON. 
 
 50."1 : 1 year: :30(~ 108000") : 2155.6 years. 
 The result indicates that the present divisions of the 
 zodiac, were made soon after the establishment of the 
 Alexandrian school of astronomy. 
 
 CHAPTER IV. 
 
 OF THE MOON - PHASES - REVOLUTIONS. 
 
 140. NEXT to the Sun the Moon naturally claims our 
 attention. She is an attendant or satellite to the earth, 
 araund which she revolves at the distance of nearly 
 240,000 miles, or more exactly 238,545 miles. Her 
 angular diameter is about half a degree, and her real diam- 
 eter 2160 miles. She is therefore a comparatively small 
 body, being only one forty-ninth part as large as the 
 earth. 
 
 The moon shines by reflected light borrowed from 
 the sun, and when full exhibits a disk of silvery bright- 
 ness, diversified by extensive portions partially shaded. 
 These dusky spots are generally said to be land, and the 
 brighter parts water ; but astronomers tell us that if ei- 
 ther are water, it must be the darker portions. Land by 
 scattering the rays of the sun's light would appear more 
 luminous than the ocean which reflects the light like a 
 mirror. By the aid of the telescope, we see undoubted 
 signs of a varied surface, in some parts composed of ex- 
 tensive tracts of level country, and in others exceedingly 
 broken by mountains and valleys. 
 
 141. The line which separates the enlightened from 
 the dark portions of the moon's disk, is called the Ter- 
 
 140. The Moon. What relation has the moon to the earth ? 
 State her distance, diameter and bulk. Is her light direct or 
 reflected ? What are the dark places in the moon generally un- 
 derstood to be ? Why would water appear darker than land ? 
 What does the telescope reveal to us respecting the moon ? 
 
LUNAR GEOGRAPHY. Ill 
 
 minator. (See Frontispiece.) As the terminator traver- 
 ses the disk from new to full moon, it appears through the 
 telescope exceedingly broken in some parts^but smooth 
 in others, indicating that portions of the lunar surface are 
 uneven while others are level. The broken regions ap- 
 pear brighter than the smooth tracts. The latter have 
 been taken for seas, but it is supposed with more prob- 
 ability that they are extensive plains, since they are still 
 too uneven for the perfect level assumed by bodies of 
 water. That there are mountains in the moon, is known 
 by several distinct indications. First, when the moon 
 is increasing, certain spots are illuminated sooner than 
 the neighboring places, appearing like bright points be- 
 yond the terminator, within the dark part of the disk, 
 in the same manner as the tops of mountains on the 
 earth are tipped with the light of the sun, in the morn- 
 ing, while the regions below are still dark. Secondly, 
 after the terminator has passed over them, they project 
 shadows upon the illuminated part of the disk, always 
 opposite to the sun, corresponding in shape to the form 
 of the mountain, and undergoing changes in length from 
 night to night, according as the sun shines upon that 
 part of the moon more or less obliquely. Many indi- 
 vidual mountains rise to a great height in the midst of 
 plains, and there are several very remarkable mountain- 
 ous groups, extending from a common center in long 
 chains. 
 
 142. That there are also valleys in the moon, is 
 equally evident. The valleys are known to be truly 
 such, particularly by the manner in which the light of 
 the sun falls upon them, illuminating the part opposite 
 to the sun while the part adjacent is dark, as is the case 
 when the light of a lamp shines obliquely into a china 
 
 141. Define the terminator. What do we learn from its rug- 
 ged appearance ? State the proofs of mountains in the moon. 
 
 142. State the proofs of valleys in the moon. When is the 
 best time for viewing the mountains and valleys of the moon. 
 
112 THE MOON. 
 
 cup. These valleys are often remarkably regular, and 
 some of them almost perfect circles. In several instan- 
 ces, a circular chain of mountains surrounds an exten- 
 sive valley, which appears nearly level, except that a 
 sharp mountain sometimes rises from the center. The 
 best time for observing these appearances is near the 
 first quarter of the moon, when half the disk is en- 
 lightened ;* but in studying the lunar geography, it is 
 expedient to observe the moon every evening from new 
 to full, or rather through her entire series of changes. 
 
 143. The various places on the moon's disk have re- 
 ceived appropriate names. The dusky regions, being 
 formerly supposed to be seas, were named accordingly ; 
 and other remarkable places have each two names, one 
 derived from some well known spot on the earth, and 
 the other from some distinguished personage. Thus 
 the same bright spot on the surface of the moon is 
 called Mount Sinai or Tycho, and another. Mount Et- 
 na or Copernicus. The names of individuals, how- 
 ever, are more used than the others. The frontispiece 
 exhibits the telescopic appearance of the full moon. A 
 few of the most remarkable points have the following 
 names, corresponding to the numbers and letters on the 
 map. (See Frontispiece.) 
 
 1. Tycho, A. Mare Humorum, 
 
 2. Kepler, B. Mare Nubium, 
 
 3. Copernicus, C. Mare Imbrium, 
 
 4. AHstarchus, D. Mare Nectaris, 
 
 5. Helicon, E. Mare Tranquilitatis, 
 
 6. Eratosthenes, F. Mare Serenitatis, 
 
 7. Plato, G. Mare Fecunditatis, 
 
 8. Archimedes, H. Mare Crisium, 
 
 9. Eudoxus, 
 10. Aristotle, 
 
 * It is earnestly recommended to the student of astronomy, to exam- 
 ine the moon repeatedly with the best telescope he can command, using 
 low powers at first, for the sake of a better light 
 
LUNAR GEOGRAPHY. 113 
 
 The frontispiece represents the appearance of the 
 moon in the telescope when full and when five days 
 old. In the latter cut, the learner will remark the rough, 
 rugged appearance of the terminator ; the illuminated 
 points beyond the terminator within the dark part of the 
 moon, which are the tops of mountains ; and the nu- 
 merous circular spaces, which exhibit valleys or caverns 
 surrounded by mountainous chains. Those circles which 
 are near the terminator into which the sun's light shines 
 very obliquely, cast deep shadows on the sides opposite 
 the sun. Those more remote from the terminator, and 
 farther within the illuminated part of the moon, into 
 which the sun shines more directly, have a greater por- 
 tion illuminated, with shorter shadows ; and those which 
 lie near the edge of the moon, most distant from the ter 
 minator, are of an oval figure, being presented obliquely 
 to the eye. 
 
 144. The heights of the lunar mountains, and the 
 depths of the valleys, can be estimated with a considera- 
 ble degree of accuracy. Some of the mountains are as 
 high as five miles, and the valleys in some instances 
 are four miles deep. Hence it is inferred that the sur- 
 face of the moon is more broken and irregular than that 
 of the earth, its mountains being higher and its valleys 
 deeper in proportion to its magnitude than that of the 
 earth: The lunar mountains in general, exhibit an ar- 
 
 143. How are places in the moon named ? Point- out the 
 most remarkable places on the map of the full moon. Point 
 out the mountains, valleys, and craters, on the cut, which rep- 
 resents the moon five days old. 
 
 144. Specify the heights of some of the lunar mountains. 
 Is the surface of the moon more or less broken than that of the 
 earth ? Are the mountains like or unlike ours ? What is the 
 first variety ? What is the shape of the insulated mountains ? 
 How can their heights be calculated ? What is said of the 
 second variety, the mountain ranges ? What .is said of the 
 circular ranges ? What is said of the central mountains ? 
 
 10* 
 
114 THE MOON. 
 
 rangement and an aspect very different from the moun- 
 tain scenery of our globe. They may be arranged un- 
 der the four following varieties. 
 
 First, Insulated Mountains, which rise from plains 
 nearly level, shaped like a sugar loaf, which may be, 
 supposed to present an appearance somewhat similar to 
 Mount Etna, or the Peak of TenerifFe. The shadows 
 of these mountains, in certain phases of the moon, are 
 as distinctly perceived, as the shadow of an upright staff, 
 when placed opposite to the sun ; and these heights can 
 be calculated from the length of their shadows. Some 
 of these mountains being elevated in the midst of exten- 
 sive plains, would present to a spectator on their sum- 
 mits, magnificent views of the surrounding regions. 
 
 Secondly, Mountain Ranges, extending in length two 
 or three hundred miles. These ranges bear a distant re- 
 semblance to our Alps, Appenines, and Andes ; but they 
 are much less in extent. Some of them appear very 
 rugged and precipitous, and the highest ranges are in 
 some places more than four miles in perpendicular alti- 
 tude. In some instances, they are nearly in a straight 
 line from northeast to southwest, as in that range called 
 the Appenines ; in other cases they assume the form of 
 a semicircle or crescent. 
 
 Thirdly, Circular Ranges, which appear on almost 
 every part of the moon's surface, particularly in its south- 
 ern regions. This is one grand peculiarity of the lunar 
 ranges, to which we have nothing similar on the earth. 
 A plain, and sometimes a large cavity, is surrounded 
 with a circular ridge of mountains, which encompasses 
 it like a mighty rampart. These annular ridges and 
 plains are of all dimensions, from a mile to forty or fifty 
 miles in diameter, and are to be seen in great numbers 
 over every region of the moon's surface ; they are most 
 conspicuous, however, near the upper and lower limbs 
 about the time of half moon. 
 
 The mountains which form these circular ridges are 
 of different elevations, from one fifth of a mile to three 
 and a half miles, and their shadows cover one half of 
 the plain at the base. These plains are sometimes on 
 
LUNAR GEOGRAPHY. 115 
 
 a level with the general surface of the moon, and in 
 other cases they are sunk a mile or more below the level 
 of the ground, which surrounds the exterior circle of the 
 mountains. 
 
 Fourthly, Central Mountains, or those which are 
 placed in the middle of circular plains. In many of the 
 plains and cavities surrounded by circular ranges cf 
 mountains there stands a single insulated mountain, 
 which rises from the center of the plain, and whose 
 shadow sometimes extends in the form of a pyramid 
 half across the plain or more to the opposite ridges. 
 These central mountains are generally from half a mile 
 to a mile and a half in perpendicular altitude. In some 
 instances they have two and sometimes three different 
 tops, w T hose shadows can be easily distinguished from 
 each other. Sometimes they are situated towards one 
 side of the plain or cavity, but, in the great majority 
 of instances, their position is nearly or exactly central. 
 The lengths of their bases vary from five to about fifteen 
 or sixteen miles. 
 
 145. The Lunar Caverns form a very peculiar and 
 prominent feature of the moon's surface, and are to 
 be seen throughout almost every region, but are most 
 numerous in the southwest part of the moon. Nearly a 
 hundred of them, great and small, may be distinguished 
 in that quarter. They are all nearly of a circular shape, 
 and appear like a very shallow egg-cup. The smaller 
 cavities appear within almost like a hollow cone, with 
 the sides tapering towards the center ; but the larger 
 ones have for the most part, flat bottoms, from the cen- 
 ter of which there frequently rises a small steep conical 
 hill, which gives them a resemblance to the circular 
 ridges^ and central mountains before described. In some 
 instances their margins are level with the general sur 
 face of the moon, but in most cases they are encircled 
 
 145. Lunar Caverns. What is said of their number, shapo 
 and appearances ? 
 
116 THE MOON. 
 
 with a high annular ridge of mountains, marked with 
 lofty peaks. Some of the larger of these cavities con 
 tain smaller cavities of the same kind and form, particu- 
 larly in their sides. The mountainous ridges which sur- 
 round, these cavities, reflect the greatest quantity of 
 light ; and hence that region of the moon in which they 
 abound, appears brighter than any other. From their 
 lying in every possible direction, they appear at and 
 near the time of full moon, like a number of brilliant 
 streaks or radiations. These radiations appear to con- 
 verge towards a large brilliant spot, surrounded by a 
 faint shade, near the lower part of the moon which is 
 named Tycho, (Frontispiece, 1,) which may be easily dis- 
 tinguished even by a small telescope. The spots named 
 Kepler and Copernicus, are each composed of a central 
 spot with luminous radiations.* 
 
 146. Dr. Herschel is supposed also to have obtained 
 decisive evidence of the existence of volcanoes in the 
 moon, not only from the light afforded by their fires, 
 but also from the formation of new mountains by the 
 accumulation of matter where fires had been seen to 
 exist, and which remained after the fires were extinct. 
 
 147. Some indications of an atmosphere about the 
 moon have been obtained, the most decisive of which 
 are derived from appearances of twilight, a phenomenon 
 that implies the presence of an atmosphere. Similar in- 
 dications have been detected, it is supposed, in eclipses 
 of the sun, denoting a transparent refracting medium 
 encompassing the moon. 
 
 146. Volcanoes. What proofs are there of their having ex- 
 isted in the moon ? 
 
 147. What evidence is there of a lunar atmosphere ? 
 
 * The foregoing accurate description of the lunar mountains and car 
 erns is from " Dick's Celestial Scenery." 
 
LUNAR GEOGRAPHY. 117 
 
 148. It has been a question with astronomers, whether 
 there is water in the moon ? The general opinion is 
 that there is none. If there were any, we should ex- 
 pect to see clouds ; or at least we should expect to find 
 the face of the moon occasionally obscured by clouds ; 
 but this is* not the case, since the spots on the moon's 
 disk, when our sky is clear, are always in full view. 
 The deep caverns,* moreover, seen in those dusky spots 
 which were supposed to be seas, are unfavorable to the 
 supposition, that they are surrounded by water ; and the 
 terminator when it passes over these places is, as already 
 remarked, too uneven to permit us to suppose that these 
 tracts are seas. 
 
 149. The improbability of our ever identifying arti- 
 ficial structures in the moon, may be inferred from the 
 fact that a line one mile in length in the moon subtends 
 an angle at the eye of only about one second. If, there- 
 fore, works of art were to have a sufficient horizontal 
 extent to become visible, they can hardly be supposed 
 to attain the necessary elevation, when we reflect that 
 the height of the great pyramid of Egypt is less than 
 the sixth part of a mile. Still less probable is it that we 
 shall ever discover any inhabitants in the moon. The 
 greatest magnifying power that has ever been applied 
 with distinctness, to the moon, does not much exceed a 
 thousand times, bringing the moon apparently a thou- 
 sand times nearer to us than when seen by the naked 
 eye. But this implies a distance still of 240 miles ; and 
 
 148. Is there water in the moon ? What proofs are there 
 to the contrary ? 
 
 149. Is it probable that artificial structures in the moon will 
 ever be identified ? How high must they be, in order to be 
 seen distinct, from the surface ? Is it probable that we shall 
 ever be able to recognize inhabitants in the moon ? What is 
 the greatest magnifying power of the telescope that has ever 
 been applied to the moon ? If we could magnify the moon 
 1 0,000 times what would still be her apparent distance ? What 
 inherent difficulty is there in employing very great magnifiers ? 
 
118 THE MOON. 
 
 could we magnify the moon ten thousand times, her ap- 
 parent distance would still be twenty-four miles, a dis- 
 tance too great to distinguish living beings. Moreover, 
 when we use such high magnifiers in the telescope, our 
 field of view is necessarily exceedingly small, so that k 
 would be a mere point that we could view at a timt . 
 This difficulty is inherent in the very nature of tele> 
 scopes, namely, that the field of view is reduced as the 
 magnifying power is increased ; and we magnify the 
 vapors and the undulations of the atmosphere, as well 
 as the moon, and by this .means impair the medium so 
 much that we should not be able to see anything with 
 distinctness. It is only to such minute objects as a star, 
 that very high powers of the telescope can ever be ap- 
 plied. 
 
 150. Some writers, however, suppose that possibly 
 we may trace indications of lunar inhabitants in their 
 works, and that they may, in like manner, recognize the 
 existence of the inhabitants of our planet. An author 
 who has reflected much on subjects of this kind, rea- 
 sons as follows : A navigator who approaches within a 
 certain distance of a small island, although he perceives 
 no Human being upon it, can judge with certainty, that 
 it is inhabited, if he perceives human habitations, villa- 
 ges, cornfields, or other traces of cultivation. In like 
 manner, if we could perceive changes or operations in 
 the moon, which could be traced to the agency of intel- 
 ligent beings, we should then obtain satisfactory evi- 
 dence, that such beings exist on that planet ; and it is 
 thought possible that such operations may be traced. 
 A telescope which magnifies 1200 times, will enable us 
 to perceive, as a visible point on the surface of the moon, 
 an object whose diameter is only about 300 feet. Such 
 
 150. What have some writers supposed with respect to the 
 probability of our tracing marks of living beings on the moon ? 
 How is it proposed to have the moon examined for this pur- 
 pose ? 
 
LUNAR GEOGRAPHY. 119 
 
 an object is not larger than many of our public edifices ; 
 and, therefore, were any such edifices rearing in the 
 moon, or were a town or city extending its boundaries, 
 or were operations of this description carrying on in a 
 district where no such edifices had previously been 
 erected, such objects and operations might probably be 
 detected by a minute inspection. Were a multitude of 
 living creatures moving from place to place in a body, 
 or were they even encamping in an extensive plain, like 
 a large army, or like a tribe of Arabs in the desert, and 
 afterwards removing, it is possible that such changes 
 might be traced by the difference of shade or color, 
 which such movements would produce. In order to de- 
 tect such minute objects and operations, it would be 
 requisite that the surface of the moon should be distrib- 
 uted among at least a hundred astronomers, each having 
 a spot or two allotted to him, as the object of his mere 
 particular investigation, and that the observations be 
 continued for a period of at least thirty or forty years, 
 during which time certain changes would probably be 
 perceived, arising either from physical causes, or from 
 the operations of living agents.* 
 
 151. It has sometimes been a subject of speculation, 
 whether it might be possible, by any symbols, to cor- 
 respond with the inhabitants of the moon. It has been 
 suggested, that if some vast geometrical figure, as a 
 square or a triangle, were erected on the plains of Siberia, 
 it might be recognized by the lunarians, and answered 
 by some corresponding signal. Some geometrical figure 
 would be peculiarly appropriate for such a telegraphic 
 commerce with the inhabitants of another sphere, since 
 these are simple ideas common to all minds. 
 
 151 . How is it proposed to carry on a telegraphic communi- 
 cation with the lunarians ? 
 
 Dick's Celestial Scenery, Ch. iv. 
 
r20 THE MOON. 
 
 PHASES OF THE MOON. 
 
 152. The changes of the moon, commonly called her 
 Phases, arise from different portions of her illuminated 
 side being turned towards the earth at different times 
 When the moon is first seen after the setting sun, hei 
 form is thlt of a bright crescent, on the side of the disk 
 next to the sun, while the other portions of the disk 
 shine with a feeble light, reflected to the moon from the 
 earth. Every night we observe the moon to be farther 
 and farther eastward of the sun, and at the same time 
 the crescent enlarges, until, when the moon has reached 
 an elongation from the sun of 90, half her visible disk 
 is enlightened, and she is said to be in her first quarter. 
 The terminator, or line which separates the illuminated 
 from the dark part of the moon, is convex towards the 
 sun from the new moon to the first quarter, and the 
 moon is said to be horned. The extremities of the 
 crescent are called cusps. At the first quarter, the ter- 
 minator becomes a straight line, coinciding with a di- 
 ameter of the disk ; but after passing this point, the ter- 
 minator becomes concave towards the sun, bounding 
 that side of the moon by an elliptical curve, when the 
 moon is said to be gibbous. When the moon arrives at 
 the distance of 180 from the sun, the entire circle is 
 illuminated, and the moon is full. She is then in oppo- 
 sition to the sun, rising about the time the sun sets. For 
 a week after the full, the moon appears gibbous again, 
 until, having arrived within 90 of the sun, she re- 
 sumes the same form as at the first quarter, being then 
 at her third quarter. From this time until new moon, 
 she exhibits again the form of a crescent before the ri- 
 sing sun, until, approaching her conjunction with the 
 
 152. Phases of the Moon. Whence do they rise ? State 
 the successive appearances of the moon from new to full. In 
 what parts of her revolution is she horned, and in what parts 
 gibbous ? When is she said to be in conjunction, and when in 
 opposition ? What are the syzigies, quadratures, and octants ? 
 Define the circle of illumination, and the ciicle of the disk. 
 
 
PHASES. . 
 
 121 
 
 sun, her narrow thread of light is lost in the solar blaze ; 
 and finally, at the moment of passing the sun, the dark 
 side is wholly turned towards us, and for some time we 
 lose sight of the moon. 
 
 The two points in the orbit corresponding to new and 
 full moon respectively, are called by the common name 
 of syzigies ; those which are 90 from the sun are 
 called quadratures ; and the points half way between 
 the syzigies and quadratures are called octants. The 
 circle which divides the enlightened from the unen- 
 lightened hemisphere of the moon, is called the circle of 
 illumination: that which divides the hemisphere that 
 is turned- towards us from the hemisphere that is turn- 
 ed from us, is called the circle of the disk. 
 
 153. As the moon is an opake body of a spherical 
 figure, and borrows her light from the sun, it is obvious 
 
 Fig. 31 
 
 that that half only which is towards the sun can be il- 
 luminated.' More or less of this side is turned towards 
 the earth, according as the moon is at a greater or less 
 elongation from the sun. The reason of the different 
 phases will be best understood from a diagram. There- 
 fore let T (Fig. 31,) represent the earth, and S the sun. 
 
 11 
 
122 THE MOON. 
 
 Let A, B, C, <fec. be successive positions of the moon. 
 At A the entire dark side of the moon being turned to- 
 wards the earth, the disk would be wholly invisible. Al 
 B, the circle of the disk cuts of a small part of the en 
 lightened hemisphere, which appears in the heavens at 
 b, under the form of a crescent. At C, the first quarter 
 the circle of the disk cuts off half the enlightened hem- 
 isphere, and a half moon is seen at c. In like manner it 
 will be seen that the appearances presented at D, E, F, 
 &c. must be those represented at d, e,f. If a round 
 body, as an apple, suspended by a string, be carried 
 around a lamp, the eye remaining fixed opposite to it at 
 the same level, the various phases of the moon will be 
 exhibited. 
 
 REVOLUTIONS OF THE MOON. 
 
 1 54. The moon revolves around the earth from west 
 to east, making the entire circuit of the heavens in about 
 271 days. 
 
 The period of the moon's revolution from any point 
 in the heavens round to the same point again, is called 
 a month. A sidereal month is the time of the moon's 
 passing from any star, until it returns to the same star 
 again. A synodical month, so called from two Greek 
 words implying that at the end of this period the two 
 bodies (the sun and moon) come together, is the time 
 from one conjunction or new moon to another. The 
 synodical month is about 29J days, or more exactly, 
 29d. 12h. 44m. 2s.S= 29.53 days. The sidereal month 
 is about two days shorter, being 27d. 7h. 43m. lls.5. 
 or 27.32 days. As the sun and moon are both revolv- 
 ing in the same direction, and the sun is moving nearly 
 
 153. How much of the moon is illuminated at once? Ex- 
 plain the phases of the moon from figure 31. 
 
 1 54. Define a month. Define a sidereal month. Also a sy- 
 nodical month. Why so called ? What is the length of the 
 Bynodical month ? Also of the sidereal month ? What is the 
 moon's daily motion ? 
 
REVOLUTIONS. 123 
 
 a degree a day, during the 27 days of the moan's revo- 
 lution, the sun must have moved 27. Now since the 
 moon passes over 360 in 27.32 days, her daily motion 
 must be 13 17'. It must therefore evidently take about 
 two days for the moon to overtake the sun. 
 
 155. The moon's orbit is inclined to the ecliptic in an 
 angle of about 5 (5 8' 48".) The moon crosses the 
 ecliptic in two opposite points called her nodes. That 
 which the moon crosses from south to north, is called 
 her ascending node, that which she crosses from north 
 to south, her descending node. The moon, therefore, is 
 never seen far from the ecliptic, but the path she pur- 
 sues through the skies, is very nearly the same as that 
 of ( the sun in his annular revolution around the earth. 
 
 156. The moon, at the same age, crosses the meridian 
 at different altitudes at different seasons of the year ; and 
 accordingly it is said to run sometimes high and some- 
 times low. The full moon, for example, will appear 
 much farther in tne south when on the meridian at one 
 period of the year than at another. The reason of this 
 may be explained as follows. When the sun is in the 
 part of the ecliptic south of the equator, the earth and 
 of course the moon, which always keeps near to the 
 earth, is in the part north of the equator. At such 
 times, therefore, the new moons, which are always 
 seen in the part of the heavens where the sun is, will 
 run far south, while the full moons, which are always in 
 the opposite part of the heavens from the sun, will run 
 high. Such is the case during the winter months ; but, 
 
 J 55. How much is the moon's orbit inclined to the ecliptic ? 
 Define the nodes. What is the ascending and what the de- 
 scending node ? 
 
 1 56. Why does the moon run high and low ? At what sea- 
 son of the year are the full moons longest above the horizon ? 
 Explain how this operates favorably to those who are near 
 the pole. 
 
124 THE MOON. 
 
 in the summer, when the sun is towards the northern 
 tropic and the earth towards the southern, the new 
 moons run high and the full moons low. This arrange- 
 ment gives us a great advantage in respect to the amount 
 of light received from the moon ; since the full moon 
 is longest above the horizon during the long nights of 
 winter, when her presence is most needed, This cir- 
 cumstance is especially favorable to the inhabitants of 
 the polar regions, the moon, when full, traversing that 
 part of her orbit which lies north of the equator, and of 
 course above the horizon of the north pole, and traver- 
 sing the portion that lies south of the equator, and be- 
 low the polar horizon, when new. During the polar 
 winter, therefore, the moon, during her second and third 
 quarters, when she gives most light, is commonly above 
 the horizon, while the sun is absent ; w^hereas, during 
 summer, while the sun is present and the light is not 
 needed, during her second and third quarters, she is be- 
 low the horizon. 
 
 157. About the time of the autumnal equinox, the 
 moon when near the full, rises about sunset Tor a num- 
 ber of nights in succession ; and as this is, in England, 
 the period of harvest,' the phenomenon is called the 
 Harvest Moon. To understand the reason of this, since 
 the moon is never far from the ecliptic, we will suppose 
 her progress to be in the ecliptic. If the moon moved 
 in the equator, then, since this great circle is at right 
 angles to the axis of the earth, all parts of it, as the 
 earth revolves, cut the horizon at the same constant 
 angle. But the moon's orbit, or the ecliptic, which is 
 here taken to represent it, being oblique to the equator, 
 cuts the 'horizon at different angles in different parts, as 
 will easily be seen by reference to an artificial globe. 
 When the first of Aries, or vernal equinox, is in the 
 
 157. Why is the harvest moon so called ? Explain its cause. 
 How is the moon's orbit inclined to the horizon at different 
 
 times ? 
 
REVOLUTIONS. 125 
 
 eastern horizon, it will be seen that the ecliptic, (and 
 consequently the moon's orbit,) makes its least angle 
 with the horizon. Now, at the autumnal equinox, the 
 sun being in Libra, the moon at the full, when she is 
 always opposite to the sun, is in Aries, and rises when 
 the sun sets. On the following evening, although she 
 has advanced in her orbit about 13, yet her progress be- 
 ing oblique to the horizon, and at a small angle with it, 
 she will be found at this time but a little way below the 
 horizon, compared with the point where she was at sun- 
 set the preceding evening. She therefore rises but little 
 later, and so for a week only a little later each evening 
 than she did the preceding night. 
 
 1 58. The moon turns on its axis in the same time in 
 which it revolves around the earth. 
 
 This is known by the moon's always keeping nearly 
 the 'same face towards us, as is indicated by the tele 
 scope, which could not happen unless her revolution on 
 her axis kept pace with her motion in her orbit. Thus 
 it will be seen by inspecting figure 22, that the earth 
 turns different faces towards the sun at different times ; 
 and if a ball having one hemisphere white and the 
 other black be carried around a lamp, it will easily be 
 seen that it cannot present the same face constantly to- 
 wards the lamp unless it turns once on its axis while 
 performing its revolution. The same thing will be ob- 
 served when a man walks around a tree, keeping his face 
 constantly towards it. Since however the motion ot 
 the moon on its axis is uniform, while the motion in its 
 orbit is unequal, the moon does in fact reveal to us a lit- 
 tle sometimes of one side and sometimes of the other. 
 Thus when the ball above mentioned is placed before 
 the eye wi^h its light side towards us, on carrying it 
 round, if it is moved faster than it is turned on its axis, 
 
 1 58. In what time does the moon turn on its axis ? Illus- 
 trate by the motion of a ball around a lamp. Is the same side 
 of the moop always turned exactly towards us ? 
 
 U* 
 
126 THE MOON. 
 
 a portion of the dark hemisphere is brought into view 
 on one side ; or if it is moved forward slower than it is 
 turned on its axis, a portion of the dark hemisphere 
 comes into view on the other side. 
 
 159. These appearances are called the moon's libra- 
 tions in longitude. The moon has also a libration in 
 latitude, so called, because in one part of her revolution, 
 more of the region around one of the poles comes into 
 view, and in another part of the revolution, more of the 
 region around the other pole ; which gives the appear- 
 ance of a tilting motion to the moon's axis. This has 
 nearly the same cause with that which occasions our 
 change of seasons. The moon's axis being inclined to 
 the plane of her orbit, and always remaining parallel to 
 itself, the circle which divides the visible from the in- 
 visible part of the moon, will pass in such a way as to 
 throw sometimes more of one pole into view, and some- 
 times more of the other, as would be the case with the 
 earth if seen from the sun. (See Fig. 22.) 
 
 The moon exhibits another phenomenon of this kind 
 called her diurnal libration, depending on the daily ro- 
 tation of the spectator. She turns the same face to- 
 wards the center of the earth only, whereas we view 
 her from the surface. When she is on the meridian, we 
 see her disk nearly as though we viewed it from the 
 center of the earth, and hence in this situation it is sub- 
 ject to little change ; but when near the horizon, our 
 circle of vision takes in more of the upper limb than 
 would be presented to a spectator at the center of the 
 earth. Hence, from this cause, we see a portion of one 
 limb while the moon is rising, which is gradually lost 
 sight of, and we see a portion of the opposite limb as 
 the moon declines to the west. It will be remarked 
 that neither of the foregoing changes implies any actual 
 motion in the moon, but that each arises from a change 
 of position in the spectator. 
 
 159. Explain lie librations in longitude. Ditto in latitude 
 Ditto the diurnal librations. 
 
REVOLUTIONS. 
 
 160. Since the succession of day and night depends 
 on the revolution of a planet on its own axis, an inhab- 
 itant of the moon would have but one day and one night 
 during the whole lunar month of 29J days. One of its 
 days, therefore, is equal to nearly 15 of ours. So pro- 
 tracted an exposure to the sun's rays, especially in the 
 equatorial regions of the moon, must occasion an exces- 
 sive accumulation of heat ; and so long an absence of 
 the sun must occasion a corresponding degree of cold. 
 Each day would be a wearisome summer ; each night a 
 severe winter.* A spectator on the side of the moon 
 which is opposite to us would never see the earth ; but 
 one on the side next to us would see the earth present- 
 ing a gradual succession' of changes during his long 
 night of 360 hours. Soon after the earth's conjunction 
 with the sun, he would have the light of the earth re- 
 flected to him, presenting at first a crescent, but enlarg- 
 ing as the earth approaches its opposition, to a great orb, 
 13 times as large as the full moon appears to us, and af- 
 fording nearly 13 times as much light. Our seas, our 
 plains, our mountains, our volcanoes, and our clouds, 
 would produce very diversified appearances, as would 
 the various parts of the earth brought successively into 
 view by its diurnal rotation. The earth while in view 
 to an inhabitant of the moon, would remain immovably 
 fixed in the same part of the heavens. For being un- 
 conscious of his own motion around the earth, as we are 
 of our motion around the sun, the earth would seem to 
 revolve around his own planet from west to east, just as 
 the moon appears to us to revolve about the earth ; but, 
 meanwhile, his rotation along with the moon on her 
 axis, would cause the earth to have an apparent motion 
 
 160. How many days would an inhabitant of the moon have 
 in a lunar month ? What vicissitudes of temperature would 
 occur in a single day ? Would a spectator on the side of the 
 moon opposite to us, ever see the earth 1 How would the earth 
 appear to a spectator on the side of the moon next to us ? 
 
 * Francceur, Uranog. p. 91. 
 
128 THE MOON. 
 
 westward at the same rate. The two motions, there- 
 fore, would exactly balance each other, and the earth 
 would appear all the while -at rest. 
 
 161. We have thus far contemplated the revolution 
 of the moon around the earth as though the earth were 
 at rest. But, in order to have just ideas respecting the 
 moon's motions, we must recollect that the moon like- 
 wise revolves along with the earth around the sun. It 
 is sometimes said that the earth carries the moon along 
 with her in her annual revolution. This language may 
 convey an erroneous idea ; for the moon, as well as the 
 earth, revolves around the sun under the influence of 
 two forces, and would continue her motion around the 
 sun were the earth removed out of the way. Indeed, 
 the moon is attracted towards the sun 2J times more 
 than towards the earth, and would abandon the earth 
 were not the latter also carried along with her by the 
 same forces. So far as the sun acts equally on both 
 bodies, their motion with respect to each other would 
 not be disturbed. Because the gravity of the moon to- 
 wards the sun is found to be greater, at the*conjunction, 
 than her gravity towards the earth, some have appre- 
 hended that, if the doctrine of universal gravitation is 
 true, the moon ought necessarily to abandon the earth. 
 In order to understand the reason why it does not do 
 thus, we must reflect, that when a body is revolving in 
 its orbit under the action of the projectile force and 
 gravity, whatever diminishes the force of gravity while 
 that of projection remains the same, causes the body to 
 approach nearer to the tangent of her orbit, and of course 
 to recede from the center ; and whatever increases the 
 amount of gravity carries the body towards the center. 
 
 161. Can it be said that the earth carries the moon around 
 the sun ? How much more is the moon attracted towards tho 
 sun than towards the earth ? Why does not the moon abandon 
 the earth ? When the sun acts equally on both bodies, does it 
 disturb their relative places ? How does the sun act upon 
 these bodies at the conjunctions and oppositions ? 
 
REVOLUTIONS. 129 
 
 Now, when the moon is in conjunction, her gravity to- 
 wards the earth acts in opposition to that towards the 
 sun, while her velocity remains too great to carry her, 
 with what force remains, in a circle about the sun, and 
 she therefore recedes from the sun, and commences her 
 revolution around the earth. On arriving at the opposi- 
 tion, the gravity of the earth conspires with that of the 
 sun, and the moon's projectile force being less than that 
 required to make her revolve in a circular orbit, when 
 attracted towards the sun by the sum of these forces, she 
 accordingly begins to approach the sun and descends 
 again to the conjunction. 
 
 162. The attraction of the sun, however, being every 
 where greater than that of the earth, the actual path of 
 the moon around the sun is every where concave to- 
 wards the latter. Still the elliptical path of the moon 
 around the earth, is to be conceived of in the same way 
 as though both bodies were at rest with respect to the 
 sun. Thus, while a steamboat is passing swiftly around 
 an island, and a man is walking slowly around a post in 
 the cabin, the line which he describes in space between 
 the forward motion of the boat and his circular motion 
 around the post, may be every where concave towards 
 the island, while his path around the post will still be 
 the same as though both were at rest. A nail in the rim 
 of a coach wheel, will turn around the axis of the wheel, 
 when the coach has a forward motion in the same man- 
 ner as when the coach is at rest, although the line ac- 
 tually described by the nail will be the resultant of both 
 motions, and very different from either. 
 
 168. We have hitherto regarded the moon as descri- 
 bing a great circle on the face of the sky, such being the 
 
 162. How is the moon's path in space with respect to the 
 sun 1 How is the elliptical path of the moon around the earth 
 to be conceived of ? How is this illustrated by the motions of 
 a man in a steamboat ? Alsc by the motions of a nail in die 
 rim of a coach wheel ? 
 
130 THE MOON. 
 
 visible orbit as seen by projection. But, on more exact 
 investigation, it is found that her orbit is not a circle, 
 and that her motions are subject to very numerous ir- 
 regularities. These will be best understood in connec- 
 tion with the causes on which they depend. The law 
 of universal gravitation has been applied with wonder- 
 ful success to their investigation, and its results have 
 conspired with those of long continued observation, to 
 furnish the means of ascertaining with great exactness 
 the place of the moon in the heavens at any given in- 
 stant of time, past or future, and thus to enable astrono- 
 mers to determine longitudes, to calculate eclipses, and 
 to solve various other problems of the highest interest. 
 A complete understanding of all the irregularities of the 
 moon's motions, must be sought for in more extensive 
 treatises of astronomy than the present ; but some gen- 
 eral acquaintance with the subject, clear and intelligible 
 as far as it goes, may be acquired by first gaining a dis- 
 tinct idea of the mutual actions of the sun, the moon, 
 and the earth. 
 
 164. The irregularities of the moon's motions, are 
 due chiefly to the disturbing influence of the sun, which 
 operates in two ways ; first, by acting unequally on the 
 earth and moon, and, secondly, by acting obliquely on 
 the moon, on account of the inclination of her orbit to 
 the ecliptic. 
 
 If the sun acted equally on the earth and moon, and 
 always in parallel lines, this action would serve only to 
 restrain them in their annual motions round the sun, and 
 would not affect their actions on each other, or their 
 motions about their common center of gravity. In that 
 case, if they were allowed to fall directly towards the 
 sun, they would fall equally, and their respective situa- 
 tions would not be affected by their descending equally 
 towards it. We might then conceive them as in a 
 plane, every part of which being equally acted on by 
 
 163. Are the motions of the moon regular or irregular ? By 
 what, general law are they explained ? 
 
REVOLUTIONS. 131 
 
 the sun, the whole plane would descend towards the 
 sun, but the respective motions of the earth and the 
 moon in this plane, would be the same as if it were 
 quiescent. Supposing then this plane and all in it, 
 to have an annual motion imprinted on it, it would 
 move regularly around the sun, while the earth and moon 
 would move in it with respect to each other, as if the 
 plane were at rest, without any irregularities. But be- 
 cause the moon is nearer the sun in one half of her orbit 
 than the earth is, and in the other half of her orbit is at 
 a greater distance than the earth from the sun, while the 
 power of gravity is always greater at a less distance ; it 
 follows, that in one half of her orbit the moon is more 
 attracted than the earth towards the sun, and in the other 
 half less attracted than the earth. The excess of the 
 attraction, in the first case, and the defect in the second, 
 constitutes a disturbing force, to which we may add an- 
 other, namely, that arising from the oblique action of the 
 solar force, since this action is not directed in parallel 
 lines, but in lines that meet in the center of the sun. 
 
