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THE 
 
 PLANETARY 
 
 AND 
 
 STELLAR WORLDS: 
 
 A POPULAR EXPOSITION 
 
 GREAT DISCOVERIES AND THEORIES 
 
 MODEEN ASTRONOMY. 
 
 IN A SERIES OF TEN LECTURES 
 
 BY 0. 1LMITCHEL, A.M. 
 
 DIRECTOR OF THE CINCINNATI OBSERVATORY. 
 
 NEW YORK: 
 CHARLES SCRIBNER. 
 
 36 PARK ROW. AND 145 NASSAU Si. 
 
 1852. 
 

 Entered, according to Act of Congress, in the year 1848, by 
 
 O. M. MITCHEL, 
 
 In the Clerk's Office of the District Court for the D : ?trict of Ohie 
 
PREFACE. 
 
 A few \vords in explanation of the circumstances under 
 which this volume is presented to the public, may not be 
 unacceptable to the reader. It is now a little more than six 
 years since the writer conceived the idea of erecting a great 
 astronomical observatory in the city of Cincinnati. My at- 
 tention had been for many years directed to this subject, by 
 the duties of the professorship, which I then held in the col- 
 lege. In attempting to communicate the great truths of astro- 
 nomy, there were no instruments at hand, to confirm and fix 
 the wonderful facts recorded in the books. Up to that period 
 our country, and the west particularly, had given but little 
 attention to practical astronomy. A few individuals, with a 
 zeal and ardor deserving of all praise, had struggled on to 
 eminence almost without means or instruments. An isolated 
 telescope was found here and there scattered through the 
 country ; but no regularly organized observatory with power- 
 ful instruments, existed within the limits of the United States, 
 so far as I know. 
 
 To attempt the building of an observatory of the first class, 
 and to furnish it with instruments of the highest order, with- 
 out any aid from the general or state government, but by the 
 voluntary contribution of all classes of citizens, was an enter- 
 prise of no common difficulty. To ascertain whether any 
 interest could be excited in the public mind, in favor of astro- 
 nomy, in the spring of 1842 a series of lectures was delivered 
 
 fiii) 
 
IV PREFACE. 
 
 in the hall of the Cincinnati College. To give an increased 
 effect to these discourses (which were unwritten, and in a 
 style of great simplicity), a mechanical contrivance was pre- 
 pared, by the aid of which the beautiful telescopic views in 
 the heavens were presented to the audience, with a brilliancy 
 and power scarcely inferior to that displayed by the most 
 powerful telescopes. To this fortunate invention were these 
 lectures, no doubt, principally indebted for the interest which 
 they produced, and which occasioned them to be attended by 
 a very large number of the intelligent persons in the city. 
 Encouraged by the large audiences, which continued through 
 two months to fill the lecture-room, and still more by the 
 request to repeat the last lecture of the course in one of the 
 great churches of the city, I matured a plan for the building 
 of an observatory, which it was resolved should be presented 
 to the audience at the close of the lecture, in case circum- 
 stances should favor. Through the kindness of a few friends, 
 who were now beginning to take a deep interest in the matter, 
 more than two thousand persons were in attendance ; and it 
 seemed that the moment had arrived for taking the first step in 
 an enterprise whose fate it was impossible to predict. 
 
 Having closed the subject under discussion, the audience 
 w r ere requested to give me a few minutes of time, for the 
 explanation of a matter which it was hoped would not be 
 received without some feelings of interest and approbation. 
 The rapid advances of astronomy in Europe were then referred 
 to — the erection of observatories in all parts of the world — -the 
 variety of magnificent instruments in Russia and Germany, in 
 France and England, and the utter deficiency of our own 
 ountry in every thing pertaining to the science of the stars. 
 
PREFACE. V 
 
 The past neglect was easily accounted for, and might be ex- 
 cused ; the future scientific character of the country rested with 
 the people, and upon them devolved the responsibility of pro- 
 viding the means for original research. In Europe, imperial 
 treasure and princely munificence could build the temples of 
 science ; under a free government no such means existed, and 
 to accomplish the erection of these great scientific institutions, 
 the intelligent liberality of the whole community was the only 
 resource. But it had been denied that this resource could be 
 relied on ; and it had been roundly asserted that, in the nature 
 of things, the United States must ever remain grossly defec- 
 tive in all the appliances for scientific research. To test the 
 truth or falsehood of these statements w r as not a difficult mat- 
 ter; and thus encouraged by the interest already manifested in 
 behalf of astronomy, I had already resolved to devote jive 
 years of faithful effort to accomplish the erection of a great 
 astronomical observatory in the city of Cincinnati. 
 
 This announcement w r as received with every mark of favor, 
 and the following simple plan was at once presented. The 
 entire amount required to erect the buildings and purchase the 
 instruments, should be divided into shares of twenty-five dol- 
 lars ; every shareholder to be entitled to the privileges of the 
 observatory, under the management of a board of control, ta 
 be elected by the shareholders. Before any subscription 
 should become binding, the names of three hundred subscribers 
 should be first obtained. This accomplished, these three hun- 
 dred should meet, organize, and elect a board, who should 
 thenceforward manage the affairs of the association. 
 
 Such is the history of the origin of the Cincinnati Astrono- 
 mical Society. Two resolutions were taken in the outset, to 
 a2 
 
VI PREFACE. 
 
 which I am indebted for any success which may have attended 
 my own personal efforts. First : To work faithfully for Jive, 
 years, during all the leisure which could be spared from my 
 regular duties. Second : Never to become angry, under any 
 provocation, while in the prosecution of this enterprise. 
 
 In three weeks the three hundred subscribers had been ob- 
 tained. No public meeting had been called ; and these names 
 had been procured by private solicitation, and a personal 
 explanation of the nature and advantages of the enterprise. So 
 soon as the number was complete, the subscribers convened, 
 organized, elected officers and a directory, and gave me a com- 
 mission to visit Europe, to procure instruments, examine ob- 
 servatories, and obtain the requisite knowledge to erect and 
 conduct the institution which it was now hoped would be one 
 day reared. 
 
 This order being received, on the second day I started for 
 New York, and on the 16th of June, 1842, sailed for Liver- 
 pool. Having visited many of the best appointed observa- 
 tories both in England and on the continent (in each and 
 every one of which I was received with a degree of kindness 
 and attention for which I acknowledge the deepest obligations), 
 and having been unsuccessful in finding, either in London or 
 Paris, an object-glass of the size required, I finally determined 
 to visit the city of Munich. The fame of the optical insti- 
 tute of the celebrated Frauenhofer had even reached the banks 
 of the Ohio ; and it was hoped that, in that great manufactory, 
 an instrument such as the society desired might be obtained, 
 if not completed, at least in such a state of forwardness as to 
 permit it to be furnished at an early day. In this I was not 
 disappointed. An object-glass of nearly twelve inches diame- 
 
PREFACE. Vll 
 
 ter, and of superior finish, was found in the cabinet of M. 
 Mertz, the successor of Frauenhofer. This glass had been 
 subjected to a severe trial in the tube of the great refractor of 
 the Munich observatory, by Dr. Lamont, and had been pro- 
 nounced of the highest quality. 
 
 To mount this glass would require about two years, at a 
 cost of nearly ten thousand dollars ; a sum considerably 
 greater than that appropriated at the time for an equatorial 
 telescope. Having made a conditional arrangement for this 
 and other instruments, I returned to Greenwich, England, 
 where, at the invitation of Professor Airy, the Astronomer 
 Royal, I remained for some time to study. Having accom- 
 plished the objects of my journey, I returned home, and ren- 
 dered a report to a very large meeting of the members of the 
 association and other citizens of Cincinnati. 
 
 During ray absence of four months, a great change had 
 occurred in the commercial affairs of the country. Every 
 thing was depressed to the lowest point, and increased in a 
 high ratio the necessary difficulties of such an undertaking ; 
 always great, even if carried forward at a time when the 
 country is prosperous. 
 
 With great difficulty the subscription was increased to an 
 amount sufficient to warrant the ordering of the great object- 
 glass already referred to. The sum of three thousand dollars 
 was collected and remitted to meet the first payment. Even 
 this fraction of the entire sum was collected with difficulty ; 
 but as the remaining part of the price of the telescope was not 
 to be paid until the completion of the instrument, it was hoped 
 that the ample time thus allowed would render the task of 
 collection comparatively easy. 
 
Viii PREFACE. 
 
 The principal instrument having been ordered, and the first 
 payment on its cost made, attention was now given to the pro- 
 curing of a suitable site for the building. Fortunately for the 
 society, the place of all others most perfectly adapted to their 
 wants, was then the property of Nicholas Longworth, Esqr. 
 It is a lofty hill-top, rising some four hundred feet above the 
 level of the city, and commanding a perfect horizon in all 
 directions. On making known to Mr. Longworth the pros- 
 pects and wants of the Astronomical Society, the writer was 
 directed by him to select four acres on the hill-top, out of a 
 tract of some twenty-five acres, and to proceed at once to en- 
 close it, as it would give him great pleasure to present it to 
 the association. On compliance with the conditions of the 
 title-bond, a deed has since been received, placing the society 
 in full possession of this elegant position. 
 
 Preparations were now made to commence the erection of 
 the building for the observatory. The grounds were enclosed, 
 a road built, rendering the access to the hill-top comparatively 
 easy, the excavations for the foundations were made, and, on 
 the 9th day of November, 1843, the corner-stone of the pier 
 which was to sustain the great Refracting Telescope, was 
 laid by John Quincy Mams, with appropriate ceremonies. 
 On this occasion Mr. Adams made his last great oration. The 
 deep interest which he had taken in astronomical science, 
 warranted the hope that he might be induced to visit the west, 
 on the occasion of laying the foundation-stone of the first great 
 popular observatory ever erected in the United States. This 
 hope was not disappointed. The unaffected devotion of this 
 truly great man to th3 interests of his country, were, perhaps, 
 never more perfectly exhibited than in his ready acquiescence 
 
PREFACE. IX 
 
 *o comply with the wishes of the astronomical society, that he 
 should perform for them the important services on which the 
 future success of this new enterprise in no small degree de- 
 pended. His high character, his advanced age, the length of 
 the journey, the inclemency of the season, all combined to 
 exhibit to his countrymen the depth of his interest in a cause 
 which could induce such sacrifices. 
 
 After the laying of the corner-stone, the lateness of the 
 season, and other causes, induced a suspension of the work on 
 the building for the winter ; and it was not resumed until May, 
 1844. In the mean time, after incredible difficulty, the entire 
 amount called for in the payment for the great telescope, 
 was collected and remitted; and, the society was left with 
 scarcely a dollar of available means, to commence the erection 
 of a building which, according to the plan, would cost some 
 seven or eight thousand dollars. 
 
 It was believed that the intelligent mechanics of Cincinnati 
 would lend their powerful aid in the accomplishment of an 
 enterprise which had progressed far enough to give some con- 
 fidence in its ultimate success. With little or no means the 
 building was commenced, trusting to activity and perseverance 
 to supply the means as the work progressed. During the 
 first week but three workmen were employed ; but by the 
 commencement of the next week the funds had been obtained 
 to pay these, and to double their number. In six weeks not 
 less than one hundred hands were at work on the hill-top and 
 in the city. Mechanics of all trades subscribed for stock, and 
 paid their subscription in work. The stone of which the 
 ouilding is erected, was quarried from the grounds of the 
 society. The lime was burnt on the hill, and every means 
 
X PREFACE. 
 
 was adopted to reduce the necessary expenditure. Payment 
 for stock in the society was received in every possible article 
 of trade ; due-bills were taken, and these were converted into 
 others which would serve in the payment of bills. 
 
 In this way the building was reared, and finally covered in, 
 without incurring any debt. But the conditions of the bond, 
 by which the lot of ground was held, required the completion 
 of the observatory in two years from its date ; and these two 
 years would expire in June, 1845. It was seen to be impos- 
 sible to carry forward the building fast enough to secure its 
 completion by the required time, without incurring some debt. 
 My own private resources were used, in the hope that a short 
 time after the finishing of the observatory would be sufficient 
 to furnish the funds to meet all engagements. The work was 
 pushed rapidly forward. In February, 1845, the great tele- 
 scope safely reached the city of Cincinnati ; and in March the 
 building was ready for its reception. I had now exhausted 
 all my private means, and, to increase the difficulty of the 
 position in which I was placed, the College edifice took fire 
 and burned to the ground. My ordinary means of support 
 were thus destroyed at a single blow. I had engaged to con- 
 duct the observatory, without compensation from the society, 
 for ten years, in the hope that my college salary would be suf- 
 ficient for my wants. It was impossible to abandon the 
 observatory. The college could not be rebuilt, at least for 
 several years, and in this emergency I found it necessary to 
 seek some means of support, least inconsistent with my duties 
 in the observatory. My public lectures at home had been 
 comparatively well received, and after much hesitation it was 
 resolved to make an experiment elsewhere. For five years I 
 
PREFACE. XI 
 
 had been pleading the cause of science among those little 
 acquainted with its technical language. I had become habitu- 
 ated to the use of such terms as were easily understood ; and 
 probably to this circumstance, more than to any other one 
 thing, am I indebted for any success which may have attended 
 my public lectures. To the citizens of Boston, Brooklyn, 
 New York, and New Orleans, for the kindness with which 
 they were pleased to receive my imperfect efforts, I am deeply 
 indebted. My lectures were never written, and no idea was 
 entertained of publishing a course, until the partiality of my 
 friends induced me to attempt this experiment. 
 