 165. To see the effects of this process, let us suppose 
 that the projectile motions of the earth and moon were 
 destroyed, and that they were allowed to fall freely to- 
 wards the sun. If the moon was in conjunction with 
 the sun, or in that part of her orbit which is nearest to 
 him, the moon would be more attracted than the earth, 
 and fall with greater velocity towards the sun ; so that 
 the distance of the moon from the earth would be in- 
 creased in the fall. If the moon was in opposition, or 
 
 164. To what cause are the inequalities of the moons mo- 
 tions chiefly due ? If the sun acted equally on the earth and 
 moon, and in parallel lines, would it disturb their motions ? If 
 allowed to fall towards the sun, how would they fall ? How 
 might we conceive them as situated in a plane ? When is the 
 moon more attracted than the earth ? When is the.earth more 
 attracted than the moon ? What constitutes the disturbing face. 
 
 165. Trace the effects of the sun, if the projectile force were 
 destroved, at conjunction, at opposition, and at quadrature. 
 
132 'THE MOON. 
 
 in the part of her orbit which is farthest from the sun, 
 she would be less attracted than the earth by the sun, 
 and would fall with a less velocity towards the sun, and 
 would be left behind ; so that the distance of the moon 
 from the earth would be increased in this case also. If 
 the moon was in one of the quarters, then the earth and 
 moon being both attracted towards the center of the 
 sun, they would both descend directly towards that cen- 
 ter, and by approaching it, they would necessarily at 
 the same time approach each other, and in this case their 
 distance from each other would be diminished. Now 
 whenever the action of the sun would increase their dis- 
 tance, if they were allowed to fall towards the sun, 
 then the sun's action, by endeavouring to separate them 
 diminishes their gravity to each other; whenever the 
 sun's action would diminish the distance, then it in- 
 creases their mutual gravitation. Hence, in the con 
 junction and opposition, that is, in the syzigies, their 
 gravity towards each other is diminished by the action 
 of the sun, while in the quadratures it is increased. 
 But it must be remembered that it is not the total action 
 of the sun on them that disturbs their motions, but only 
 that part of it which tends at one time to separate them, 
 and at another time to bring them nearer together. The 
 other and far greater part, has no other effect than to 
 retain them in their annual course around the sun. 
 
 166. The figure of the moon's orbit is an ellipse, hav- 
 ing the earth in one of the foci. 
 
 The greatest and least distances of the moon from the 
 earth, are nearly 64 and 56, the radius of the earth being 
 taken for unity. Hence, taking the arithmetical mean, 
 we find that the mean distance of the moon from the 
 
 166. What is the figure of the moon's orbit ? What are the 
 greatest and least distances of the moon from the earth ? De- 
 fine the terms perigee and apogee. What numbers express the 
 greatest and least distance of the sun from the earth ? How 
 does the eccentricity of the lunar orbit, compare with that of 
 the solar ? 
 
REVOLUTIONS. 133 
 
 earth is very nearly 60 times the radius of the earth. 
 The point in the moon's orbit nearest the earth, is 
 called her perigee ; the point farthest from the earth, 
 her apogee. 
 
 The greatest and least distances of the sun are re- 
 spectively as the numbers 32.583, and 31.517. By com- 
 paring this ratio with that of the distances of the moon, 
 it will be seen that the latter vary much more than the 
 former, and consequently that the lunar orbit is much 
 more eccentric than the solar. The eccentricity of the 
 moon's orbit is in fact ^ of its mean distance from the 
 earth, while that of the earth is only $ of its mean dis- 
 tance from the sun, 
 
 167. The moon 1 s nodes constantly shift their positions 
 in the ecliptic from east to west, at the rate of 19 35' per 
 annum, returning to the same points in 18.6 years. 
 
 Suppose the great circle of the ecliptic marked out on 
 the face of the sky in a distinct line, and let us observe, 
 at any given time, the exact point where the moon 
 crosses this line, which we will suppose to be close to a 
 certain star ; then, on its next return to that part of the 
 heavens, we shall find that it crosses the ecliptic sensi- 
 bly to the westward of that star, and so on, farther and 
 farther to the westward every time it crosses the ecliptic 
 at either node. This fact is expressed by saying that 
 the nodes retrograde on the ecliptic, and that the line 
 which joins them, or the line of the nodes, revolves from 
 east to west. 
 
 1 68. The period occupied by the sun in passing from 
 one of the moon's nodes until it comes round to the 
 same node again, is called the synodical revolution of the 
 node. This period is shorter than the sidereal year, be- 
 ing only about 3461 days. For since the node shifts its 
 
 167. How do the moon's nodes shift their position ? In 
 what time do they make a complete revolutin in the ecliptic ? 
 Explain what is mean* by saying that the nodes retrogade. 
 
 12 
 
134 THE MOON. 
 
 place to the westward 19 35' per annum, the sun, in 
 his annual revolution, comes to it so much before he 
 completes his entire circuit ; and since the sun moves 
 about a degree a day, the synodical revolution of the 
 node is 365 -19=346, or more exactly, 346.619851. 
 The time from one new moon, or from one full moon, 
 to another, is 29.5305887 days. Now 19 synodical rev- 
 olutions of the nodes contain very nearly 223 of these 
 periods. 
 
 For 346.619851 x 19 = 6585.78. 
 And 29.5305887x223 = 6585.32. 
 Hence, if the sun and moon were to leave the moon's 
 node together, after the sun had been round to the same 
 node 19 times, the moon would have made very nearly 
 223 conjunctions with the sun, and would therefore, at 
 the end of this period meet at the same node, to repeat 
 the same circuit. And since eclipses of the sun and 
 moon depend upon the relative position of the sun, the 
 moon, and node, these phenomena are repeated in nearly 
 the same order, in each of those periods. Hence, this 
 period, consisting of about 18 years and 10 days, under 
 the name of the Saros, was used by the Chaldeans and 
 other ancient nations in predicting eclipses. 
 
 169. The Metonic Cycle is not the same with the Sa- 
 ros, but consists of 19 tropical years. During this pe- 
 riod the moon makes very nearly 235 synodical revolu- 
 tions, and hence the new and full moons, if reckoned 
 by periods of 19 years, recur at the same dates. If, for 
 example, a new moon fell on the fiftieth day of one 
 cycle, it would also fall on the fiftieth day of each suc- 
 
 168. What is meant by the synodical revolution of the node ? 
 How many new moons occur in 19 synodical revolutions of the 
 node ? Why was this period used in predicting eclipses ? What 
 was it called ? 
 
 169. What is the period of the Metonic Cycle ? How many 
 conjunctions of the moon with the sun occur during this pe- 
 riod ? What use did the Athenians make of this lunar cycle ? 
 
REVOLUTIONS. 135 
 
 ceeding cycle ; and, since the regulation of games, 
 feasts, and* fasts, has been made very extensively ac- 
 cording to new or full moons, hence this lunar cycle has 
 been much used both in ancient and modern times. 
 The Athenians adopted it 433 years before the Christian 
 era, for the regulation of their calendar, and had it in- 
 scribed in letters of gold on the walls of the temple of 
 Minerva. Hence the term Golden Number, which de- 
 notes the year of the lunar cycle. 
 
 170. The line of the apsides of the moon's orbit re- 
 volves from west to east through her whole orbit in about 
 nine years. 
 
 If, in any revolution of the moon, we should accu- 
 rately mark the place in the heavens where the moon 
 comes to its perigee, (which would be known by the 
 moon's apparent diameter being then greatest,) we should 
 find, that at the next revolution, it would come to its 
 perigee at a point a little farther eastward than before, 
 and 'so on at every revolution, until, after nine years, it 
 would come to its perigee at nearly the same point as at 
 first. This fact is expressed by saying that the perigee 
 and of course the apogee, revolves, and that the line 
 which joins these two points, or the line of the apsides, 
 also revolves. 
 
 171. The inequalities of the moon's motions are di- 
 vided into periodical and secular. Periodical inequal- 
 ities are those which are completed in comparatively 
 short periods. Secular inequalities are those which 
 are completed only in very long periods, such as cen- 
 turies or ages. Hence the corresponding terms peri- 
 odical equations and secular equations. As an exam- 
 ple of a secular inequality, we may mention the ac- 
 celeration of the moon's mean motion. It is discov- 
 ered, that the moon actually revolves around the earth 
 
 170. In what period does the line of the apsides revolve? 
 Explain what is meant by this. 
 
136 THE MOON. 
 
 in less time now than she did in ancient times. The 
 difference however is exceedingly small, being only 
 about 10" in a century, but increases from century to 
 century as the square of the number of centuries. This 
 remarkable fact was discovered by Dr. Halley,* In a 
 lunar eclipse' the moon's longitude differs from that of 
 the sun, at the middle of the eclipse, by exactly 180 ; 
 and since the sun's longitude at any given time of the 
 year is known, if we can learn the day and hour when 
 an eclipse occurs, we shall of course know the longitude 
 of the sun and moon. Now in the year 721 before the 
 Christian era, on a specified day and hour, Ptolemy re- 
 cords a lunar eclipse to have happened, and to have been 
 observed by the Chaldeans. The moon's longitude, 
 therefore, for that time is known ; and as we know the 
 mean motions of the moon at present, starting from that 
 epoch, and computing, as may easily be done, the place 
 which the moon ought to occupy at present at any given 
 time, she is found to be actually nearly a degree and a 
 half in advance of that place. Moreover, the same con- 
 clusion is derived from a comparison of the Chaldean 
 observations with those made by an Arabian astronomer 
 of the tenth century. 
 
 This phenomenon at first led astronomers to appre- 
 hend that the moon encountered a resisting medium, 
 which, by destroying at every revolution a small portion 
 of her projectile force, would have the effect to bring 
 her nearer and nearer to the earth and thus to augment 
 her velocity. But in 1786, La Place demonstrated that 
 
 171 . How are the inequalities of the moon's motions divided? 
 What are periodical inequalities ? What are secular inequali- 
 ties ? Give an example of a secular inequality. How is it 
 known that the moon's motions are accelerated ? What is the 
 amount of the acceleration per century ? Will they a' ways 
 continue to be accelerated ? 
 
 * Astronomer Royal of Great Britain, and cotemporary with Sir Isaac 
 Newton. 
 
ECLIPSES. 137 
 
 this acceleration is one of the legitimate effects of the 
 sun's disturbing force, and is so connected with changes 
 in the eccentricity of the earth's orbit, that the moon 
 will continue to be accelerated while that eccentricity 
 diminishes, but when the eccentricity has reached its 
 minimum (as it will do after many ages) and begins to 
 increase, then the moon's motion will begin to be re- 
 tarded, and thus her motions will oscillate forever about 
 a mean value. 
 
 CHAPTER V. 
 
 * 
 
 OF ECLIPSES. 
 
 172. AN Eclipse of the moon happens when the moon 
 in its revolution around the earth, falls into the earth's 
 shadow. An Eclipse of the sun happens when the 
 moon coming between the earth and the sun, covers 
 either a part or the whole of the solar disk. 
 
 The earth and the moon being both opake globular 
 bodies exposed to the sun's light, they cast shadows op- 
 posite to the sun like any other bodies on which the 
 sun shines. Were the sun of the same size with the 
 earth and the moon, then the lines drawn touching the 
 surface of the sun, and the surface of the earth or moon 
 (which lines form the boundaries of the shadow) would 
 be parallel to each other, and the shadow would be a 
 cylinder infinite in length ; and were the sun less than 
 the earth or the moon, the shadow would be an increas- 
 ing cone, its narrower end resting on the earth ; but as 
 
 172. When does an eclipse of the moon happen ? When 
 does an eclipse of the sun happen ? Were the sun of the same 
 size with the earth and moon, how would their shadows be ? 
 How if less than these bodies ? How are they in fact? Ex- 
 plain by figure 32 
 
 12* 
 
138 
 
 THE MOON. 
 
 the sun is vastly greater than either of these bodies* 
 the shadow of each is a cone, whose base rests on the 
 body itself, and which comes to a point or vertex at a 
 certain distance behind the body. These several cases 
 are represented in the following diagrams. 
 
 173. It is found by calculation, that the length of the 
 moon's shadow is, on an average, just about sufficient to 
 reach to the earth, but the moon is sometimes farther 
 from the earth than at others. (Art. 166.) When she is 
 nearer than usual, the shadow reaches considerably be- 
 yond the surface of the earth. Also the moon as well 
 as the earth, is at different distances from the sun at dif- 
 ferent times, and its shadow is longest when it is far- 
 thest from the sun. Now when both these circumstan- 
 ces conspire, that is, when the moon is in her perigee 
 and in her aphelion, her shadow extends nearly 15000 
 miles beyond the center of ,the earth, and covers a space 
 
 173. How does the moon's shadow compare with her dis- 
 tance from the earth ? When does her shadow extend farthest 
 beyond the center of the earth ? What is the greatest breadth 
 of her shadow where it falls on the surface of the earth ? What 
 is the length of the earth's shadow ? When only can an eclipse 
 of the sun take place ? When only can an eclipse of the moon 
 occur ? Explain from figure 33. What is the moon's Pen- 
 umbra ? 
 
ECLIPSES. 139 
 
 on the surface of the earth 170 miles broad. The 
 earth's shadow is towards a million of miles in length, 
 and more than three and a half times as long as the dis- 
 tance from the earth to the moon ; and it is also at the 
 distance of the moon three times as broad as the moon 
 itself. An eclipse of the sun can take place only at new 
 moon, when the sun and moon meet in the same part of 
 the heavens, for then only can the moon come between 
 us and the sun ; and an eclipse of the moon can occur 
 only when the sun and moon are in opposite parts of 
 the heavens, or at full moon, for then only can the moon 
 fall into the shadow of the earth. 
 
 The nature of eclipses will be clearly understood from 
 the following representation. This figure exhibits the 
 
 Fig. 33. 
 
 relative position of the sun, the earth, and the moon, 
 both in a solar and in a lunar eclipse. - It is evident from 
 the figure, that if a spectator were situated where the 
 moon's shadow strikes the earth, the moon would cut off 
 from him the view of the sun, or the sun would be to- 
 tally eclipsed. Or, if he were within a certain distance 
 of the shadow on either side, the moon would be partly 
 between him and the sun, and would intercept from 
 him more or less of the sun's light, according as he was 
 nearer to the shadow or farther from it. If he were at 
 c, or , he would just see the moon entering upon the 
 
140 THE MOON. 
 
 sun's disk ; if he were nearer the shadow than either of 
 these points, he would have a portion of the sun's light 
 cut oft* from his view, and the moment he entered the 
 shadow itself, he would lose sight of the sun. To all 
 places between c or d and the shadow, the sun would 
 cast a partial shadow of the moon, growing deeper and 
 deeper as it approached the true shadow. This partial 
 shadow is called the moon's Penumbra. In like man- 
 ner, as the moon approaches the earth's shadow in a lu- 
 nar eclipse, as soon as she arrives at , the earth begins 
 to intercept from her a portion of the sun's light, or she 
 falls into the earth's penumbra. She continues to lose 
 more and more of the sun's light as she draws near to 
 the shadow, and hence her disk becomes gradually ob- 
 scured, until it enters the shadow, where the sun's light 
 is entirely lost. 
 
 174. As the sun and earth are both situated in the 
 plane of the ecliptic, if the moon 1 also revolved around 
 the earth in this plane, we should have a solar eclipse at 
 every new moon, and a lunar eclipse at every full 
 moon ; for m the former case the moon would come di- 
 rectly between us and the sun, and in the latter case, 
 the earth would come directly between the sun and the 
 moon. But the moon's path is inclined to the ecliptic 
 about 5, and the center of the moon may be all this 
 distance from the center of the sun, at new moon, and 
 the same distance from the center of the earth's shadow 
 at full moon. It is true the moon extends across her 
 path, one half her breadth lying on each side of it, and 
 the sun likewise reaches from the ecliptic a distance 
 equal to half his breadth. But these luminaries to- 
 gether make but little more than a degree, and conse- 
 quently their two semi-diameters would occupy only 
 
 174. Why do we not have a solar eclipse every new moon, 
 and a lunar eclipse every full moon ? Explain how eclipses 
 occur only when the sun is near one of the moon's nodes, by 
 figure 34. 
 
ECLIPSES. 141 
 
 about half a degree of the five degrees from one orbit 
 to the other. Also the earth's shadow where the moon 
 crosses it extends from the ecliptic., less than three 
 fourths of a degree, so that the semi-diameter of the 
 moon and of the earth's shadow, would together reach 
 but little way across the space that may in certain cases 
 separate the two luminaries from each other when they 
 are in opposition. Thus suppose we could take hold 
 of the circle in the figure that represents the moon's 
 orbit, (Fig. 31,) and lift the moon up five degrees above 
 the plane of the paper, it is evident that the moon 
 as seen from the earth, would appear in the heavens 
 five degreess above the sun, and of course would cut off 
 none of his light, and that the moon at the full would 
 pass the shadow of the earth five degrees below it, and 
 would suffer no eclipse. But in the course of the sun's 
 apparent revolution around the earth once a year, he is 
 successively in every part of the ecliptic ; consequently, 
 the conjunctions and oppositions of the sun and moon 
 may occur at any part of the ecliptic, and of course at 
 the two points where the moon's orbit crosses the eclip- 
 tic, that is, at the nodes, for the sun must necessarily 
 come to each of these nodes once a year. If then the 
 moon overtakes the sun just as she is crossing his path, 
 
 Fig. 34. 
 
 she will hide more or less of his disk from us. Since, 
 also, the earth's shadow is always directly opposite to 
 the sun, if the sun is at one of the nodes, the shadow 
 
142 THE MOON. 
 
 must extend in the direction of the other node, so as to 
 lie directly across the moon's path, and if the moon over- 
 takes it there, she will pass through it and be eclipsed. 
 Thus in figure 34, let BN represent the sun's path, and 
 AN the moon's, N being the place of the node ; then it v 
 evident that if the two luminaries at new moon be s 
 far from the node, that the distance between their centers 
 is greater than their semi-diameters, no eclipse can hap- 
 pen ; but if that distance is less than this sum as at 
 JE, F, then an eclipse will take place, but if the position 
 be as at C, D, the two bodies will just touch one another. 
 If A denote the earth's shadow instead of the sun, the 
 same illustration will apply to an eclipse of the moon. 
 
 175. Since bodies are defined to be in conjunction 
 when they are in the same part of the heavens, and to 
 be in opposition when they are in opposite parts of the 
 heavens, it may not appear how the sun and moon can 
 be in conjunction as at A and B, when they are still at 
 some distance from each other. But it must be recol- 
 lected that bodies are in conjunction when they have the 
 same longitude, in which case they are both situated in 
 the same great circle perpendicular to the ecliptic, that 
 is, in the same secondary to the ecliptic. One of the 
 bodies may be much farther from the ecliptic than the 
 other ; still, if the same secondary to the ecliptic passes 
 through them both, they will be in conjunction or oppo- 
 sition. 
 
 176. In a total eclipse of the moon, its disk is still 
 visible, shining with a dull red light. This light cannot 
 be derived directly from the sun, since the view of the 
 sun is completely hidden from the moon ; nor by reflex- 
 ion from the earth, since the illuminated side of the 
 
 175. Is it necessary for two bodies to be precisely together 
 in order to be in conjunction ? 
 
 176. Why is the disk of the moon still visible in a total 
 eclipse of the moon ? 
 
ECLIPSES. 143 
 
 earth is wholly turned from the moon ; but it is owing 
 to refraction from the earth's atmosphere^ by which a 
 few scattered rays of the sun are bent round into the 
 earth's shadow and conveyed to the moon, sufficient in 
 number to afford the feeble light in question. 
 
 177. It is impossible fully to understand the method 
 vf calculating eclipses, without a knowledge of trigo- 
 nometry ; still it is not difficult to form some general no- 
 tion of the process. It may be readily conceived that, 
 by long continued observations on the sun and moon, 
 the exact places which they will occupy in the heavens 
 at any future times, may be forseen and laid down in 
 tables of the sun and moon's motions ; that we may thus 
 ascertain by inspecting the tables the exact instant when 
 these two bodies will appear together in the heavens, or 
 be in conjunction, and when they will be 180 apart, 
 or in opposition. Moreover, since the exact place of the 
 moon's node among the stars at any particular time is 
 known to astronomers, it cannot be difficult to determine 
 when the new or full moon occurs in the same part of 
 the heavens as that where the node is projected as seen 
 from the earth. In short, as astronomers can easily de- 
 termine what will be the relative position of the sun, 
 the moon, and the moon's nodes for any given time, 
 they can tell when these luminaries will meet so near 
 the node as to produce an eclipse of the sun, or when 
 they will be in opposition so near the node as to produce 
 an eclipse of the moon. 
 
 178. Let us endeavor to form a just conception of the 
 manner in which these three bodies, the sun, the earth, 
 and the moon, are situated with respect to each other at 
 the time of a solar eclipse. First, suppose the conjunction 
 to take place at the node. Then the straight line which 
 connects the center of the sun and the earth, also passes 
 
 177. What science must be known in order fully to under- 
 stand the mode of calculating eclipses ? Explain the general 
 principles of the calculation. 
 
144 THE MOON. 
 
 through the center of the moon, and coincides with the 
 axis of its shadow ; and, since the earth is bisected by 
 the plane of the ecliptic, the shadow would traverse the 
 earth in the direction of the terrestrial ecliptic, from 
 west to east, passing over the middle regions of the 
 earth. Here the diurnal motion of the earth being in 
 the same direction with the shadow, but with a less ve- 
 locity, the shadow will appear to move with a speed 
 equal only to the difference between the two. Secondly, 
 suppose the moon is on the north side of the ecliptic at 
 the time of conjunction, and moving towards her de- 
 scending node, and that the conjunction takes place 
 as far from the node as an eclipse can happen. The 
 shadow will not fall in the plane of the ecliptic, but 
 a little northward of it, so as just to graze the earth 
 near the pole of the ecliptic. The nearer the conjunc- 
 tion comes to the node, the farther the shadow will fall 
 from the pole of the ecliptic towards the equatorial re- 
 gions. 
 
 179. The leading particulars respecting an ECLIPSE 
 OF THE SUN, are ascertained very nearly like those of a 
 lunar eclipse. The shadow of the moon travels over a 
 portion of the earth, as the shadow of a small cloud, seen 
 from an eminence in a clear day, rides along over hills 
 and plains. Let us imagine ourselves standing on the 
 moon ; then we shall see the earth partially eclipsed by 
 the shadow of the moon, in the same manner as we 
 now see the moon eclipsed by the earth's shadow. 
 
 But, although the general characters of a solar eclipse 
 might be investigated on these principles, so far as re- 
 spects the earth at large, yet as the appearances of the 
 same eclipse of the sun are very different at different 
 places on the earth's surface, it is necessary to calculate 
 
 178. Explain the relative position of the sun, the earth, and 
 the moon, in a solar eclipse. Explain the circumstances when 
 the conjunction takes place at the node, and when it occurs at 
 a distance from the node. 
 
ECLIPSES. 145 
 
 its peculiar aspects for each place separately, a circum- 
 stance which makes the calculation of a solar eclipse 
 much more complicated and tedious than of an eclipse 
 of the moon. The moon, when she enters the shadow 
 of the earth, is deprived of the light of the part immer- 
 sed, and that part appears black alike to all places where 
 the moon is above the horizon. But it is not so with a 
 solar eclipse. We do not see this by the shadow cast 
 on the earth, as we should do if we stood on the moon, 
 but by the interposition of the moon between us and the 
 sun ; and the sun may be hidden from one observer 
 while he is in full view of another only a few miles dis- 
 tant. Thus, a small insulated cloud sailing in a clear 
 sky, will, for a few moments, hide the sun from us, and 
 from a certain space near us, while all the region around 
 is illuminated. 
 
 We have compared the motion of the moon's shadow 
 over the surface of the earth to that of a cloud ; but its 
 velocity is incomparably greater. The mean motion of 
 the moon around the earth is about 33' per hour ; but 
 33' of the moon's orbit is 2280 miles, and the shadow 
 moves of course at the same rate, or 2280 miles per 
 hour, traversing the entire disk of the earth in less than 
 four hours. 
 
 180. The diameter of the moon's shadow where it 
 eclipses the earth can never exceed 170 miles, and com- 
 monly falls much short of that ; and the greatest por- 
 tion of the earth's surface ever covered by the moon's 
 penumbra is about 4393 miles. 
 
 181. The apparent diameter of the moon is sometimes 
 larger than that of the sun, sometimes smaller, and 
 
 179. How are the leading particulars of an eclipse of the sun 
 ascertained ? How illustrated by the motion of a cloud ? In 
 what respects does the calculation of a solar differ from that of 
 a lunar eclipse ? How does the shadow of the moon cempare 
 with that of a cloud in velocity ? 
 
 13 
 
146 
 
 THE MOON. 
 
 sometimes exactly equal to it. Suppose an observer 
 placed on the right line which joins the centers of the 
 sun and moon ; if the apparent diameter of the moon is 
 greater than that of the sun, the eclipse will be total. If 
 the two diameters are equal, the moon's shadow just 
 reaches the earth, and the sun is hidden but for a mo- 
 ment from the view of spectators situated in the line 
 which the vertex of the shadow describes on the surface 
 of the earth. But if, as happens when the moon comes 
 to her conjunction in that part of her orbit which is to- 
 wards her apogee, the moon's diameter is less than the 
 sun's, then the observer will see a ring of the sun en- 
 circling the moon, constituting an Annular Eclipse, as in 
 figure 35. 
 
 Fig. 35. 
 
 180. What cannot the diameter of the moon's shadow 
 where it eclipses the earth, exceed ? What is the greatest 
 portion of the earth's surface ever covered by the moon's pe- 
 numbra ? 
 
 181 . How does the moon's apparent diameter compare with 
 the sun'* ? When will the eclipse b total, and when annular ? 
 
ECLIPSES. 147 
 
 182. Eclipses of the sun are modified by the eleva- 
 tion of the moon above the horizon, since its apparerft 
 diameter is augmented as its altitude is increased. This 
 effect, combined with that of parallax, may so increase 
 or diminish the apparent distance between the centers of 
 the sun and moon, that from this cause alone, of two 
 observers at a distance from each other, one might see 
 an eclipse which was not visible to the other. If the 
 horizontal diameter of the moon differs but little from 
 the apparent diameter of the sun, the case might occur 
 where the eclipse would be annular over the places 
 where it was observed morning and evening, tyit total 
 where it was observed at mid-day. 
 
 The earth in its diurnal revolution and the moon's 
 shadow both move from west to east, but the shadow 
 moves faster than the earth ; hence the moon overtakes 
 the sun on its western limb and crosses it from west to 
 east. The excess of the apparent diameter of the moon 
 above that of the sun in a total eclipse is so small, that 
 total darkness seldom continues longer than four minutes, 
 and can never continue so long as eight minuutes. An 
 annular eclipse may last 12m. 24s. 
 
 183. Eclipses of the sun are more frequent than those 
 of the moon. Yet lunar eclipses being visible to every 
 part of the terrestrial hemisphere opposite to the sun,, 
 while those of the sun are visible only to the small por- 
 tion of the hemisphere on which the moon's shadow 
 falls, it happens that for any particular place on the 
 earth, lunar eclipses are more frequently visible than 
 solar. In any year, the number of eclipses of both lu- 
 
 182. How are eclipses of the sun modified by the elevation 
 of the moon above the horizon ? How might the same eclipse 
 appear total to one observer and annular to another ? How 
 long cin total darkness continue in a solar eclipse ? How long 
 may an annular eclipse last ? 
 
 183. Which are most frequent, solar or lunar eclipses ? Why 
 does an eclipse'of the moon sometimes happen at the next full 
 moon after an eclipse of the sun ? 
 
148 REVOLUTIONS. 
 
 t 
 
 Binaries cannot be less than two nor more than seven : 
 the most usual number is four, and it is very rare to 
 have more than six. A total eclipse of the moon fre- 
 quently happens at the next full moon after an eclipse 
 of the sun. For since, in an eclipse of the sun, the sun 
 is at or near one of the moon's nodes, the earth's shadow 
 must be at or near the other node, and may not have 
 passed far from the node before the moon overtakes it. 
 
 184. In total eclipses of the sun, there has sometimes 
 been observed a remarkable radiation of light from the 
 margin of the sun. This has been ascribed to an illu- 
 mination of the solar atmosphere, but it is with more 
 probability owing to the zodiacal light, which at that 
 time is projected around the sun, and which is of such 
 dimensions as to extend far beyond the solar orb.* 
 
 A total eclipse of the sun is one of the most sublime 
 and impressive phenomena of nature. Among barbarous 
 tribes it is ever contemplated with fear and astonish- 
 ment, while among cultivated nations it is recognized, 
 from the exactness with which the time of occurrence 
 and the various appearances answer to the prediction, as 
 affording one of the proudest triumphs of astronomy. 
 By astronomers themselves it is of course viewed with 
 the highest interest, not only as verifying their calcula- 
 tions,- but as contributing to establish beyond all doubt 
 the certainty of those grand laws, the truth of which is 
 involved in the result. During the eclipse of June, 
 1806, which was one of the most remarkable on record, 
 the time of total darkness, as seen by the author of this 
 work, was about mid-day. The sky was entirely cloud- 
 
 1 84. How is the radiation of light around the margin of the 
 sun in a total eclipse of the sun, accounted for ? How have 
 eclipses of the sun been regarded among barbarous tribes ? 
 How among civilized nations 1 How by astronomers ? Givo 
 some account of the great eclipse of 1806. 
 
 * See an excellent description and delineation of this appearance as 
 it was exhibited in the eclipse of 1806, in the Transactions ol the Al- 
 bany Institute, by the late Chancellor JDe Witt 
 
ECLIPSES 149 
 
 less, but -as the period of total obscuration approached, a 
 gloom pervaded all nature. When the sun was wholly 
 lost sight of, planets and stars came into view ; a fearful 
 pall hung upon the sky, unlike both to night and to 
 twilight ; and, the temperature of the air rapidly de- 
 clining, a sudden chill came over the earth. Even the 
 animal tribes exhibited tokens of fear and agitation. 
 
 185. The word Eclipse is derived from a Greek word, 
 (exleiytg,) which signifies to fail, to faint, or swoon 
 away, since the moon at the period of her greatest 
 brightness falling into the shadow of the earth, was im- 
 agined by the ancients to sicken and swoon, as if she 
 were going to die. By some very ancient nations she 
 was supposed at such times to be in pain, and hence 
 lunar eclipses were called the labors of the moon, (Iuna3 
 labores ;) and, in order to relieve her fancied distress, they 
 lifted torches high in the atmosphere, blew horns and 
 trumpets, beat upon brazen vessels, and even, after the 
 eclipse was over, they offered sacrifices to the moon. 
 The opinion also extensively prevailed, that it was in 
 the power of witches, by their spells and charms, not 
 only to darken the moon, but to bring her down from 
 her orbit, and to compel her to shed her baleful influences 
 upon the earth. In a solar eclipse also, especially when 
 total, the sun was supposed to turn away his face in ab- 
 horrence of some atrocious crime, that either had been 
 perpetrated or was about to be perpetrated, and to 
 threaten mankind with everlasting night, and the de- 
 struction of the world. 
 
 The Chinese, who from a very high period of anti- 
 quity have been great observers of eclipses, although 
 they did not take much notice of those of the moon, re- 
 garded eclipses of the sun in general as unfortunate, but 
 especially such as occurred on the first day of the year. 
 
 185. From what is the word eclipse derived ? What ideas 
 bad certain ancient nations respecting eclipses ? With what 
 ceremonies did they observe them ? How were eclipses re- 
 garded among the Chinese ? 
 
 13* 
 
150 THE MOON. 
 
 These were thought to forbode the greatest calamities 
 to the emperor, who on such occasions did not receive 
 the usual compliments of the season. When an eclipse 
 of the sun was expected from the predictions of their as- 
 ^tronomers, they made great preparation at court for ob- 
 serving it ; and as soon as it commenced, a blind man 
 beat a drum and a great concourse assembled, and the 
 Mandarins, or nobility, appeared in state. 
 
 186. From 1831 to 1838, was a period distinguished 
 for great eclipses of the sun, in which time there were no 
 less than five, of the most remarkable character. The 
 next total eclipse of the sun, visible in the United States, 
 will occur on the 7th of August, 1869. 
 
 CHAPTER VI. 
 
 OF LONGITUDE. TIDES. 
 
 187. As eclipses of the sun afford one of the most 
 approved methods of finding the longitude of places, our 
 attention is naturally turned next towards that subject, 
 
 The ancients studied astronomy in order that they 
 might read their destinies in the stars : the moderns that 
 they may securely navigate the ocean. A large portion 
 of the refined labors of modern astronomy, has been di- 
 rected towards perfecting the astronomical tables with 
 the view of finding the longitude at sea, an object 
 manifestly worthy of the highest efforts of science, con- 
 sidering the vast amount of property and of human life 
 involved in navigation. 
 
 188. The difference of longitude between two places, 
 may be found by any method by which we can ascertain 
 
 1S6. What recent period has abounded with great eclipses 
 of the sun ? When will the next total eclipse of the sun occur ? 
 
 1 87. For what purpose did the ancients study astronomy ? 
 For what purpose do the moderns study it ? 
 
LONGITUDE. 151 
 
 the difference of their local times, at the same instant of 
 absolute time. 
 
 As the earth turns on its axis from west to east, any 
 place that lies eastward of another will come sooner un- 
 der the sun, or will have the sun earlier on the meridian, 
 and consequently, in respect to the hour of the day, will 
 be in advance of the other at the rate of one hour for 
 every 15, or four minutes of time for each degree. Thus, 
 to a place 15 east of Greenwich, it is 1 o'clock, P. M. 
 when it is noon at Greenwich; and to a place 15 west 
 of that meridian, it is 11 o'clock, A. M. at the same in- 
 stant. Hence the difference of time at any two places, 
 indicates their difference of longitude. 
 
 189. The easiest method of finding the longitude is 
 by means of an accurate time piece, or chronometer. Let 
 us set out from London with a chronometer accurately 
 adjusted to Greenwich time, and travel eastward to a 
 certain place, where the time is accurately kept, or may 
 be ascertained by observation. We find, for example, 
 that it is 1 o'clock by our chronometer, when it is 2 
 o'clock and 30 minutes at the place of observation. 
 Hence the longitude is 15 x 1.5=22i E. Had we trav- 
 elled westward until our chronometer was an hour and 
 a half in advance of the time at the place of observa- 
 tion, (that is, so much later in the day,) our longitude 
 would have been 22^ W. But it would not be neces- 
 sary to repair to London in order to set our chronometer 
 to Greenwich time. This might be done at any obser- 
 vatory, or any place whose longitude has been accu- 
 
 188. How may the difference of longitude between two pla- 
 ces be found ? How many degrees of longitude correspond to 
 one hour in time ? How many minutes to one degree ? 
 
 189. Explain the method of finding the longitude by the 
 chronometer. To what time is it set ? How do we ascertain 
 the longitude of a place by it ? Would it be necessary to re- 
 pair to Greenwich to regulate our chronometer ? What is said 
 oi the accuracy of some chronometers ? Why is not this 
 method adapted to general use ? 
 
152 THE MOON. 
 
 rately determined. For example, the time at New YorR 
 is 4h. 56m. 4s.5 behind that of Greenwich. If, there- 
 fore, we set our chronometer so much before the true 
 time at New York, it will indicate the time at Green- 
 wich. Moreover, on arriving at different places any 
 where on the earth, whose longitude is accurately known, 
 we may learn whether our chronometer keeps accurate 
 time or not, and if not, the amount of its error. Chro- 
 nometers have been constructed of such an astonishing 
 degree of accuracy, as to deviate but a few seconds in a 
 voyage from London to Baffin's Bay and back, during an 
 absence of several years. But chronometers which are 
 sufficiently accurate to be depended on for long voya- 
 ges, are too expensive for general use, and the means of 
 verifying their accuracy are not sufficiently easy. More- 
 over, chronometers, by being transported from one place 
 to another, change their daily rate, or depart from that 
 mean rate which they preserve at a fixed station, A 
 chronometer, therefore, cannot be relied on for determin- 
 ing the longitudes of places where the greatest degree of 
 accuracy is. required, especially where the instrument is 
 conveyed over land, although the uncertainty attendant 
 on one instrument may be nearly obviated by employing 
 several and taking their mean results. 
 
 190. Eclipses of the sun and moon are sometimes 
 used for determining the longitude. The exact instant 
 of immersion or of emersion, or any other definite mo- 
 ment of the eclipse which presents itself to two distant 
 observers, affords the means of comparing their difference 
 of time, and hence of determining their difference of 
 longitude. Since the entrance of the moon- into the 
 earth's shadow, in a lunar eclipse, is seen at the same 
 instant of absolute time at all places where the eclipse 
 is visible, this observation would be a very suitable one 
 for finding the longitude were it not that, on account of 
 
 1 90. Explain how to find the longitude by eclipses of the sun 
 and moon. What objections are there to this method, both in 
 lunar and solar eclipses ? 
 
LONGITUDE. .153 
 
 the increasing darkness of the penumbra near the boun 
 claries of the shadow, it is difficult to determine the pre 
 cise instant when the moon enters the shadow. By 
 taking observations on the immersions of known spots 
 on the lunar disk, a mean result may be obtained which 
 will give the longitude with tolerable accuracy. In an 
 eclipse of the sun, the instants of immersion and emer- 
 sion may be observed with greater accuracy, although, 
 since these do not take place at the same instant of ab- 
 solute time, the calculation of the longitude from obser- 
 vations on a solar eclipse are complicated and laborious. 
 
 191. The lunar method of finding the longitude, at 
 sea, is in many respects preferable to every other. It 
 consists in measuring (with a sextant) the angular dis- 
 tance between the moon and the sun, or between the 
 moon and a star, and then turning to the Nautical Alma- 
 nac,* and finding what time it was at Greenwich when 
 that distance was the same. The moon moves so rap- 
 idly, that this distance will not be the same except at 
 very nearly the same instant of absolute time. For ex- 
 ample, at 9 o'clock, A. M., at a certain place, we find the 
 angular distance of the moon and the sun to be 72 ; 
 and, on looking into the Nautical Almanac, we find that 
 the time when this distance was the same for the me- 
 ridian of Greenwich was 1 o'clock, P. M . ; hence we 
 infer that the longitude of the place is four hours, or 60 
 west. 
 