 Such are the circumstances under which this effort to trace 
 the career of the human mind, in its researches among the 
 stars, has been undertaken. No one science, perhaps, so per- 
 fectly illustrates the gradual growth and development of the 
 powers of human genius. The movement of the mind has 
 been constantly onward — its highest energies have ever been 
 called into requisition — and there never has been a time when 
 astronomy did not present problems not only equal to all that 
 man could do, but passing beyond the limits of his greatest 
 intellectual vigor. Hence, in all ages and countries, the abso- 
 lute strength of human genius may be measured by its reach 
 to unfold the mysteries of the stars. 
 
 It will be seen that in the following lectures one single 
 object has engaged*the attention of the writer — the structure 
 of the universe, so far as revealed by the mind of man. 
 The uses of science have in no way been considered. The 
 effects on the mind, on society, on civilization, on commerce, 
 on religion, have not been permitted to mar the unity of the 
 original design. The onward, steady, triumphant march of 
 
XU PREFACE. 
 
 mind, in its study and exploration of the universe of God, has 
 been my only object, the single theme of the entire series. 
 
 I may be pardoned for a single word, before taking leave of 
 the reader, touching the condition of our country with refer- 
 ence to practical astronomy. Within a few years an entire 
 revolution on this subject has occurred. The reproach which 
 once rested on the United States has been removed. Several 
 magnificent instruments now adorn the observatories of the 
 New World, and the contributions of American astronomers, 
 to science, are beginning to change the scientific character of 
 our country in the eyes of the old World. It is gratifying 
 to know that several institutions, with ample means of support, 
 now exist in our country, to which the interests of American 
 science are committed with entire confidence. The obser- 
 vatories at Washington, Cambridge, Philadelphia, and George- 
 town, are amply provided with instruments, and an efficient 
 corps of observers are constantly occupied in their use. 
 
 For a long time to come, one principal object will engage 
 the instruments of the Cincinnati observatory, viz., the explo- 
 ration of the heavens south of the equator, and the re-measure- 
 ment of Striive's double stars in that region. Should this work 
 progress but slowly, let it be remembered that the director of 
 the observatory has no assistant, out of his own immediate 
 family, and must devote a large portion of his time to other 
 duties, far more closely allied to the earth than the stars. 
 
 Cincinnati Observatory, 
 
 Mount Mams, May, 1848. 
 
TABLE OF CONTENTS. 
 
 LECTURE I. 
 
 AN EXPOSITION OF THE PROBLEM WHICH THE HEAVENS PRE- 
 SENT FOR SOLUTION. 
 
 First revolution of the Heavens witnessed by man, 18. The 
 curiosity excited and its effects, 19. Object of the course, 20. 
 The astronomer lives in all ages, 22. First problem to distinguish 
 between real and apparent motion, 23. The relations of the sun, 
 and earth, and moon, 24. The wandering stars or planets, 25. 
 Fixed stars, points of reference, 27. Complexity of the planetary 
 movements, 28. Discovery of the true center of motion, 29. The 
 planets form a system; their orbits, laws, stability, 31. Pertur- 
 bations, 32. Analytic machinery, 33. Examination of the starry 
 heavens, 34. Distance of the fixed stars to be determined, 35. 
 Motions among the stars, 36. The binary systems; movement 
 of the sun in space, 37. Investigations yet to be made, and pro- 
 bable success, 39. 
 
 LECTURE II. 
 
 THE DISCOVERIES OF THE PRIMITIVE AGES. 
 
 The founder of the science of astronomy unknown, 42. First 
 discovery on the moon, 43. Her motion among the stars and her 
 phases, 44. Cause of the phases sought; two revolutions of the 
 moon discovered, 45. First ideas of the constellations; North 
 Star, 47. Motions of the sun and moon among the stars ; the 
 starry heavens surround the earth, 48. First measure of the year, 
 49. A moving star discovered, 50. Periods of the planets deter- 
 mined, 53. The sun's apparent motion the subject of perplexity, 
 55. The equinoxes and solstices, 56. Inequality in the sun's 
 motion detected, 57. The construction of the sphere, 58. Its 
 uses in observing, 59. Eclipses of the sun and moon and their 
 effects, 60. Explanation of solar eclipses; discovery of the moon's 
 reflective light, and explanation of her phases, 61. Lunar eclipses 
 explained; prediction of the first eclipse, 65. Value of recorded 
 eclipses, 68. 
 
 B Cxiii) 
 
XIV TABLE OF CONTENTS. 
 
 LECTURE III. 
 
 THEORIES FOR THE EXPLANATION OF THE MOTIONS OF THE 
 HEAVENLY BODIES. 
 
 The names of early discoverers lost, 70. Chaldean period 
 found among many nations; the days of the week, and their names, 
 place of the vernal equinox, 71. Precession of the equinoxes, 73. 
 Astronomy of the primitive ages, and condition of the mind at the 
 beginning of the era reached by history, 75. Causes retarding 
 the progress of astronomy, 77. The confounding of true and 
 apparent motion; immobility of the earth and its central position, 
 78. The Greek astronomers, Pythagoras, Nicetas, Hipparchus, 
 Ptolemy, 80. System of Ptolemy, 82. Astronomy cultivated by 
 the Arabs, 82. The era of modern science commences, 84. Co- 
 pernicus and his discoveries, 86. His system promulged with 
 great caution, 87. Kepler, the character of his mind, his mode 
 of research, 91. His great discoveries; he finds the orbits of the 
 planets, 92. Detects his second law, 93. His efforts to find the 
 third law successful. 98. Importance of these laws, 99. 
 
 LECTURE IV. 
 
 DISCOVERY OF THE GREAT LAWS OF MOTION AND GRAVITATION 
 
 The philosophy of Aristotle — its hold on the mind, 101. Cha- 
 racteristics of Galileo's mind, 102. He detects the errors of Aris- 
 totle, 103. Attacks his theories, and demonstrates their falsehood 
 by experiment, 104. Driven from Pisa by his enemies, 105. 
 Discovers the law of falling bodies, 106. Adopts the Copernican 
 theory, 107. Constructs a telescope, 108. His discoveries in the 
 moon, and among the planets and fixed stars, 110. Phases of 
 Venus, 111. Questions relating to the planetary motions, 113. 
 Laws of motion; the centrifugal force, 114. Problem presented 
 for solution to Newton, 116. Discoveries of Descartes; conjec- 
 tures of Kepler, 117. Measure of the moon's distance and of the 
 earth's circumference, 118. The law of gravitation — Newton's 
 first effort to demonstrate the truth of this law, 121. He finally 
 shows that the moon is ever falling towards the earth, and proves 
 the law, 124. Enunciation of his great law, 125. Discovers 
 that the planets may revolve in conic sections, 126. Contrast 
 between Kepler's and Newton's methods of research, 128. 
 