 191. Explain the lunar method of finding the longitude. 
 What measurements are made ? How do we find the corres- 
 ponding time at Greenwich ? 
 
 * The Nautical Almanac, is a book published annually by the British 
 Board of Longitude, containing various tables and astronomical infor- 
 mation for the use of navigators. The American Almanac also con- 
 tains a variety of astronomical information, peculiarly interesting to the 
 people of the United States, in connexion with a vast amount ot 
 statistical matter. It is well deserving of a place in the library of the 
 student. 
 
154 THE MOON. 
 
 The Nautical Almanac contains the true angular dis- 
 tance of the moon from the sun, from the four large 
 planets, (Venus, Mars, Jupiter, and Saturn,) and from 
 nine bright fixed stars, for the beginning of every third 
 hour of mean time for the meridian of Greenwich ; and 
 the mean time corresponding to any intermediate hour, 
 may be found by proportional parts.* 
 
 192. It would be a very simple operation to determine 
 the longitude by Lunar Distances, if the process as de- 
 scribed in the preceding article were all that is neces- 
 sary ; but the various circumstances of parallax, refrac- 
 tion, and dip of the horizon, would differ more or less at 
 the two places, even were the bodies, whose distances 
 were taken, in view from both, which is not necessarily 
 the case. The observations, therefore, require to be 
 reduced to the center of the earth, being cleared of the 
 effects of parallax and refraction. Hence, three obser- 
 vers are necessary in order to take a lunar distance in 
 the most exact manner, viz. two to measure the altitudes 
 of the two bodies respectively, at the same time that 
 the third takes the angular distance between them. 
 The altitudes of the two luminaries at the time of ob- 
 servation must be known, in order to estimate the effects 
 of parallax and refraction. 
 
 193. Although the lunar method of finding the longi- 
 tude at sea has many advantages over the other meth- 
 ods in use, yet it also has its disadvantages. One is, the 
 great exactness requisite in observing the distance of 
 the moon from the sun or star, as a small error in the 
 distance makes a considerable error in the longitude. 
 The moon moves at the rate of about a degree in two 
 
 192. What difficulties are there in this method ? Why are 
 three observers necessary ? 
 
 193. What are the objections to this method ? What is the 
 error of the best tables now in use ? 
 
 * See Bowditch's Navigator, Tenth Ed. p. 226. 
 
LONGITUDE. 155 
 
 hours, or one minute of space in two minutes of time. 
 Therefore, if we make an error of one minute in ob- 
 serving the distance, we make an error of two minutes 
 in time, or 30 miles of longitude at the equator. A sin- 
 gle observation with the best sextant, may be liable to 
 an error of more than half a minute ; but the accuracy 
 of the result may be much increased by a mean of sev- 
 eral observations taken to the east and west of the moon. 
 The imperfection of the lunar tables was until recently 
 considered as an objection to this method. Until within a 
 few years, the best lunar tables were frequently errone- 
 ous to the amount of one minute, occasioning an error 
 of 30 miles. The error of the best tables now in use 
 will rarely exceed 7 or 8 seconds. 
 
 / TIDES. 
 
 r~* 
 
 194. (The tides are an alternate rising and falling of 
 
 the waters of the ocean, at regular intervals. They have 
 a maximum and a minimum twice a day, twice a month, 
 and twice a year. Of the daily tide, the maximum is 
 called High tide, and the minimum Low tide. The 
 maximum for the month is called Spring tide, and the 
 minimum Neap tide. The rising of the tide is called 
 Flood and its falling Ebb tide. 
 
 Similar tides, whether high or low, occur on opposite 
 sides of the earth at once. Thus at the same time that it 
 is high tide at any given place, it is also high tide on the 
 inferior meridian, and the same is true of the low tides. 
 
 The interval between two successive high tides is 
 12h. 25m.; or, if the same tide be considered as return- 
 ing to the meridian, after having gone around the globe, 
 
 194. What are the tides ? When have they a maximum and 
 a minimum ? Define the terms High and Low, Spring and 
 Neap, Flood and Ebb tides. What two tides occur at the same 
 time ? What is the intervalbetween two successive high tides ? 
 How much later is the tide of to-day than the same tide of 
 yesterday ? What is the average height of the tide for the 
 whole globe ? To what extreme height does it sometimes rise ? 
 Have inland lakes and seas any tides ? 
 
156 THE MOON 
 
 its return is about 50 minutes later than it occurred on 
 the preceding day. In this respect, as well as in various 
 others, it corresponds very nearly to the motions of the 
 moon. 
 
 The average height for the whole globe is about 2J 
 feet ; or, if the earth were covered uniformly with a 
 stratum of water, the difference between the two diam- 
 eters of the oval would be 5 feet, or more exactly 5 feet 
 and 8 inches ; but its actual height at various places is 
 very various, sometimes rising to 60 or 70 feet, and 
 sometimes being scarcely perceptible. At the same 
 place also, the phenomena of the tides are very different 
 at different times. 
 
 Inland lakes and seas, even those of the largest class, 
 as Lake Superior, or the Caspian, have no perceptible 
 tide. 
 
 195. Tides are caused by the unequal attraction of 
 the sun and moon upon different parts of the earth. 
 
 Suppose the projectile force by which the earth is car- 
 ried forward in her orbit, to be suspended, and the earth 
 to fall towards one of these bodies, the moon, for exam- 
 ple, in consequence of their mutual attraction. Then, 
 if all parts of the earth fell equally towards the moon, 
 no derangement of its different parts would result, any 
 more than of the particles of a drop of water in its de- 
 scent to the ground. But if one part fell faster than an- 
 other, the different portions would evidently be separa- 
 ted from each other. Now this is precisely what takes 
 place with respect to the earth in its fall towards the 
 moon. The portions of the earth in the hemisphere 
 next to the moon, on account of being nearer to the 
 center of attraction, fall faster than those in the oppo- 
 site hemisphere, and consequently leave them behind. 
 The solid earth, on account of its cohesion, cannot obey 
 
 195. State the cause of the tides. What would be the con- 
 sequence were the earth abandoned to the force exerted by 
 the moon alone ? 
 
TIDES. 
 
 157 
 
 this impulse, since all its different portions constitute 
 one mass, which is acted on in the same manner as 
 though it were all collected in the center ; but the wa- 
 ters on the surface, moving freely under this impulse, 
 endeavor to desert the solid mass and fall towards the 
 tnoon. For a similar reason the waters in the opposite 
 hemisphere falling less towards the moon than the solid 
 earth are left behind, or appear to rise from the center 
 of the earth. 
 
 196. Let DEFG (Fig. 36,) represent the globe ; and, 
 for the sake of illustrating the principle, we will sup- 
 pose the waters entirely to cover the globe at a uniform 
 depth. Let defg represent the solid globe, and the cir- 
 
 Fig. 3G. 
 
 cular ring exterior to it, the covering of waters. Let C 
 be the center of gravity of the solid mass, A that of the 
 hemisphere next to the moon, (for the center of gravity 
 of a ring is within the ring,) and B that of the remoter 
 hemisphere. Now the force of attraction exerted by 
 the moon, acts in the same manner as though the solid 
 mass were all concentrated in C, and the waters of each 
 hemisphere at A and B respectively ; and (the moon be- 
 
 1 96. Explain the tides upon the doctrine of the center of 
 gravity. Where would the tide-wave always be seen were it 
 not for impediments ? What are these ? 
 
 14 
 
158 THE MOON. 
 
 ing supposed above E) it is evident that A will tend to 
 leave C, and C to leave B behind. The same must evi- 
 dently be true of the respective portions of matter, of 
 which these points are the centers of gravity. The wa- 
 ters of the globe will thus be reduced to an oval shape, 
 being elongated in the direction of that meridian which 
 is under the moon, and flattened in the intermediate 
 parts, and most of all at points ninety degrees distant 
 from that meridian. 
 
 Were it not, therefore, for impediments which prevent 
 the force from producing its full effects, we might expect 
 to see the great tide-wave, as the elevated crest is called, 
 ahvays directly beneath the moon, attending it regularly 
 around the globe. But the inertia of the waters pre- 
 vents their instantly obeying the moon's attraction, and 
 the friction of the waters on the bottom of the ocean, 
 still farther retards its progress. It is not therefore until 
 several hours (differing at different places) after the 
 moon has passed the meridian of a place, that it is high 
 tide at that place. 
 
 197. The sun has a similar action to the moon, but 
 only one third as great. On account of the great mass 
 of the sun compared with that of the moon, we might 
 suppose that his action in raising the tides would be 
 greater than that of the moon ; but the nearness of the 
 moon to the earth more than compensates for the sun's 
 greater quantity of matter. Let us, however, form a just 
 conception of the advantage which the moon derives 
 from her proximity. It is not that her actual amount of 
 attraction is thus rendered greater than that of the sun ; 
 but it is that her attraction for the different parts of the 
 earth is very unequal, while that of the sun is nearly 
 uniform. It is the inequality of this action, and not the 
 absolute force, that produces the tides. The diameter of 
 the earth is ^ of the distance of the moon, while it is 
 less than of the distance of the sun. 
 
 197. Explain the action of the sun in raising the tide ? Why 
 is its effect less than that of the moon ? 
 
19* 
 
 TIDES. 159 
 
 Having now learned the general cause of the 
 tides, we will next attend to the explanation of particu- 
 lar phenomena. 
 
 The Spring tides, or those which rise to an unusual 
 height twice a ntonth, are produced by the sun and 
 moon's acting together ; and the Neap tides, or those 
 which are unusually low twice a month, are produced 
 by the sun and moon's acting in opposition to each 
 other. The Spring tides occur at the syzigies: the 
 Neap tides at the quadratures. At the time of new moon, 
 the sun and moon both being on tli same side of the 
 earth, and acting upon it in the same line, their actions 
 conspire, and the sun may be considered as adding so 
 much to the force of the moon. We have already ex- 
 plained how the moon contributes to raise a tide on the 
 opposite side of the earth. But the sun as well as the 
 moon raises its own tide-wave, which, at new moon, 
 coincides with the lunar tide-wave. At full moon, also, 
 the two luminaries conspire in the same way to raise 
 the tide ; for we must recollect that each body contri- 
 butes to raise the tide on the opposite side of the earth 
 as well as on the side nearest to it. At both the con- 
 junctions and oppositions, therefore, that is, at the syzi- 
 gies, we have unusually high tides. But here also the 
 maximum effect is not at the moment of the syzigies, 
 but 36 hours afterwards. 
 
 At the quadratures, the solar wave is lowest where the 
 lunar wave is highest ; hence the low tide produced by 
 the sun is subtracted from high water and produces the 
 Neap tides. Moreover, at the quadratures the solar 
 wave is highest where the lunar wave is lowest, and 
 hence is to be added to the height of low water at the 
 time of Neap tides. Therefore the difference between 
 high and low water is only about half as great at Neap 
 tide as at Spring tide. 
 
 198. What is the cause of the Springtides ? Also of the 
 Neap tides 1 How long after the syzigies does the highest 
 tide occur ? 
 
160 THE MOON 
 
 199. The variations of distance in the sun are not 
 great enough to influence the tides very materially, but 
 the variations in the moon's distance have a striking 
 effect. The tides which happen when the rnoon is in 
 perigee, are considerably greater than when she is in 
 apogee ; and if she happens to be in perigee at the time 
 of the syzigies, the Spring tide is unusually high. 
 When this happens at the equinoxes, the highest tides 
 of the year are produced. 
 
 200. The declinations of the sun and moon have a 
 considerable influence on the height of the tide. When 
 the moon, for example, has no declination, or is in the 
 
 equator, as in figure 37,* the two tides will be exactly 
 equal on opposite sides of the meridian in the same 
 parallel. Thus a place in the parallel TT' will have 
 
 199. How do the variations in the moon's distance from the 
 earth affect the tides ? How are the tides when the moon is in 
 perigee ? How when she in apogee ? When are the highest 
 tides of the year produced ? 
 
 * Diagrams like these are apt to mislead the learner, by exhibiting the 
 protuberance occasioned by the tides as much greater than the reality. 
 We must recollect that it amounts, at the highest, to only a very few 
 feet in eight thousand miles. Were the diagram, therefore, drawn in 
 just proportions, the alteration of figure produced by the tides would 
 be wholly insensible. 
 
TIDES. 
 
 161 
 
 the height of one tide T2 and the other tide T'3. 
 The tides are in this case greatest at the equator, and 
 diminish gradually to the poles, where it will be low 
 water during the whole day. When the moon is 
 on the north side of the equator, as in figure 38, at 
 her greatest northern declination, a place describing 
 the parallel TT will have T'3 for the height of the 
 
 Fig. 38. 
 
 tide when the moon is on the superior meridian, and T2 
 for the height at the same time on the inferior me- 
 ridian. Therefore, all places north of the equator will 
 have the highest tide when the moon is above the hor- 
 izon, and the lowest when she is below it ; the differ- 
 ence of the tides diminishing towards the equator, where 
 they are equal. In like manner, (the moon being still 
 at M, Fig. 38, that is, having northern declination,) 
 places south of the equator have the highest tides when 
 the moon is below the horizon, -and the lowest when she 
 is above it. The circumstances are all reversed when 
 the moon is south of the equator. 
 
 201. The motion of the tide- wave, it should be re- 
 marked, is not a. progressive motion, but a mere undula- 
 tion, and is to be carefully distinguished from the cur- 
 
 200 Explain the effect of the declinations of the sun and 
 moon upon the tides. How will the upper and lower tides cor- 
 respond when the moon is in the equator ? How when the 
 moon is north of the equator ? Explain by figures 37, 38. 
 
 14* 
 
162 THE MOON. 
 
 rents to which it gives rise. If the ocean completely 
 covered the earth, the sun and moon being in the equa- 
 tor, the tide-wave would travel at the same rate as the 
 earth on its axis. Indeed, the correct way of conceiv- 
 ing of the tide-wave, is to consider the moon at rest, 
 and the earth in its rotation from west to east, as bringing 
 successive portions of water under the moon, which 
 portions being elevated successively at the same rate as 
 the earth revolves on its axis, have a relative motion 
 westward in the same degree. 
 
 202. The tides of rivers, narroib bays, and shores 
 far from the main body of the ocean, are not produced 
 in those places by the direct action of the sun and moon, 
 but are subordinate waves propagated from the great 
 tide-wave. 
 
 Lines drawn through all the adjacent parts of any 
 tract of water, which have high water at the same time, 
 are called cotidal lines. We may, for instance, draw a 
 line through all places in the Atlantic Ocean which 
 have high tide in a given day at 1 o'clock, and another 
 through all places which have high tide at 2 o'clock. 
 The cotidal line for any hour may be considered as rep- 
 resenting the summit or ridge of the tide-wave at that 
 time ; and could the spectator, detached from the earth, 
 perceive the summit of the wave, he woulclsee it travel- 
 ing round the earth in the open ocean once in twenty- 
 four hours, followed by another twelve hours distant, 
 and both sending branches into rivers, bays, and other 
 openings into the main land. These latter are called 
 Derivative tides, while those raised directly by the ac- 
 tion of the sun and moon, are called Primitive tides. 
 
 201. Is the motion of the tide-wave progressive? if the 
 ocean completely covered the earth and the sun and moon were 
 in the equator, how would the tide-wave travel ? What is trie 
 most correct way of conceiving of the tide-wave ? 
 
 202. How are the tides of rivers, &c. produced ? Define 
 cotidal lines. What does the cotidai line for any hour repre- 
 sent ? Distinguish between Primitive and Derivative tides. 
 
TIDES. 163 
 
 The velocity with which the wave moves, will 
 depend on various circumstances, but principally on the 
 depth, and probably on the regularity of the channel. 
 If the depth be nearly uniform, the cotidal lines will be 
 nearly straight and parallel. But if some parts of the 
 channel are deep while others are shallow, the tide will 
 be detained by the greater friction of the shallow places, 
 and the cotidal lines will be irregular. The direction 
 also of the derivative tide, may be totally different from 
 that of the primative. Thus, (Fig. 39,) if the great 
 
 Fig. 39. 
 
 tide-wave, moving from east to west, be represented by 
 the lines 1, 2, 3, 4, the derivative tide which is propa- 
 gated up a river or bay, will be represented by the co- 
 tidal lines 3, 4, 5, 6, 7. Advancing faster in the channel 
 than next the bank, the tides will lag behind towards 
 the shores, and the cotidal lines will take the form of 
 curves as represented in the diagram. 
 
 203- On what will the velocity of the tide- wave depend ? 
 "What circumstances will retard it ? Explain figure 39. 
 
164 THE MOON. ^ 
 
 204. On account of the retarding influence of shoals, 
 and an uneven, indented coast, the tide-wave travels 
 more slowly along the shores of an island than in the 
 neighbouring sea, assuming convex figures at a little dis- 
 tance from the island and on opposite sides of it. These 
 convex lines sometimes meet and become blended in 
 such a manner as to create singular anomalies in a sea 
 much broken by islands, as well as on coasts indented 
 with numerous bays and rivers. Peculiar phenomena 
 are also produced, when the tide flows in at opposite 
 extremities of a reef or island, as into the two opposite 
 ends of Long Island Sound. In certain cases a tide- 
 wave is forced into a narrow arm of the sea, and pro- 
 duces very remarkable tides. The tides of the Bay of 
 Fundy (the highest in the world) sometimes rise to 
 the height of 60 or 70 feet ; and the tides of the rivei 
 Severn, near Bristol in England, rise to the height of 40 
 feet. 
 
 205. The Unit of Altitude of any place, is the height 
 of the maximum tide after the syzigies, being usually 
 about 36 hours after the new or full moon. But as the 
 amount of this tide would be affected by the distance of 
 the sun and moon from the earth, and by their declina- 
 tions, these distances are taken at their mean value, and 
 the luminaries are supposed to be in the equator ; the 
 observations being so reduced as to conform to these cir- 
 cumstances. The unit of altitude can be ascertained 
 by observation only. The actual rise of the tide de- 
 pends much on the strength and direction of the wind. 
 When high winds conspire with a high flood tide, as is 
 frequently the case near the equinoxes, the tide often 
 
 204. How does the tide-wave travel along the shores of an 
 island ? How are the great tides of the Bay of Fundy accounted 
 for? How high do they rise there, and at Bristol in England ? 
 
 205. Define the unit of altitude. By what circumstances is 
 the unit of altitude affected ? How is it ascertained ? State 
 it for several places. 
 
TIDES. 165 
 
 rises to a very unusual height. We subjoin from the 
 American Almanac a few examples of the unit of alti- 
 tude for different places. 
 
 Feet. 
 
 Cumberland, head of the Bay of Fundy, 71 
 Boston, 11J 
 
 New Haven, 8 
 
 New York, 5 
 
 Charleston, S. C., 6 
 
 206. The Establishment of any port is the mean in- 
 terval between noon and the time of high water, on the 
 day of new or full moon. As the interval for any given 
 place is always nearly the same, it becomes a criterion 
 of the retardation of the tides at that platfe. On ac- 
 count of the importance to navigation of a correct 
 knowledge of the tides, the British Board of Admiralty, 
 at the suggestion of the Royal Society, recently issued 
 orders to their agents in various important naval stations, 
 to have accurate observations made on the tides, with 
 the view of ascertaining the establishment and various 
 other particulars respecting each station ; and the gov- 
 ernment of the United States is prosecuting similar in- 
 vestigations respecting our own ports. 
 
 207. According to Professor Whewell, the tides on 
 the coast of North America are derived from the great 
 tide-wave of the South Atlantic, which runs steadily 
 northward along the coast to the mouth of the Bay of 
 Fundy, where it meets the northern tide-wave flowing 
 in the opposite direction. Hence he accounts for the 
 high tides of the Bay of Fundy. 
 
 208. The largest lakes and inland seas have no per- 
 ceptible tides. This is asserted by all writers respect- 
 
 206. What, is the establishment, of a port ? What efforts 
 have been made to obtain accurate observations on the tides ? 
 
166 THE MOON. 
 
 ing the Caspian and Euxine, and the same is found to 
 be true of the largest of the North American lakes, 
 Lake Superior. 
 
 Although these several tracts of water appear large 
 when taken by themselves, yet they occupy but smal 1 
 portions of the surface of the globe, as will appear e\ 
 ident from the delineation of them on an artificial globe. 
 Now we must recollect that the primitive tides are pror 
 duced by the unequal action of the sun and moon upon 
 the different parts of the earth ; and that it is only at 
 points whose distance from each other bears a consider- 
 able ratio to the whole distance of the sun or the moon, 
 that the inequality of action becomes manifest. The 
 space required is larger than either of these tracts of 
 water. It is obvious also that they have no opportunity 
 to be subject to a derivative tide. 
 
 209. To apply the theory of universal gravitation to 
 all the varying circumstances that influence the tides, 
 becomes a matter of such intricacy, that La Place pro- 
 nounces " the problem of the tides" the most difficult 
 problem of celestial mechanics. 
 
 210. The Atmosphere that envelops the earth, must 
 evidently be subject to the action of the same forces as 
 the covering of waters, and hence we might expect a 
 rise and fall of the barometer, indicating an atmospheric 
 tide corresponding to the tide of the ocean. La Place 
 has calculated the amount of this aerial tide. It is too 
 inconsiderable to be detected by changes in the barom- 
 eter, unless by the most refined observations. Hence it 
 is concluded, that the fluctuations produced by this cause 
 are too slight to affect meteorological phenomena in any 
 appreciable degree. 
 
 207. How are the tides on the coast of North America de- 
 rived ? 
 
 208. Why have lakes and seas no tides ? 
 
 209. What is said of the difficulty of applying the principle 
 of universal gravitation to all the circumstances of the tides ? 
 
167 
 
 CHAPTER 
 
 OF THE PLANETS - THE INFERIOR PLANETS, MERCURY 
 
 AND VENUS. 
 
 211. THE name planet signifies a wanderer* and is 
 applied to this class of bodies because they shift their 
 positions in the heavens, whereas the fixed stars con- 
 stantly maintain the same places with respect to each 
 other. The planets known from a high antiquity, are 
 Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To 
 these, in 1781, was added Uranus,f (or Herschel,as it 4s 
 sometimes called from the name of its discoverer,) and, 
 as late as the commencement of the present century, 
 four more were added, namely, Ceres, Pallas, Juno, and 
 Vesta. These bodies are designated by the following 
 characters : 
 
 1. Mercury $ 7. Ceres ? 
 
 2. Venus $ 8. Pallas $ 
 
 3. Earth -0 9. Jupiter U 
 
 4. Mars $ 10. Saturn T? 
 
 5. Vesta fi 11. Uranus *& 
 
 6. Juno 
 
 The foregoing are called the primary planets. Sev- 
 eral of these have one or more attendants, or satellites, 
 
 210. Has the atmosphere any tide ? Is it sufficient to influ- 
 ence meteorological phenomena 1 
 
 211. Whence is the name planet derived ? Which of the 
 planets have been long known ? Which have been added in 
 modern times ? Mark on paper or on the black board, the 
 several characters by which the planets are designated. Dis- 
 tinguish between the primary and the secondary planets. What 
 bodies have satellites ? State the whole number of planets. 
 
 From the Greek n\avnrr,i. t From 
 
168 THE PLANETS. 
 
 which revolve around them, as they revolve around the 
 sun. The earth has one satellite, namely, the moon ; 
 Jupiter has four ; Saturn, seven ; and Uranus, six. These 
 bodies also are planets, but in distinction from the others 
 they are called secondary planets. Hence, the whole 
 number of planets are 29; viz. 11 primary, and IS sec 
 ondary planets. 
 
 212. With the exception of the four new planets, 
 'ihese bodies have their orbits very nearly in the same 
 plane, and are never seen far from the ecliptic. Mer- 
 cury, whose orbit is most inclined of all, never departs 
 farther from the ecliptic than about 7, while most of 
 the other planets pursue very nearly the same path with 
 the earth, in their annual revolutions around the sun. 
 The new planets, hpwever, make wider excursions from 
 the plane of the ecliptic, amounting, in the case of Pal- 
 las, to 
 
 213. Mercury and Venus are called inferior planets, 
 because they have their orbits nearer to the sun than 
 that of the earth ; while all the others, being more dis- 
 tant from the sun than tfrB earth, are called superior 
 planets. The planets present great diversity among 
 themselves in respect to distance from the sun, magni- 
 tude, time of revolution, and density. They differ also 
 in regard to satellites, of which, as we have seen, three 
 have respectively four, six, and seven, while more than 
 half have none at all. It will aid the memory, and 
 render our view of the planetary system more clear and 
 comprehensive, if we classify, as far as possible, the x 
 various particulars comprehended under the foregoing 
 heads. 
 
 212. Near what great circle are the orbits of all the planets ? 
 How far does Pallas deviate from the ecliptic ? 
 
 213. Why are Mercury and Venus called Inferior planets ? 
 Why are the other planets called superior ? What diversities 
 do the planets exhibit among themselves ? 
 
DISTANCES FROM THE SUN. 169 
 
 214. DISTANCES FROM THE SUN. 
 
 1. Mercury, . . 37,000,000 
 
 2. Venus, . . 68,000,000 
 
 3. Earth, . . 95,000,000 
 
 4. Mars, . . 142,000,000 
 
 5. Vesta, _ . . 225,000,000 
 
 6. Juno, . . ) 
 
 7. Ceres, . . V 261,000,000 
 S.Pallas, . . ) 
 
 9. Jupiter, . . 485,000,000 
 
 10. Saturn, . . 890,000,000 
 
 11. Uranus, . 1800,000,000 
 
 The dimensions of the planetary system are seen 
 from this table to be vast, comprehending a circular 
 space thirty six hundred millions of miles in diameter. 
 A railway car, travelling constantly at the rate of 20 
 miles an hour, would require more than 20,000 years to 
 cross the orbit of Uranus. 
 
 It may aid the memory to remark, that in regard to 
 the planets nearest the sun, the distances increase in an 
 arithmetical ratio, while those most remote, increase in 
 a geometrical ratio. Thus, if we add 30 to the distance 
 of Mercury, it gives us nearly that of Venus ; 30 more 
 gives that of the Earth ; while Saturn is nearly twice 
 the distance of Jupiter, and Uranus twice the distance 
 of Saturn. Between the orbits of Mars and Jupiter, a 
 great chasm appeared, which broke the continuity of the 
 series ; but the discovery of the new planets has filled 
 the void. 
 
 214. State the distance of each of the planets from the sun. 
 What is said of the dimensions of the planetary system ? How 
 do the distances of those planets which are nearest the sun in- 
 crease 1 Also those which are more distant ? How may the 
 mean distances of the planets from the sun be determined ? 
 Give an example in computing the distance of Jupiter. 
 
 15 
 
170 THE PLANETS. 
 
 The mean distances of the planets from the sun, may 
 be determined by means of Kepler's law, that the squares 
 of the periodical times are as the cubes of the distances. 
 Thus the earth's distance being previously ascertained 
 by means of the sun's horizontal parallax, and the pe- 
 riod of any other planet, as Jupiter, being learned from 
 observation, we say as 3G5.256 2 : 43S2.585 2 * : : I 3 : 
 5.202 3 , which equals the cube of Jupiter's distance from 
 the sun, and its root equals that distance itself. 
 / 
 
 215. MAGNITUDES. 
 
 Diam. in Miles. Mean apparent Diam. Volume. 
 
 Mercury, ;. . . 3140 6".9 T V 
 
 Venus, . . '_. 7700 61".9 ^ 
 
 Earth, . . . 7912 1 
 
 Mars, . . . 4200 6".3 T 
 
 Ceres, . . . 160 0".5 
 
 Jupiter, . . . 89000 36".7 1281 
 
 Saturn, . . . 79000 16".2 995 
 
 Uranus, . . . 35000 4".0 80 
 
 We remark here a great diversity in regard 4o magni- 
 tude, a diversity which does not appear to be subject to 
 any definite law. While Venus, an inferior planet, is 
 f as large as the earth, Mars, a superior planet is only y, 
 while Jupiter is 1281 times as large. Although several 
 of the planets, when nearest to us, appear brilliant and 
 large when compared with the fixed stars, yet the angle 
 which they subtend is very small, that of Venus, the 
 greatest of all, never exceeding about 1', or more exactly 
 61 ".9, and that of Jupiter being when greatest only 
 about f of a minute. 
 
 215. State the diameter of each of the planets. -What diver- 
 sities occur in regard to their magnitudes ? How great angles 
 do Venus and Jupiter subtend ? 
 
 * This is the number of days in one revolution of Jupiter. 
 
PERIODIC TIMES MERCURY AND VENUS. 171 
 
 216. PERIODIC TIMES. 
 
 Revolution in its orbit. Mean daily motion. 
 
 Mercury, 3 months, or 88 days, 4 5' 32 '.6 
 
 Venus, 7| " 224 1 36' 7".8 
 
 Earth, 1 year, " 365 " 59' 8".3 
 
 Mars, 2 years, " 687 " 31' 26".7 
 
 Ceres, 4 " "1681 12' 50".9 
 
 Jupiter, 12 " 4332 " 4' 59".3 
 
 Saturn, 29 " 10759 " 2' 0".6 
 
 Uranus, 84 " " 30686 " 0' 42".4 
 
 From this view, it appears that the planets nearest the 
 sun move most rapidly. Thus Mercury performs nearly 
 350 revolutions while Uranus performs one. This is 
 evidently not owing merely to the greater dimensions of 
 the orbit of Uranus, for the length of its orbit is not 50 
 times that of the orbit of Mercury, while the time em- 
 ployed in describing it is 350 times that of Mercury. 
 Indeed this ought to follow from Kepler's law that the 
 squares of the periodical times are as the cubes of the 
 distances, from which it is manifest that the times of 
 revolution increase fasten than the dimensions of the or- 
 bit. Accordingly, the apparent progress of the most 
 distant planets is exceedingly slow, the daily rate, of 
 Uranus being only 42'',4 per day ; so that for weeks and 
 months, and even years, this planet but slightly changes 
 its place among the stars. 
 
 THE INFERIOR PLANETS, MERCURY AND VENUS. 
 
 217. The inferior planets, Mercury and Venus, hav- 
 ing their orbits so far within that of the earth, appear to 
 us as attendants upon the sun. Mercury never appears 
 farther from the sun than 29 (28 48') and seldom so 
 
 216. State the periodic time of each of the planets. Which 
 planets move most rapidly ? How many revolutions does Mer- 
 cury perform while Uranus performs one ? What is the daily 
 rate of Uranus ? 
 
172 
 
 THE PLANETS. 
 
 far ; and Venus never more than about 47 (4T 12'). 
 Both planets, therefore, appear either in the west soon 
 after sunset, or in the east a little before sunrise. In 
 high latitudes, where the twilight is prolonged, Mercury 
 
 can seldom be seen with the naked eye, and then only 
 at the periods of 'its greatest elongation.* The reason 
 of this will readily appear from the following diagram. 
 
 Fig. 40. 
 
 Let S (Fig. 40,) represent the sun, ADB the orbit of 
 Mercury, and E the place of the Earth. Each of the 
 planets is seen at its greatest elongation, when a line, 
 EA or EB in the figure, is a tangent to its orbit. Then 
 the sun being at S' in the heavens, the planet will be 
 
 217. What is Mercury's greatest elongation from the sun ? 
 What is Venus's ? What is said respecting the difficulty of see- 
 ing Mercury ? Explain by figure 40. 
 
 * Copernicus is said to have lamented on his death-bed that he had 
 never been able to obtain a sight of Mercury, and Delambre saw it but 
 twice. 
 
MERCURY AND VENUS. 173 
 
 seen at A' and B', when at its greatest elongations, and 
 will appear no further from the sun than the arc S'A' or 
 S'B' respectively. 
 
 218. A planet is said to be in Conjunction with the 
 sun, when it is seen in the same part of the heavens 
 with the sun, or when it has the same longitude. Mer- 
 cury and Venus have each two conjunctions, the inferior, 
 and the superior. The inferior conjunction is its posi- 
 tion when in conjunction on the same side of the sun 
 with the earth, as at C in the figure : the superior con- 
 junction is its position when on the side of the sun most 
 distant from the earth, as at D. 
 
 219. The period occupied by a planet between two 
 successive conjunctions with the earth, is called its sy- 
 nodical revolution. Both the planet and the earth being 
 in motion, the time of the synodical revolution exceeds 
 that of the sidereal revolution of Mercury or Venus ; 
 for when the planet comes round to the place where it 
 before overtook the earth, it does not find the earth at 
 that point, but far in advance of it- Thus, let Mercury 
 come into inferior conjunction with the earth at C, (Fig. 
 40.) In about 88 days, the planet will come round to 
 the same point again; but meanwhile the earth has 
 moved forward through the arc EE', and will continue 
 to move while the planet is moving more rapidly to over- 
 take her, the case being analogous to that of the hour 
 and minute hand of a clock. 
 
 The synodical period of Mercury is 1 16, and of Venus 
 584 days. 
 
 218. When is a planet said to be in conjunction with the 
 sun ? What conjunctions have the inferior planets ? 
 
 219. Define the synodical revolution. How does this period 
 compare with the sidereal revolution ? Explain by figure 40. 
 What is the synodical period of Mercury and Venus respect* 
 ively ? 
 
 15* 
 
174 THE PLANETS. 
 
 ( 
 
 220. The motion of an inferior planet is direct in 
 passing through its superior conjunction, and retrogade 
 in passing through its inferior conjunction. Thus Ve- 
 nus, while going from B through D to A, (Fig. 40,) 
 moves in the order of the signs, or from west to east, 
 and would appear to traverse the celestial vault B'S'A' 
 from right to left ; but in passing from A through C to 
 B, her course would be retrogade, returning on the same 
 arc from left to right. If the earth were at rest, there- 
 fore, (and the sun, of course, at rest,) the inferior planets 
 would appear to oscillate backwards and forwards across 
 the sun. But, it must be recollected, that the earth is 
 moving in the same direction with the planet, as respects 
 the signs, but with a slower motion. This modifies the 
 motions of the planet, accelerating it in the superior and 
 retarding it in the inferior conjunctions. Thus in figure 
 40, Venus while moving through BDA would seem to 
 move in the heavens from B' to A 7 were the earth at 
 rest ; but meanwhile the earth changes its position from 
 E to E' by which means the planet is not seen at A' 
 but at A", being accelerated by the arc A' A" in conse- 
 quence of the earth's motion. On the other hand, when 
 the planet is passing through its inferior conjunction 
 ACB, it appears to move backwards in the heavens from 
 A' to B' if the earth is at rest, but from A' to B" if the 
 earth has in the mean time moved from E to E' being 
 retarded by the arc B'B". Although the motions of the 
 earth have the effect to accelerate the planet in the superi- 
 or conjunction, and to retard it in the inferior, yet, on ac- 
 count of the greater distance, the apparent motion of the 
 planet is much slower in the superior than in the infe- 
 rior conjunction. 
 
 221. When passing from the superior to the inferior 
 conjunction, or from the inferior to the superior conjunc- 
 
 220. When is the motion of an inferior planet direct and 
 when retrograde ? Explain by figure 40. If the earth were at 
 rest, how would the inferior planets appear to move ? Show 
 how the earth's motion modifies the apparent motions. 
 
MERCURY AND VENUS. 175 
 
 tion through the greatest elongations, the inferior plan- 
 ets are stationary. 
 
 If the earth were at rest, the stationary points would 
 be at the greatest elongations as at A and B, for then the 
 planet would be moving directly towards or from the 
 earth, and would be seen for some time in the same 
 place in the heavens ; but the earth itself is moving 
 nearly at right angles to the line of the planet's motion, 
 that is, the line which is drawn from the earth to the 
 planet through the point of greatest elongation ; hence a 
 direct motion is given to the planet by this cause. When 
 the planet, however, has passed this line by its superior 
 velocity, it soon overcomes this tendency of the earth to 
 give it a relative motion eastward, and becomes retro- 
 grade as it approaches the inferior conjunction. Its sta- 
 tionary point obviously lies between its place of greatest 
 elongation, and the place where its motion becomes re- 
 trograde. Mercury is stationary at an elongation of 
 from 15 to 20 from the sun ; and Venus at about 29. 
 
 222. Mercury and Venus exhibit to the telescope, pha- 
 ses similar to those of the moon. 
 
 When on the side of their inferior conjunction, these 
 planets appear horned, like the moon in her first and last 
 quarters ; and whqn on the side of their superior con- 
 junctions they appear gibbous. At the moment of su- 
 perior conjunction, the whole enlightened orb of the 
 planet is turned towards the earth, and the appearance 
 would be that of the full moon, but the planet is too 
 near the sun to be commonly visible. 
 
 These different phases show these bodies are opake, 
 and shine only as they reflect to us the light of the sun ; 
 and the same remark applies to all the planets. 
 
 221. When are the inferior planets stationary ? Why are 
 they not stationary at the points of greatest elongation ? At what 
 elongation are Mercury and Venus stationary respectively ? 
 
 222. What phases do Mercury and Venus exhibit ? Explain 
 by figure 40, Whence do these bodies derive their light ? Is 
 the same true of the other planets ? 
 
176 THE PLANETS. 
 
 223. The orbit of Mercury is the most eccentric, and 
 the most inclined of all the planets ;* while that ofi Ve- 
 nus varies but little from a circle, and lies much nearer 
 to the ecliptic. 
 
 The eccentricity of the orbit of Mercury is nearly 
 its semi-major axis, while that of Venus is only y^ ; 
 the inclination of Mercury's orbit is 7, while that of 
 Venus is less than 3J. Mercury, on account of his dif- 
 ferent distances from the earth, varies much in his appa- 
 rent diameter, which is only 5" in the apogee, but 12" 
 in the perigee. The inclination of his orbit to his equa- 
 tor being very great, the changes of his seasons must be 
 proportionally great. 
 