 LECTURE V. 
 
 UNIVERSAL GRAVITATION APPLIED TO THE EXPLANATION OF 
 THE PHENOMENA OF THE SOLAR SYSTEM. 
 
 The era of physical astronomy commences, 132. A theoretic 
 system proposed and discussed; a central sun and solitary planet, 
 
TABLE OF CONTEXTS. XV 
 
 133. Planets and satellites added and their effects considered, 
 136. How the imagined system may be made the system of na- 
 ture, 137. Discussion of the relative motions of the sun. moon 
 and earth, under the action of their mutual influences. 139. The 
 moon's acceleration ; motion of her apsides, nodes, &c, and the 
 discovery of the change in the figure of the earth's orbit, 146. 
 Perplexity occasioned by the seeming discrepancy between the 
 observed and computed motion of the moon's perigee, 149. Fi- 
 nally removed by Clairault, 150. Changes in the earth's figure 
 occasioned by its rotation, 153. The form of equilibrium reached, 
 155. The precession of the equinoxes caused by the protuberant 
 matter at the earth's equator, 157. 3Ioon affected by the re- 
 dundant matter at the earth's equator, 160. Wonderful questions 
 answered by an examination of the moon, 161. 
 
 LECTURE VI. 
 
 THE STABILITY OF THE PLANETARY SYSTEM. 
 
 Rapid survey of the system, 165. General characteristics of 
 the planets, 166. What phenomena gravitation must account for, 
 167. Stability not the sole object of the Creator, 168. Laws of 
 matter selected in wisdom, 170. By how much does the central 
 force diminish the primitive velocity of a planet ! 171. Changes 
 in the elements of the orbits of the planets, 174. The eccentri- 
 city. 175. Stability of the principal axes, 176. Motion of the 
 perihelion. 177. The inclinations, 180. The lines of nodes, 181. 
 The periodic times, 183. Stability of the great system, 185. Of 
 the system of the earth and moon, 186. Of Jupiter's svstem, 
 187. * Of Saturn's system, 190. 
 
 LECTURE VII. 
 
 THE DISCOYERY OF THE NEW PLANETS. 
 
 Kepler's speculations, 194. Discovery of Uranus, 195. Bode's 
 law of interplanetary spaces, 196. The astronomical congress 
 of Lilienthal, in 1800, 198. Piazzi's discovery of a new planet, 
 Ceres ; its loss and rediscovery, 200. The symmetry of the sys- 
 tem destroyed by the discovery of Pallas, 201. Olbers's theory of 
 the bursting of a planet, 202. Discovery of Juno and Vesta. 203. 
 Hen eke discovers iVstrea and Hebe, 204. Hind discovers Iris 
 and Flora, 204. Search for a planet beyond Uranus commenced, 
 206. Causes of this search. 207. Leverrier's researches on Mer- 
 cury, 209. Its transit in May, 1845,211. Leverrier presents his 
 computations to the French Academy, 212. Popular exhibition 
 of his reasoning, 215. The hypothetical planet found by Galle, 
 of Berlin, 216. Adams's computations, 217. The new planet 
 detected by its disc,218. Walker's computations, 2 19. Pierce's 
 views. 22*1. Leverrier claims Neptune to be the planet of 
 theorv. 
 
XVI TABLE OF CONTENTS. 
 
 LECTURE VIII. 
 
 THE COMETARY WORLDS 
 
 Characteristics of comets, 223. Reduced to law by Newton, 
 225. The comet of 1680, 226. Halley's comet of 1682, 227. Its 
 return in 1759 predicted, 229. Its return in 1835,231. Won- 
 derful changes in its magnitude, 233. Encke's comet, 235. Ap- 
 proaching the sun, 236. Resisting medium, 237. Biela's comet, 
 238. Fears excited of collision with the earth, in 1832,239. Its 
 nebulous character, 240. Its double character in 1846. Sepa- 
 ration of the comets, 242. Vast periods of some comets, 244. 
 Comets seen to transit the sun's disc, 246. Comets accounted for 
 by Laplace's nebular hypothesis, 247. Herschel's theory of the 
 physical condition of comets, 250. His theory accounts for the 
 diminishing period of Encke's comet, 251. Zodiacal light, 252. 
 
 LECTURE IX. 
 
 THE SCALE ON WHICH THE UNIVERSE IS BUILT. 
 
 Scale of the planetary system, 253. Radius of the earth's orbit 
 too small a unit, 254. The velocity of light determined from the 
 eclipses of Jupiter's satellites, and employed as a unit, 256. 
 Parallax of the fixed stars, 258. No parallax sensible to the 
 naked eye, 260. Great distance of the fixed stars inferred from 
 this fact, 261. Bradley's researches for parallax, 263. Discovery 
 of nutation and its value, 264. Discovery of aberration — its 
 explanation, 266. Herschel's researches for parallax, 269. Dis- 
 covery of the revolving stars, 270. Power of modern telescopes, 
 271. Bessel discovers the parallax of 61 Cygni, 273. 
 
 LECTURE X. 
 
 THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 
 
 Distances separating man from the stars, 290. Various diffi- 
 culties in the research for their motions, 291. Hipparchus dis- 
 covers a new and brilliant star, 292. The new star of 1572, 293. 
 The new star of 1604, 294. The disappearance of old stars, 295. 
 Changes of Algol, 295. Periodical stars, 296. Gravitation ex- 
 tended to the sphere of the fixed stars, 297. Periods of some of 
 the binary systems, 298. Herschel sounds the depth of the Milky 
 Way, 299. Seeks the direction of the solar motion, 300. His 
 reasoning, 302. Argelander's research for the point towards 
 which the solar system is moving, 306. Struve's investigation 
 for the quantity of angular motion of the system, as seen from 
 stars of the first magnitude, 308. His father's research for the 
 relative distances of stars of different magnitudes, 310. Peters's 
 research for the parallax of stars of the second magnitude, 311. 
 Maedler's theory of the central sun, 319. The attributes of God, 
 as displayed in the universe, 324. 
 
THE 
 
 STRUCTURE OF THE UNIVERSE. 
 
 INTRODUCTORY LECTURE. 
 
 AN EXPOSITION OF THE PROBLEM WHICH THE HEAVENS 
 PRESENT FOR SOLUTION. 
 