 These different aspects of an inferior planet will be 
 easily understood from Fig. 41, where the earth is at E, 
 
 Fig. 41. 
 
 and the planet is represented in various positions in its 
 revolutions around the sun. When at A, in the supe- 
 rior conjunction, the whole enlightened disk is turned 
 towards us ; at D, in the inferior conjunction, the en- 
 lightened side is turned entirely from us ; and at the 
 quadratures B and C, half the disk is in view. Between 
 A and B, and A and C, the planet is gibbous, like the 
 moon in her second and third quarters ; and between B 
 
 223. What is said of the eccentricity and inclination of the 
 orbit of Mercury ? How does the apparent diameter of Mer 
 cury vary ? How are his changes of seasons ? 
 
 * The new planets of course excepted 
 
MERCURY AND VENUS. 177 
 
 ?wid D, and C and D, the planet is horned, like the moon 
 in her first and last quarters. 
 
 224. An inferior planet is brightest at a certain point 
 between its greatest elongation and inferior conjunction. 
 
 Its maximum brilliancy would happen at the inferior 
 conjunction, (being then nearest to us,) if it shined by 
 its own light ; but in that position its dark side is turned 
 towards us. Still, its maximum cannot be when. most 
 of the illuminated side is towards us ; for then, being at 
 the superior conjunction, it is at its greatest distance 
 from us. The maximum must therefore be somewhere 
 between the two. Venus gives her greatest light when 
 about 40 from the sun. 
 
 225. Mercury and Venus oik revolve on their axes, 
 in nearly the same time with the earth. 
 
 The diurnal period of Mercury is 24h. 5m. 28s., and 
 that of Venus 23h. 21m. 7s. The revolutions on their 
 axes have been determined by means of some spot or 
 mark seen by the telescope, as the revolution of the sun 
 on his axis is ascertained by means of his spots. 
 
 226. Venus is regarded as the most beautiful of the 
 planets, and is well known as the morning and evening 
 star. The most ancient nations did not indeed recog- 
 nize the evening and morning star as one and the same 
 body, but supposed they were different planets, and ac- 
 cordingly gave them different names, calling the morn- 
 ing star Lucifer, and the evening star Hesperus. At her 
 period of greatest splendor, Venus casts a shadow, and is 
 sometimes visible in broad daylight. Her light is then 
 estimated as equal to that of twenty stars of the first 
 
 224. When is an inferior planet brightest 1 Why not when 
 nearest to us 1 Why not when most of the illuminated side is 
 turned towards us 1 
 
 225. In what time do Mercury and Yenus, respectively, re- 
 volve on their axes 1 How are these periods ascertained 1 
 
178 THE PLANETS. 
 
 magnitude. At her period of greatest elongation, Ve- 
 nus is visible from three to four hours after the setting 
 or before the rising of the sun. 
 
 227. Every eight years, Venus forms her conjunctions 
 with the sun in the same part of the heavens. 
 
 For, since the synodical period of Venus is 584 days, 
 and her sidereal period 224.7, 
 
 224.7 : 360: : 584 : 935.6=the arc of longitude de- 
 scribed by Venus between the first and second conjunc- 
 tions. Deducting 720, or two entire circumferences, 
 the remainder, 21 #.6, shows how far the place of the 
 second conjunction is in advance of the first. Hence, 
 in five synodical revolutions, or 2920 days, the same 
 point must have advanced 215.6x 5 = 1078, which is 
 nearly three entire circumferences, so that at the end of 
 five synodical revolutions, occupying 2920 days, or 8 
 years, the conjunction of Venus takes place nearly in 
 the same place in the heavens as at first. 
 
 Whatever appearances of this planet, therefore, arise 
 from its position with respect to the earth and the sun, 
 they are repeated every eight years in nearly the same 
 form. 
 
 TRANSITS OF THE INFERIOR PLANETS. 
 
 228. The Transit of Mercury or Venus, is its passage 
 across the sun's disk, as the moon passes over it in a solar 
 eclipse. 
 
 As a transit takes place only when the planet is in 
 inferior conjunction, at which time her motion is retro- 
 grade, it is always from left to right, and the planet is 
 seen projected on the solar disk in a black round spot. 
 
 226. What erroneous notions had the ancients respecting the 
 morning and evening star ? What is said of the brilliancy ot 
 Venus at her greatest splendor ? How long may Venus be in 
 sight after sunset ? 
 
 227. What happens to Venus every eight years ? 
 
MERCURY AND VENUS. 
 
 Were the orbits of the inferior planets coincident with 
 the plane of the earth's orbit, a transit would occur to 
 some part of the earth at every inferior conjunction. 
 But the orbit of Venus makes an angle of 3^ with the 
 ecliptic, ana Mercury an angle of 7 ; and, moreover, 
 the apparent diameter of each of these bodies is very 
 small, both of which circumstances conspire to render a 
 transit a comparatively rare occurrence, since it can hap- 
 pen only when the sun, at the time of an inferior con- 
 junction, chances to be at or extremely near the planet's 
 node. The nodes of Mercury lie in longitude 46 and 
 226, points which the sun passes through in May and 
 November. It is only in these months, therefore, that 
 transits of Mercury can occur. For a similar reason, 
 those of Venus occur only in June and December. Since, 
 however, the nodes of both planets have a small retro- 
 grade motion, the months in which transits occur will 
 change in the course of ages 
 
 229. Transits of Mercury occur more frequently than 
 those of Venus. The periodic times of Mercury and 
 the earth are so adjusted to each other, that Mercury 
 performs nearly 29 revolutions while the earth performs 
 7. If, therefore, the two bodies meet at the node in any 
 given year, seven years afterwards they will meet nearly 
 at the same node, and a transit may take place, accord- 
 ingly, at intervals of 7 years. But 54 revolutions of 
 Mercury correspond still nearer to 13 revolutions of the 
 
 228. What is meant by the transit of Mercury or Venus ? 
 When only can a transit take place ? What angles do the or- 
 bits of Venus and Mercury respectively make with the ecliptic ? 
 In what months does the sun pass through the nodes of each 
 of these planets ? 
 
 229. Which planet has the most frequent-transits ? What is 
 the shortest interval of the transits of Mercury ? What are the 
 longer intervals ? When will the next occur ? What are in- 
 tervals of the transits of Venus ? When was the last transit 
 of Venus, and when will the next occur ? 
 
380 THE PLANETS. 
 
 earth, and therefore a transit is still more probable after 
 intervals of 13 years. At intervals of 33 years, transits 
 of Mercury are exceedingly probable, because in that 
 time Mercury makes almost exactly 137 revolutions. 
 Intermediate transits however may occur at the other 
 node, these intervals having reference merely to the 
 same node. Thus transits of Mercury happened at the 
 ascending node in 1815, and 1822, at intervals of 
 7 years ; and at the descending node in 1832, which 
 will return in 1845, after an interval of 13 years. Tran- 
 sits of Venus arte much more unfrequent than those of 
 Mercury, Eight revolutions of the earth are completed 
 in nearly the same time as thirteen revolutions of Venus, 
 and hence two transits of Venus may occur at an in- 
 terval of 8 years, as was the case at the last return of 
 this phenomenon, one transit having occurred in 1761, 
 and another in 1769. But if a transit does not happen 
 after 8 years, it will not happen, at the same node, until 
 an interval of 235 years ; but intermediate transits may 
 occur at the other node. The next transit of Venus will 
 take place in 1874, being 235 years after the first that was 
 ever observed, which occurred in the year 1639. In the 
 mean time, as already mentioned, two transits have oc- 
 curred at the other node, at intervals of 8 years. 
 
 230. The great interest attached by astronomers to a 
 transit of Venus, arises from its furnishing the most accu- 
 rate means in our power of determining the sun's hori- 
 zontal parallax an element of great importance, since it 
 leads us to a knowledge of the distance of the earth from 
 the sun, and, consequently, by the application of Kepler's 
 aw, (Art. 130,) of the distances of all the other planets. 
 Hence, in 1769, great efforts were made throughout the 
 civilized world, under the patronage of different govern- 
 
 230. Why is so much interest attached to the transits ol 
 Venus ? What efforts were made to observe it in 1769 ? Why 
 cannot we ascertain the horizontal parallax of the sun in the 
 same way as we do that of the moon ? 
 
MERCURY AND VENUS. 181 
 
 ments, to observe this phenomenon under circumstances 
 the most favorable for determining the parallax of the 
 sun. 
 
 The common methods of finding the parallax of a 
 heavenly body cannot be relied on to a greater degree 
 of accuracy than 4". In the case of the moon, whose 
 greatest parallax amounts to about 1, this deviation 
 from absolute accuracy is not material ; but it amounts 
 to nearly half the entire parallax of the sun. 
 
 231. If the sun and Venus were equally distant from 
 us, they would be equally affected by parallax as viewed 
 by spectators in different parts of the earth, and hence 
 their relative situation would not be altered by it ; but 
 since Venus, at the inferior conjunction, is only about 
 one third as far off as the sun, her parallax is propor- 
 tionally greater, and therefore spectators at distant points 
 will see Venus projected on different parts of the so- 
 lar disk, as the planet traverses the disk. Astron- 
 omers avail themselves of this circumstance to ascer- 
 tain the sun's horizontal parallax. In order to make 
 the difference as large as possible very distant pla- 
 ces are selected for observation. Thus in the transit 
 of 1769, among the places selected, two of the most 
 favorable were Wardhuz in Lapland, and Oteheite, one 
 of the South Sea Islands. 
 
 The appearance of Venus on the sun's disk, being 
 that of a well defined black spot, and the exactness with 
 which the moment of external or internal contact may 
 be determined, are,circumstances favorable to the exact- 
 ness of the result ; and astronomers repose so much con- 
 fidence in the estimation of the sun's horizontal parallax 
 as derived from the observations on the transit of 1769, 
 that this important element is thought to be ascertained 
 
 231. How is Venus projected on the sun to spectators in 
 different parts of the earth ? What places were selected for 
 observing the transit of 1769 ? 
 
 16 
 
182 THE PLANETS. 
 
 within ^ of a second. The general result of all these 
 observations gives the sun's horizontal parallax 8".6, or 
 more exactly, 8."5776. 
 
 232. During the transits of Venus over the sun's disk 
 in 1761 and 1769, a sort of penumbral light was ob- 
 served around the planet by several astronomers, which 
 was thought to indicate an atmosphere. This appear- 
 ance was particularly observable while the planet was 
 coming on and going off the solar disk. The total im- 
 mersion and emersion were not instantaneous ; but as 
 two drops of water when about to separate, form a liga- 
 ment between them, so there was a dark shade stretched 
 out between Venus and the sun, and when the ligament 
 broke, the planet seemed to have got about an eighth part 
 of her diameter from the limb of the sun. The various 
 accounts of the two transits abound with remarks like 
 these, which indicate the existence of an atmosphere 
 about Venus of nearly the density and extent of the 
 earth's atmosphere. Similar proofs of the existence of 
 an atmosphere around this planet, are derived from ap- 
 pearances of twilight. 
 
 The elder astronomers imagined they had discovered 
 a satellite accompanying Venus in her transit. If Venus 
 had in reality any satellite, the fact would be obvious at 
 her transits, as the satellite would be projected near the 
 primary on the sun's disk ; but later astronomers have 
 searched in vain for any appearances of the kind, and 
 the inference is that former astronomers were deceived 
 by some optical illusion. 
 
 Astronomers have detected very high mountains on 
 Venus, sometimes reaching to the elevation of 22 miles ; 
 and it is remarkable that the highest mountains in Ve- 
 nus, in Mercury, in the moon, and in the earth, are al- 
 ways in the southern hemisphere. 
 
 232. What indications have been observed of an atmos- 
 phere about Venus ? Has Venus any Satellite ? What is said 
 of the mountains of Venus ? 
 
SUPERIOR PLANETS. 183 
 
 CHAPTER VIII. 
 
 OP THE SUPERIOR PLANETS MARS, JUPITER, SATURN, AND 
 
 URANUS CERES, PALLAS, JUNO, AND VESTA. 
 
 233. THE Superior planets are distinguished from the 
 Inferior, by being seen at all distances from the sun 
 from to 180. Having tfeeir orbits exterior to that 
 of the earth, they of course never come between us and 
 the sun, that is, they never have any inferior conjunction 
 like Mercury and Venus, but they are sometimes seen in 
 superior conjunction, and sometimes in opposition. Nor 
 do they, like the inferior planets, exhibit to the telescope 
 different phases, but, with a single exception, they al- 
 ways present the side that is turned towards the earth 
 fully enlightened. This is owing to their great distance 
 from the earth ; for were the spectator to stand upon the 
 sun, he would of course always have the illuminated 
 side of each of the planets turned towards him ; but, 
 so distant are all the superior planets except Mars, that 
 they are viewed by us very nearly in the same manner 
 as they would be if we actually stood on the sun. 
 
 234. MARS is a small planet, his diameter being only 
 about half of that of the earth, or 4200 miles. He also, 
 at times, comes nearer to the earth than any other planet 
 except Venus. His mean distance from the sun is 
 142,000,000 miles; but his orbit is so eccentric that his 
 distance varies much in different parts of his revolution. 
 Mars is always very near the ecliptic, never varying from 
 
 233. Name the Superior Planets. How are they distin- 
 guished from the Inferior ? Whidh of them exhibits phases ? 
 Why do not the rest ? 
 
 234. Mars. State his diameter Mean distance from the 
 sun inclination of his orbit. How distinguished from the 
 other planets ? Why do his brightness and apparent magni- 
 tude vary so much ? Illustrate by figure 42. 
 
184 
 
 THE PLANETS. 
 
 it 2. He is distinguished from all the planets by his 
 deep red color, and fiery aspect ; but his brightness and 
 apparent magnitude vary much at different times, being 
 sometimes nearer to us than at others, by the whole di- 
 ameter of the earth's orbit-, that is, by about 190,000,000 
 of miles. When Mars is on the same side of the sun 
 with the earth, or at his opposition, he comes within 
 47,000,000 miles of the earth, and rising about the time 
 the sun sets, surprises us by his magnitude and splen- 
 dor ; but when he passes to the other side of the sun to 
 his superior conjunction, he dwindles to the appearance 
 of a small star, being then 237,000,000 miles from us. 
 Thus, let M (Fig. 42,) represent Mars in opposition, 
 and M' in the superior conjunction, while E represents 
 the earth. It is obvious that in the former situation, the 
 planet must be nearer to the earth than in the latter 
 by the whole diameter of the earth's orbit. 
 
 Tig. 42. 
 
 235. Mars is the only one of the superior planets 
 which exhibits phases. When he is towards the quad- 
 ratures at Q or Q', it is evident from the figure that 
 only a part of the circle of illumination is turned towards 
 
MARS. 185 
 
 the earth, such a portion of the remoter part of it being 
 concealed from our view as to render the form more or 
 less gibbous. 
 
 236. When viewed with a powerful telescope, the 
 surface of Mars appears diversified with numerous vari- 
 eties of light and shade. The region around the poles 
 is marked by white spots, which vary their appearance 
 with the changes of seasons in the planets. Hence Dr. 
 Herschel conjectured that they were owing to ice and 
 snow, which alternately accumulates and melts, accord- 
 ing to the position of each pole with respect to the sun. 
 It has been cpmmon ta ascribe the ruddy light of this 
 planet to an extensive and dense atmosphere, which was 
 said to be distinctly indicated, by the gradual diminution 
 of light observed in a star as it approached very near to 
 the planet in undergoing an occultation ; but more re- 
 cent observations afford no such evidence of an atmos- 
 phere. 
 
 237. By observations on the spots, we learn that Mars 
 revolves on his axis in very nearly the same time with 
 the earth, (24h. 39m. 21s.3) ; and that the inclination of 
 his axis to that of his orbit is also nearly the same, 
 being 30 18' 10".8. 
 
 As the diurnal rotation of Mars is nearly the same as 
 that of the earth, we might expect a similar flattening at 
 the poles, giving to the planet a spheroidal figure. In- 
 deed the compression or ellipticity of Mars greatly ex- 
 ceeds that of the earth, being no less than 1 4 of the 
 equatorial diameter, while that of the earth is only 
 
 235. Show why Mars should exhibit phases. 
 
 236. How is the surface of Mars diversified ? What is seen 
 around the poles ? What indications are there of ice and 
 snow ? To what is the ruddy hue of Mars ascribed ? 
 
 237. How do we learn his revolution on his axis ? In what 
 time does it take place ? What is the figure of Mars ? How 
 does its ellipticity compare with that of the earth ? 
 
 16* 
 
186 
 
 THE PLANETS. 
 
 This remarkable flattening of the poles of Mars has been 
 supposed to arise from a great variation of density in the 
 planet in different parts. 
 
 238. JUPITER is distinguished from all the other plan- 
 ets by his vast magnitude. His diameter is 89,000 
 miles, and his volume 1280 times that of the earth. 
 His figure is strikingly spheroidal, the equatorial being 
 larger than the polar diameter in the proportion of 107 
 to 100. Such a figure might naturally be expected 
 from the rapidity of his diurnal rotation, which is ac- 
 complished in about 10 hours. A place on the equa- 
 tor of Jupiter must turn 27 times as fast |is on the ter- 
 restrial equator. The distance of Jupiter from the sun 
 is nearly 490,000,000 miles, and his revolution around 
 the sun occupies nearly 12 years. 
 
 239. The view of Jupiter through a good telescope, 
 (Fig. 43,) is one of the most magnificent and interesting 
 spectacles in astronomy. The disk expands into a large 
 
 Fig. 43. 
 
 and bright orb like the full moon ; the spheroidal figure 
 wtych theory assigns to revolving spheres, is here pal- 
 
 238. Jupiter. State his diameter, volume, figure, revolu- 
 tion on his axis, velocity of his equator, distance from the sun, 
 periodic time. 
 
JUPITER* 187 
 
 pably exhibited to the eye ; across the disk, arranged 
 in parallel stripes, are discerned several dusky bands, 
 called belts ; and four bright satellites, always in at- 
 tendance, and ever varying their positions, compose a 
 splendid retinue. Indeed, astronomers gaze with pecu- 
 liar interest on Jupiter and his moons, as affording a 
 miniature representation of the whole solar system, 
 repeating on a smaller scale, the same revolutions, and 
 exemplifying, in a manner more within the compass 
 of our observation, the same laws as regulate the 
 entire assemblage of sun and planets. 
 
 240. The Belts of Jupiter are variable in their num- 
 ber and dimensions. With the smaller telescopes, only 
 one or two are seen across the equatorial regions ; but 
 with more powerful instruments, the number is in- 
 creased, covering a great part of the whole disk. Dif- 
 ferent opinions have been entertained by astronomers 
 respecting the cause of the belts ; but they have gen- 
 erally been regarded as clouds formed in the atmo- 
 sphere of the planet, agitated by winds, as is indicated 
 by their frequent changes, and made to assume the 
 form of belts parallel to the equator by currents that 
 circulate around the planet like the trade winds and 
 other currents that circulate around our globe. Sir 
 John Herschel supposes that the belts are not ranges 
 of clouds, but portions of the planet itself brought into 
 view by the removal of clouds and mists, that exist in 
 the atmosphere of the planet through which are open- 
 ings made by currents circulating around Jupiter. 
 
 241. The Satellites of Jupiter may be seen with a 
 telescope of very moderate powers. Even a common 
 spy glass will enable us to discern them. Indeed one or 
 two of them have been occasionally seen with the naked 
 eye. In the largest telescopes, they severally appear as 
 
 239. What does the telescopic view of Jupiter exhibit ? 
 Why do astronomers regard it with so much interest ? 
 
 240. Describe Jupiter's Belts to what are thgx ascribed ? 
 
 Bh 
 
 OF T;I-. 
 
 UNIVERSITY j 
 /*... P!-. J 
 
168 
 
 THE PLANETS. 
 
 bright as Sirius. With such an instrument, the view of 
 Jupiter with his moons and belts is truly a magnificent 
 spectacle, a world within itself. As the orbits of the 
 satellites do not deviate far from the plane of the eclip- 
 tic, and but little from the equator of the planet, they 
 are usually seen in nearly a straight line with each other 
 extending across the central part of the disk. 
 
 242. Jupiter's satellites are distinguished from one 
 another by the denominations of first, second, third, and 
 fourth, according to their relative distances from Jupiter, 
 the first being that which is nearest to him. Their ap- 
 parent motion is oscillatory, like that of a pendulum, 
 going alternately from their greatest elongation on one 
 side to their greatest elongation on the other, sometimes 
 in a straight line, and sometimes in an elliptical curve, 
 according to the different points of view in which we 
 observe them from the earth. They are sometimes sta- 
 tionary ; their motion is alternately direct and retro- 
 grade ; and, in short, they exhibit in miniature all the 
 phenomena of the planetary system. Various partic- 
 ulars of the system are exhibited in the following table. 
 The distances are given in radii of the primary. 
 
 Satellite. 
 
 Diameter. 
 
 Mean Distance. 
 
 Sidereal Revolution. 
 
 1 
 
 2 
 3 
 4 
 
 2508 
 2068 
 3377 
 
 2890 
 
 6.04853 
 9.62347 
 15.35024 
 26.99835 
 
 Id. 18h. 28m. 
 3 13 14 
 7 3 43 
 16 16 32 
 
 Hence it appears, first, that Jupiter's satellites are all 
 except the second, somewhat larger than the moon, but 
 that the second satellite is the smallest, and the third 
 the largest of the whole, but the diameter of the latter 
 is only about -fa part of that of the primary ; secondly, 
 that the distance of the innermost satellite from the planet 
 
 241. How do the satellites appear to the telescope ? 
 
 242. Describe the motions of the satellites magnitudes 
 distances periods of revolution. 
 
JUPITER. 189 
 
 is three times his diameter, while that of the outermost 
 satellite is nearly fourteen times his diameter ; thirdly, 
 that the first satellite completes his revolution around the 
 primary in one day and three fourths, while the fourth 
 satellite requires nearly sixteen and three fourths days. 
 
 243. The orbits of the satellites are nearly or quite 
 circular, and deviate but little from the plane of the 
 planet's equator, and of course are but slightly inclined 
 to the plane of its orbit. They are, therefore, in a sim- 
 ilar situation with respect to Jupiter as the moon would 
 be with respect to the earth if her orbit nearly coincided 
 with the ecliptic, in which case she would undergo an 
 eclipse at every opposition. 
 
 244. The eclipses of Jupiter's satellites, in their gen- 
 eral conception, are perfectly analogous to those of the 
 moon, but in their detail they differ in several particulars. 
 Owing to the much greater distance of Jupiter from the 
 sun, and its greater magnitude, the cone of its shadow is 
 much longer and larger than that of the earth. On this 
 account, as well as on account of the little inclination of 
 their orbits to that of their primary, the three inner sat- 
 ellites of Jupiter pass through the shadow, and are totally 
 eclipsed at every revolution. The fourth satellite, ow- 
 ing to the greater inclination of its orbit, sometimes 
 though rarely escapes eclipse, and sometimes merely 
 grazes the limits of the shadow or suffers a partial 
 eclipse. These eclipses, moreover, are not seen, as is 
 the case with those of the moon, from the center of 
 their motion, but from a remote station, and one whose 
 situation with respect to the line of the shadow is vari- 
 able. This, of course, makes no difference in the times 
 of the eclipses, but a very great one in their visibility, 
 
 243. What is the shape of their orbits ? How situated with 
 regard to the plane of the planet's orbit ? 
 
 244. Describe the phenomena of their eclipses. Which of 
 them escapes an eclipse ? Are these eclipses seen in different 
 parts of the earth at the same moment of absolute time t 
 
190 THE PLANETS. 
 
 and in their apparent situations with respect to the 
 planet at the moment of their entering or quitting the 
 shadow. 
 
 245. The eclipses of Jupiter's satellites present some 
 curious phenomena, which will be understood from th 
 following diagrams. 
 
 Fig. 44. 
 
 Let A, B, C, I), (Fig. 44,) represent the earth in dif- 
 ferent parts of its orbit ; J, Jupiter in his orbit sur- 
 rounded by his four satellites the orbits of which are 
 marked 1, 2, 3, 4. At a the first satellite enters the 
 shadow of the planet, and emerges from it at b, and ad- 
 vances to its greatest elongation at c. The other satellites 
 traverse the shadow in a similar .manner. These ap- 
 pearances will be modified by the place the earth hap- 
 pens to occupy in its orbit, being greatly altered by per- 
 spective ; but their appearances for any given night as 
 exhibited at Greenwich, are calculated and accurately 
 laid down in the Nautical Almanac. 
 
 When one of the satellites is passing between Jupiter 
 and the sun it casts its shadow on the primary as the 
 
 245. Describe the phenomena of the eclipses from figure 44. 
 Will these appearances be affected by the relative position of 
 the earth, with respect to the planet ? Does the shadow of a 
 satellite or the satellite itself ever make a transit across the 
 disk of the planet ? 
 
JUPITER. 191 
 
 moon casts its shadow on the earth in a solar eclipse. 
 We see with the telescope, the shadow traversing the 
 disk. Sometimes the satellite itself is seen projected on 
 the disk ; but being illuminated as well as the primary, 
 it is not so easily distinguished as Venus or Mercury, 
 when seen on the sun's disk, since, at the time of their 
 transits, their dark sides are turned towards us. The 
 manner in which these phenomena take place, as seen 
 from the earth in the several positions, A, B, C, D, may 
 be conceived by attentively inspecting the figure. It 
 will be seen, that when the earth is at A or C, the im- 
 mersions and emersions must take place close to the disk 
 of the planet, but that, in other positions of the earth, as 
 at B or D, the satellite will be seen to enter and leave 
 the shadow at some distance from the primary. 
 
 246. The eclipses of Jupiter's satellites have been 
 studied with great attention by astronomers, on account 
 of their affording one of the easiest methods of deter- 
 mining the longitude. On this subject Sir J. Herschel 
 remarks : The discovery of Jupiter's satellites by Gali- 
 leo, which was one of the first fruits of the invention of 
 the telescope, forms one of the most memorable epochs 
 in the history of astronomy. The first astronomical so- 
 lution of the great problem of " the longitude," the 
 most important problem for the interests of mankind 
 that has ever been brought under the dominion of strict 
 scientific principles, dates immediately from their dis- 
 covery. The final and conclusive establishment of the 
 Copernican system of astronomy, may also be considered 
 as referable to the discovery and study of this exquisite 
 miniature system, in which the laws of the planetary 
 motions, as ascertained by Kepler, and especially that 
 which connects their periods and distances, were speed- 
 ily traced, and found to be satisfactorily maintained. 
 
 246. Why have the eclipses of Jupiter's satellites been stud- 
 ied with so much attention ? Who first discovered these eclip- 
 ses ? What bearing has the system of Jupiter and his satel- 
 lites upon the Copernican system of astronomy ? 
 
192 THE PLANETS. 
 
 a* 
 
 247. The entrance of one of Jupiter's satellites into 
 the shadow of the primary being seen like the entrance 
 of the moon into the earth's shadow, at the same mo- 
 ment of absolute time, at all places where the planet is 
 visible, and being wholly independent of parallax ; be- 
 ing, moreover, predicted beforehand with great accuracy 
 for the instant of its occurrence at Greenwich, and given 
 in the Nautical Almanac ; this would seem to be one of 
 those events (Art. 188,) which are peculiarly adapted for 
 finding the longitude. It must be remarked, however, 
 that the extinction of light in the satellite at its immer- 
 sion, and the recovery of its light at its emersion, are not 
 instantaneous but gradual; for the satellite, like the 
 moon, occupies some time in entering into the shadow 
 or in emerging from it, which occasions a progressive 
 dimunition or increase of light. The better the light 
 afforded by the telescope with which the observation is 
 made, the later the satellite will be seen at its immer- 
 sion, and the sooner at its emersion.* In noting the 
 eclipses even of the first satellite, the time must be con- 
 sidered as uncertain to the amount of 20 or 30 seconds ; 
 and those of the other satellites involve still greater un- 
 certainty. Two observers, in the same room, observing 
 with different telescopes the same eclipse, will frequently 
 disagree in noting its time to the amount of 15 or 20 
 seconds ; and the difference will be always the same 
 way. 
 
 Better methods, therefore, of finding the longitude are 
 now employed, although the facility with which the 
 necessary observations can be made, and the little calcu- 
 lation required, still render this method eligible in many 
 
 247. Explain how these eclipses are used in finding the lon- 
 gitude. What imperfections attend this method ? Is this meth- 
 od much employed at present ? Why can it not be used at 
 sea? 
 
 * This is the reason why observers are directed in the Nautical Al- 
 manac to use telescopes of ?. certain power. 
 
SATURN. 193 
 
 cases where extreme accuracy is not important. As a 
 telescope is essential for observing an eclipse of one of 
 the satellites, it is obvious that this method cannot be 
 practiced at sea. 
 
 248. The grand discovery of the progressive motion 
 of light, was first made by observations on the eclipses 
 of Jupiter's satellites. In the year 1 675, it was remarked 
 by Roemer, a Danish astronomer, on comparing together 
 observations of these eclipses during many successive 
 years, that they take place sooner by about sixteen min- 
 utes, (16m.26s.6) when the earth is on the same side of 
 the sun with the planet, than when she is on the oppo- 
 site side. This difference he ascribed to the progressive 
 motion of light, which takes that time to pass through the 
 diameter of the earth's orbit, making the velocity of light 
 about 1 92,000 miles per second. So great a velocity star- 
 tled astronomers at first, and produced some degree of 
 distrust of this explanation of the phenomenon ; but the 
 subsequent discovery of what is called the aberration of 
 light, led to an independent estimation of the velocity of 
 light with almost precisely the same result. 
 
 249. SATURN comes next in the series as we recede 
 from the sun, and has, like Jupiter, a system within it- 
 self, on a scale of great magnificence. In size it is, next 
 to Jupiter, the largest of the planets, being 79,000 miles 
 in diameter, or about 1,000 times as large as the earth. 
 It has likewise belts on its surface and is attended by 
 seven satellites. But a still more wonderfnl appendage 
 is its Ring, a broad wheel encompassing the planet at a 
 great distance from it. We have already intimated that 
 Saturn's system is on a grand scale. As, however, Sat- 
 
 248. How was the progressive motion of light first discovered ? 
 Explain the manner of the discovery. How long is light in 
 traversing the diameter of the earth's orbit ? What is its ve- 
 locity per second ? How does this agree with that derived 
 from the aberration of light ? 
 
 17 
 
194 THE PLANETS. 
 
 urn is distant from us nearly 900,000,000 miles, we are 
 unable to obtain the same clear and striking views of 
 his phenomena as we do of the phenomena of Jupiter, al- 
 though they really present a more wonderful mechanism. 
 
 250. Saturn's ring, when viewed with telescopes of 
 a high power, is found to consist of two concentric rings, 
 separated from each other by a dark space. Although 
 this division of the rings appears to us, on account of 
 our immense distance, as only a fine line, yet it is in re- 
 ality an interval of not less than about 1800 miles. The 
 dimensions of the whole system are in round numbers 
 as follows : 
 
 Miles. 
 
 Diameter of the planet, . . . . V) 79,000 
 From the surface of the planet to the inner ring, 20,000 
 Breadth of the inner ring, .... 17,000 
 Interval between the rings, .... 1,800 
 
 Breadth of the outer ring, .... 10,500 
 Extreme dimensions from outside to outside, 176,000 
 
 Fig. 45. 
 
 The figure represents Saturn as it appears to a power- 
 ful telescope, surrounded by its rings, and having its body 
 striped with dark belts, somewhat similar but broader 
 
 249. Saturn. State his diameter and volume, number of 
 atellites, ring, distance from the sun. 
 
SATURN. 195 
 
 and less strongly marked than those of Jupiter, and 
 owing doubtless to a similar cause. That the ring is a 
 solid opake substance, is shown by its throwing its shad- 
 ow on the body of the planet on the side nearest the sun 
 and on the other side receiving that of the body. From 
 the parallelism of the belts with the plane of the ring, 
 it may be conjectured that the axis of rotation of the 
 planet is perpendicular to that plane ; and this conjec- 
 ture is confirmed by the occasional appearance of exten- 
 sive dusky spots on its surface, which when watched 
 indicate a rotation parallel to the ring in lOh. 29m. 17s. 
 This motion, it will be remarked, is nearly the same 
 with the diurnal motion of Jupiter, subjecting places on 
 the equator of the planet to a very swift revolution, and 
 occasioning a high degree of compression at the poles, 
 the equatorial being to the polar diameter in the high 
 ratio of 11 to 10. It requires a telescope of high mag- 
 nifying powers and a strong light, to give a full and 
 striking view of Saturn with his rings and belts and sat- 
 tellites ; for we must bear in mind, that in the distance 
 of Saturn one second of angular measurement corres- 
 ponds to 4,000 miles, a space equal to the semi-diameter 
 of our globe. But with a telescope of moderate powers, 
 the leading phenomena of the ring itself may be ob- 
 served. 
 
 251. Saturn 1 s ring, in its revolution awund the sun, 
 always remains parallel to itself. 
 
 If we hold opposite to the eye a circular ring or disk 
 like a piece of coin, it will appear as a complete circle 
 when it is at right angles to the axis of vision, but when 
 oblique to that axis it will be projected into an ellipse 
 
 250. How is the ring divided by large telescopes? State the 
 several dimensions of Saturn and his rings. Describe tho 
 figure. i|pw is the ring inferred to be a solid opake sub- 
 stance ? In what time does Saturn revolve on his axis ? What 
 figure does this give to the planet ? What kind of telescope is 
 required to see the phenomena of Saturn to advantage ? 
 
196 THfc PLANETS. 
 
 more ,and more flattened as its obliquity is increased, 
 until, when its plane coincides with the axis of vision, 
 it is projected into a straight line. Let us place on the 
 table a lamp to represent the sun, and holding the ring 
 at a certain distance inclined a little towards the lamp, 
 let us carry it round the lamp always keeping it parallel 
 to itself. During its revolution it will twice present its 
 edge to the lamp at opposite points, and twice at places 
 90 distant from those points, it will present its broadest 
 face towards the lamp. At intermediate points, it will 
 exhibit an ellipse more or less open, according as it is 
 nearer one or the other of the preceding positions. It 
 will be seen also that in one half of the revolution the 
 lamp shines on one side of the ring, and in the other 
 half of the revolution on the other side. Such would 
 be the successive appearances of Saturn's ring to a spec- 
 tator on the sun ; and since the earth is, in respect to 
 so distant a body as Saturn, very near the sun, these 
 appearances are presented to us in nearly the same man- 
 ner as though we viewed them from the sun. Accord 
 dingly, we sometimes see Saturn's ring under the form 
 of a broad ellipse, which grows continually more and 
 more acute until it passes into a line, and we either lose 
 sight of it altogether, or by the aid of the most power- 
 ful telescopes, we see it as a fine thread of light drawn 
 across the disk and projecting out from it on each side. 
 As the whole revolution occupies 30 years, and the edge 
 is presented to the sun twice in the revolution, this last 
 phenomenon, namely, the disappearance of the ring, 
 takes place every 15 years. 
 
 252. The learner may perhaps gain a clearer idea of 
 the foregoing appearances from the following diagram : 
 
 Let A, B, C, &c. represent successive positions of Sat- 
 urn and his ring in different parts of his orbit, while 
 
 251. How is the position of the ring with respdfct to itself 
 m all parts of its revolution ? How may the various appear- 
 ances of the ring be represented ? 
 
SATURN. 
 
 197 
 
 abc represents the orbit of the earth.* Were the ring 
 when at C and G perpendicular to the CG, it would be 
 seen by a spectator situated at a or d a perfect circle, 
 but being inclined to the line of vision 28 4', it is pro- 
 jected into an ellipse. This ellipse contracts in breadth 
 
 46. 
 
 as the ring passes towards its nodes at A and E, where 
 it dwindles into a straight line. From E to G the ring 
 opens again, becomes broadest at G, and again contracts 
 till it becomes a straight line at A, and from this point 
 expands till it recovers its original breadth at C. These 
 successive appearances are all exhibited to a telescope of 
 moderate powers. The ring is extremely thin, since the 
 smallest satellite, when projected on it, more than covers 
 it. The thickness is estimated at 100 miles. 
 
 253. Saturn's ring shines wholly by reflected light 
 derived from the sun. This is evident from the fact, 
 that that side only which is turned towards the sun is 
 enlightened ; and it is remarkable, that the illumination 
 of the ring is greater than that of the planet itself, but 
 
 252. Explain the revolution of the ring by figure 46. 
 
 253. Whence does the ring derive its light ? What causes 
 occasion the disappearance of the ring ? At what intervals 
 do these disappearances occur ? 
 
 * It may be remarked by the learner, that .these orbits are made so 
 elliptical, not to represent the eccentricity of either the earth's or Sat- 
 urn's 01 bit, but merely as the projection of circles seen very obliquely, 
 
 17* 
 
198 THE PLANETS. 
 
 the outer ring is less bright than the inner. Although, 
 as we have already remarked, we view Saturn's ring 
 nearly as though we saw it from the sun, yet the plane 
 of the ring produced may pass between the earth and 
 the sun, in which case also the ring becomes invisi- 
 ble, the illuminated side being wholly turned from us. 
 Thus when the ring is approaching its node at E, a spec- 
 tator at a would have the dark side of the ring presented 
 to him. The ring was invisible in 1833, and will be 
 invisible again in 1847. The northern side of the ring 
 will be seen until 1845, when the southern side will 
 come into view. 
 
 It appears, therefore, that there are three causes for 
 the disappearance of Saturn's ring ; first, when the edge 
 of the ring is presented to the sun ; secondly, when the 
 edge is presented to the earth ; and thirdly, when the un- 
 illuminated side is towards the earth. 
 
 254. Saturn's ring revolves in its own plane in about 
 10i hours, (lOh. 32m. 15s.4). La Place inferred this 
 from the doctrine of universal gravitation. He proved 
 that such a rotation was necessary, otherwise the matter 
 of which the ring is composed would be precipitated 
 upon its primary. He showed that in order to sustain 
 itself, its period of rotation must be equal to the time of 
 revolution of a satellite, circulating around Saturn at a 
 distance from it equal to that of the middle .of the ring, 
 which period would be about 10^ hours. By means of 
 spots in the ring, Dr. Herschel followed the ring in its 
 rotation, and actually found its period to be the same as 
 assigned by La Place, a coincidence which beautifully 
 exemplifies the harmony of truth. 
 