 The subject to which your attention is invited, 
 claims no specific connexion with the every day 
 struggle of human life. Far away from the earth on 
 which we dwell, in the blue ocean of space, thou- 
 sands of bright orbs, in clusterings and configura- 
 tions of exceeding beauty, invite the upward gaze of 
 man, and tempt him to the examination of the won- 
 derful sphere by which he is surrounded. The starry 
 heavens do not display their glittering constellations 
 in the glare of day, while the rush and turmoil of 
 business incapacitate man for the enjoyment of their 
 solemn grandeur. It is in the stillness of the mid- 
 night hour, when all nature is hushed in repose, when 
 the hum of the world's on going is no longer heard, 
 that the planets roll and shine, and the bright stars, 
 trooping through the deep heavens, speak to the wil- 
 ling spirit that would learn their mysterious being. 
 
 Often have I swept backward in imagination six 
 thousand years, and stood beside our Great Ances- 
 
 B2 (IT) 
 
18 STRUCTURE OF THE UNIVERSE. 
 
 tor, as he gazed for the first time upon the going 
 down of the sun. What strange sensations must 
 have swept through his bewildered mind, as he watch- 
 ed the last departing ray of the sinking orb, uncon- 
 scious whether he should ever behold its return. 
 Wrapt in a maze of thought, strange and startling, 
 his eye long lingers about the point at which the 
 sun had slowly faded from his view. A mysterious 
 darkness, hitherto unexperienced, creeps over the face 
 of nature. The beautiful scenes of earth, which 
 through the swift hours of the first wonderful day of 
 his existence, had so charmed his senses, are slowly 
 fading one by one from his dimmed vision. A gloom 
 deeper than that which covers earth, steals across the 
 mind of earth's solitary inhabitant. He raises his 
 inquiring gaze towards heaven, and lo ! a silver 
 crescent of light, clear and beautiful, hanging in the 
 western sky, meets his astonished eye. The young 
 moon charms his untutored vision, and leads him up- 
 ward to her bright attendants, which are now steal- 
 ing one by one, from out the deep blue sky. The 
 solitary gazer bows, and wonders, and adores. The 
 hours glide by— the silver moon is gone — the stars are 
 rising — slowly ascending the heights of heaven — and 
 solemnly sweeping downward in the stillness of 
 the night. The first grand revolution to mortal vision 
 is nearly completed. A faint streak of rosy light is 
 seen in the east — it brightens — the stars fade — the 
 planets are extinguished — the eye is fixed in mute 
 astonishment on the growing splendor, till the first 
 rays of the returning sun dart their radiance on the 
 young earth and its solitary inhabitant. To him " the 
 evening and the morning were the first day." 
 
INTRODUCTORY LECTURE. 19 
 
 The curiosity excited on this first solemn night — the 
 consciousness that in the heavens God had declared 
 his glory — the eager desire to comprehend the mys- 
 teries that dwell in these bright orbs, have clung to 
 the descendants of him who first watched and won- 
 dered, through the long lapse of six thousand years. 
 In this boundless field of investigation, human genius 
 has won its most signal victories. — Generation after 
 generation has rolled away, age after age has swept 
 silently by, but each has swelled by its contribution 
 the stream of discovery. — One barrier after another 
 has given way to the force of intellect — mysterious 
 movements have been unravelled — mighty laws have 
 been revealed — ponderous orbs have been weighed, 
 their reciprocal influences computed, their complex 
 wanderings made clear, until the mind, majestic 
 in its strength, has mounted step by step up the 
 rocky height of its self-built pyramid, from whose star- 
 crowned summit it looks out upon the grandeur of 
 the universe, self-clothed with the prescience of a 
 God.- — With resistless energy it rolls back the tide 
 of time, and lives in the configuration, of rolling 
 worlds a thousand years ago, or more wonderful, it 
 sweeps away the dark curtain from the future, and 
 beholds those celestial scenes which shall greet the 
 vision of generations when a thousand years shall 
 have rolled away, breaking their noiseless waves 
 on the dim shores of eternity. 
 
 To trace the efforts of the human mind in this 
 long and ardent struggle, to reveal its hopes and 
 fears, its long years of patient watching, its moments 
 of despair and hours of triumph — to develop the means 
 by which the deep foundations of the rock-built pyra- 
 
20 STRUCTURE OF THE UNIVERSE. 
 
 mid of science have been laid, and to follow it as it 
 slowly rears its stately form from age to age, until its 
 vertex pierces the very heavens — these are the ob- 
 jects, proposed for accomplishment, and these are the 
 topics to which I would invite your earnest attention. 
 The task is one of no ordinary difficulty. It is no 
 feast of fancy, with music and poetry, with eloquence 
 and art, to enchain the mind. Music is here— but 
 it is the deep and solemn harmony of the spheres. 
 Poetry is here— but it must be read in the characters 
 of light, written on the sable garments of night. 
 Architecture is here — but it is the colossal structure 
 of sun and system, of cluster and universe. Eloquence 
 is here — but " there is neither speech nor language. — 
 Its voice is not heard," yet its resistless sweep comes 
 over us in the mighty periods of revolving worlds. 
 
 Shall we not listen to this music, because it is 
 deep and solemn? Shall we not read this poetry, 
 because its letters are the stars of heaven? — Shall 
 we refuse to contemplate this architecture, because 
 " its architraves, its archways, seem ghostly from in- 
 finitude." Shall we turn away from this surging 
 eloquence, because its utterance is made through 
 sweeping worlds ? No — the mind is ever inquisitive, 
 ever ready to attempt to scale the most rugged steeps. 
 Wake up its enthusiasm— fling the light of hope on 
 its pathway, and no matter how rough, and steep, 
 and rocky it may prove, onward! is the word which 
 charms its willing powers. 
 
 It is not my wish or design to introduce you to 
 the dark technicalities of science, neither do I propose 
 to rest satisfied with the barren statement of the 
 results which have been reached by the efforts of 
 
INTRODUCTORY LECTURE. 21 
 
 genius. While on the one hand I shall endeavor to 
 shun all attempt at critical scientific demonstration, 
 which could only be intelligible to the professed 
 student of astronomy, I shall on the other hand 
 fearlessly attempt such an exposition of the processes 
 and trains of reasoning by which great truths have 
 been elicited, as to show to every intelligent mind 
 that the problem is not impossible ; by simplicity of 
 language, by familiar illustrations, to fling light 
 enough upon these mysterious propositions, to show 
 a pathway, though it be dim and rugged, still a 
 pathway, which if pursued shall certainly lead to a 
 full and perfect solution. I ask, then, no critical 
 previous knowledge of the subject, on the part of 
 those who would follow me in the wonderful devel- 
 opments which I am about to attempt. Give me 
 but your earnest and unbroken attention. Go with 
 me in imagination, and join in the nightly vigils of 
 the astronomer, and while his mind with powerful 
 energy struggles with difficulty, join your own sym- 
 pathetic efferts with his — hope with his hope — trem- 
 ble with his fears — rejoice with his triumphs. Lend 
 me but this kind of interest, and my task is already 
 half accomplished. 
 