 255. Although the rings are very nearly concentric with 
 the planet, yet recent measurements of extreme delicacy 
 
 254 In what time does the ring revolve in its own plane ? 
 How was this re volution inferred to exist before it was actually 
 observed ? 
 

 SATURN. 199 
 
 have demonstrated, that the coincidence is not mathe- 
 matically exact, but that the center of gravity of 'the rings 
 describes around that of the body a very minute orbit. 
 This fact, unimportant as it may seem, is of the utmost 
 consequence to the stability of the system of rings. * Sup- 
 posing them mathematically perfect in their circular form, 
 and exactly concentric with the planet, it is demonstrable 
 that they would form (in spite of their centrifugal force) 
 a system in a state of unstable equilibrium, which the 
 slightest external power would subvert not by causing 
 a rupture in the substance of the rings but by precip- 
 itating them unbroken on the surface of the planet. 
 The ring may be supposed of an unequal breadth in its 
 different parts, and as consisting of irregular solids, 
 whose common center of gravity does not coincide with 
 the center of the figure. Were it not for this distribu- 
 tion of matter, its equilibrium would be destroyed by 
 the slightest force, such as the attraction of a satellite, 
 and the ring would finally precipitate itself upon the 
 planet. 
 
 As the smallest difference of velocity between the 
 planet and its rings must infallibly precipitate the rings 
 upon the planet, never more to separate, it follows either 
 that their motions in their common orbit round the sun, 
 must have been adjusted to each other by an external 
 power, with the minutest precision, or that the rings 
 must have been formed about the planet while subject 
 to their common orbitual motion, and under the full and 
 free influence of all the acting forces. 
 
 The rings of Saturn must present a magnificent spec- 
 tacle from those regions of the planet which lie on their 
 enlightened sides, appearing as vast arches spanning the 
 sky from horizon to horizon, and holding an invariable 
 situation among the stars. On the other hand, in the 
 region beneath the dark side, a solar eclipse of 15 years 
 
 255. Are the rings concentric with the planet ? What ad- 
 vantage results from this arrangement ? How must the rings 
 appear when seen from the planets ? 
 
200 THE PLANETS. 
 
 in duration, under their shadow, must afford (to our 
 ideas) an inhospitable abode to animated beings, but ill 
 compensated by the full light of its satellites. But we 
 shall do wrong to judge of the fitness or unfitness of 
 their condition from what we see around us, when, per- 
 haps, the very combinations which convey to our minds 
 only images of horror may be in reality theatres of the 
 most striking and glorious displays of beneficent con- 
 trivance. (Sir J. Herschel.) 
 
 256. Saturn is attended by seven satellites. Although 
 bodies of considerable size, their great distance prevents 
 their being visible to any telescopes but such as afford a 
 strong light and high magnifying powers. The outer- 
 most satellite is distant from the planet more than 30 
 times the planet's diameter, and is by far the largest of 
 the whole. It is the only one of the series whose theory 
 has been investigated further than suffices to verify Kep- 
 ler's law of the periodic times, which is found to hold 
 food here as well as in the system of Jupiter. It ex- 
 ibits, like the satellites of Jupiter, periodic variations of 
 light, which prove its revolution on its axis in the time 
 of a sidereal revolution about Saturn. The next satellite 
 in order, proceeding inwards, is tolerably conspicuous ; 
 the three next are very minute, and require pretty pow- 
 erful telescopes to see them ; while the two interior sat- 
 ellites, which just skirt the edge of the ring, and move 
 exactly in its plane, have never been discovered but with 
 the most powerful telescopes which human art has yet 
 constructed, and then only under peculiar circumstances. 
 At the time of the disappearance of the rings (to ordinary 
 telescopes) they were seen by Sir William Herschel 
 with his great telescope, projected along the edge of the : Jjj 
 ring, and threading like beads the thin fibre of light to 
 
 256. What is the number of Saturn's satellites ? How far 
 distant from the planet is the outermost satellite ? Do the sat- 
 ellites follow Kepler's third law ? Which of the satellites are 
 easily seen ? Do they undergo eclipses ? 
 
URANUS. 201 
 
 which the ring is then reduced. Owing to the obliquity 
 of the ring, and of the orbits of the satellites to that of 
 their primary, there are no eclipses of the satellites, the 
 two interior ones excepted, until near the time when the 
 ring is seen edgewise. 
 
 257. URANUS is the remotest planet belonging to our 
 system, and is rarely visible except to the telescope. Al- 
 though his diameter is more than four times that of the 
 earth, (35,112 miles,) yet his distance from the sun is 
 likewise nineteen times as great as the earth's distance, 
 or about 1,800,000,000 miles. His revolution around 
 the sun occupies nearly 84 years, so that his position in 
 the heavens for several years in succession is nearly sta- 
 tionary. His path lies very nearly in the ecliptic, being 
 inclined to it less than one degree, (46 X 28".44.) 
 
 The sun himself when seen from Uranus dwinflles al- 
 most to a star, subtending as it does an angle of only 
 1 / 40" ; so that the surface of the sun would appear 
 there 400 times less than it does to us. 
 
 This planet was discovered by Sir William Herschel 
 on the 1 3th of March 1781. His attention was attracted 
 to it by the largeness of its disk in the telescope ; and 
 finding that it shifted its place among the stars, he at 
 first took it for a comet, but soon perceived that its orbit 
 was not eccentric like the orbits of comets, but nearly 
 circular like those of the planets. It was then recog- 
 nized as a new member of the planetary system, a con- 
 clusion which has been justified by all succeeding ob- 
 servations. 
 
 258. Uranus is attended by six satellites. So minute 
 objects are they, that they can be seen only by powerful 
 telescopes. Indeed, the existence of more than two is 
 still considered as somewhat doubtful. These two, 
 
 257. Uranus. State his diameter distance from the sun ^ 
 periodic time inclination of his orbit. How would the sun 
 appear from Uranus ? State the history of his discovery 
 
602 THE PLANETS. 
 
 however, offer remarkable, and indeed qui'e unexpected 
 and unexampled peculiarities. Contrary to the unbro- 
 ken analogy of the whole planetary system, the planes 
 of their orbits are nearly perpendicular to the ecliptic, 
 being inclined no less than 78 58' to that plane, and in 
 these orbits their motions are retrograde ; that is, instead 
 of advancing from west to east around their primary, as 
 is the case with all the other planets and satellites, they 
 move in the opposite direction. With this exception, all 
 the motions of the planets, whether around their own 
 axes, or around the sun, are from west to east. The sun, 
 himself, turns on his axis from west to east ; all the pri- 
 mary planets revolve around the sun from west to east ; 
 their revolutions on their own axes are, also in the same 
 direction ; all the secondaries, with the single exception 
 above-mentioned, move about their primaries from west 
 to east ; and, finally, such of the secondaries as have 
 been discovered to have a diurnal revolution, follow the 
 same course. Such uniformity among so many motions, 
 could have resulted only from forces impressed upon 
 them by the same omnipotent hand ; and few things in 
 the creation more distinctly proclaim that God made the 
 world. 
 
 THE NEW PLANETS, CERES, PALLAS, JUNO, AND VESTA. 
 
 259. THE commencement of the present century was 
 rendered memorable in the annals of astronomy, by the 
 discovery of four new planets between Mars and Jupiter. 
 Kepler, from some analogy which he found to subsist 
 among the distances of the planets from the sun, had 
 long before suspected the existence of one at this dis- 
 tance ; and his conjecture was rendered more probable 
 by the discovery of Uranus, which follows the analogy 
 
 258. By how many satellites is Uranus attended ? What is 
 said of their minuteness ? What remarkable peculiarities have 
 they ? In what direction are the motions of all the bodies in 
 the solar system ? What does this fact indicate with respect to 
 their origin ? 
 
NEW PLANETS. 203 
 
 >f the other planets. So strongly, indeed, were astrono- 
 mers impressed with the idea that a planet would be 
 found between Mars and Jupiter, that, in the hope of 
 discovering it, an association was formed on the conti 
 nent of Europe of- twenty-four observers, who divided 
 the sky into as many zones, one of which was allotted 
 to each member of the association. The discovery of 
 the first of these bodies was however made accidentally 
 by Piazzi, an astronomer of Palermo, on the first of Jan- 
 uary, 1801. It was shortly afterwards lost sight of on 
 account of its proximity to the sun, and was not seen 
 again until the close of the year, when it was re-discov- 
 ered in Germany. Piazzi called it Ceres, in honor of 
 the tutelary goddess of Sicily ; and her emblem, the 
 sickle?, has been adopted as its appropriate symbol. 
 
 The difficulty of finding Ceres induced Dr. Olbers, of 
 Bremen, to examine with particular care all the small 
 stars that lie near her path, as seen from the earth ; and 
 while prosecuting these observations, in March, 1802, he 
 discovered another similar body, very nearly at the same 
 distance from the sun, and resembling the former in 
 many other particulars. The discoverer gave to this se- 
 cond planet the name of Pallas, choosing for its symbol 
 the lance $ , the characteristic of Minerva. 
 
 260. The most surprising circumstance connected 
 with the discovery of Pallas, was the existence of two 
 planets at nearly the same distance from the sun, and 
 apparently having a common node. On account of this 
 singularity, Dr. Olbers was led to conjecture that Ceres 
 and Pallas are only fragments of a larger planet, which 
 had formerly circulated at the same distance, and been 
 shattered by some internal convulsion. The hypothesis 
 suggested the probability that there might be other frag 
 
 259. Name the New Planets. When were they discovered ? 
 What had been conjectured previous to their discovery ? Who 
 discovered the first ? What is its name ? How was Pallas dis 
 covered ? 
 
204 THE PLANETS. 
 
 ments, whose orbits, however they might differ in ec 
 centricity and inclination, might be expected to cross the 
 ecliptic at a common point, or to have the same node. 
 Dr. Olbers, therefore, proposed to examine carefully every 
 month, the two opposite parts of the heavens in which 
 the orbits of Ceres and Pallas intersect one another, with 
 a view to the discovery of other planets, which might 
 be sought for in those parts with greater chance of suc- 
 cess than in a wider zone, embracing the entire limits 
 of these orbits. Accordingly, in 1804, near one of the 
 nodes of Ceres and Pallas, a third planet was discovered. 
 This was called Juno, and the character $ was adopted 
 for its symbol, representing the starry sceptre of the 
 queen of Olympus. Pursuing the same researches, in 
 1807, a fourth planet was discovered, to which was 
 given the name of Vesta, and for its symbol the char- 
 acter ft was chosen an altar surmounted with a censer 
 holding the sacred fire. 
 
 After this historical sketch, it will be sufficient to clas- 
 sify under a few heads the most interesting particulars 
 relating to the New Planets. 
 
 261. The average distance of these bodies from the 
 sun is 261,000,000 miles; and it is remarkable that 
 their orbits are very near together. Taking the distance 
 of the earth from the sun for unity, their respective dis- 
 tances are 2.77, 2.77, 2.67, 2.37. 
 
 As they are found to be governed, like the other mem- 
 bers of the solar system, by Kepler's law, that regulates 
 the distances and times. of revolution, their periodical 
 times are of course pretty nearly equal, averaging about 
 4^ years. 
 
 In respect to the inclination of their orbits, there is 
 considerable diversity. The orbit of Vesta is inclined 
 
 260. How do Ceres and Pallas compare in distance from the 
 sun and the place of their nodes ? What hypothesis did Olbers 
 adopt ? State the circumstances connected with the discovery 
 of Juno and Vesta. 
 
MOTIONS OF THE PLANETARY SYSTEM. 205 
 
 to the ecliptic only about 7, while that of Pallas is more 
 than 34. They all therefore have a higher inclination 
 than the orbits of the old planets, and of course make 
 excursions from the ecliptic beyond the limits of the 
 Zodiac. 
 
 The eccentricity of their orbits is also, in general, 
 greater than that of the old planets ; and the eccentrici- 
 ties of the orbits of Pallas and Juno exceed that of the 
 orbit of Mercury. 
 
 Their small size constitutes one of their most remark- 
 able peculiarities. The difficulty of estimating the ap- 
 parent diameters of bodies at once so very small and so 
 far off, would lead us to expect different results in the 
 actual estimates. Accordingly, while Dr. Herschel es- 
 timates the diameter of Pallas at only 80 miles, Schroe- 
 ter places it as high as 2,000 miles, or about the size of 
 the moon. The volume of Vesta is estimated at only 
 one fifteen thousandth part of the earth's, and her surface 
 is only about equal to that of the kingdom of Spain. 
 These little bodies are surrounded by atmospheres of 
 great extent, some of which are uncommonly luminous, 
 and others appear to consist of nebulous or vapory mat- 
 ter. These planets in general shine with a more vivid 
 light than might be expected from their great distance 
 and diminutive size. 
 
 CHAPTER IX. 
 
 MOTIONS OF THE PLANETARY SYSTEM QUANTITY OP MAT- 
 TER IN THE SUN AND PLANETS STABILITY OF THE SO- 
 LAR SYSTEM. 
 
 262. WE have waited until the learner may be sup- 
 posed to be familiar with the contemplation of the heav- 
 
 261. What is the average distance of the New Planets from 
 the sun ? How do these orbits lie with respect to each other? 
 Are they subject to Kepler's third law ? What is their average 
 periodical time ? What is said of the inclination of their or- 
 bits ? Also, of the eccentricity ? What "is their size ? 
 
 18 
 
206 THE PLANETS. 
 
 enly bodies, individually, before inviting his attention to 
 a systematic view of the planets, and of their motions 
 around the sun. The time has now arrived for entering 
 more advantageously upon this subject, than could have 
 been done at an earlier period. 
 
 There are two methods of arriving at a knowledge of 
 the motions of the heavenly bodies. One is to begin 
 with the apparent, and from these to deduce the real 
 motions ; the other is, to begin with considering things 
 as they really are in nature, and then to inquire why 
 they appear as they do. The latter of these methods is 
 by far the more eligible ; it is much easier than the 
 other, and proceeding from the less difficult to that which 
 is more difficult, from motions that are very simple to 
 such as are complicated, it finally puts the learner in pos- 
 session of the whole machinery of the heavens. We 
 shall, in the first place, therefore, endeavor to introduce 
 the learner to an acquaintance with the simplest motions 
 of the planetary system, and afterwards to conduct him 
 gradually through such as are more complicated and dif- 
 ficult. 
 
 263. Let us first of all endeavor to acquire an adequate 
 idea of absolute space, such as existed before the crea- 
 tion of the" world. We shall find it no easy matter to 
 form a correct notion of infinite space ; but let us fix our 
 attention, for some time, upon extension alone, devoid of 
 every thing material, without light or life, and without 
 bounds. Of such a space we could not predicate the 
 ideas of up or down, east, west, north, or south, but all 
 reference to our own horizon (which habit is the most 
 difficult of all to eradicate from the mind) must be com- 
 pletely set aside. Into such a void we would introduce 
 the SUN. We would contemplate this body alone, in 
 the midst of boundless space, and continue to fix the at- 
 
 262. What are the two methods of studying the motions of 
 the heavenly bodies ? Which method is bust ? What motions 
 will be first considered ? 
 
MOTIONS OF THE PLANETARY SYSTEM. 207 
 
 tention upon this object, until we had fully settled its 
 relations to the surrounding void. The ideas of up and 
 down would now present themselves, but as yet there 
 would be nothing to suggest any notion of the cardinal 
 points. We suppose ourselves next to be placed on the 
 surface of the sun, and the firmament of stars to be 
 lighted up. The slow revolution of the sun on his axis, 
 would be indicated by a corresponding movement of the 
 stars in the opposite direction ; and in a period equal to 
 more than 25 of our days, the spectator would see the 
 heavens perform a complete revolution around the sun, 
 as he now sees them revolve around the earth once in 
 24 hours. The point of the firmament where no mo- 
 tion appeared, would indicate the position of one of the 
 poles, which being called North, the other cardinal points 
 would be immediately suggested. 
 
 Thus prepared, we may now enter upon the conside- 
 ration of the planetary motions. 
 
 264. Standing on the sun, we see all the planets mo 
 ving slowly around the celestial sphere, nearly in the 
 same great highway, and in the same direction from 
 west to east. They move, however, with very unequal 
 velocities. Mercury makes very perceptible progress 
 from night to night, like the moon revolving about the 
 earth, his daily progress eastward being one third as 
 great as that of the moon, since he completes his entire 
 revolution in about three months. If we watch the 
 course of this planet from night to night, we observe it 
 in its revolution, to cross the ecliptic in two opposite 
 points of the heavens, and wander about 7 from that 
 plane at its greatest distance from it. Knowing the po- 
 sition of the orbit of Mercury with respect to the ecliptic, 
 we may now, in imagination, represent that orbit by a 
 
 263. How can we form a correct idea of absolute space ? 
 What can we predicate of such a space ? If the sun were pla- 
 ced in such a void, what new ideas would present themselves ? 
 should we get a knowledge of the cardinal points ? 
 
208 THE PLANETS. 
 
 great circle passing through the center of the planet and 
 the center of the sun, and cutting the plane of the eclip- 
 tic in two opposite points at an angle of 7, We may 
 imagine the* intersection of these two great circles- with 
 the celestial vault to be marked out in plain and palpa- 
 ble lines on the face of the sky ; but we must bear in 
 mind that these orbits are mere mathematical planes, 
 having no permanent existence in nature, any more than 
 the path of an eagle flying through the sky ; and if we 
 conceive of their orbits marked on the celestial vault, 
 we must be careful to attach to the representation the 
 same notion as to a thread or wire, carried round to trace 
 out the course pursued by a horsfi. in a race-ground.* 
 
 The planes of both the ecliptic and the orbit of Mer- 
 cury, may be conceived of as indefinitely extended to a 
 great distance until they meet the sphere of the stars ; 
 but the lines which the earth and Mercury describe in 
 those planes, that is, their orbits may be conceived of as 
 comparatively near to the sun. Could we now for a 
 moment be permitted to imagine that the planes of the 
 ecliptic, and of the orbit of Mercury, were made of thin 
 plates of glass, and that the paths,of the respective plan- 
 ets were marked out on their planes in distinct lines, we 
 should perceive the orbit of the earth to be alnrrtost a per- 
 fect circle, while that of Mercury would appear distinctly 
 elliptical. But having once made use of a palpable sur- 
 
 264. Where must the spectator be placed in order to see the 
 real motions of the planets ? How would the motions of the 
 several planets appear from this station ? State the particular 
 movements of Mercury. How may we imagine the ecliptic 
 and the orbit of Mercury to be represented on the sky ? How 
 shall we conceive of the planes of these orbits as distinguished 
 from the orbit itself ? 
 
 * It would seem superfluous to caution the reader on so plain a point, 
 did not the experience of the instructor constantly show that young 
 learners, from the habit of seeing the celestial motions represented in 
 orreries and diagrams, almost always fall into the absurd notion of con- 
 sidering the orbits of the planets as having a distinct and independent 
 existence. 
 
MOTIONS OF THE PLANETARY SYSTEM. 209 
 
 face and visible lines to aid us in giving position and fig- 
 ure to the planetary orbits, let us now throw aside these 
 devices, and hereafter conceive of these planes and or- 
 bits as they are in nature, and learn to refer a body to a 
 mere mathematical plane, and to trace its path in that 
 plane through absolute space. 
 
 265. A clear understanding of the motions of Mercury 
 and of the relation of its orbit to the plane of the eclip- 
 tic, will render it easy to understand the same particulars 
 in regard to each of the other planets. Standing on the 
 sun we should see each of the planets pursuing a similar 
 course to that of Mercury, all moving from west to east, 
 with motions differing from each other chiefly in two re- 
 spects, namely, in their velocities, and in the distances 
 to which they ever recede from the ecliptic. 
 
 The earth revolves about the sun very much like Ve- 
 nus, and to a spectator on the sun, the motions of these 
 two planets would exhibit much the same appearances. 
 We have supposed the observer to select the plane of 
 the earth's orbit as his standard of reference, and to see 
 how each of the other orbits is related to it ; but such a 
 selection of the ecliptic is entirely arbitrary ; the specta- 
 tor on the sun, who views the motions of the planets as 
 they actually exist in nature, would make no such dis- 
 tinction between the different orbits, but merely inquire 
 how they were mutually related to each other. Taking, 
 however, the ecliptic as the plane to which all the others 
 are referred, we do not, as in the case of the other plan- 
 ets, inquire how its plane is inclined, nor what are its 
 nodes, since it has neither inclination nor node. 
 
 26(K The attempt to exhibit the motions of the solar 
 system, and the positions of the planetary orbits by 
 
 265. If we stood on the sun, how should we see each of the 
 planets revolve ? Why is the earth's orbit selected as the stan- 
 dard of reference ? Would the spectator on the sun make any 
 such distinction ? 
 
210 THE PLANETS. 
 
 means of diagrams, or even orreries, is usually a failure 
 The student who relies exclusively on such aids as 
 these, will acquire ideas on this subject that are both in- 
 adequate and erroneous. They may aid reflection, but 
 can never supply its place. The impossibility of rep- 
 resenting things in their just proportions will be evident 
 when we reflect, that to do this, if, in an orrery, we 
 make Mercury as large as a cherry, we should require to 
 represent the sun by a globe six feet in diameter. If we 
 preserve the same proportions in regard to distance, we 
 must place Mercury 250 feet, and Uranus 12,500 feet, 
 or more than two miles from the sun. The mind of the 
 student of astronomy must, therefore, raise itself from 
 such imperfect representations of celestial phenomena as 
 are afforded by artificial mechanism, and, transferring his 
 contemplations to the celestial regions themselves, he 
 must conceive of the sun and planets as bodies that bear 
 an insignificant ratio to the immense spaces in which 
 they circulate, resembling more a few little birds flying 
 in the open sky, than they do the crowded machinery of 
 an orrery. 
 
 267. Having acquired as correct an idea as we are 
 able of the planetary system, and of the positions of the 
 orbits with respect to the ecliptic, let us next inquire 
 into the nature and causes of the apparent motions. 
 
 The apparent motions of the planets are exceedingly 
 unlike the real motions, a fact which is owing to two 
 causes ; first, we mew them out of the center of their or- 
 bits ; secondly, we are ourselves in motion. From the 
 first cause, the apparent places of the planets are greatly 
 changed by perspective ; and from the second cause, 
 
 266. What is said of the attempt to represent the positions 
 and motions of the solar system by diagrams and orreries ? 
 Give examples. 
 
 267. Are the apparent motions of the planets like the real 
 motions ? What makes, them different ? How does each cause 
 operate 1 What is the heliocentric place, and what the geo- 
 centric place of a planet ? 
 
MOTIONS OF THE PLANETARY SYSTEM. 211 
 
 we attribute to the planets changes of place which arise 
 from our own motions of which we are unconscious. 
 
 The situation of a heavenly body as seen from the 
 center of the sun is called its heliocentric place ; as seen 
 from the center of the earth, its geocentric place. The 
 geocentric motions of the planets must, according to 
 what has just been said, be far more irregular and com- 
 plicated than the heliocentric. 
 
 268. The apparent motions of the Inferior Planets as 
 seen from the earth, have been already explained in ar- 
 ticles 216 and 217 ; from which it appeared, that Mer- 
 cury and Venus move backwards and forwards across 
 the sun, the former never being seen farther than 29 
 and the latter never more than 47 from that luminary. 
 It was also shown that while passing from the greatest 
 elongation on one side to the greatest elongation on the 
 other side, through the superior conjunction, the apparent 
 motions of these planets are accelerated by the motion 
 of the earth ; but that while moving through the infe- 
 rior conjunction, at which time their motions are retro- 
 grade, they are apparently retarded by the earth's mo- 
 tion. Let us now see what are the geocentric motions 
 of the Superior Planets. 
 
 269. Let A, B, C, (Fig. 47,) represent the earth in 
 different positions in its orbit, and M a superior planet as 
 Mars, and NR an arc of the concave sphere of the 
 heavens. First, suppose the planet to remain at rest in 
 M, and let us see what apparent motions it will receive 
 from the real motions of the earth. When the earth is 
 at B, it will see the planet in the heavens at N ; and as 
 the earth moves successively through, C, D, E, F, the 
 planet will appear to move through O, P, Q,, R. B and 
 F are the two points of greatest elongation of the earth 
 from the sun as seen from the planet ; hence between 
 
 268. Describe the apparent motions of Mercury and Venus 
 from figure 40. 
 
212 
 
 THE PLANETS. 
 
 these two points, while passing through the part of her 
 orbit most remote from the planet, (when the planet is 
 seen in superior conjunction,) the earth by her own mo- 
 Fig. 47. 
 
 tion gives an apparent motion to the planet in the order 
 of the signs that is, the apparent motion given by the 
 earth is direct. But in passing from F to B through A, 
 when the planet is seen in opposition, the apparent mo- 
 tion given to the planet by the earth's motion is from R 
 to N, and is therefore retrograde. As the arc described 
 by the earth, when the motion is direct, is much greater 
 than when the motion is retrograde, while the apparent 
 arc of the heavens described by the planet from N to R 
 in the one case, and from R to N in the other, is the 
 
 269. Describe the motions of the Superior Planets from fig- 
 ure 47. The planet remaining at rest, what apparent motions 
 will the motion of the earth impart to it, when in opposition ? 
 What when in superior conjunction ? 
 
MOTIONS OF THE PLANETARY SYSTEM. 213 
 
 same in both cases, the retrograde motion is much swifter 
 than the direct, being performed in much less time. 
 
 270. But the superior planet is not in fact at rest, as 
 we have supposed, but is all the while moving east- 
 ward, though with a slower motion than the earth. In- 
 deed, with respect to the remotest planets as Saturn and 
 Uranus, the forward motion is so exceedingly slow that 
 the above representation is nearly true for a single year. 
 Still, the effect of the real motions of all the superior 
 planets eastward, is to increase the direct apparent mo- 
 tion communicated by the earth and to diminish the ret- 
 rograde motion. 
 
 If Mars stood still while the earth went round the 
 sun, then a second opposition as at A, would occur at 
 the end of one year from the first ; but while the earth 
 is performing this circuit, Mars is also moving the same 
 way, more than half as fast, so that when the earth re- 
 turns to A, the planet has already performed more than 
 half the same circuit, and will have completed its whole, 
 revolution before the earth comes up with it. Indeed, 
 Mars, -after having been once seen in opposition, does not 
 come into opposition again until after two years and 
 fifty days. And since the planet is then comparatively 
 very near to us, and appears very large and bright, rising 
 unexpectedly about the time the sun sets, he surprises 
 the world as though it were some new celestial body. 
 But on account of the slow progress of Saturn and Ura- 
 nus, we find after having performed one circuit around 
 the sun, that they are but little advanced beyond where 
 we left them at the last opposition. The time between 
 one opposition of Saturn and another is only a year and 
 thirteen days. 
 
 It appears, therefore that the superior planets steadily 
 pursue their course around the sun, but that their appar- 
 
 270. How does the real motion of the planet modify the fore 
 going results ? How in respect to the remotest planets, as Ura 
 nus, and how in respect to a nearer planet as Mars ? How 
 often is Mars in opposition ? What is his appearance then 7 
 
214 THE PLANETS, 
 
 ent retrograde motion when in opposition, is occasioned 
 by our passing by them with a swifter motion, like the 
 apparent backward motion of a vessel when we over- 
 take it and pass rapidly by it in a steamboat. 
 
 QUANTITY OP MATTER IN THE SUN AND PLANETS. 
 
 271. It would seem at first view very improbable that 
 an inhabitant of this earth should be able to weigh the 
 sun and planets, and estimate the exact quantity of mat- 
 ter which they severally contain. But the principles of 
 Universal Gravitation conduct us to this result, by a 
 process remarkable for its simplicity. By comparing the 
 relations of a few elements that are known to us, we 
 ascend to the knowledge of such as appeared to be be- 
 yond the pale of human investigation. We learn the 
 quantity of matter in a body from the force of gravity 
 it exerts, and this force is estimated by its effects. 
 Hence worlds are weighed with as much ease as a peb- 
 ble or an article of merchandise. 
 
 272. The sun contains about 355,000 times as much 
 matter as the earth, and 800 times as much matter as all 
 the planets. This however, is owing rather to its great 
 size than to the specific gravity of its materials, for the 
 density of the sun is only one fourth as great as that of 
 the earth. The earth is nearly 5 times as heavy as 
 water, but the sun is only a little heavier than that fluid. 
 The planets near the sun are in general more dense than 
 
 271. What is said of the apparent difficulty of weighing the 
 sun and planets ? What great principles lead us to this re- 
 sult ? How do we learn the quantity of matter in the bodies 
 of the solar system ? 
 
 272. How much more matter does the sun contain than the 
 earth ? How much more than all the planets ? What is the 
 density of the sun compared with that of the earth ? How 
 much heavier is the earth than water ? How much heavier is 
 the sun than water ? Which of the planets have the greatest 
 density \ How heavy is Mercury ? How heavy is Saturn ? 
 
STABILITY OP THE SOLAR SYSTEM. 215 
 
 those more remote ; Mercury being heavier than lead, 
 while Saturn is as light as a cork. The decrease in 
 density however, is not entirely regular, since Venus is 
 a little lighter than the earth, while Jupiter is heavier 
 than Mars, and Uranus than Saturn. 
 
 STABILITY OF THE SOLAR SYSTEM. 
 
 273. The perturbations occasioned by the motions of 
 the planets by their action on each other are very nu- 
 merous, since every body in the system exerts an attrac- 
 tion on every other, in conformity with the law of Uni- 
 versal Gravitation. Venus and Mars, approaching as 
 they do at times comparatively near to the earth, sen- 
 sibly disturb its motions, and the satellites of the re- 
 moter planets greatly disturb each other's movements. 
 
 274. The derangement which the planets produce in 
 the motion of one of their number will be very small in 
 the course of one revolution ; but this gives us no secu- 
 rity that the derangement may not become very large 
 in the course of many revolutions. The cause acts per- 
 petually, and it has the whole extent of time to work in. 
 Is it not easily conceivable then, that in the lapse of ages, 
 the derangements of the motions of the planets may 
 accumulate, the orbits may change their form, and their 
 mutual distances may be much increased or diminished ? 
 Is it not possible that these changes may go on without 
 
 273. What is said of the perturbations occasioned by the ac- 
 tion of the planets on each other ? Which planets in particu- 
 lar, disturb the motions of the earth ? 
 
 274. How is the derangement produced by the planets upon 
 any one of them, in a single revolution ? What may be the 
 ultimate effect of these disturbing forces ? What would be 
 tiie consequence of increasing the eccentricity of the earth's 
 orbit or of bringing the moon nearer the earth or of alter- 
 ing the positions of the planets with respect to that of the 
 earth ? What changes are actually going on in the motions 
 of the heavenly bodies ? 
 
216 THE PLANETS. 
 
 limit, and end in the complete subversion and ruin of the 
 system? If, for instance, the result of this mutual 
 gravitation should be to increase considerably the eccen- 
 tricity of the earth's orbit, or to make the moon approach 
 continually nearer and nearer to the earth at every revo- 
 lution, it is easy to see that in the one case, our year 
 would change its character, producing a far greater ir- 
 regularity in the distribution of the solar heat : in the 
 other, our satellite must fall to the earth, occasioning a 
 dreadful catastrophe. If the positions of the planetary 
 orbits with respect to that of the earth, were to change 
 much, the planets might sometimes come very near us, 
 and thus increase the effect of their -attraction beyond cal- 
 culable limits. Under such circumstances we might have 
 years of unequal length, and seasons of capricious tem- 
 perature ; planets and moons of portentous size and as- 
 pect glaring and disappearing at uncertain intervals ; tides 
 like deluges sweeping over whole continents ; and, per- 
 haps, the collision of two of the planets, and the conse- 
 quent destruction of all organization on both of them. 
 The fact really is, that changes are taking -place in the 
 motions of the heavenly bodies, which have gone on 
 progressively from the first dawn of .science. The ec- 
 centricity of the earth's orbit has been diminishing from 
 the earliest observations to our times. The moon has 
 been moving quicker from the time of the first recorded 
 eclipses, and is now in advance by about four times her 
 own breadth, of what her own place would have been if 
 it had not been affected by this acceleration. The ob- 
 liquity of the ecliptic also, is in a state of diminution, 
 and is now about two fifths of a degree less than it was 
 in the time of Aristotle. (Whewell, in the Bridgewater 
 Treatises, p. 128.) 
 
 275. But amid so many seeming causes of irregular- 
 ity, and ruin, it is worthy of grateful notice, that effec- 
 tual provision is made for the stability of the solar sys- 
 tem. The full confirmation of this fact, is among the 
 grand results of Physical Astronomy. Newton did not 
 undertake to demonstrate either the stability or insta- 
 
STABILITY OF THE SOLAR SYSTEM. 217 
 
 bility of the system. The decision of this point re- 
 quired a great number of preparatory steps and simplifi- 
 cations, and such progress in the invention and improve- 
 ment of mathematical methods, as occupied the best 
 nathematicians of Europe for the greater part of the 
 ast century. Towards the end of that time, it was 
 'hown by La Grange and La Place, that the arrange- 
 ments of the solar system are stable ; that, in the 
 iong run, the orbits and motions remain unchanged; 
 and that the changes in the orbits, which- take place in 
 shorter periods, never transgress certain very moderate 
 limits. Each orbit undergoes deviations on this side 
 and on that side of its average state ; but these devia- 
 tions are never very great, and it finally recovers from 
 them, so that the average is preserved. The planets 
 produce perpetual perturbations in each other's motions, 
 but these perturbations are not indefinitely progressive, 
 but periodical, reaching a maximum value and then di- 
 minishing. The periods which this restoration requires 
 are for the most part enormous, not less than thou- 
 sands, and in some instances millions of years. Indeed 
 some of these apparent derangements, have been going 
 on in the same direction from the creation of the world. 
 But the restoration is in the sequel as complete as the 
 derangement ; and in the mean time the disturbance 
 never attains a sufficient amount seriously to affect the 
 stability of the system. (Whewell, in the Brid^ewater 
 Treatises, p. 128.) I have succeeded in demonstrating 
 (says La Place) that, whatever be the masses of the plan- 
 ets, in consequence of the fact that they all move in the 
 same direction, in orbits of small eccentricity, and but 
 slightly inclined to each other, their secular irregulari- 
 ties are periodical and included within narrow limits ; 
 so that the planetary system will only oscillate about a 
 
 275. Is the system stable ? Did Newton prove this ? Who 
 fully established this point ? Have all the inequalities of the 
 planetary motions a fixed period ? How long are some of these 
 periods ? 
 
 19 
 
218 COMETS. 
 
 mean state, and will never deviate from it except by 3 
 very small quantity. The ellipses of the planets have 
 been and always will be nearly circular. The ecliptic 
 will never coincide with the equator ; and the entire ex- 
 tent of the variation in its inclination, cannot exceed 
 three degrees. 
 
 276. To these observations of La Place, Professor 
 Whewell adds the following on the importance, to the 
 stability of the solar system, of the fact that those plan- 
 ets which have great masses have orbits of small eccen- 
 tricity. The planets Mercury and Mars, which have 
 much the largest eccentricity among the old planets, are 
 those of which the masses are much the smallest. The 
 mass of Jupiter is more than two thousand times that of 
 either of these planets. If the orbit of Jupiter were as 
 eccentric as that of Mercury, all the security for the sta- 
 bility of the system, which analysis has yet pointed out, 
 would disappear. The earth and the smaller planets 
 might, by the near approach of Jupiter at his perihelion, 
 change their nearly circular orbits into very long ellipses, 
 and thus might fall into the sun, or fly off into remote 
 space. It is further remarkable that in the newly discov- 
 ered planets, of which the orbits are still more eccentric 
 than that of Mercury, the masses are still smaller, so that 
 the same provision is established in this case also. 
 
 CHAPTER X. 
 
 OF COMETS. 
 
 277. A COMET, when perfectly formed, consists of 
 three parts, the Nucleus, the Envelope, and the Tail. 
 The Nucleus, or body of the comet, is generally distin- 
 guished by its forming a bright point in the center of 
 the head, conveying the idea of a solid, or at least of a 
 
 276. What planets have orbits of small eccentricity ? How 
 does this fact contribute to the stability of the system ? 
 
COMETS. 219 
 
 very dense portion of matter. Though it is usually ex- 
 ceedingly small when compared with the other parts of 
 the comet, yet it sometimes subtends an angle capable 
 of being measured by the telescope. The Envelope, 
 (sometimes called the coma) is a dense nebulous cover- 
 ing, which frequently renders the edge of the nucleus 
 so indistinct, that it is extremely difficult to ascertain its 
 diameter with any degree of precision. Many comets 
 have no nucleus, but present only a nebulous mass ex- 
 tremely attenuated on the confines, but gradually in- 
 creasing in density towards the center. Indeed there is 
 a regular gradation of comets, from such as are com- 
 posed merely of a gaseous or vapory medium, to those 
 which have a well defined nucleus. In some instances 
 on record, astronomers have detected with their tele- 
 scopes small stars through the densest part of a comet. 
 The Tail is regarded as an expansion or prolongation 
 of the coma;* and, presenting as it sometimes .does, a 
 train of appalling magnitude, and of a pale, disastrous 
 light, it confers on this class of bodies, their peculiar 
 celebrity. 
 
 Fig 48. 
 
 These several parts are exhibited in figure 48, which 
 represents the appearance of the comet of 1680. 
 
 277. Of what three parts does a comet consist ? Describe 
 each. 
 
220 COMETS. 
 
 278. The number of comets belonging to the solar 
 system, is probably very great. Many, no doubt, escape 
 observation by being above the horizon in the day time. 
 Seneca mentions, that during a total eclipse of the sun, 
 which happened 60 years before the Christian era, a 
 large and splendid comet suddenly made its appearance, 
 being very near the sun. The elements of at least 130 
 have been computed, and arranged in a table for future 
 comparison. Of these six are particularly remarkable, 
 viz. the comets, of 1680, 1770, and 1811; and those 
 which bear the names of Halley, Biela, and Encke. 
 The comet of 1680, was remarkable not only for its as- 
 tonishing size and splendor, and its near approach to the 
 sun, but is celebrated for having submitted itself to the 
 observations of Sir Isaac Newton, and for having en- 
 joyed the signal honor of being the first comet whose 
 elements were determined on the sure basis of math- 
 ematics. The comet of 1770, is memorable for the 
 change's its orbit has undergone by the action of Jupiter, 
 as will be more particularly related in the sequel. The 
 comet of 1811 was the most remarkable in its appear- 
 ance of all that have been seen in the present century. 
 It had scarcely any perceptible nucleus, but its train 
 
 Fig. 49. 
 
 4 . 
 
 was very long and broad, as is represented in figure 49. 
 Halley's comet (the same which re-appeared in 1835) is 
 
COMETS 221 
 
 distinguished as that whose return was first successfully 
 predicted, and whose orbit is best determined ; and 
 Biela's and Encke's comets are well known for their 
 short period^ of revolution, which subject them fre- 
 quently to the view of astronomers. 
 
 279. In magnitude and brightness comets exhibit a 
 great diversity. History informs us of comets so bright 
 as to be distinctly visible in the day time, even at noon 
 and in the brightest sunshine. Such was the comet 
 seen at Rome a little before the assassination of Julius 
 Caesar. The comet of 1680 covered an arc of the heav- 
 ens of 97, and its length was estimated at 123,000,000 
 miles. That of 1811, had a nucleus of only 428 miles 
 in diameter, but a tail 132,000,000 miles long. Had it 
 been coiled around the earth like a serpent, it would 
 have reached round more than 5,000 times. Other com- 
 ets are of exceedingly small dimensions, the nucleus 
 being estimated at only 25 miles ; and some which are 
 destitute of any perceptible nucleus, appear to the largest 
 telescopes, even when nearest to us, only as a small 
 speck of fog, or as a tuft of down. The majority of 
 comets can be seen only by the aid of the telescope. 
 
 The same comet, indeed, has often very different as- 
 pects, at its different returns. Halley's comet in 1305 
 was described by the historians of that age, as the comet 
 of terrific magnitude ; (cometa horrendce magnitudinis ;) 
 in 1456 its tail reached from the horizon to the zenith, 
 and inspired such terror, that by a decree of the Pope of 
 Rome, public prayers were offered up at noon-day in all 
 the Catholic churches to deprecate the wrath of heaven, 
 while in 1682, its tail was only 30 in length, and in 1759 
 
 278. What is said of the number of comets? How many 
 have been arranged in a table. Specify the six that are most 
 remarkable. State particulars respecting each. 
 
 279. What is said of the magnitude and brightness of com- 
 ets ? What \vas the length of the comet of 1680 ? Ditto of 
 1811 ? Has the same comet different aspects at different re- 
 turns ? Example in Halley's comet. 
 
 19* 
 
222 COMETS. 
 
 it was visible only to the telescope, until after it had pas- 
 sed the perihelion. At its recent return in 1835, the 
 greatest length of the tail was about 12. These changes 
 in the appearances of the same comet, are partly owing 
 to the different positions of the earth wifh respect to 
 them, being sometimes much nearer to them when they 
 cross its track than at others ; also one spectator so situ- 
 ated as to see the coma at a higher angle of elevation or 
 in a purer sky than another, will see the train longer than 
 it appears to another less favorably situated ; but the 
 extent of the changes are such as indicate also a real 
 change in magnitude and brightness. 
 
 280. The periods of comets in their revolutions 
 around the sun, are equally various. Encke's comet, 
 which has the shortest known period, completes its rev- 
 olution in 3^ years, or more accurately, in 1208 days ; 
 while that of 1811 is estimated to have a period of 3383 
 years. 
 
 281. The distances to which different comets recede 
 from the sun, are also very various. While Encke's 
 comet performs its entire revolution within the orbit of 
 Jupiter, Halley's comet recedes from the sun to twice 
 the distance of Uranus, or nearly 3600,000,000 miles. 
 Some comets, indeed, are thought to go to a much 
 greater distance from the sun than this, while some even 
 are supposed to pass into parabolic or hyperbolic orbits, 
 and never to return. 
 
 282. Comets shine by reflecting the light of the sun. 
 In one or two instances they have exhibited distinct 
 phases, although the nebulous matter with which the 
 nucleus is surrounded, would commonly prevent such 
 
 280. How arc the periods of comets ? What is that of 
 Encke's comet, and that of the comet of 1811 ? 
 
 281. How are the distances of comets from the sun ? Coin- 
 pare Encke's and Halley's. Do comets always return to the sun ? 
 
COMETS. 223 
 
 phases from being distinctly visible, even when they 
 would otherwise be apparant. Moreover, certain quali- 
 ties of polarized light enable the optician to decide 
 whether the light of a given body is direct or reflected ; 
 and M. Arago, of Paris, by experiments of this kind on 
 the light of the comet of 1819, ascertained it to be re- 
 flected light. 
 
 283. The tail of a comet usually increases very much 
 as it approaches the sun ; and it frequently does not reach 
 its maximum until after the perihelion passage. In re- 
 ceding from the sun, the tail again contracts, and nearly 
 or quite disappears before the body of the comet is en- 
 tirely out of sight. The tail is frequently divided into 
 two portions, the central parts, in the direction of the 
 axis, being less bright than the marginal parts. In 
 1744, a comet appeared which had six tails, spread out 
 like a fan. 
 
 The tails of comets extend in a direct line from the 
 sun, although more or less curved, like a I >ng quill or 
 feather, being convex on the side next to the direction 
 in which they are moving a figure which may result 
 from the less velocity of the portions most remote from 
 the sun. Expansions of the Envelope have also been 
 at times observed on the side next the sun, but these 
 seldom attain any considerable length. 
 
 284. The quantity of matter in comets is exceedingly 
 small. Their tails consist of matter of such tenuity that 
 the smallest stars are visible through them. They can 
 only be regarded as great masses of thin vapor, suscepti- 
 ble of being penetrated through their whole substance by 
 
 282. Do comets shine by direct or by reflected light ? Do 
 they exhibit phases ? How is it known that their light is re- 
 flected and not direct light ? 
 
 283. How are the tails of comets affected by being near the 
 sun ? How many tails have some comets ? In what direction 
 is the tail in respect to the snn ? 
 
224 COMETS. 
 
 the sunbeams, and reflecting them alike from their inte- 
 rior parts and from their surfaces. It appears, perhaps, 
 incredible that so thin a substance should be visible by 
 reflected light, and some astronomers have held that the 
 matter of comets is self-luminous ; but it requires but 
 very little light to render an object visible in the night, 
 and a light vapor may be visible when illuminated 
 throughout an immense stratum, which could not be 
 seen if spread over the face of the sky like a thin cloud. 
 From the extremely small quantity of matter of these 
 bodies, compared with the vast spaces they cover, New- 
 ton calculated that if all the matter constituting the 
 largest tail of a comet, were to be compressed to the 
 same density with atmospheric air, it would occupy no 
 more than a cubic inch. This is incredible, but still 
 the highest clouds that float in our atmosphere, must be 
 looked upon as dense and massive bodies, compared with 
 the filmy and all but spiritual texture of a comet. 
 
 285. The small quantity of matter in comets is proved 
 by the fact, that they have sometimes passed very near 
 to some of the planets without disturbing their motions 
 in any appreciable degree. Thus the comet of 1770, in 
 its way to the sun, got entangled among the satellites of 
 Jupiter, and remained near them four months, yet it did 
 not perceptibly change their motions. The same comet 
 also came veiy near the earth ; so near, that, had its 
 mass been equal to that of the earth, it would have 
 caused the earth to revolve in an orbit so much larger 
 than at present, as to have increased the length of the 
 year, 2h. 47rn. Yet it produced no sensible effect on 
 the length of the year, and therefore its mass, as is shown 
 by La Place, "could not have exceeded y^V? of that of 
 the earth, and might have been less than this to any ex- 
 
 284. How is the quantity of matter in comets ? Of what do 
 the tails consist ? Can a substance so thin shine by reflected 
 light ? What opinion had Newton of the extreme tenuity of 
 the material of comets' tails ? 
 
COMETS. 225 
 
 tent. It may indeed be asked, what proof we nave that 
 comets have any matter, and are not mere reflections of 
 light. The answer is, that, although they are not able 
 by their own force of attraction to disturb the motions 
 of the planets, yet they are themselves exceedingly dis- 
 turbed by the action of the planets, and in exact con- 
 formity with the laws of universal gravitation. A deli- 
 cate compass may be greatly agitated by the vicinity of 
 a mass of iron, while the iron is not sensibly affected by 
 the attraction of the needle. 
 
 286. By approaching very near to a large planet, a 
 comet may have its orbit entirely changed. This fact 
 is strikingly exemplified in the history of the comet of 
 1770. At its appearance in 1770, its orbit was found to 
 be an ellipse, requiring for a complete revolution only 
 5| years ; and the wonder was, that it had not been seen 
 before, since it was a very large and bright comet. As- 
 tronomers suspected that its path had been changed, and 
 that it had been recently compelled to move in this short 
 ellipse, by the disturbing force of Jupiter and his satel- 
 lites. The French Institute, therefore, offered a high 
 prize for the most complete investigation of the elements 
 of this comet, taking into account any circumstances 
 which could possibly have produced an alteration in its 
 course. By tracing back the movements of this comet 
 for some years previous to 1770, it was found that, at 
 the beginning of 1767, it had entered considerably within 
 the sphere of Jupiter's attraction. Calculating the amount 
 of this attraction from the known proximity of the two 
 bodies, it was found what must have been its orbit pre- 
 vious to the time when it became subject to the disturb- 
 ing action of Jupiter. The result showed that it then 
 
 285. How is the small quantity of matter in comets proved 
 How was this indicated by the comet of 1770 ? What did its 
 quantity of matter not exceed as compared with the earth's ? 
 May we not infer that they have no matter ? 
 
226 COMETS. 
 
 moved in an ellipse of greater extent, having a period of 
 50 years, and having its perihelion instead of its aphelion 
 near Jupiter. It was therefore evident why, as long as 
 it continued to circulate in an orbit so far from the cen- 
 ter of the system, it was never visible from the earth. 
 In January 1767, Jupiter and the comet happened to be 
 very near one another, and as both were moving in the 
 same direction, and nearly in the same plane, they re- 
 mained in the neighborhood of each other for several 
 months, the planet being between the comet and the 
 sun. The consequence was, that the comet's orbit was 
 changed into a, smaller ellipse, in which its revolution 
 was accomplished in 5 years. But as it was approach- 
 ing the sun in 1779, it happened again to fall in with 
 Jupiter. It was in the month of June, that the attrac- 
 tion of the planet began to have a sensible effect ; and 
 it was not until the month of October following, that 
 they were finally separated. 
 
 At the time of their nearest approach, in August, Ju- 
 piter was distant from the comet only T T of its distance 
 from the sun, and exerted an attraction upon it 225 
 times greater than that of the sun. By reason of this 
 powerful attraction, Jupiter being farther from the sun 
 than the comet, the latter was drawn out into a new or- 
 bit, which even at its perihelion came no nearer to the 
 sun than the planet Ceres. In this third orbit, the comet 
 requires about 20 years to accomplish its revolution; 
 and being at so great a distance from the earth, it is in- 
 visible, and will forever remain so, unless, in the course 
 of ages, it may undergo new perturbations, and move 
 again in some smaller orbit as before. 
 
 286. How may a comet have its orbit changed ? How was 
 the orbit of the comet of 1770 changed? How was this fact as- 
 certained ? What action did Jupiter exert upon it in 1 767, and 
 again in 1779 ? How far was Jupiter from the comet at -the 
 time of their nearest approach 1 How many years does it now 
 require to perform its revolution ? 
 
ORBITS AND MOTIONS OF COMETS. 227 
 
 ORBITS AND MOTIONS OP COMETS. 
 
 287. The planets, as we have seen, (with the excep- 
 tion of the four new ones, which seem to be an interme- 
 diate class of bodies between planets and comets,) move 
 in orbits which are nearly circular, and all very near to 
 the plane of the ecliptic, and all move in the same direc- 
 tion from west to east. But the orbits of comets are far 
 more eccentric than those of the planets ; they are in- 
 clined to the ecliptic at various angles, being sometimes 
 even nearly perpendicular to it ; and the motions of 
 comets are sometimes retrograde. 
 
 288. The Elements of a comet are five, viz. (1) The 
 perihelion distance ; (2) longitude of the perihelion ; (3) 
 longitude of the node ; (4) inclination of the orbit ; (5) 
 time of the perihelion passage. 
 
 The investigation of these elements is a problem ex- 
 tremely intricate, requiring for its solution, a skilful and 
 laborious application of the most refined analysis. This 
 difficulty arises from several circumstances peculiar to 
 comets. In the first place, from the elongated form of 
 the orbits which these bodies describe, it is during only 
 a very small portion of their course, that they are visible 
 from the earth, and the observations made in that short 
 period, cannot afterwards be verified on more convenient 
 occasions ; whereas in the case of the planets, whose or- 
 bits are nearly circular, and whose movements may be 
 followed uninterruptedly throughout a complete revolu- 
 tion, no such impediments to the determination of their 
 orbits occur. In the second place, there are many com- 
 ets which move in a direction opposite to the order of 
 the signs in the zodiac, and sometimes nearly perpen- 
 dicular to the plane of the ecliptic ; so that their appa- 
 
 287. How do the orbits of comets differ from those of planets ? 
 
 288. What particulars are called the elements of a comet ? 
 What is said of the difficulty of determining these elements ? 
 Specify the several reasons of this difficulty. 
 
COMETS. 
 
 rent course through the heavens is rendered extremely 
 complicated, on account of the contrary motion of the 
 earth. In the third place, as there may be a multitude 
 of elliptic orbits, whose perihelion distances are equal, 
 (see p. 100,) it is obvious that, in the case of very ec- 
 centric orbits, the slightest change in the position of the 
 curve near the vertex, where alone the comet can be ob- 
 served, must occasion a very sensible difference in the 
 length of the orbit ; and therefore, though a small error 
 produces no perceptible discrepancy between the ob- 
 served and the calculated course, while the comet re- 
 mains visible from the earth, its effect when diffused 
 over the whole extent of the orbit, may acquire a most 
 material or even a fatal importance. 
 
 289. On account of these circumstances, it is found 
 exceedingly difficult to lay down the path which a comet 
 actually follows through the whole system, and least of 
 all, possible to ascertain with accuracy, the length of the 
 major axis of the ellipse, and consequently the periodical 
 revolution.* An error of only a few seconds may cause 
 a difference of many hundred years. In this manner, 
 though Bessel determined the revolution of the comet of 
 1769 to be 2089 years, it was found that an error of no 
 more than 5" in observation, would alter the period either 
 to 2678 years, or to 1692. Some astronomers, in calcula- 
 ting the orbit of the great comet of 1680, have found the 
 length of its greater axis 426 times the earth's distance 
 from the sun, and consequently its period 8792 years ; 
 whilst others estimate the greater axis 430 times the 
 earth's distance, which alters the period to 8916 years. - 
 
 289. Is it easy to ascertain the major axis of a comet's orbit, 
 and its periodic time ? What difference would an error of a few 
 seconds occasion ? Give examples of this. 
 
 * For when we know the length of the major axis, we can find tht 
 periodic time by Kepler's law, which applies as well to comets as t 
 planets. 
 
[OTIONS AND ORBITS OF COMETS. 
 
 229 
 
 Newton and Halley, however, judged that this comet 
 accomplished its revolution in only 570 years. 
 
 290. The appearances of the same comet at different 
 periods of its return are so various, that we can never 
 pronounce a given comet to be the same with one that 
 has appeared before, from any peculiarities in its physi- 
 cal aspect. The identity of a comet with one already 
 on record, is determined by the identity of the elements. 
 It was by this means that Halley first established the 
 identity of the comet which bears his name, with one 
 that had appeared at several preceding ages of the world, 
 of which so many particulars were left on record, as to 
 enable him to calculate the elements at each period. 
 These were as in the following table. 
 
 Time ot appear. 
 
 Inclin. of the orbit. 
 
 Lon. of Node. 
 
 Lon. of Per. 
 
 Per. Dist. 
 
 Course. 
 
 1456 
 1531 
 1607 
 
 1682 
 
 17 56' 
 17 56 
 17 02 
 17 42 
 
 48 30' 
 49 25 
 50 21 
 
 50 48 
 
 30i 00 
 301 38 
 302 16 
 301 36 
 
 0.58 
 0.57 
 0.58 
 0.58 
 
 Retrograde 
 
 M 
 
 (( 
 
 On comparing these elements, no doubt could be en- 
 tertained that they belonged to one and the same body ; 
 and since the interval between the successive returns 
 was seen to be 75 or 76 years, Halley ventured to pre- 
 dict that it would again return in 1758. Accordingly, 
 the astronomers who lived at that period, looked for its 
 return with the greatest interest. It was found, how- 
 ever, that on its way towards the sun it would pass very 
 near to Jupiter and Saturn, and by their action on it, it 
 would be retarded for a long time. Clairaut, a distin- 
 guished French mathematician, undertook the laborious 
 task of estimating the exact amount of this retardation, 
 and found it to be no less than 618 days, namely, 100 
 
 290. Can we identify a comet with one that has been seen 
 before, by its appearance ? How is this identity determined ? 
 How was Halley's comet proved to be the same with one that 
 had appeared before ? How was its return predicted ? What 
 causes alter the periods of its return ? 
 
 20 
 
280 COMETS. 
 
 days by the action of Jupiter, and 518 days by that of 
 Saturn, This would delay its appearance until early in 
 the year 1759, and Clairaut fixed its arrival at the peri- 
 helion within a month of April 13th. It came to the 
 perihelion on the 12th of March. 
 
 291. The return of Halley's comet in 1835, was 
 looked for with no less interest than in 1759. Several 
 of the most accurate mathematicians of that age had cal- 
 culated its elements with inconceivable labor. Their 
 zeal was rewarded by the appearance of the expected 
 visitant at the time and place assigned ; it travelled the 
 northern sky presenting the very appearances, in most 
 respects, that had been anticipated ; and came to its pe- 
 rihelion on the 16th of November, within two days of 
 the time predicted by Pontecoulant, a French mathe- 
 matician who had, it appeared, made the most success- 
 ful calculation.* On its previous return, it was deemed 
 an extraordinary achievement to have brought the pre- 
 diction within a month of the actual time. 
 
 Many circumstances conspired to render this return of 
 Bailey's comet an astronomical event of transcendent 
 interest. Of all the celestial bodies', its history was the 
 most remarkable ; it afforded most triumphant evidence 
 of the truth of the doctrine of universal gravitation, and 
 of course of the received laws of astronomy ; and it in- 
 spired new confidence in the power of that instrument, 
 (the Calculus,) by means of which its elements had been 
 investigated. 
 
 292. Encke's comet, by its frequent returns, (once in 
 3 years,) affords peculiar facilities for ascertaining the 
 
 291 How was the return of Halley's comet in 1835 re- 
 garded by astronomers ? What circumstances conspired to 
 produce this feeling ? 
 
 * See Professor Loomis's Observations on Halley's Comet. Amer. 
 Jour. Science, 30, 209. 
 
ORBITS AND MOTIONS OF COMETS. 231 
 
 laws of its revolution ; and it has kept the appointments 
 made for it with great exactness. On its late return 
 (1839) it exhibited to the telescope a globular mass of 
 nebulous matter, resembling fog, and moved towards its 
 perihelion with great rapidity. 
 
 But what has made. Encke's comet particularly fa- 
 mous, is its having first revealed to us the existence of a 
 Resisting Medium in the planetary spaces. It has long 
 been a question, whether the earth and planets revolve 
 in a perfect void, or whether a fluid of extreme rarity 
 may not be diffused through space. A perfect vacuum 
 was deemed most probable, because no such effects on 
 the motions of the planets could be detected as indicated 
 that they encountered a resisting medium. But a feather 
 or a lock of cotton propelled with great velocity, might 
 render obvious the resistance of a medium which would 
 not be perceptible in the motions of a cannon ball. Ac- 
 cordingly, Encke's comet is thought to have plainly suf- 
 fered a retardation from encountering a resisting medium 
 in the planetary regions. The effect of this resistance, 
 from the first discovery of the comet to the present time, 
 has been to diminish the time of its revolution about 
 two days. Such a resistance by destroying a part of the 
 projectile force, would cause the comet to approach 
 nearer to the sun, and thus to have its periodic time 
 shortened. The ultimate effect of this cause will be to 
 bring the comet nearer to the sun at every revolution, 
 until it finally falls into that luminary, although many 
 thousand years will be required to produce this catas- 
 trophe. It is conceivable, indeed, that the effects of 
 such a resistance may be counteracted by the attraction 
 of one or more of the planets, near which it may pass in 
 its successive returns to the sun. 
 
 292. Are the elements of Encke's comet calculated with ex- 
 actness 1 What was its appearance in 1839 ? What has made 
 it peculiarly famous ? Why should it be so favorable for detec- 
 ting a resisting medium ? What has been its effect on the 
 motions of the comet ? What will be its ultimate effect ? 
 
232 COMETS. 
 
 293. It is peculiarly interesting to see a portion of 
 matter, of a tenuity exceeding the thinnest fog, pursuing 
 its path in space, in obedience to the same laws as those 
 which regulate such large and heavy bodies as Jupiter 
 or Saturn. In a perfect void, a speck of fog if propelled 
 by a suitable projectile force, would revolve around the 
 sun, and hold on its way through the widest orbit, with 
 as sure and steady a pace as the heaviest and largest 
 bodies in the system. 
 
 294. Of the physical nature of comets, little is under- 
 stood. It is usual to account for the variations which 
 their tails undergo, by referring them to the agencies of 
 heat and cold. The intense heat to which they are 
 subject in approaching so near the sun as some of them 
 do, is alleged as a sufficient reason for the great expan- 
 sion of thin nebulous atmospheres forming their tails ; 
 and the inconceivable cold to which they are subject in 
 receding to such a distance from the sun, is supposed to 
 account for the condensation of the same matter until it 
 returns to its original dimensions. Thus the great comet 
 of 1680, at its perihelion, approached 166 times nearer 
 the sun than the earth, being only 130,000 miles from 
 the surface of the sun. The heat which it must have 
 received, was estimated to be equal to 28,000 times that 
 which the earth receives in the same time, and 2000 
 times hotter than red hot iron. This temperature would 
 be sufficient to volatilize the most obdurate substances, 
 and to expand- the vapor to vast dimensions ; and the op- 
 posite effects of the extreme cold to which it would be 
 
 293. Does the extreme tenuity of this body prevent its mov- 
 ing in obedience to the laws that regulate the motions of the 
 largest bodies in the system ? 
 
 294. Is the physical nature of comets well understood ? How 
 are the variations in the lengths of their tails accounted for ? 
 How near did the comet of 1680 approach to the sun ? What 
 heat did it acquire ? Does this account for the direction of tho 
 tail ? How is that accounted for by some writers ? 
 
ORBITS AND MOTIONS OF COMETS. 233 
 
 subject in the regions remote from the sun, would be ad- 
 equate to condense it into its former volume. 
 
 This explanation, however, does not account for the 
 direction of the tail, extending as it usually does, only 
 in a line opposite to the sun. Some writers therefore, 
 as Delambre, suppose that 'the nebulous matter of the 
 comet after being expanded to such a volume, that the 
 particles are no longer attracted to the nucleus unless by 
 the slightest conceivable force, are carried off* in a direc- 
 tion from the sun, by the impulse of the solar rays them- 
 selves. But to assign such a power of communicating 
 motion to the sun's rays while they have never been 
 proved to have any momentum, is unphilosophical ; and 
 we are compelled to place the phenomena of comets' 
 tails among the points of astronomy yet to be explained. 
 
 295. Since those comets which have their perihelion 
 very near the sun, like the comet of 1680, cross the or- 
 bits of all the planets, the possibility that one of them 
 may strike the earth, has frequently been suggested. 
 Still it may quiet our apprehensions on this subject, to 
 reflect on the vast extent of the planetary spaces, in 
 which these bodies are not crowded together as we see 
 them erroneously represented in orreries and diagrams, 
 but are sparsely scattered at immense distances from 
 each other. They are like insects flying in the expanse 
 of heaven. If a comet's tail lay with its axis in the 
 plane of the ecliptic when it was near the sun, we can 
 imagine that the tail might sweep over the earth ; but 
 the tail may be situated at any angle with the ecliptic 
 as well as in the same plane with it, and the chances 
 
 295. What is said respecting the possibility of a comet's stri- 
 king the earth ? What considerations may quiet our apprehen- 
 sions ? How might the case be if the tail lay in the plane of 
 the ecliptic ? Is it probable that a comet will cross the ecliptic 
 precisely a^ the place of the earth's path ? Have comets ac- 
 tually approached near to the earth ? What would be the con- 
 sequences were a comet to strike the earth ? 
 
284 COMETS. 
 
 that it will not be in the same plane, are almost infinite. 
 It is also extremely improbable that a comet will cross 
 the plane of the ecliptic precisely at the earth's path in 
 that plane, since it may as probably cross it at any other 
 point, nearer or more remote from the sun. Still some 
 comets have occasionally approached near to the earth. 
 Thus Biela's comet in returning to the sun in 1832, 
 crossed the ecliptic very near to the earth's track, and 
 had the earth been then at that point of its orbit, it might 
 have passed through a portion of the nebulous atmos- 
 phere of the comet. The earth was within a month of 
 reaching that point. This might at first view seem to 
 involve some nazard ; yet we must consider that a 
 month short, implied a distance of nearly 50,000,000 
 miles. La Place has assigned the consequences that 
 would ensue in case of a direct collision between the 
 earth and a comet ; but terrible as he has represented 
 them on the supposition that the nucleus of the comet 
 is a solid body, yet considering a comet (as most of them 
 doubtless are) as a mass of exceedingly light nebulous 
 matter, it is not probable, even were the earth to make 
 its way directly through a comet, that a particle of the 
 comet would reach the earth. The portions encountered 
 by the earth, would be arrested by the atmosphere, and 
 probably inflamed ; and they would perhaps exhibit, on 
 a more magnificent scale than was ever before observed, 
 the phenomena of shooting stars, or meteoric showers. 
 
PART III. OF THE FIXED STARS AND THE SYS- 
 TEM OF THE WORLD. 
 
 CHAPTER I. 
 
 OF THE FIXED STARS CONSTELLATIONS. 
 
 296. THE FIXED STARS are so called, because, to 
 common observation, they always maintain the same 
 situations with respect to one another. 
 
 The stars are classed by their apparent magnitudes. 
 The whole number of magnitudes recorded are sixteen, 
 of which the first six only are visible to the naked eye ; 
 the rest are telescopic stars. These magnitudes are not 
 determined by any very definite scale, but are merely 
 ranked according to their relative degrees of brightness, 
 and this is left in a great measure to the decision of the 
 eye alone. The brightest stars to the number of 15 or 
 20, are considered as stars of the first magnitude ; the 50 
 or 60 next brightest, of the second magnitude ; the next 
 200 of the third magnitude ; and thus the number of 
 each class increases rapidly as we descend the scale, so 
 that no less than fifteen or twenty thousand are included 
 within the first seven magnitudes. 
 
 297. The stars have been grouped in Constellations 
 from the most remote antiquity ; a few, as Orion, Bootes, 
 and Ursa Major, are mentioned in the most ancient wri- 
 tings under the same names as they bear at present. 
 The names of the constellations are sometimes founded 
 
 296. Fixed Stars. Why so called ? How classed ? Into 
 how many magnitudes are they divided ? How many are there 
 of each magnitude ? 
 
236 FIXED STARS. 
 
 on a supposed resemblance to the objects to which the 
 names belong ; as the Swan and the Scorpion were evi- 
 dently so denominated from their likeness to those ani- 
 mals ; but in most cases it is impossible for us to find 
 any reason for designating a constellation by the figure 
 of the animal or the hero which is employed to repre- 
 sent it. These representations were probably once 
 blended with the fables of pagan mythology. The 
 same figures, absurd as they appear, are still retained for 
 the convenience of reference ; since it is easy to find 
 any particular star, by specifying the part of the figure 
 to which it belongs, as when we say a star is in the neck 
 of Taurus, in the knee of Hercules, or in the tail of the 
 Great Bear. This method furnishes a general clue to 
 its position ; but the stars belonging to any constellation 
 are distinguished according to their apparent magnitudes 
 as follows : first, by the Greek letters, Alpha, Beta, 
 Gamma, &c. Thus Alpha Orionis, denotes the largest 
 star in Orion ; Beta Andromeda, the second star in An- 
 dromeda ; and Gamma Leonis, the third brightest star 
 in the Lion. Where the number of the Greek letters is 
 insufficient to include all the stars in a constellation, 
 recourse is had to the letters of the Roman alphabet, a, 
 b, c, &c. ; and, in cases where these are exhausted, the 
 final resort is to numbers. This is evidently necessary, 
 since the largest constellations contain many hundrerds 
 or even thousands of stars. Catalogues of particular 
 stars have also been published by different astronomers, 
 each author numbering the individual stars embraced in 
 his list, according to the places they respectively occupy 
 in the catalogue. These references to particular cata- 
 logues are sometimes entered on large celestial globes. 
 Thus we meet with a star marked 84 H., meaning that 
 
 297. Constellations. How long known ? Which are men- 
 tioned in the most ancient writings ? How far are the names 
 founded on resemblance ? Why are the ancient figures still 
 retained ? How are the individual stars of a constellation dis- 
 tinguished ? What is said df catalogues of the stars ? 
 
FIXED STARS. 237 
 
 this is its number in Herschel's catalogue ; or 140 M., de- 
 noting the place the star occupies in the catalogue of 
 Mayer. 
 
 298. The earliest catalogue of the stars was made by 
 Hipparchus of the Alexandrian school, about 140 years 
 before the Christian era. A new star appearing in the 
 firmament, he was induced to count the stars and to re- 
 cord their positions, in order that posterity might be able 
 to judge of the permanency of the constellations. His 
 catalogue contains all that were conspicuous to the 
 naked eye in the latitude of Alexandria, being 1022. 
 Most persons unacquainted with the actual number of 
 the stars which compose the visible firmament, would 
 suppose it to be much greater than this ; but it is found 
 that the catalogue of Hipparchus, embraces nearly all 
 that can now be seen in the same latitude, and that on 
 the equator, when the spectator has the northern and 
 southern hemispheres both in view, the number of stars 
 that can be counted does not exceed 3000. A careless 
 view of the firmament in a clear night, gives us the im- 
 pression of an infinite multitude of stSrs ; but when we 
 begin to count them, they appear much more sparsely 
 distributed than we supposed, and large portions of the 
 sky appear almost destitute of stars. 
 
 By the aid of the telescope, new fields of stars present 
 themselves of boundless extent ; the number contin- 
 ually augmenting as the powers of the telescope are in- 
 creased. Lalande, in his Histoire Celeste, has registered 
 the positions of no less than 50,000 ; and the whole 
 number visible in the largest telescopes amounts to many 
 millions. 
 
 299. It is strongly recommended to the learner to ac- 
 quaint himself with the leading constellations at least, 
 
 298. Why did Hipparchus make a catalogue ? How many 
 stars did he number ? What is the greatest number that can 
 be seen by the naked eye in both hemispheres ? How many 
 can be seen by the telescope ? 
 
238 FIXED STARS. 
 
 and with a few of the most remarkable individual stars. 
 The task of learning them is comparatively easy, and 
 hardly any kind of knowledge, attained with so little 
 labor, so amply rewards the possessor. It will generally 
 be advisable, at the outset, to get some one already ac- 
 quainted with the stars, to point out a few of the mo?, 
 conspicuous constellations, those of the Zodiac for ex 
 ample ; the learner may then resort to maps of the stars, 
 or what is much better, to a celestial globe,* and fill up 
 the outline by tracing out the principal $tars in each 
 constellation as there laid down. By adding one new 
 constellation to his list every night, and reviewing those 
 already acquired, he will soon become familiar with the 
 stars, and will greatly augment his interest and improve 
 his intelligence in celestial observations, and practical 
 astronomy. 
 
 CONSTELLATIONS. 
 
 300. We will point out particular marks by which the 
 leading constellations may be recognized, leaving it to 
 the learner, after he has found a constellation, to trace 
 out additional members of it by the aid of the celestial 
 globe, or by maps of the stars. Let us begin with the 
 Constellations of the Zodiac, which succeeding each 
 other as they do in a known order, are most easily 
 found. 
 
 ARIES (The RAM) is a small constellation, known by 
 two bright stars which form his head, Alpha and Beta 
 Arietis. These two stars are four degreesf apart, and 
 directly south of Beta at the distance of one degree, is 
 
 299. Specify the directions for learning the constellations. 
 
 * For the method of rectifying the globe so as to represent the ap- 
 pearance of the heavens on any particular evening, see page 34, Art. 
 61. 
 
 t These measures are not intended to be stated with exactness, but 
 only with such a degree of accuracy as may serve for a general guide. 
 
CONSTELLATIONS. 289 
 
 a smaller star, Gamma Arietis. It has been already 
 intimated (Art. 139) that the vernal equinox probably 
 was near the head of Aries, when the signs of the Zo- 
 diac received their present names. 
 
 TAURUS (The BULL) will be readily found by the 
 seven stars or Pleiades, which lie in his neck. The 
 largest star in Taurus is Aldebaran, in the Bull's eye, a 
 star of the first magnitude, of a reddish color somewhat 
 resembling the planet Mars. Aldebaran and four other 
 stars in the face of Taurus, compose the Hyades. 
 
 GEMINI (The TWINS) is known by two very bright 
 stars, Castor and Pollux, four degrees asunder. Castor 
 (the northern) is of the first, and Pollux of the second 
 magnitude. 
 
 CANCER (The CRAB.) There are no large stars in this 
 constellation, and it is regarded as less remarkable than 
 any other in the Zodiac. It contains however an inter- 
 esting group of small stars, called Prcesepe or the Neb- 
 ula of Cancer, which resembles a comet, and is often 
 mistaken for one, by persons unacquainted with the 
 stars. With a telescope of very moderate powers this 
 nebula is converted into a beautiful assemblage of ex- 
 ceedingly bright stars. 
 
 LEO (The LION) is a very large constellation, and has 
 many interesting members. Regulus (Alpha Leonis) 
 is a star of the first magnitude, which lies directly in the 
 ecliptic, and is much used in astronomical observations. 
 
 300. Constellations of the Zodiac. Aries. How known ? 
 How far are the two brightest stars apart ? Where was the 
 vernal equinox situated when the signs of the Zodiac received 
 their present names ? 
 
 Taurus. How found ? Name the largest star in Taurus. 
 What stars compose the Hyades ? 
 
 Gemini. How known 1 How far are Castor and Pollux 
 asunder ? Of what magnitudes are they respectively ? 
 
 Cancer. Are there any large stars in Cancer ? What is 
 said of Praesepe ? 
 
 Leo. What is its size ? What is said of Regulus ? Where 
 is the sickle ? Where is Denebola situated ? 
 
24 r FIXED STARS. 
 
 North of Regulus lies a semi-circle of bright stars, form- 
 ing a sickle of which Regulus is the handle. Denebola, 
 a star of the second magnitude, is in the Lion's tail, 25 
 north east of Regulus. 
 
 VIRGO (The VIRGIN) extends a considerable way 
 from west to east, but contains only a few bright stars. 
 Spica, however, is a star of the first magnitude, and 
 lies a little east of the place of the autumnal equinox. 
 Twenty-two degrees north of Spica, is Vindemiatrix, in 
 the arm of Virgo, a star of the third magnitude. 
 
 LIBRA (The BALANCE) is distinguished by three large 
 stars, of which the two brightest constitute the beam 
 of the balance, and the smallest forms the top or handle. 
 
 SCORPIO (The SCORPION) is one of the finest of the 
 constellations. His head is formed of five bright stars 
 arranged in the arc of a circle, which is crossed in the 
 center by the ecliptic nearly at right angles, near the 
 brightest of the five, Beta Scorpionis. Nine degrees 
 southeast of this, is a remarkable star of the first mag- 
 nitude, of a reddish color, called Cor Scorpionis, or An- 
 tares. South of this a succession of bright stars sweep 
 round towards the east, terminating in several small 
 stars, forming the tail of the Scorpion. 
 
 SAGITTARIUS (The ARCHER.) Northeast of the tail of 
 the Scorpion, are three stars in the arc of a circle which 
 constitute the bow of the Archer, the central star being 
 the brightest, directly west of which is a bright star 
 which forms the arrow. 
 
 CAPRICORNUS (The GOAT) lies northeast of Sagittarius, 
 and is known by two bright stars, three degrees apart, 
 which form the head. 
 
 Virgo. Extent from east to west ? What is said of Spica, 
 and of Vindemiatrix ? 
 
 Libra. How distinguished ? 
 
 Scorpio. His appearance ? His head how formed ? Where 
 is Antares situated ? 
 
 Sagittarius. Describe his bow. 
 
 Capricornus. Where situated from Sagittarius ? How 
 known ? 
 
CONSTELLATIONS. 241 
 
 AQUARIUS (The WATER BEARER) is recognized by 
 two stars in a line with Alpha Capricorni, forming the 
 shoulders of the figure. These two stars are 10 apart, 
 and 4 southeast is a third star, which, together with the 
 other two, makes an acute triangle, of which the west- 
 ernmost is the vertex. 
 
 PISCES (The FISHES) lie between Aquarius and Aries. 
 They are not distinguished by any large stars, but are 
 connected by a series of small stars, that form a crooked 
 line between them. Piscis Australis, the Southern 
 Fish, lies directly below Aquarius, and is known by a 
 single bright star far in the south, having a declination 
 of 30. The name of this star is Fomalhaut, and it is 
 much used in astronomical measurements. 
 
 301. The Constellations of the Zodiac, being first 
 well learned, so as to be easily recognized, will facil- 
 itate the learning of others that lie north and south of 
 them. Let us therefore next review the principal North- 
 ern Constellations, beginning north of Aries and pro- 
 ceeding from west to east. 
 
 ANDROMEDA, is characterized by three stars of the sec- 
 ond magnitude, situated in a straight line, extending 
 from west to east. The middle star is about 17 north 
 of Beta Arietis. It is in the girdle of Andromeda, and 
 is named Mirach. The other two lie at about equal 
 distances, 14 west and east of Mirach. The western 
 star, in the head of Andromeda, lies in the Equinoctial 
 Colure. The eastern star, Alamak, is situated in the 
 foot. 
 