 Before proceeding to an actual exposition of the 
 structure of the Heavens, I propose in this introductory 
 lecture to announce the nature of the problem, which 
 the mind has essayed to resolve, and to point out the 
 more important auxiliaries, mental and mechanical, 
 which it has conjured to its aid. If the difficulties of 
 this problem should overwhelm the mind, let it be 
 remembered that the astronomer has ever lived, and 
 never dies. The sentinel upon the watchtower is 
 
22 STRUCTURE OF THE UNIVERSE. 
 
 relieved from duty, but another takes his place, and 
 the vigil is unbroken. No — the astronomer never dies. 
 He commences his investigations on the hill tops of 
 Eden — he studies the stars through the long centuries 
 of antideluvian life. The deluge sweeps from the 
 earth its inhabitants, their cities and their monu- 
 ments — but when the storm is hushed, and the heav- 
 ens shine forth in beauty, from the summit of Mount 
 Arrarat the astronomer resumes his endless vigils. 
 In Babylon he keeps his watch, and among the Egyp- 
 tian priests he inspires a thirst for the sacred mys- 
 teries of the jl oars. The plains of Shinar — the temples 
 of India — the pyramids of Egypt, are equally his 
 watching places. When science fled to Greece, his 
 home was in the schools of her philosophers; and 
 when darkness covered the earth for a thousand 
 years, he pursues his never ending task from amidst 
 the burning deserts of Arabia. When science dawn- 
 ed on Europe, the Astronomer was there — toiling with 
 Copernicus — watching with Tycho — suffering with Ga- 
 lileo — triumphing with Kepler. Six thousand years 
 have rolled away since the grand investigation com- 
 menced. We stand at the terminus of this vast pe- 
 riod, and looking back through the long vista of de- 
 parted years, mark with honest pride the successive 
 triumphs of our race. Midway between the past and 
 future, we sweep backward and witness the first rude 
 effort to explain the celestial phenomena — we may 
 equally stretch forward thousands of years, and al- 
 though we cannot comprehend what shall be the 
 condition of astronomical science at that remote pe- 
 riod, of one thing we are certain — the past, the pre- 
 sent, and the future, constitute but one unbroken 
 
INTRODUCTORY LECTURE. 23 
 
 chain of observations, condensing all time, to the 
 astronomer, into one mighty now. 
 
 From the vantage ground which we occupy, it will 
 not -be difficult to announce so much of the great 
 problem as has already been resolved, and to form 
 some approximate conception of what remains for 
 future ages to accomplish. 
 
 In the exposition about to be attempted, I do not 
 propose, to present any trains of reasoning, or any 
 results which may have been reached. These shall 
 engage our attention hereafter. At present permit 
 me simply to translate into language th , questions 
 which the visible heavens propound. 
 
 The most cursory examination of the celestial 
 vault reveals the fact, that not one solitary object, 
 visible to the eye, is at rest. Motion is the attribute 
 of sun and moon and planets and stars. The earth 
 we inhabit alone remains fixed, to the senses. 
 
 The first great problem propounded for human 
 ingenuity, is to sever real motion from that which is 
 unreal and only apparent. To accomplish this, some 
 knowledge of the form of the earth which we inhabit 
 must be obtained. Not only must we acquire a 
 knowledge of its figure, but in like manner we must 
 learn with certainty its actual condition, whether of 
 rest or motion. If at absolute rest in the centre of 
 the universe, then the rising sun, the setting mooiij 
 the revolving heavens, are real exhibitions, and must 
 be examined as such. On the contrary, should it be 
 found to be impossible to predicate of the earth ab- 
 solute immobility, then arises the complicated ques- 
 tion, how many motions belong to it ? and with what 
 velocity does it move ? If a motion of rotation exist, 
 
24 ^ - STRUCTURE OF THE UNIVERSE. 
 
 what is the position of the axis about which it re- 
 volves, and is this axis permanent or changeable? 
 If a motion of translation in space must be adopted, 
 then whither is the earth urging its flight ? what the 
 nature of the path described ? the velocity of its move- 
 ment, and the laws by which it is governed ? These 
 are some of the questions which present themselves 
 in the outset, touching the condition of the earth, on 
 whose surface the astronomer is located, in his re- 
 searches of the heavens. 
 
 Beyond the limits of the earth, a multitude of ob- 
 jects present themselves for examination: and first 
 of all the sun, the great source of life and light and 
 heat, demands the attention of the student of the 
 heavens. That some inscrutable tie binds it to the 
 earth, or the earth to it, was early recognised in the 
 fact, that whether the sun was moving or at rest, 
 the relative distance of it and the earth never changed 
 by any great amount; and whatever changes did occur, 
 were all obliterated in a short period and the distance 
 by which these bodies are separated was restored to 
 its primitive value, to recommence its cycle of changes 
 in the same precise order. — Here then was a grand 
 problem, to determine the relations existing between 
 the sun and earth; to endue with motion that one of 
 these bodies which did move, and to fix the limits 
 within which the observed changes occurred, both in 
 time and distance. 
 
 While the connection between the sun and earth 
 was certain, a mutual dependence between the earth 
 and the other great source of light, the moon, was 
 equally manifest. The invariability in the apparent 
 diameter of the moon, demonstrates the fact, that 
 
INTRODUCTORY LECTURE. 25 
 
 whether the earth were moving or stationary, the 
 moon never parts company with our planet. In all 
 her wanderings among the fixed stars, in her elonga- 
 tions from the sun, in her wondrous phases and 
 perpetual changes, some invisible hand held her at 
 the same absolute distance from the earth. But to 
 decide whether this power resided in the earth or 
 the moon, or in both, to explain these wondrous 
 changes from the silver crescent of the western sky 
 to the full orb which rose with the setting sun, 
 pouring a flood of light over all the earth, to develop 
 the mysterious connection between the disappear- 
 ance of the moon and those terrific phenomena, the 
 going out of the sun in dim eclipse — these furnished 
 themes for investigation requiring long centuries of 
 patient watching, of never ending toil. 
 
 Passing out from the sun and moon to the more 
 distant stars, among the brightest of those which 
 gemmed the nocturnal heavens, a few were found 
 differing from all the rest in the fact that they wan- 
 dered from point to point, and at the end of inter- 
 vals widely differing among themselves, swept round 
 the entire heavens, and returned to their starting 
 point, to recommence their ceaseless journies. These 
 were named planets, wanderers, in contradistinction 
 to the host of stars which were fixed in position, 
 unchanged from century to century. 
 