 PERSEUS lies directly north of the Pleiades, and con- 
 tains several bright stars. About 18 from the Pleiades 
 
 Aquarius. How recognized ? How far apart are the shoul- 
 ders of Aquarius ? 
 
 Pisces. Where situated ? How connected ? Where is 
 Piscis Australis situated ? By what name is it commonly 
 known ? 
 
 301 Northern Constellations. Andromeda, how character- 
 ized ? Where are Mirach and Alamak situated ? 
 
 21 
 
242 FIXED STARS. 
 
 is Algol, a star of the second magnitude in the Head of 
 Medusa, which forms a part of the figure ; and 9 north- 
 east of Algol is Algenib, of the same magnitude in the 
 back of Perseus. Between Algenib and the Pleiades are 
 three bright stars, at nearly equal intervals, which com- 
 pose the right leg of Perseus. 
 
 AURIGA (the WAGONER) lies directly east of Perseus, 
 and extends nearly parallel to that constellation from 
 north to south. Capella a very white and beautiful 
 star of the first magnitude, distinguishes this constella- 
 tion. The feet of Auriga are near the Bull's Horns. 
 
 The LYNX comes next, but presents nothing particu- 
 larly interesting, containing no stars above the fourth 
 magnitude. 
 
 LEO MINOR consists of a collection of small stars 
 north of the sickle in Leo, and south of the Great Bear. 
 Its largest star is only of the third magnitude. 
 
 COMA BERENICES is a cluster of small stars, north of 
 Denebola, (a star in the tail of the Lion,) and of the head of 
 Virgo. About 12 north of Berenice's Hair, is a single 
 bright star called Cor Caroli, or Charles's Heart. 
 
 BOOTES, which comes next, is easily found by means 
 of Arcturus, a star of the first magnitude, of a reddish 
 color, which is situated near the knee of the figure. 
 Arcturus is accompanied by three small stars forming a 
 triangle a little to the southwest. Two bright stars 
 Gamma and Delta Bootis, form the shoulders, and 
 Beta of the third magnitude is in the head of the 
 figure. 
 
 CORONA BOREALIS, (The CROWN>) which is situated east 
 
 Perseus. How situated with respect to the Pleiades ? 
 Where is Algol ? Where is Algenib 1 What stars compose 
 the right leg of Perseus ? 
 
 Auriga. How situated from Perseus ? What large star dis- 
 tinguishes this constellation ? Where are the feet of Auriga ? 
 
 Lynx. Size of its stars ? 
 
 Leo Minor. Where situated ? Size of its largest star ? 
 
 Coma Berenices. Describe it. Where is Cor Caroli ? 
 
 Bootes. What large star is in this constellation ? 
 
UNIVERSITY 
 
 OF 
 
 t Q Kl\ ^ 
 
 of Bootes, is very easily recognized, composed as it is of 
 a semi-circle of bright stars. In the center of the bright 
 crown, is a star of the second magnitude, called Gem- 
 ma ; the remaining stars are all much smaller. 
 
 HERCULES, lying between the Crown on the west and 
 the Lyre on the east, is very thick set with stars, most 
 of which are quite small. The Constellation covers a 
 great extent of the sky, especially from N. to S., the 
 head terminating within 15 of the equator, and marked 
 by a star of the third magnitude, called Ras Algethi, 
 which is the largest in the Constellation. 
 
 OPHIUCUS js situated directly south of Hercules, ex- 
 tending some distance on both sides of the equator, the 
 feet resting on the Scorpion. The head terminates near 
 the head of Hercules, and like that, is marked by a 
 bright star within 5 of Alpha Herculis. Ophiucus is 
 represented as holding in his hands the SERPENT, the 
 head of which, consisting of three bright stars, is sit- 
 uated a little south of the Crown. The folds of the 
 serpent will be easily followed by a succession of bright 
 stars which extend a great way to the east. 
 
 AQTJILA (The EAGLE) is conspicuous for three bright 
 stars in its neck, of which the central one, Altair, is a 
 very brilliant white star of the first magnitude. Anti- 
 nous lies directly south of the Eagle, and north of the 
 head of Capricornus. 
 
 DELPHINUS (The DOLPHIN) is a small but beautiful 
 Constellation, a few degrees east of the Eagle, and is 
 characterized by four bright stars near to one another, 
 forming a small rhombic square. Another star of the 
 same magnitude 5 south, makes the tail. 
 
 Corona Borealis. Describe it. Where is Gemma situated ? 
 
 Hercules. Between what two constellations is it ? What 
 is said of its extent ? Where is Ras Algethi ? 
 
 Ophiucus. Where is it from Hercules ? How is it repre- 
 sented ? 
 
 Aquila. How distinguished ? Where is Altair 1 Where is 
 Ajitinous ? 
 
 The Dolphin- Describe it. 
 
244 FIXED STARS, 
 
 PEGASUS lies between Aquarius on the southwest arid 
 Andromeda on the northeast. It contains but few large 
 stars. A very regular square of bright stars is composed 
 of Alpha Andromeda, and the three largest stars in Pe- 
 gasus, namely, Sckeat, Markab, and Algenib. The 
 sides composing this square are each about 15. Alge- 
 nib is situated in the Equinoctial Colure. 
 
 302. We may now review the Constellations which 
 surround the North Pole, within the circle of perpetual 
 apparition. (Art. 38.) 
 
 URSA MINOR (The LITTLE BEAR) lies nearest the 
 pole. The Pole-star, Polaris, is in the extremity of the 
 tail, and is of the third magnitude. Three stars in a 
 straight line 4 or 5 apart, commencing with the Pole- 
 star, lead to a trapezium of four stars, and the whole 
 seven form together a dipper, the trapezium being the 
 body, and the three stars the handle. 
 
 URSA MAJOR (The GREAT BEAR) is situated between 
 the pole and the Lesser Lion, and is usually recognized 
 by the figure of a larger and more perfect dipper, which 
 constitutes the hinder part of the animal. This has also 
 seven stars, four in the body of the dipper, and three in 
 the handle. All these are stars of much celebrity The 
 two in the western SKJ of the dipper, Alpha and Beta, are 
 called Pointers, on account of their always being in a 
 right line with the Pole-star, and therefore affording an 
 easy mode of finding that. The first star in the tail, next 
 the body, is named Alioth, and the second Mizar. The 
 head of the Great Bear lies far to the westward of the 
 
 Pegasus. Between what two constellations is it situated? 
 How may a square be formed of certain stars in this constel- 
 lation ? 
 
 302. Northern Constellations. Ursa Minor. How situated 
 with respect to the pole ? Show how the dipper in this con- 
 stellation is formed ? 
 
 Ursa. Major. Where situated ? How recognized ? What 
 are the Pointers ? Where is Alioth Mizar ? Of what is the 
 head composed ? 
 
CONSTELLATIONS. 24 
 
 Pointers, and is composed of numerous small stars ; and 
 the feet are severally composed of two small stars very 
 near to each other. 
 
 DRACO (The DRAGON) winds round between the Great 
 and the Little Bear ; and commencing with the tail, be- 
 tween the Pointers and the Pole-star, it is easily traced 
 by a succession of bright stars extending from west to 
 east, passing under Ursa Minor, it returns westward, and 
 terminates in a triangle which forms the head of Draco, 
 near the feet of Hercules, northwest of Lyra. 
 
 CEPHEUS lies eastward of the breast of the Dragon, 
 but has no stars above the third magnitude. 
 
 CASSIOPEIA is known by the figure of a chair, com- 
 posed of four stars which form the legs, and two which 
 form the back. This constellation lies between Perseus 
 and Cepheus, in the Milky Way. 
 
 CYGNUS (The SWAN) is situated also in the Milky Way, 
 some distance southwest of Cassiopeia, towards the Ea- 
 
 f 1 5. Three bright stars, which lie along the Milky 
 ay, form the body and neck of the Swan, and two 
 others in a line with the middle one of the three, one 
 above and one below, constitute the wings. This Con- 
 stellation is among the few, that exhibit some resem- 
 blance to the animals whose names they bear. 
 
 LYRA (The LYRE) is directly west of the Swan, and 
 is easily distinguished by a beautiful white star of the 
 first magnitude, Alpha Lyrce. 
 
 303. The Southern Constellations are comparatively 
 few in number. We shall notice only the Whale, Orion, 
 the Greater and Lesser Dog, Hydra, and the Crow. 
 
 Draco. How situated with respect to the two Bears ? 
 Trace its course ? 
 
 Cepheus. How situated from Draco ? 
 
 Cassiopeia. How known ? Where situated ? 
 
 Cygnus. How situated 1 Of what stars formed ? Has this 
 constellation any resemblance to a Swan ? 
 
 303. Southern Constellations. Cetus. Its extent ? Size 
 of its stars ? What is said of Menkar, and of Mira ? 
 21* 
 
246 FIXED STARS. 
 
 CETUS (The WHALE) is distinguished rather for its 
 extent than its brilliancy, reaching as it does through 
 40 of longitude, while none of its stars except one, 
 are above the third magnitude. Menkar (Alpha Ceti) 
 in the mouth, is a star of the second magnitude, and 
 several other bright stars directly south of Aries, make 
 the head and neck of the Whale. Mira (Omicron 
 Ceti) in the neck of the Whale is a variable star. 
 
 ORION is one of the largest and most beautiful of the 
 constellations, lying southeast of Taurus. A cluster of 
 small stars form the head ; two large stars, Betalgeus of 
 the first and Bellatrix of the second magnitude, make 
 the shoulders ; three more bright stars compose the 
 buckler, and three the sword ; and Rigel, another star of 
 the first magnitude, makes one of the feet. In this 
 Constellation there are 70 stars plainly visible to the 
 naked eye, including two of the first magnitude, four of 
 the second, and three of the third. 
 
 CANIS MAJOR lies S. E. of Orion, and is distinguished 
 chiefly by its containing the largest of the fixed stars, 
 Siriug. 
 
 CANIS MINOR a little north of the equator, between 
 Canis Major and Gemini, is a small Constellation, con- 
 sisting chiefly of two stars, of which Procyon is of the 
 first magnitude. 
 
 HYDRA has its head near Procyon, consisting of a 
 number of stars of ordinary brightness. About 17 S. 
 E. of the head, is a star of the second magnitude, form- 
 ing the heart, (Cor Hydrce ;) and eastward of this, is 
 a long succession of stars of the fourth and fifth magni- 
 tudes composing the body and the tail, and reaching a 
 few degrees south of Spica Virginis. 
 
 Orion. What is said of its size and beauty ? Describe its 
 different parts. How many stars does it contain which are 
 visible to the naked eye ? 
 
 Canis Major. Where situated -from Orion ? What large 
 star is in it ? 
 
 Cams Minor. Where situated ? What large star does it 
 contain ? 
 
 Hydra. Trace its course. 
 
CLUSTERS OF STARS. 247 
 
 CORVUS (The CROW) is represented as standing on the 
 tail of Hydra. It consists of small stars, onlv three of 
 which are as large as the third magnitude. 
 
 304. The foregoing brief sketch is designed merely 
 to aid the student in finding the principal constellations 
 and the largest fixed stars. When we have once learned 
 to recognize a constellation by some characteristic marks, 
 we may afterwards fill up the outline by the aid of a 
 celestial globe or a map of the stars. It will be of little 
 avail however, merely to commit this sketch to memory ; 
 but it will be very useful for the student at once to ren- 
 der himself familiar with it, from the actual specimens 
 which every clear evening presents to his view. 
 
 CHAPTER II. 
 
 VF CLUSTERS OF STARS NEBULA VARIABLE STARS 
 
 TEMPORARY STARS DOUBLE STARS. 
 
 305. IN various parts of the firmament are seen large 
 groups or clusters, which, either by the naked eye, or by 
 the aid of the smallest telescope, are perceived to con- 
 sist of a great number of small stars. Such are the 
 Pleiades, Coma Berenices, and Prsesepe or the Bee-hive 
 in Cancer. The Pleiades, or Seven stars, as they are 
 called, in the neck of Taurus, is the most conspicuous 
 cluster. When we look directly at this group, we can. 
 not distinguish more than six stars, but by turning the 
 eye sideways* upon it, we discover that there are many 
 
 Corvus. How represented ? 
 
 305. Clusters. Name a few of the largest. Pleiades, 
 where situated ? How many stars does it contain ? What 
 is said of Coma Berenices, and of the Bee-hive ? 
 
 * Indirect vision is far more delicate than direct. Thus we can see 
 the Zodiacal Light or a Comet's Tail, much more distinctly and better 
 denned, if we fix one eye on a part of the heavens at some distance, and 
 turn the other eye obliquely upon the object. 
 
248 FIXED STARS. 
 
 more. Telescopes show 50 or 60 stars crowded to* 
 gether and apparently insulated from the other parts of 
 the heavens. Coma Berenices has fewer stars, but they 
 are of a larger class than those which compose the Plei- 
 ades. The Bee-hive or Nebula of Cancer as it is called, 
 is one of the finest objects of this kind for a small tel- 
 escope, being by its aid converted into a rich congeries 
 of shining points. The head of Orion affords an exam- 
 ple of another cluster, though less remarkable than the 
 others. 
 
 306. Nebulce are those faint misty appearances which 
 resemble comets, or a small speck of fog. The Galaxy 
 or Milky Way, presents a continued succession of large 
 nebulae. A very remarkable Nebula, visible to the naked 
 eye, is seen in the girdle of Andromeda. No powers of 
 the telescope have been able to resolve this into separate 
 stars. Its dimensions are astonishingly great. In diam- 
 eter it is about 15'. The telescope reveals to us innumer- 
 able objects of this kind. Sir William Herschel has given 
 catalogues of 2000 Nebulae, and has shown that the neb- 
 ulous matter is distributed through the immensity of 
 space in quantities inconveivably great, and in separate 
 parcels of all shapes and sizes, and of all degrees of 
 brightness between a mere milky appearance and the 
 condensed light of a fixed star. Finding that the gra- 
 dations between the two extremes were tolerably regu- 
 lar, he thought it probable that the nebulae form the ma- 
 terials out of which nature elaborates suns and systems ; 
 and he conceived that, in virtue of a central gravitation, 
 each parcel of nebulous matter becomes more and more 
 condensed, and assumes a rounded form. He inferred 
 from the eccentricity of its shape, and the effects of the 
 mutual gravitation of its particles, that it acquires gradu- 
 
 306. Nebula. What are they ? What is said of the nebula 
 in the girdle of Andromeda ? How many nebulae has Sir W. 
 Herschel included in his catalogue 1 What are his ideas re 
 specting nebulae ? 
 
NEKUL.E. 249 
 
 ally a rotary motion ; that the condensation goes on in 
 creasing until the mass acquires consistency and solidity 
 and all the characters of a comet or a planet ; that by a 
 still further process of condensation, the body becomes a 
 real star, self-shining ; and that thus the waste of the ce- 
 lestial bodies, by the perpetual diffusion of their light, is 
 continually compensated and restored by new formations 
 of such bodies, to replenish forever the universe with 
 planets and stars. 
 
 307. These opinions are recited here rather out of re- 
 spect to their notoriety and celebrity, than because we 
 suppose them to be founded on any better evidence than 
 conjecture. The Philosophical Transactions for many 
 years, both before and after the commencement of the 
 present century, abound with both the observations and 
 speculations of Sir William Herschel. The former are 
 deserving of all praise ; the latter of much less confi- 
 dence. Changes, however, are going on in some of the 
 nebulae, which plainly show that they are not, like plan- 
 ets and stars, fixed and permanent creations. Thus the 
 great nebula in the girdle of Andromeda, has very much 
 altered its structure since it first became an object of tele- 
 scopic observation. Many of the nebulae are of a globu- 
 lar form, (Fig. 50,) but frequently they present the ap- 
 pearance of a rapid increase of numbers towards the cen- 
 (Fiff. 50.) (Fig. 51.) 
 
 ter, (Fig. 51,) the anterior boundary being irregular, 
 and the central parts more nearly spherical. 
 
 307. What is said of Herschel's speculations and of his ob- 
 servations 1 What changes occur in the nebulae ? What 
 forms have they ? 
 
250 FIXED STARS. 
 
 308. The nebula in the sword of Orion is particularly 
 celebrated, being very large and of a peculiarly interest- 
 ing appearance. According to Sir John Herschel, its 
 nebulous character is very different from what might be 
 supposed to arise from the assemblage of an immense 
 collection of small stars. It is formed of little flocculent 
 masses like wisps of clouds ; and such wisps seem to 
 adhere to many small stars at its outskirts, and especially 
 to one considerable star which it envelops with a neb- 
 ulous atmosphere of considerable extent and singular 
 figure. 
 
 Descriptions, however, can convey but a very imper- 
 fect idea of this wonderful class of astronomical objects, 
 and we would therefore urge the learner studiously to 
 avail himself of the first opportunity he may have to 
 view them through a large telescope, especially the Neb- 
 ula of Andromeda and of Orion. 
 
 309. Nebulous Stars are such as exhibit a sharp and 
 brilliant star surrounded by a disk or atmosphere of neb- 
 ulous matter. These atmospheres in some cases present 
 a circular, in others an oval figure ; and in some in- 
 stances, the nebula consists of a long, narrow spindle- 
 shaped ray, tapering away at both ends to points. 
 
 Planetary Nebulcs constitute another variety, and are 
 very remarkable objects. They have, as their name 
 imports, exactly the appearance of planets. Whatever 
 may be their nature, they must be of enormous magni- 
 tude. One of them is to be found in the parallel of 
 Gamma Aquarii, and about 5m. preceding that star. Its 
 apparent diameter is about 20 X/ . Another in the Con- 
 stellation Andromeda, presents a visible disk of 12", per- 
 fectly defined and round. Granting these objects to be 
 
 308. Whatsis said of the nebula in the sword of Orion ? 
 Can the nebulae be fully learned from description ? 
 
 309. Nebulous stars-r-what are they? What forms have 
 their atmospheres ? -Planetary nebulas, their appearance ? 
 What apparent diameters have they 1 What is said of their 
 light ? 
 
VARIABLE STARS. 251 
 
 equally distant from us with the stars, their real dimen- 
 sions must be such as, on the lowest computation, would 
 fill the orbit of Uranus. It is no less evident that, if they 
 be solid bodies, of a solar nature, the intrinsic splendor 
 of their surfaces must be almost infinitely inferior to 
 that of the sun. A circular portion of the sun's disk, 
 subtending an angle of 20", would give a light equal to 
 100 full moons ; while the objects in question are hardly, 
 if at all, discernible with the naked eye. 
 
 310. The Galaxy or Milky Way is itself supposed 
 by some to be a nebula of which the sun forms a com- 
 ponent part ; and hence it appears so much greater than 
 other nebulae only in consequence of our situation with 
 respect to it, and its greater proximity to our system. 
 So crowded are the stars in some parts of this zone, that 
 Sir William Herschel, by counting the stars in a single 
 field of his telescope, estimated that 50,000 had passed 
 under his review in a zone two degrees in breadth du- 
 ring a single hour's observation. Notwithstanding the 
 apparent contiguity of the stars which crowd the galaxy, 
 it is certain that their mutual distances must be incon- 
 ceivably great. 
 
 311. VARIABLE STARS are those which undergo a pe- 
 riodical change of brightness. One of the most remark- 
 able is the star Mira in the Whale, (Omicron Ceti.) It 
 appears once in 1 1 months, remains at its greatest bright- 
 ness about a fortnight, being then, on some occasions, 
 equal to a star of the second magnitude. It then de- 
 creases about three months, until it becomes completely 
 invisible, and remains so about five months, when it 
 again becomes visible, and continues increasing during 
 the remaining three months of its period. 
 
 Another very remarkable variable star is Algol (Beta 
 Persei.) It is usually visible as a star of the second magni- 
 
 310. Galaxy or Milky Way what is said respecting it? 
 Give an example of -the multitude of stars in it ? 
 
252 FIXED STAKS. 
 
 tude, and continues such for 2d. 14h. when it suddenly 
 begins to diminish in splendor, and in about 3^ hours is 
 reduced to the fourth magnitude. It then begins again 
 to increase, and in 3^ hours more, is restored to its usual 
 brightness, going through all its changes in less than 
 three days. This remarkable law of variation appears 
 strongly to suggest the revolution round it of some opake 
 body, which, when interposed between us and Algol, 
 cuts off a large portion of its light. It is (says Sir J. 
 Herschel) an indication of a high degree of activity in 
 regions where, but for such evidences, we might con- 
 clude all lifeless. Our sun requires almost nine times 
 this period to perform a revolution on its axis. On the 
 other hand, the periodic time of an opake revolving 
 body, sufficiently large, which would produce a similar 
 temporary obscuration of the sun, seen from a fixed star, 
 would be less than fourteen hours. 
 
 The duration of these periods is extremely various. 
 While that of Beta Persei above mentioned, is less than 
 three days, others are more than a year, and others many 
 years. 
 
 312. TEMPORARY STARS are new stars which have ap- 
 peared suddenly in the firmament, and after a certain in- 
 terval, as suddenly disappeared and returned no more. 
 
 It was the appearance of a new star of this kind 125 
 years before the Christian era, that prompted Hipparchus 
 to draw up a catalogue of the stars, the first on record. 
 Such also was the star which suddenly shone out A. D 
 389, in the Eagle, as bright as Venus, and after remain- 
 ing three weeks disappeared entirely. At other periods, 
 at distant intervals, similar phenomena have presented 
 themselves. Thus the appearance of a star in 1572, 
 was so sudden, that Tycho Brahe returning home one 
 
 311. Variable stars what are they ? What is said of Mira ? 
 Also of Algol ? How are their periods of revolution ? 
 
 312. Temporary stars what are they 7 Give examples. 
 Do they ever return ? Do stars ever disappear ? 
 
DOUBLE STARS. 203 
 
 day was surprized to find a collection of country people 
 gazing at a star which he was sure did not exist half an 
 hour before. It was then as bright as Sirius, and con- 
 tinued to increase until it surpassed Jupiter when bright- 
 est, and was visible at mid-day. In a month it began 
 to diminish, and in three months afterwards it had en- 
 tirely disappeared. 
 
 It has been supposed by some that in a few instances, 
 the same star has returned, constituting one of the peri- 
 odical or variable stars of a long period. 
 
 Moreover, on a careful re-examination of the heavens, 
 and a comparison of catalogues, many stars are now 
 found to be missing. 
 
 313. DOUBLE STARS are those which appear single to 
 the naked eye, but are resolved into two by the tele- 
 scope ; or, if not visible to the naked eye, are seen in the 
 telescope so close together as to be recognized as objects 
 of this class. Sometimes three or more stars are found 
 in this near connexion, constituting triple or multiple 
 stars. Castor, for example, when seen by the naked 
 eye, appears as a single star, but in a telescope even of 
 moderate powers, it is resolved into two stars of between 
 the third and fourth magnitudes, within 5" of each other. 
 These two stars are nearly of equal size, but frequently 
 one is exceedingly small in comparison with the other, 
 resembling a satellite near its primary, although in dis- 
 tance, in light, and in other characteristics, each has all 
 the attributes of a star, and the combination therefore 
 cannot be that of a planet with a satellite. In some in- 
 stances, also, the distance between these objects is much 
 less than 5", and in many cases it is less than \". The 
 extreme closeness, together with the exceeding minute- 
 ness of most of the double stars, requires the best tele- 
 
 313 Double stars what are they? What are multiple 
 stars ? Give an, example of a double star ? How do the two 
 stars sometimes differ ? What is required in order to observe 
 most of the double stars ? 
 
 22 
 
254 FIXED STARS. 
 
 scopes united with the most acute powers of observa- 
 tion. Indeed, certain of these objects are regarded as 
 the severest tests, both of the excellence of the instru- 
 ment and of the skill of the observer. The following 
 diagram represents four double stars, as seen with ap- 
 propriate magnifiers. No. 1. exhibits Epsilon Bootis with 
 a power of 350 ; No. 2, Rigel with a power of 130 ; 
 No. 3, the Pole-star with a power of 100 ; and No. 4, 
 Castor with a power of 300. 
 
 Fig. 52. 
 1 2 3 4 
 
 314. Our knowledge of the double stars almost com- 
 menced with Sir William Herschel, about the year 1780. 
 At the time he began his search for them, he was ac- 
 quainted with only four. Within five years, he discov- 
 ered nearly 700 double stars.* In his memoirs, pub- 
 lished in the Philosophical Transactions, he gave most 
 accurate measurements of the distances between the two 
 stars, and of the angle which a line joining the two, 
 formed with the parallel of declination. These data 
 would enable him, or at least posterity, to judge whether 
 these minute bodies ever change their position with re- 
 spect to each other. 
 
 314. Who began the discovery of double stars ? When did 
 he publish his account of them ? By whom have these re- 
 searches been since prosecuted 1 What two circumstances add 
 a high degree of interest to the phenomena of the double stars ? 
 
 During his life he observed in all, 2400 double stars. 
 
MOTIONS OP THE FIXED STARS. 255 
 
 Since 1821, these researches have been prosecuted 
 with great zeal and industry by Sir James South and 
 Sir John Herschel in England, and by Professor Struve 
 at Dorpat in Russia ; and the whole number of double 
 stars now known, amounts to several thousands. Two 
 circumstances add a high degree of interest to the phe- 
 nomena of the double stars the first is, that a few of 
 them at least are found to have a revolution around 
 each other, and the second, that they are supposed to 
 afford the means of obtaining the parallax of the fixed 
 stars. Of these topics we shall treat in the next chapter. 
 
 CHAPTER III. 
 
 OF THE MOTIONS OF THE FIXED STARS DISTANCES 
 
 NATURE. 
 
 315. IN 1803, Sir William Herschel first determined 
 and announced to the world, that there exist among the 
 stars, separate systems, composed of two stars revolving 
 about each other in regular orbits. These he denomin- 
 ated Binary Stars, to distinguish them from other 
 double stars where no such motion is detected, and 
 whose proximity to each other may possibly arise from 
 casual juxta-position, or from one being in the range of 
 the other. Between fifty and sixty instances of changes 
 to a greater or less amount of the relative position of 
 double stars, are mentioned by Sir William Herschel ; 
 and a few of them had changed their places so much 
 within 25 years, and in such order, as to lead him to the 
 conclusion that they performed revolutions, one around 
 the other, in regular orbits. 
 
 315. Binary^Stars. Who first discovered this class of 
 bodies ? How are they distinguished from ordinary double 
 stars 1 What conclusions did Sir W. Herschel draw respect- 
 ing them ? 
 
'256 
 
 FIXED STARS. 
 
 316. These conclusions have been fully confirmed by 
 later observers, so that it is now considered as fully es- 
 tablished, that there exist among the fixed stars, binary 
 systems, in which two stars perform to each other the 
 office of sun and planet, and that the periods of revolu- 
 tion of more than one such pair have been ascertained 
 with something approaching to exactness. Immersions 
 and emersions of stars behind each other have been ob- 
 served, and real motions among them detected rapid 
 enough to become sensible and measurable in very short 
 intervals of time. The following table exhibits the 
 present state of our knowledge on this subject.* 
 
 Names. 
 
 Period in years. 
 
 Major axis of the orbit. 
 
 Eccentricity. 
 
 >?Corona3, 
 Cancri, 
 Ursse Majoris, 
 70 Ophiuchi 
 Castor, 
 ffCoronae, 
 61 Cygni, 
 yVirginis, 
 vLeonis. 
 
 43.40 
 55.00 
 58.26 
 80.34 
 252.66 
 286.00 
 452.00 
 628.90 
 1200.00 
 
 
 
 
 
 7 X/ .714 
 8.784 
 16.172 
 7.358 
 30.860 
 24.000 
 
 0.4164 
 0.4667 
 
 0.7582 
 0.6112 
 
 0.8335 
 
 
 From this table it appears, first, that the periods of the 
 double stars are very various, ranging, in the case of 
 those already ascertained, from forty-three years to one 
 
 316. Have the conclusions of Herschel been confirmed by 
 others ? What doctrine is now considered as fully established ? 
 How are the periods of the double stars ? What is the figure of 
 their orbits ? Which is the most remarkable of the Binary 
 stars ? What is its size ? How long since it was first observed 
 to be double ? What changes has it undergone since ? When 
 did it pass its perihelion ? 
 
 * Those who do not understand the Greek letters, can pass over thi 
 table to the inferences which follow. 
 
MOTIONS OP THE FIXED STARS. 257 
 
 thousand ; secondly, that their orbits are very small 
 ellipses, more eccentric than those of the planets, the 
 greatest of which (that of Mercury) having an eccentri- 
 city of only about .2 of the major axis. 
 
 The most remarkable of the binary stars is Gamma 
 Virginis, on account not only of the length of its period, 
 but also of the great diminution of apparent distance, 
 and rapid increase of angular motion about each other 
 of the individuals composing it. It is a bright star of 
 the fourth magnitude, and its component stars are almost 
 exactly equal. It has been known to consist of two 
 stars since the beginning of the eighteenth century, their 
 distance being then between six and seven seconds ; so 
 that any tolerably good telescope would resolve it. 
 Since that time they have been constantly approaching, 
 and are at present hardly more than a single second asun- 
 der ; so that no telescope that is not of a very superior 
 quality, is competent to show them otherwise than as a 
 single star, somewhat lengthened in one direction. It 
 fortunately happens that Bradley (Astronomer Royal) in 
 1718, noticed, and recorded in the margin of one of his 
 observation books, the apparent direction of their line of 
 junction, as being parallel to that of two remarkable 
 stars Alpha and Delta of the same constellation, as seen 
 by the naked eye, a remark which has been of signal 
 service in the investigation of their orbit. It is found 
 that it passed its perihelion, August 18th, 1834. 
 
 317. The revolutions of the binary stars have assured 
 us of that most interesting fact, that the law of gravita- 
 tion extends to the fixed stars. Before these discoveries, 
 we could not decide except by a feeble analogy that this 
 law transcended the bounds of the solar system. In- 
 
 17. What great fact have the revolutions of the binary stars 
 revealed to us ? How was this doctrine limited before this 
 discovery ? Are these revolutions those of a planetary or 
 cometary nature ? 
 
 22* 
 
258 FIXED STARS. 
 
 deed, our belief of the fact rested more upon our idea of 
 unity of design in all the works of the Creator, than 
 upon any certain proof ; but the revolution of one star 
 around another in obedience to forces which must be 
 similar to those that govern the solar system, establishes 
 the grand conclusion, that the law of gravitation is truly 
 the law of the material universe. 
 
 We have the same evidence (says Sir John Herschel) 
 of the revolutions of the binary stars about each other, 
 that we have of those of Saturn and Uranus about the 
 sun ; and the correspondence between their calculated 
 and observed places in such elongated ellipses, must be 
 admitted to carry with it a proof of the prevalence of the 
 Newtonian law of gravity in their systems, of the very 
 same nature and cogency as that of the calculated and 
 observed places of comets round the center of our own 
 system. 
 
 But (he adds) it is not with the revolution of bodies 
 of a planetary or cometary nature round a solar center 
 that we are now concerned ; it is with that of sun 
 around sun, each, perhaps, accompanied with its train of 
 planets and their satellites, closely shrouded from our 
 view by the splendor of their respective suns, and crowd- 
 ed into a space, bearing hardly a greater proportion to 
 the enormous interval which separates them, than the 
 distances of the satellites of our planets from their pri- 
 maries, bear to their distances from the sun itself. 
 
 318. Some of the fixed stars appear to have a real mo- 
 tion in space. 
 
 There are several apparent changes of place among 
 the stars which arise from real changes in the earth, 
 which, as we are not conscious of them, we refer to the 
 stars ; but there are other motions among the stars which 
 
 318. Have any of the fixed stars a real motion in space ? 
 Are the places of the stars as described in ancient times by 
 Ptolemy nearly the same as at present ? To what conclu- 
 sions on this subject are we now forced ? 
 
MOTIONS OP THE FIXED STARS. 259 
 
 cannot result from any changes in the earth, but must 
 arise from changes in the stars themselves. Such mo- 
 tions are called the proper motions of the stars. Nearly 
 2000 years ago, Hipparchus and Ptolemy made the most 
 accurate determinations in their power of the relative 
 situations of the stars, and their observations have been 
 transmitted to us in Ptolemy's Almagest ; from which it 
 appears that the stars retain at least very nearly the same 
 places now as they did at that period. Still the more 
 accurate methods of modern Astronomers, have brought 
 to light minute changes in the places of certain stars, 
 which force upon us the conclusion, either that our solar 
 system causes an apparent displacement of certain stars, 
 by a motion of its own in space, or that they have them- 
 selves a proper motion. Possibly, indeed, both these 
 causes may operate. 
 
 319. If the sun, and of course the earth which accom- 
 panies him, is actually in motion, the fact may become 
 manifest from the apparent approach of the stars in the 
 region which he is leaving, and the recession of those 
 which lie in the part of the heavens towards which he 
 is travelling. Were two groves of trees situated on a 
 plain at some distance apart, and we should go from one 
 to the other, the trees before us would gradually appear 
 farther and farther asunder, while those we left behind 
 would appear to approach each other. Some years since, 
 Sir William Herschel supposed he had detected changes 
 of this kind among two sets of stars in opposite points 
 of the heavens, and announced that the solar system 
 was in motion towards a point in the constellation Her- 
 cules ; but other astronomers have not found the changes 
 question such as would correspond to this motion, or 
 
 319. If the solar system is really in motion, how may the 
 fact become manifest ? Towards what constellation did Sir 
 William Herschel suppose it moving ? Has the opinion been 
 confirmed by later observers ? 
 
260 FIXED STARS. 
 
 to any motion of the sun ; and while it is a matter of 
 general belief that the sun has a motion in space, the 
 fact is not considered as yet entirely proved 
 
 320. In most cases where a proper motion in certain 
 stars has been suspected, its annual amount has been so 
 small, that many years are required to assure us, that the 
 effect is not owing to some other cause than a real pro- 
 gressive motion in the stars themselves-; but in a few 
 instances the fact is too obvious to admit of any doubt. 
 Thus the two stars 61 Cygni, which are nearly equal, 
 have remained constantly at the same, or nearly at the 
 same distance of 15" for at least fifty years past. Mean- 
 while they have shifted their local situation in the 
 heavens, 4? 23" the annual proper motion of each star 
 being 5 /x .3, by which quantity this system is every year 
 carried along in some unknown path, by a motion which 
 for many centuries must be regarded as uniform and rec- 
 tillinear. A greater proportion of the double stars than 
 of any other indicate proper motions, especially the bi- 
 nary stars or those which have a revolution around each 
 other. Among stars not double, and no way differing 
 from the rest in any other obvious particular, Mu Cassi- 
 opeia has the greatest proper motion of any yet ascer- 
 tained, amounting to nearly 4" annually. 
 
 DISTANCES OF THE FIXED STARS. 
 
 321. We cannot ascertain the actual distance of any 
 of the fixed stars, but can certainly determine that the 
 nearest star is more than (20,000,000,000,000,) twenty 
 billions of miles from the earth. 
 
 320. What length of time is required in order to detect 
 proper motions in the stars ? What changes have occurred in 
 the two stars 61 Cygni? What sort of stars indicate proper 
 motions ? Of stars not double, what star has the greatest 
 proper motion ? 
 
DISTANCES OF THE FIXED STARS. 261 
 
 For all the measurements relating to the distances of 
 the sun and planets, the radius of the earth furnishes the 
 base line. (Art. 96.) The length of this line being 
 known, and the horizontal parallax of the body, whose 
 distance is sought, we readily obtain the distance by tne 
 solution of a right angled triangle. But any star viewed 
 from the opposite sides of the earth, would appear from 
 Doth stations, to occupy precisely the same situation in 
 the celestial sphere, and of course it would exhibit no 
 horizontal parallax. 
 
 But astronomers have endeavored to find a parallax in 
 some of the fixed stars, by taking the diameter of the 
 earths orbit as a base line. Yet even a change of posi- 
 tion amounting to 190 millions of miles, proves insuffi- 
 cient to alter the place of a single star, from which it is 
 concluded that the stars have not even any annual par- 
 allax ; that is, the angle subtended by the semi-diameter 
 of the earth's orbit, at the nearest fixed star is insensible. 
 The errors to which instrumental measurements are sub- 
 ject, arising from the defects of the instruments them- 
 selves, from refraction, and from various other sources of 
 inaccuracy, are such, that the angular determinations of 
 arcs of the heavens cannot be relied on to less than I". 
 But the change of place in any star when viewed at op- 
 posite extremities of the earth's orbit, is less than 1", and 
 therefore cannot be appreciated by direct measurement. 
 It follows, that, when viewed from the nearest star, the 
 diameter of the earth's orbit would be insensible. 
 
 322. Taking, however, the annual parallax of a fixed 
 star at 1", it can be demonstrated that the distance of 
 the nearest fixed star must exceed 95000000x200000 
 190000000x100000, or one hundred thousand times 
 
 321 . What do we know respecting the distances of the fixed 
 stars ? Have the fixed stars any parallax ? What is taken as 
 the base line for measuring the parallax ? What angle is 
 greater than would be subtended by the diameter of the earth's 
 oirbit as seen from the nearest fixed star ? 
 
262 FIXED STABS. 
 
 one hundred and ninety millions of miles. Of a dis- 
 tance so vast we can form no adequate conceptions, and 
 even seek to measure it only by the time that light, 
 (which moves more than 192,000 miles per second, and 
 passes from the sun to the earth in 8m. 13.3sec.,) would 
 take to traverse it, which is found to be more than threv 
 and a half years. 
 
 If these conclusions are drawn with respect to the 
 largest of the fixed stars, which we suppose to be vastly 
 nearer to us than those of the smallest magnitude, the 
 idea of distance swells upon us when we attempt to es- 
 timate the remoteness of the latter. As it is uncertain, 
 however, whether the difference in the apparent magni- 
 tudes of the stars is owing to a real difference, or merely 
 to their being at various distances from the eye, more or 
 less uncertainty must attend all efforts to determine the 
 relative distances of the stars ; but astronomers generally 
 believe, that the lower orders of stars are vastly more 
 distant from us than the higher. Of some stars it is 
 said, that thousands of years would be required for their 
 light to travel down to us. 
 