 Hence arose a new and profound series of investi- 
 gations: where were these wandering stars urging 
 their flight? Were their motions real or apparent? 
 Were their distances equal or unequal ? Did any tie 
 bind them to the earth, or to the sun, or to each other? 
 Were their distances from the earth constant or 
 C 
 
26 STRUCTURE OF THE UNIVERSE. 
 
 variable? Were their motions irregular, or guided 
 by law ? Did they accomplish their revolutions among 
 the fixed stars in regular curves, or in lawless wan- 
 derings? Among all the moving bodies, sun, moon, 
 and planets, could any principle of association be 
 traced which might bind them together and form them 
 into a common system? 
 
 To resolve these profound questions, a critical watch 
 is kept on all the moving bodies. Their pathway 
 is among the stars, and to these ever during points of 
 light their positions are constantly referred. If be- 
 yond the limits of the moving bodies a dark veil had 
 been drawn so as to have excluded the light of the 
 stars, at the first glance it might seem that by such 
 a change, simplicity would have been introduced, and 
 the perplexity arising from the motion of the planets 
 among the profusely scattered stars, would have been 
 removed. But let us not judge too hastily. Blot out 
 the stars, and give to the sun, moon and planets a 
 blank heavens in which to move, and the possibility 
 of unraveling their mysterious motions, mutual re- 
 lations, and common laws, is gone forever. 
 
 This will become manifest when we reflect that 
 on such a change, not a fixed point in all the heavens 
 would remain, to which we could refer a moving 
 planet. They must then be referred to each other, and 
 the motion due to the one, would become inextricably 
 involved in that due to the other, and neither could 
 be determined with any precision. Like the ocean 
 islands which guided the early mariners, so God 
 has given to us the stars of heaven as the fixed points 
 to which we can ever refer, in all parts of their 
 
INTRODUCTORY LECTURE. 27 
 
 revolutions, the places of the wandering planets, 
 and the swiftly revolving moon. 
 
 As the necessity for accuracy in watching the 
 movements of the planets became more apparent, 
 the attention was directed to the acquisition of the 
 means by which this might be accomplished. Hence 
 we find in the earliest ages the astronomer grouping 
 the fixed stars into constellations — breaking up the 
 great sphere of the heavens into fragments, the more 
 easily to study its parts in detail. Not only are the 
 stars of each constellation numbered, their brilliancy 
 noted, but their relative places in the constellation 
 and to each other, are fixed with all the precision 
 which the rude means then in use permitted. Names 
 are fixed to these different groupings, when or where 
 or by whom we know not. Neither history nor tra- 
 dition lead us back to this first breaking up of the 
 heavens, but the names then bestowed on the fragmen- 
 tary parts, the richer constellations, have survived the 
 fall of empires, and are fixed forever in the heavens. 
 
 Possessing now a thorough knowledge of the ob- 
 jects among which the planets were moving, and the 
 means of measuring with approximate accuracy, their 
 distance from the stars along their path, it became 
 possible to trace a planet in its career, and to note the 
 changes of its velocity. New and wonderful discover- 
 ies were thus made. It was found that all the planets 
 moved with an irregular velocity. Sometimes swiftly 
 advancing among the fixed stars, then slowly relaxing 
 their speed, they actually stopped, turned backward in 
 their career, stopped again, and then, at first slowly 
 but afterwards more rapidly, resumed their onward 
 motion. These strange and anomalous motions, differ- 
 
28 STRUCTURE OF THE UNIVERSE. 
 
 ing from anything remarked in the sun and moon, 
 furnished new themes for discussion, new problems 
 for solution. While the phenomena above alluded 
 to became known, the same chain of observations 
 revealed the remarkable fact, that the periods of 
 revolution of the planets, though differing for each 
 one of the group, were identical for any one indi- 
 vidual, and moreover, that a simple curve marked out 
 the pathway of sun, moon and planets, among the 
 fixed stars, and that all these wandering bodies were 
 confined to a narrow zone or belt in the heavens. 
 
 Centuries had now rolled away, nay, even thou- 
 sands of years had slowly glided by, since the mind 
 had first given itself to the examination of the heav- 
 ens, and while discovery after discovery had reward- 
 ed the zeal of the observer in every age, yet the 
 grand object of research, the distinction between ac- 
 tual and apparent motion, had thus far eluded the 
 utmost efforts of human genius. But a brighter day 
 was dawning. Each successive effort tore away 
 some petty obstruction which impeded the march of 
 mind upward towards the lofty region of truth. Facts 
 grew and multiplied. Phenomena striking and di- 
 versified, were collated and compared. The mind 
 in imagination took leave of the earth as the cen- 
 tre of all these complex movements, inexplicable on 
 its surface, and naturally urged its flight towards 
 the sun. There it paused and rested, and from 
 this fixed point looked out upon the circling orbs, 
 and lo! the complexity of their movements melted 
 away. The centre was found — the mystery solved — 
 the ponderous earth rescued from its false position, roll- 
 ed in its place among the planets, one of the great 
 
INTRODUCTORY LECTURE. 29 
 
 family that swept in beauty and harmony about their 
 common parent the sun. 
 
 The mind now stood upon the first platform of 
 the rocky pyramid which it had been slowly rearing 
 and with which it had been slowly rising, through long 
 centuries of ceaseless toil. One grand point had been 
 gained. Darkness had given way to light, but the 
 great problem of the universe was yet to be resolved. 
 All this long and arduous struggle had only revealed 
 what the problem was. Appearances were now 
 separated from realities, and with a fresh and invigo- 
 rated courage the human mind now gives its energies 
 to the accomplishment of definite objects, no longer 
 working uncertainly in the dark, but with the clear 
 light of truth to guide and conduct the investigation. 
 
 Possessed of these extraordinary advantages, the 
 advance now became rapid and brilliant, as it had 
 previously been slow and discouraging. That the 
 planets, reckoning the earth as one, constituted a 
 mighty family of worlds, was now manifest — whether 
 linked singly to the sun, or mutually influencing each 
 other, was the grand question. This great problem 
 rested upon the resolution of a multitude of subordi- 
 nate ones. The actual curve constituting the plan- 
 etary orbits, the magnitude of these orbits, their actual 
 position in space, the values and directions of their 
 principal lines, the laws of their motion, all these 
 and many more questions of equal importance and 
 intricacy presented themselves in the outset of the 
 examination now fairly commenced. Human skill 
 was exhausted in the contrivance and construction 
 of mechanical aids by which the movements of the 
 planets might be watched with the greater accuracy. 
 c2 
 
30 STRUCTURE OF THE UNIVERSE. 
 
 Partial success crowned these extraordinary efforts, 
 but there yet remained delicate investigations which 
 with the utmost skill in observing escaped the farthest 
 reach of man's eagle gaze, and seemed to bid de- 
 fiance to all his powers. 
 