 323. We have said that the stars have no annual par- 
 allax ; yet it may be observed that astronomers are not 
 exactly agreed on this point. Dr. Brinkley, a late emi- 
 nent Irish astronomer, supposed that he had detected an 
 annual parallax in Alpha Lyrae amounting to l x/ .13 and 
 in Alpha Aquilae of l x/ .42. These results were contro- 
 verted by Mr. Pond, of the Royal Observatory of Green- 
 wich ; and Mr. Struve of Dorpat, has shown that in a 
 number of cases, the parallax is in a direction opposite 
 to that which would arise from the motion of the earth. 
 Hence it is considered doubtful whether in all cases of 
 
 322. If we take the parallax at 1", what must the distance 
 be ? What time would it take light to traverse this space 1 
 How much farther off than this may some of the smaller stars be? 
 
 323. Is it entirely settled that the fixed stars have no paral- 
 lax ? What did Dr. Brinkley assert 1 Have his observations 
 been confirmed ? 
 
DISTANCE OF THE FIXED STARS. 263 
 
 an apparent parallax, the effect is not wholly due to 
 errors of observation. 
 
 324. Indirect methods have been proposed for ascer- 
 taining the parallax of the fixed stars by means of obser- 
 vations on the double stars. If the two stars composing 
 a double star are at different distances from us, parallax 
 would affect them unequally, and change their relative 
 positions with respect to each other ; and since the ordi- 
 nary sources of error arising from the imperfection of 
 instruments, from precession, and refraction, would be 
 avoided, (since they would affect both objects alike, and 
 therefore would not disturb their relative positions,) 
 measurements taken with the micrometer of changes 
 much less than \" may be relied on. Sir John Herschel 
 proposes a method by which changes may be determined 
 which amount to only ^ of a second.* 
 
 The immense distance of the fixed stars is inferred 
 also from the fact, that the largest telescopes do not in- 
 crease their apparent magnitude. They are still points, 
 when viewed with the highest magnifiers, although 
 they sometimes present a spurious disk, which is owing 
 to irradiation.'f 
 
 324. What indirect methods have been proposed for ascer- 
 taining the parallax of the fixed stars ? State the particulars 
 of this method. How minute changes of place is it supposed 
 may be detected. How do the largest telescopes affect their 
 apparent magnitudes ? 
 
 * Very recent intelligence informs us, that Prof. Bessel of Konigs- 
 berg, has obtained decisive evidence of an annual parallax in 61 Cygni, 
 amounting to 0" .3136. This makes the distance of that star, equal to 
 657700 times 95 millions of miles a distance which it would take light 
 10.3 years to traverse. 
 
 t Irradiation is an enlargement of objects beyond their proper bounds, 
 in consequence of the vivid impression of light on the eye. It is sup- 
 posed to increase the apparent diameters of the sun and moon from three 
 to four seconds, and to create an appearance of a disk in a fixed star, 
 which, when this cause is removed, ia seen as a mere point. 
 
264 FIXED STARS. 
 
 NATURE OF THE STARS. 
 
 325. The stars are bodies greater than our earth. If 
 this were not the case they could not be visible at such 
 an immense distance. Dr. Wollaston, a distinguished 
 English philosopher, attempted to estimate the magni- 
 tudes of certain of the fixed stars from the light which 
 they afford. By means of an accurate photometer (an 
 instrument for measuring the relative intensities of light) 
 he compared the light of Sirius with that of the sun. 
 He next inquired how far the sun must be removed from 
 us in order to appear no brighter than Sirius. He found 
 the distance to be 141,400 times its present distance. 
 But Sirius is more than 200,000 times as far off as the 
 sun. Hence he inferred that, upon the lowest compu- 
 tation, Sirius must actually give out twice as much 
 light as the sun ; or that, in point of splendor, Sirius 
 must be at least equal to two suns. Indeed, he has ren- 
 dered it probable that the light of Sirius is equal to 
 fourteen suns. 
 
 326. The fixed stars are suns. We have already seen 
 that they are large bodies ; that they are immensely 
 farther off than the farthest planet ; that they shine by 
 their own light ; in short, that their appearance is, in all 
 respects, the same as the sun would exhibit if removed 
 to the region of the stars. Hence we infer, that they 
 are bodies of the same kind with the sun. 
 
 We are justified therefore by a sound analogy, in con- 
 cluding that the stars were made for the same end as 
 the sun, namely, as the centers of attraction to other 
 planetary worlds, to which they severally dispense light 
 and heat. Although the starry heavens present, in a 
 clear night, a spectacle of ineffable grandeur and beauty, 
 
 325. Nature of the stars. How large are the stars compared 
 with the earth ? How did Dr. Wollaston endeavor to estimate 
 the magnitudes of certain fixed stars ? How distant would this 
 method make Sirius ? T * how many suns is Sirius equal ? 
 
SYSTEM OP THE WORLD. 265 
 
 yet it must be admitted that the chief purpose of the 
 stars could not have been to adorn the night, since by 
 far the greatest part of them are wholly invisible to the 
 naked eye ; nor as landmarks to the navigator, for only a 
 very small proportion of them are adapted to this pur- 
 pose ; nor, finally, to influence the earth by their attrac- 
 tions, since their distance renders such an effect entirely 
 insensible. If they are suns, and if they exert no im- 
 portant agencies upon our world, but are bodies evidently 
 adapted to the same purpose as our sun, then it is as ra- 
 tional to suppose that they were made to give light and 
 heat, as that the eye was made for seeing and the ear 
 for hearing. It is obvious to inquire next, to what they 
 dispense these gifts if not to planetary worlds ; and why 
 to planetary worlds, if not for the use of percipient be- 
 ings ? We are thus led, almost inevitably, to the idea 
 of a Plurality of Worlds ; and the conclusion is forced 
 upon us, that the spot which the Creator has assigned to 
 us is but a humble province of his boundless empire.* 
 
 CHAPTER IV. 
 
 OP THE SYSTEM OP THE WORLD. 
 
 327. The arrangement of all the bodies that compose 
 the material universe, and their relations to each other, 
 constitute the System of the World. 
 
 It is otherwise called the Mechanism of the Heavens ; 
 and indeed, in the System of the World, we figure to 
 ourselves a machine, all the parts of which have a mu- 
 
 326. Prove that the fixed stars are suns. For what purpose 
 were they made ? Could they have been designed to adorn the 
 night ? or as landmarks to the navigator ? If they are suns, for 
 what farther purpose were they designed ? 
 
 * See this argument, in its full extent, in Dick's Celestial Scer,ery. 
 23 
 
266 SYSTEM OF THE WORLD. 
 
 tual dependence, and conspire to one great end. " The 
 machines that are first invented (says Adam Smith) to 
 perform any particular movement, are always the most 
 complex ; and succeeding artists generally discover that 
 with fewer wheels and with fewer principles of motion 
 than had originally been employed, the same effects may 
 be more easily produced. The first systems, in the 
 same manner, are always the most complex ; and a par- 
 ticular connecting chain or principle is generally thought 
 necessary to unite every two seemingly disjointed ap- 
 pearances ; but it often happens, that one great cpnnect- 
 ing principle is afterwards found to be sufficient, to bind 
 together all the discordant phenomena that occur in a 
 whole species of things." This remark is strikingly 
 applicable to the origin and progress of systems of as 
 tronomy. 
 
 328. From the visionary notions which are generally 
 understood to have been entertained on this subject by 
 the ancients, we are apt to imagine that they knew less 
 than they actually did of the truths of astronomy. But 
 Pythagoras, who lived 500 years before the Christian 
 era, was acquainted with many important facts in our 
 science, and entertained many opinions respecting the 
 system of the world which are now held to be true. 
 Among other things well known to Pythagoras were the 
 following : 
 
 1. The principal Constellations. These had begun to 
 be formed in the earliest ages of the world. Several of 
 them bearing the same names as at present, are men- 
 tioned in the writings of Hesiod and Homer ; and tile 
 * sweet influences of the Pleiades" and the " bands of 
 Orion," are beautifully alluded to in the book of Job. 
 
 2. Eclipses. Pythagoras knew both the causes of 
 eclipses and how to predict them ; not indeed in the ac- 
 
 327. What constitutes the System of the World ? Under 
 what image do we figure it to ourselves ? What properties 
 characterize the machines first invented ? 
 
ASTRONOMICAL KNOWLEDGE OF THE ANCIENTS. 267 
 
 curate manner now employed, but by means of the Saros. 
 (Art. 168.) 
 
 3. Pythagoras had divined the true system of the 
 world, holding that the sun and not the earth, (as was 
 generally held by the ancients, even for many ages after 
 Pythagoras,) is the center around which all the planets 
 revolve, and that the stars are so many suns, each the 
 center of a system like our own. Among lesser things, 
 he knew that the earth is round ; that its surface is nat- 
 urally divided into five Zones ; and that the ecliptic is 
 inclined to the equator. He also held that the earth re- 
 volves daily on its axis, and yearly around the sun ; that 
 the galaxy is an assemblage of small stars ; and that it 
 is the same luminary, namely, Venus, that constitutes 
 bofh the morning and the evening star, whereas, all the 
 ancients before him had supposed that each was a sepa- 
 rate planet, and accordingly the morning star was called 
 Lucifer, and the evening star Hesperus. He held also 
 that the planets were inhabited, and even went so far as 
 to calculate the size of some of the animals in the moon. 
 Pythagoras was so great an enthusiast in music, that he 
 not only assigned to it a conspicuous place in his system 
 of education, but even supposed the heavenly bodies 
 themselves to be arranged at distances corresponding to 
 the diatonic scale, and imagined them to pursue their sub- 
 lime march to notes created by their own harmonious 
 movements, called the " music of the spheres ;" but he 
 maintained that this celestial concert, though loud and 
 grand, is not audible to the feeble organs of man, but 
 only to the gods. 
 
 329. With few exceptions, however, the opinions of 
 Pythagoras on the System of the World, were founded 
 
 328. What is said of our usual estimate of the knowledge of 
 astronomy possessed by the ancients 1 What things were 
 known to Pythagoras ? How early were the principal constel- 
 lations known 1 What did Pythagoras know of eclipses ? Also 
 respecting the System of the World ? What lesser things did 
 he know ? What notions had he of the music of the spheres ? 
 
'268 SYSTEM OF THE WORLD. 
 
 in truth. Yet they were rejected by Aristotle and by 
 most succeeding astronomers down to the time of Coper- 
 nicus, and in their place was substituted the doctrine of 
 Crystalline Spheres, first taught by Eudoxus. Accord- 
 ing to this system, the heavenly bodies are set like gems 
 in hollow solid orbs, composed of crystal so pellucid that 
 no anterior orb obstructs in the least the view of any of 
 the orbs that lie behind it. The sun and the planets 
 have each its separate orb ; but the fixed stars are all set 
 in the same grand orb ; and beyond this is another still, 
 the Primum Mobile, which revolves daily from east to 
 west, and carries along with it all the other orbs. Above 
 the whole, spreads the Grand Empyrean, or third heav- 
 ens, the abode of perpetual serenity. 
 
 To account for the planetary motions, it was supposed 
 that each of the planetary orbs as well as that of the sun, 
 has a motion of its own eastward, while it partakes of 
 the common diurnal motion of the starry sphere. Aris- 
 totle taught that these motions are effected by a tutelary 
 genius of each planet, residing in it, and directing its 
 motions, as the mind of man directs his motions. 
 
 330. On coming down to the time of Hipparchus, who 
 flourished about 150 years before the Christian era, we 
 meet with astronomers who acquired far more accurate 
 knowledge of the celestial motions. Previous to this 
 period, celestial observations were made chiefly with the 
 naked eye, but Hipparchus was in possession of instru- 
 ments for measuring angles, and knew how to resolve 
 spherical triangles. He ascertained the length of the 
 year within 6m. of the truth. He discovered the eccen- 
 tricity of the solar orbit, (although he supposed the sun 
 actually to move uniformly in a circle, but the earth to 
 be placed out of the center,) and the positions of the 
 
 329. Were the opinions of Pythagoras generally embraced 
 by the ancients ? What was the doctrine of Crystalline 
 Spheres ? How were the planetary motions accounted for ? 
 
 330. When did Hipparchus flourish ? How did he make 
 his observations ? What great facts did he ascertain ? 
 
THE PTOLEMAIC SYSTEM. 269 
 
 sun's apogee and perigee. He formed very accurate es- 
 timates of the obliquity of the ecliptic, and of the preces- 
 sion of the equinoxes. He computed the exact period 
 of the synodic revolution of the moon, and the inclina- 
 tion of the lunar orbit ; discovered the motion of her 
 node and of her line of apsides ; and made the first at- 
 tempts to ascertain the horizontal parallaxes of the sun 
 and moon. 
 
 Such was the state of astronomical knowledge when 
 Ptolemy wrote the Almagest, in which he has transmit- 
 ted to us an encyclopedia of the astronomy of the an- 
 cients. 
 
 331. The systems of the world which have been most 
 celebrated are three the Ptolemaic, the Tychonic, and 
 the Copernican. We shall conclude this part of our 
 work with a concise statement and discussion of each 
 of th&se systems of the Mechanism of the Heavens. 
 
 THE PTOLEMAIC SYSTEM. * 
 
 332. The doctrines of the Ptolemaic System were not 
 originated by Ptolemy, but being digested by him out of 
 materials furnished by various hands, it has come down 
 to us under the sanction of his name. 
 
 According to this system, the earth is the center of 
 the universe, and all the heavenly bodies daily revolve 
 around it from east to west. In order to explain the 
 planetary motions, Ptolemy had recourse to deferents and 
 epicycles an explanation devised by Apollonius one of 
 the greatest geometers of antiquity. He conceived that, 
 in the circumference of a circle, having the earth for its 
 center, there moves the center of another circle, in the 
 circumference of which the planet actually revolves. 
 The circle surrounding the earth was called the deferent. 
 
 331. What are the most celebrated Systems of the World? 
 
 332. Ptolemaic System. Did Ptolemy originate this sys- 
 tem? State the outlines of it. What was the deferent? 
 What was the epicycle ? 
 
 23* 
 
270 
 
 SYSTEM OF THE WORLD. 
 
 while the smaller circle whose center was always in the 
 periphery of the deferent, was called the epicycle. The 
 motion in each was supposed to be uniform. Lastly, it 
 was conceived that the motion of the center of the epi- 
 cycle in the circumference of the deferent, and of the 
 planet in that of the epicycle, are in the same directions. 
 
 333. But these views will be better understood from a 
 diagram. Therefore, let ABC (Fig. 53,) represent the 
 deferent, E being the earth a little out of the center. 
 
 Let abc represent the epicycle, having its center at v, on 
 the periphery of the deferent. Conceive the circumfer- 
 ence of the deferent to be carried about the earth every 
 twenty four hours in the order of the letters ; and at the 
 
 333. Explain the Ptolemaic System by figure 53. 
 
THE PTOLEMAIC SYSTEM. 271 
 
 same time, let the center v of the epicycle abed, have a 
 slow motion in the opposite direction, and let a body re- 
 volve in this circle in the direction abed. Then a body 
 revolving in the circle abed, and at the same time having 
 a motion eastward in common with the circle, would 
 describe the looped curves khnnop. At I and m, and at 
 n and o, it would appear stationary, because in these 
 points its motion would be either directly towards or 
 from the spectator. The motion would be direct from 
 k to /, being in the order of the signs, and retrograde 
 from I to m ; direct again from m to n, and retrograde 
 from n to o. 
 
 334. Such a deferent and epicycle may be devised 
 for each planet as will fully explain all its ordinary mo- 
 tions ; but it is inconsistent with the phases of Mercuiy 
 and Venus, which being between us and the sun on 
 both sides of the epicycle, would present their dark 
 sides towards us in both these positions, whereas at one 
 of the conjunctions they are seen to shine with full 
 face. It is moreover absurd to speak of a geometrical 
 center which has no bodily existence, moving around the 
 earth on the circumference of another circle ; and hence 
 some suppose that the ancients merely assumed this hy- 
 pothesis as affording a convenient geometrical represen- 
 tation of the Phenomena, a diagram simply, without 
 conceiving the system to have any real existence in na- 
 ture. 
 
 335. The objections to the Ptolemaic system, in gen- 
 eral, are the following : First, it is a mere hypothesis, 
 having no evidence in its favor, except that it explains 
 the phenomena. Tljis evidence is insufficient of itself, 
 since it frequently happens that each of two hypotheses, 
 
 334. State the objections to this mode of representing the 
 motions of the planets. Why is it inconsistent with the phases 
 of Mercury and Venus ? What is said of the supposition of a 
 geometrical center moving around the earth ? 
 
'272 SYSTEM OP THE WORLD. 
 
 directly opposite to each other, will explain all the known 
 phenomena. But the Ptolemaic system does not even 
 do this, as it is inconsistent with the phaaes of Mercury 
 and Venus, as already observed. Secondly, now that 
 we are acquainted with the distances of the remoter 
 planets, and especially of the fixed stars, the swiftness 
 of motion implied in a daily revolution of the starry 
 firmament around the earth, renders such a motion 
 wholly incredible. Thirdly, the centrifugal force that 
 would be generated in these bodies, especially in the 
 sun, renders it impossible that they can continue to re- 
 volve around the earth as a center. 
 
 These reasons are sufficient to show the absurdities 
 of the Ptolemaic System of the World. 
 
 THE TYCHONIC SYSTEM. 
 
 336. Tycho Brahe, like Ptolemy, placed the earth in 
 the center of the universe, and accounted for the diur- 
 nal motions in the same manner as Ptolemy had done, 
 namely, by an actual revolution of the whole host of 
 heaven around the earth every twenty four hours. But 
 he rejected the scheme of deferents and epicycles, and 
 held that the moon revolves about the earth as the cen- 
 ter of her motions ; that the sun and not the earth, is 
 the center of the planetary motions ; and that the sun 
 accompanied by the planets moves around the earth 
 once a year, somewhat in the manner that we now con- 
 ceive of Jupiter and his satellites as revolving around 
 the sun. 
 
 337. The system of Tycho serves to explain all the 
 common phenomena of the planetary motions, but it is 
 encumbered with the same objections as those that have 
 
 335. State the objections to the Ptolemaic System in general. 
 Does it explain all the phenomena ? What swiftness of motion 
 does it imply ? 
 
 336. Tychonic System. State its leading points. 
 
THE COPERNICAN SYSTEM. 273 
 
 been mentioned as resting against the Ptolemaic system, 
 namely, that it is a mere hypothesis ; that it implies an 
 incredible swiftness in the diurnal motions ; and that it 
 is inconsistent with the known laws of unive/sal grav- 
 itation. But if the heavens do not revolve, the earth 
 must, and this brings us to the system of Copernicus. 
 
 THE "COPERNICAN SYSTEM. 
 
 338. Copernicus was born at Thorn in Prussia in 
 1473. The system that bears his name was the fruit of 
 forty years of intense study and meditation upon the 
 celestial motions. As already mentioned, (Art. 6,) it 
 maintains (1) That the apparent diurnal motions of the 
 heavenly bodies, from east to west is owing to the real 
 revolution of the earth on its own axis from west to east ; 
 and (2) That the sun is the center around which the 
 earth and planets all revolve from west to east. It rests 
 on the following arguments : 
 
 First, the earth revolves on its own axis. 
 
 1. Because this supposition is vastly more simple. 
 
 2. It is agreeable to analogy, since all the other plan- 
 ets that afford any means of determining the question, 
 are seen to revolve on their axes. 
 
 3. The spheriodal figure of the earth, is the figure of 
 equilibrium, that results from a revolution on its axis. 
 
 4. The diminished weight of bodies at the equator, 
 indicates a centrifugal force arising from such a rev- 
 olution. 
 
 5. Bodies let fall from a high eminence, fall eastward 
 of their base, indicating that when farther from the cen- 
 ter of the earth they were subject to a greater velocity, 
 which in consequence of their inertia, they do not en- 
 tirely lose in descending to the lower level. 
 
 337. How far does the Tychonic System explain the plan- 
 etary motions ? With what objections is it encumbered ? 
 
 338. Copernican System. Who was Copernicus ? State' 
 the principles of his System. State the five reasons why tho 
 earth revolves on its axis. 
 
#74 SYSTEM OP THE WORLD. 
 
 339. Secondly, the planets, including the earth, revolve 
 about the sun. 
 
 1. The phases of Mercury and Venus are precisely 
 such, as would result from their circulating around the 
 sun in orbits within that of the earth ; but they are 
 never seen in opposition, as they would be if they cir- 
 culate around the earth. 
 
 2. The superior planets do indeed revolve around the 
 earth ; but they also revolve around the sun, as is evi- 
 dent from their phases and from the known dimensions 
 of their orbits ; and that the sun and not the earth, is the 
 center of their motions, is inferred from the greater sym- 
 metry of their motions as referred to the sun than as re- 
 ferred to the earth, and especially from the laws of grav- 
 itation which forbid our supposing that bodies so much 
 larger than the earth, as some of these bodies are, can 
 circulate permanently around the earth, the latter re- 
 maining all the while at rest. 
 
 3. The annual motion of the earth itself is indicated 
 also by the most conclusive arguments. For, first, since 
 all the planets with their satellites, and the comets, re- 
 volve about the sun, analogy leads us to infer the same 
 respecting the earth and its satellites. Secondly, The 
 motions of the satellites, as those of Jupiter and Saturn, 
 indicate that it is a law of the solar system that the 
 smaller bodies revolve about the larger. Thirdly, on 
 the supposition that the earth performs an annual revolu 
 tion around the sun, it is embraced along with the plan- 
 ets, in Kepler's law, that the squares of the times are as 
 the cubes of the distances ; otherwise, it forms an ex- 
 ception, and the only known exception to this law. 
 
 340. It only remains to inquire, whether there sub- 
 sist higher orders of relations between the stars them- 
 selves. 
 
 339. State the three reasons why the planets revolve about 
 the sun how argued from the phases of Mercury and Venus 1 
 from the aspects and positions of the superior planets ? from 
 the annual motion of the earth ? 
 
THE COPBRNICAN SYSTEM. 275 
 
 The revolutions of the binary stars afford conclusive 
 evidence of at least subordinate systems of suns, gov- 
 erned by the same laws as those which regulate the mo- 
 tions of the solar system. The nebulce also compose 
 peculiar systems, in which the members are evidently 
 bound together by some common relation. 
 
 In these marks of organization, of stars associated 
 together in clusters, of sun revolving around sun, 
 and of nebulae disposed in regular figures, we recognize 
 different members of some grand system, links in one 
 great chain that binds together all parts of the universe ; 
 as we see Jupiter and his satellites combined in one sub- 
 ordinate system, and Saturn and his satellites in another, 
 each a vast kingdom, and both uniting with a num- 
 ber of other individual parts to compose an empire still 
 more vast. 
 
 341. This fact being now established, that the stars 
 are immense bodies like the sun, and that they are sub- 
 ject to the laws of gravitation, we cannot conceive how 
 they can be preserved from falling into final disorder and 
 ruin, unless they move in harmonious concert like the 
 members of the solar system. Otherwise, those that 
 are situated on the confines of creation, being retained 
 by no forces from without, while they are subject to the 
 attraction of all the bodies within, must leave their sta- 
 tions, and move inward with accelerated velocity, and 
 thus all the bodies in the universe would at length fall 
 together in the common center of gravity. The im- 
 mense distance at which the stars are placed from each 
 other, would indeed delay such a catastrophe ; but such 
 must be the ultimate tendency of the material world, un- 
 
 340. Proofs of higher orders of relations among the stars 
 themselves from the binary stars from the nebulae. What 
 do we recognize in these marks of organization ? 
 
 341. How are these systems preserved from falling into dis- 
 order and ruin ? How should we be justified in inferring that 
 other worlds are not subject to forces which operate to hasten 
 their decay? To what final conclusions are we led? 
 
276 SYSTEM OF THE WORLD. 
 
 less sustained in one harmonious system by nicely ad- 
 justed motions. To leave entirely out of view our con- 
 fidence in the wisdom and preserving goodness of the 
 Creator, and reasoning merely from what we know of 
 the stability of the solar system, we should be justified 
 in inferring, that other worlds are not subject to forces 
 which operate only to hasten their decay, and to involve 
 them in final ruin. 
 
 We conclude, therefore, that the material universe is 
 one great system ; that the combination of planets with 
 their satellites constitutes the first or lowest order of 
 worlds ; that next to these planets are linked to suns ; 
 that these are bound to other suns, composing % a still 
 higher order in the scale of being ; and, finally, that all 
 the different systems of worlds, move around their com- 
 mon center of gravity. 
 
SUPPLEMENT, 
 
 CONTAINING AN ACCOUNT OF THE LATES1 DISCOV- 
 ERIES IN ASTRONOMY. 
 
 Art. I. GREAT COMET OF 1843. On the 28th of Feb- 
 ruary, 1843, the attention of numerous observers, in 
 various parts of the world, was arrested by a comet 
 seen at noonday a little eastward of the sun. It re- 
 sembled a white cloud of great density, being nearly 
 equally brilliant through its whole length, which at 
 this time was estimated by different observers to be 
 about three degrees. During the first week in March, 
 the appearance of the comet in the southern hemi- 
 sphere was splendid and magnificent, enhanced, in 
 both respects, by the transparency of a tropical sky, 
 and the higher angle of elevation above that at which 
 it was seen by northern observers. At Pernambuco, 
 in South America, on the 4th of March, it presented a 
 golden hue ; and it was, as described by the com- 
 mander of a ship, so brilliant as to throw a strong 
 light on the sea. 
 
 At New Haven, the comet was first seen after sun- 
 set on the 5th of March, and by the writer on the 6th. 
 It then lay far in the southwest. On account of the 
 presence of the moon, it was not seen under the most 
 favorable circumstances until the evening of the 17th. 
 It then stretched along the southern sky from the point 
 of sunset to the bright star Sirius, covering a space 
 40 deg. in length, but unusually limited in breadth, 
 the whole figure resembling that of a long goose-quill, 
 being similarly curved. It was, at first, of a delicate 
 rose-red color, but afterwards nearly a pure white. 
 
278 DISTANCES OF THE STARS. 
 
 All the astronomers of the age have concurred in 
 the opinion, that this is one of the most remarkable 
 exhibitions of a comet ever witnessed, although they 
 are not fully agreed respecting the elements of its 
 orbit, or its periodic time. Some maintain that its 
 time of revolution is 175 years, and consequently that 
 the present is its first return since 1668; but others 
 think that its true period is 21 f years, and that it will 
 visit our sphere again in 1865. It passed its perihelion 
 on the 27th of February, at which time it almost 
 grazed the surface of the sun, approaching nearer to 
 that luminary than any comet hitherto observed. Its 
 motions at this time were astonishingly swift, and its 
 brilliancy such as to induce the belief that it was at a 
 white heat through its whole extent. 
 
 Art II. DISTANCES OP THE STARS. After many fruit- 
 less and delusory efforts to measure the immense in- 
 terval that separates us from the fixed stars, the great 
 Prussian astronomer, Bessel, in the year 1838, deter- 
 mined this interesting and important element by ob- 
 servations on a double star in the Swan, (61 Cygni.) 
 
 By observations of the last degree of refinement, 
 conducted for a period of several years, a parallax 
 (see page 36) was decisively indicated amounting to 
 about one third of a second; or, more exactly, to 
 0".3483, implying a distance of 592,200 times the 
 mean distance of the earth from the sun ; or a space 
 which it would take light, moving at the rate of 
 twelve millions of miles per minute, 9 years to tra- 
 verse. To form some familiar notions of this distance, 
 let us suppose a railway-car to travel night and day 
 at the rate of twenty miles an hour, we should find it 
 would take it about 547 years to reach the sun ; but 
 to reach 61 Cygni would require 324,000,000 of years. 
 
 The observations of Bessel enabled him to estimate 
 also the period of revolution of the two stars compo- 
 sing the Binary System (see p. 255) of 61 Cygni, and 
 the dimensions of the orbit ; and he found the period 
 
NEW PLANETS. 279 
 
 about 540 years, and the length of the orbit about 2| 
 times that of Uranus. Knowing also the distance of 
 this star, we can now determine, from its proper mo- 
 tion (five seconds a year) the velocity with which it 
 moves : this is found to be forty-four miles per second, 
 more than double that of the earth in its orbit 
 amounting to about one "thousand millions of miles 
 per annum. 
 
 On account of the smallness of the supposed paral- 
 lax thus found, it would not be unreasonable still to 
 entertain a lingering suspicion, that it is nothing more 
 than the unavoidable imperfection of instrumental 
 measurements; but the most satisfactory evidence 
 which the world can have that such is not the fact 
 in the present instance, but that the parallax is truly 
 found, is that the most celebrated astronomers of the 
 age, after rigorous scrutiny, have acknowledged the 
 reality and soundness of the determination. 
 
 Several other stars have of late been supposed to 
 indicate a'parallax ; and one of them, (Alpha Centauri,) 
 the brightest star of the Centaur, a constellation of the 
 southern hemisphere, is thought by some to be nearer 
 to us than 61 Cygni, having a parallax of nine-tenths 
 of a second, The evidence, however, upon which this 
 case and several similar cases of supposed parallax 
 rest, is not such as to have inspired so high a degree 
 of confidence as the determination by Bessel, and it is 
 still claimed only that the distance of one star, namely, 
 61 Cygni, is accurately measured. 
 
 Art. III. NEW PLANETS. The discovery of the planet 
 Neptune by a distinguished French astronomer, Le 
 Verrier, is one of the most remarkable events in as- 
 tronomy ; both its existence and its place in the heav- 
 ens having been determined by mathematical calcula- 
 tion, founded on the doctrine of universal gravitation, 
 before it was seen by the telescope. The method of 
 investigation, although laborious and intricate, is not 
 difficult to be understood, and may be explained in 
 
280 NEW PLANETS. 
 
 very simple terms. The planet Uranus has long been 
 known to be subject to certain irregularities in its 
 revolution around the sun, not accounted for by all 
 the known causes of perturbation. In some cases, 
 the deviation from the true place, as given by the 
 latter, differs from actual observation two minutes of 
 a degree, a quantity, indeed, which seems small, but 
 which is still far greater than occurs in the case of the 
 other planets, Jupiter and Saturn for example, and far 
 too great to satisfy the extreme accuracy required by 
 modern astronomy. This long since suggested to as- 
 tronomers the possibility of one or more additional 
 planets, hitherto undiscovered, which, by their attrac- 
 tions, exerted on Uranus a great disturbing influence. 
 Le Verrier, assuming the existence of such a planet, 
 applied himself, by the aid of the most profound math- 
 ematical calculations guided by the law of gravitation, 
 to the inquiry : Where is it situated at what distance 
 from the sun and in what point of the starry heavens ? 
 As Saturn is nearly twice as far from the sun as Ju- 
 piter, and Uranus just twice as far as Saturn, he in- 
 ferred that, if a planet exists beyond Uranus, its dis- 
 tance is probably twice that of Uranus, or about thirty- 
 six millions of miles from the sun. After reasoning 
 from analogy, and the doctrine of universal gravita- 
 tion, respecting the position and quantity of matter 
 which a body must have in order to occasion the per- 
 turbations of Uranus to be accounted for, and sub- 
 mitting the whole to mathematical calculation, he was 
 enabled to say that the planet was just then passing 
 its opposition, and was consequently most favorably 
 situated for observation, and, on account of the slow- 
 ness of its motion, would remain in a very favorable 
 position for three months afterwards. Le Verrier 
 wrote to M. Galle, a practical astronomer of Berlin, 
 communicating his latest results, and requesting him 
 to reconnoitre for the stranger, directing his telescope 
 to a point about five degrees eastward of the well- 
 known star Delta Capricorni. That astronomer no 
 
 
NEW PLANETS. 281 
 
 sooner pointed his telescope to the region assigned, 
 than he at once recognised the body, its place being 
 only 52 minutes of a degree distant from thje position 
 marked out for it by Le Verrier, and its apparent di- 
 ameter being almost the same that he had assigned. 
 
 By a singular coincidence, a young mathematician 
 of the University of Cambridge, (Eng.,) Mr. Adams, 
 had, without the least knowledge of what M. Le Ver- 
 rier was doing, arrived at the same great result. But 
 having failed to publish his paper until the world was 
 made acquainted with the facts through the other 
 medium, he has lost much of the honor which the 
 priority of the discovery would have gained for him. 
 Thus two distinguished mathematicians, unknown to 
 each other, and by entirely independent processes, ar- 
 rived at the same results, as regarded both the exist- 
 ence of the supposed planet, and the region of the 
 starry heavens where at that time it lay concealed ; 
 and, to crown all, astronomers, in obedience to the 
 directions of one of them, pointed their telescopes to 
 the spot, and found it there. The conviction on the 
 mind of every one was, that nothing but absolute truth 
 could abide a test so unequivocal. 
 
 This is justly regarded as one of the greatest results 
 ever reached by pure mathematical reasoning; and 
 nothing could better convince us of the power of the 
 Calculus, (the highest branch of mathematical science,) 
 as an instrument for guiding human thought in the 
 investigation of truth, than its pointing out the place 
 of a body, which had lain concealed in the starry fir- 
 mament from the creation of the world to the present 
 time, and which is so small as to be visible only to a 
 large telescope. It is like finding a single pearl buried 
 in the depths of the ocean, or a grain of gold hidden 
 among the sands of the seashore. Nor has any dis- 
 covery ever more fully illustrated the immutability of 
 truth, and its fertility, or that property by which the 
 discovery of one great truth conducts the human mind 
 to others which before lay entirely beyond its reaoh. 
 
282 CENTER OF THE UNIVERSE. 
 
 This, as well as many other great truths hidden in the 
 abysses of the universe, is among the legitimate fruits 
 of Newton's grand discovery the law of Universal 
 Gravitation. ^. 
 
 One satellite accompanying Neptune has already 
 been discovered, and the existence of another satellite, 
 and of a ring resembling that of Saturn, is strongly 
 suspected, but is not fully confirmed. 
 
 Asteroids. In addition to the four small planets, 
 Ceres, Pallas, Juno, and Vesta, discovered near the 
 beginning of the present century, and having their 
 orbits in the long space between Mars and Jupiter, 
 five more similar bodies have recently been revealed 
 to us, lying in the same region of the heavens, namely 
 Astrcea, Iris, Hebe, Flora, and Metis. Like the former, 
 they are very small bodies, as faint stars visible only 
 to the telescope, and are characterized by orbits of 
 greater eccentricity than those of the old planets. 
 This multiplication of asteroids faintly countenances 
 the hypothesis of Dr. Olbers, one of the original dis- 
 coverers of this class of bodies, that " they are frag- 
 ments of a single large planet that once occupied the 
 same region between Mars and Jupiter." 
 
 Art. IV. CENTER OF THE UNIVERSE. At the end of the 
 preceding work, we have suggested reasons for be- 
 lieving that the whole host of heaven revolve around 
 a common center. Dr. Maedler, of the Imperial Ob- 
 servatory at Dorpat, has recently not only asserted 
 this doctrine, but has endeavored to show the exact 
 position of that center. He fixes it jn the Pleiades, 
 and asserts that Alcyone, the brightest star of this 
 group, is the true " central sun," around which all the 
 stars of our visible firmament revolve, in obedience to 
 the law of universal gravitation. The proofs of this 
 remarkable hypothesis are deemed too incomplete, at 
 present, to command entire assent ; but the method of 
 investigation pursued by this distinguished astrono- 
 mer, opens a new field of observation and of specula- 
 
TELESCOPES. 283 
 
 tion, and promises to lend a new interest to inquirers 
 into the mechanism of the heavens. 
 
 Art. V. TELESCOPES. Practical Astronomy has of 
 late been enriched with a number of great telescopes, 
 which have discovered new wonders in the starry 
 heavens. The most remarkable of these are the grand 
 Reflector constructed by Lord Rosse, an Irish noble- 
 man, and the great Refractors belonging respectively 
 to the Pulkova, the Cincinnati, and the Cambridge 
 observatories. 
 
 Lord Rosse's telescope considerably exceeds in di- 
 mensions the great 40 feet reflector of Sir William 
 Herschel, being 50 feet in focal length, and having a 
 diameter of 6 feet ; whereas that of the Herschelian 
 telescope was only 4 feet. This unexampled magni- 
 tude makes this instrument superior to all others in 
 light, and fits it pre-eminently for observations on the 
 most remote and obscure celestial objects, as the faint- 
 est nebulae, for example. But its unwieldy size, and 
 its liability to loss of power by the tarnishing or tem- 
 porary blurring of the great speculum, will render it 
 far less available for actual research than the great 
 refractors which come in competition with it. 
 
 Until recently, it was thought impossible to form 
 achromatic object-glasses for telescopes of more than 
 about five inches diameter ; but they have been suc- 
 cessively enlarged, until we can no longer set bounds 
 to the dimensions which they may finally assume. 
 The Pulkova telescope (at St. Petersburg) has a clear 
 aperture of about 15 inches and a focal length of 22 
 feet. That of Cincinnati is somewhat smaller, its ob- 
 ject-glass being 12 inches in diameter, and its length 
 17 feet. The telescope recently acquired by Harvard 
 University, is perhaps the finest refractor hitherto 
 constructed. Its dimensions are nearly the same with 
 those of the Pulkova instrument, but its performances 
 are thought to be superior even to that. It has recently 
 added to the system of Saturn an eighth satellite. 
 
284 TELESCOPES. 
 
 These magnificent telescopes have afforded views 
 of celestial 'objects, more splendid and exciting than 
 any previously enjoyed by man. In a scientific point 
 of view, the most interesting of these revelations con- 
 sist in the resolution of Nebulae before deemed irre- 
 solvable, and thus countenancing the idea that this 
 term is applicable only to the comparative powers of 
 our instruments ; that, if any objects of this class re- 
 main unresolved, it will only be because the telescope 
 has not yet acquired the requisite power to separate 
 them into stars. Under these mighty instruments, 
 what was before a faint wisp of fog on the confines 
 of creation, expands suddenly into innumerable suns, 
 composing a glorious firmament of stars. The Cam- 
 bridge telescope has succeeded in the resolution of the 
 great Nebula of Orion, more complete than had been 
 effected even by Lord Rosse's " Leviathan Reflector," 
 and is thus proved to be one of the finest instruments 
 (probably the finest refractor) in the world. 
 
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