 To conquer these difficulties, one of two things 
 must be accomplished : either man must sweep out 
 from earth towards the distant planets, to gain a 
 nearer and more accurate view, or else bring them 
 down from their lofty spheres to subject themselves 
 to his scrutinizing gaze. How hopeless the accom- 
 plishment of either of these impossible alternatives. 
 But who shall prescribe the limits of human genius ? 
 In studying the phenomena of the passage of light 
 through transparent crystalized bodies, a principle is 
 discovered which lets in a gleam of hope on the dis- 
 heartened mind. It seizes this principle, converts it to 
 its use, and arms itself with an instrument more won- 
 derful than any that fancy in its wildest dreams ever 
 pictured to the imagination. With the potent aid of 
 this magic instrument, the astronomer no longer is 
 bound hopelessly to his native earth; without indeed 
 quitting in person its surface, his eye gifted with 
 superhuman power, ranges the illimitable fields of 
 space. He visits the moon, and finds a world with its 
 lofty mountains and spreading valleys. The star- 
 like planets swell into central worlds, with their cir- 
 cling moons, and myriads of fixed stars, hitherto be- 
 yond the reach of human vision, stand revealed in all 
 their sparkling beauty. It is as if the united ranges 
 of a thousand eyes were all concentrated in a single 
 one. 
 
 A new era now dawns on the world. The delicate 
 
INTRODUCTORY LECTURE. 31 
 
 and invisible irregularities of the planetary motions 
 are now fully revealed, and the data rapidly accumu- 
 late by means of which the last grand question is 
 to be resolved. The orbitual curves are determined. 
 The laws of the revolving planets are revealed. A 
 mysterious relation between the distances of the 
 planets from the sun and their periods of revolution 
 unites them positively into one grand family group. 
 That they are bound to the sun by some inscrutable 
 power, is certain, and it now remains to determine 
 the law of increase and decrease of this force for all 
 possible distances. This last truth is finally achieved, 
 and the wisdom of God is vindicated in the beautiful 
 structure of our grand system. 
 
 The second lofty platform is reached in the mighty 
 pyramid, whose summit is now nearing the stars of 
 heaven. From this elevation the mind looks out 
 upon the circling planets and their revolving satellites, 
 and the mysterious comet, and ventures to propound 
 the question, do these bodies so interfere with the 
 movements of each other, as to affect permanently 
 the structure by which the equilibrium and stability of 
 the entire system is guarantied ? 
 
 To answer this question, a new train of investiga- 
 tion is commenced, satellite is weighed against 
 planet, and planet against the sun, until the mass 
 of matter contained in each individual of the system 
 becomes accurately known. Then is undertaken the 
 grand problem of perturbations. The telescope re- 
 veals the fact that slow and mysterious changes are 
 going on in the mean motions of the moon, in the 
 figure of the planetary orbits, and in the relative po- 
 nitions which these orbits hold to each other. Are 
 
32 STRUCTURE OF THE UNIVERSE. 
 
 these changes ever progressive ? If this be true, then, 
 does the system contain within itself the seeds of de- 
 cay, the elements of its own destruction. Slowly but 
 surely as the solemn tread of time, the end must come, 
 and one by one planet and satellite and comet, sink 
 forever in the sun. Long and arduous was the strug- 
 gle to reach the true answer to this difficult question. 
 The entire solution involved a multitude of parts. 
 
 When the mutual dependence of the multitude of 
 bodies constituting our system was discovered, when 
 planet, and satellite, and comet, were found to feel 
 and sway to the influence which each exerted on the 
 other, the simplicity of their movements was gone for 
 ever ; orbits once fixed in the heavens, slowly swung 
 away from their moorings ; the beautiful precision 
 which had to all appearance marked the planetary 
 curves, was destroyed. The regularity of their motions 
 was changed into irregularity, and a system of com- 
 plexity which seemed to bid defiance to all effort at 
 comprehension, presented itself to the human intellect. 
 
 It was no less than this — given, a system of revolv- 
 ing worlds, mutually operating on each other ; re- 
 quired, their magnitudes, masses, distances, motions, 
 and positions, at the close of a thousand revolutions. 
 What mind possessed the gigantic power to grasp 
 this mighty problem ? Reason was lost in wander- 
 ing mazes, and the brightest intellect sunk clouded 
 in gloom. 
 
 In this dilemma, the mind turns inward on its own 
 resources. As the physical man climbs some moun- 
 tain height by successive efforts, rising higher and 
 higher, scaling rock after rock, and mounting precipice 
 after precipice, by the use of strength comparatively 
 
INTRODUCTORY LECTURE. 33 
 
 feeble, resting and recruiting as it becomes exhausted 
 was it impossible, to contrive some mental machinery 
 which might give to the reason the power of pros- 
 ecuting its difficult researches, in such manner thai 
 it might stop and rest, and not lose what it hai 
 already gained in its onward movement ? 
 
 Geometry had invigorated the reason, as exercise 
 toughens and strengthens the muscles of the human 
 frame. But it had given to the mind no mechanical 
 power, wherewith to conquer the difficulties which 
 rose superior to its natural strength. Archimides 
 wanted but a place whereon to stand, and with his 
 potent lever he would lift the world. The astronomer 
 demands an analogous mental machinery to trace 
 out the complex wanderings of a system of worlds. 
 What the human mind demands and resolves to find, 
 it never fails to discover. The infinitesimal analysis is 
 reached, its principles developed, its resistless power, 
 compelled into the service of human reason. I shall 
 not now stop to explain the nature of this analysis. 
 Its power and capacity alone engage our attention at 
 the present. Once having seized on a wandering 
 planet, it never relaxes its hold, no matter how com- 
 plicated its movements, how various the influences to 
 which it may be subjected, how numerous its revolu- 
 tions, no escape is possible. This subtle analysis 
 clings to its object, tracing its path and fixing its place 
 with equal ease, at the beginning, middle, or close of 
 a thousand revolutions, though each of these should 
 require a century for its accomplishment. 
 
 Armed with this analysis, which the mind had crea- 
 ted for its use, giving to it a strength only commensu- 
 rate with the increased power which had been given 
 
34 STRUCTURE OF THE UNIVERSE. 
 
 to the human eye, it concentrated its energies once 
 more upon this last greatest problem. One by one 
 these strong holds give way, the resistless power of 
 analysis marches onward from victory to victory, until 
 finally the sublime result is reached, the system is 
 stable, the equilibrium is perfect ; slowly rocking to 
 and fro in periods which stun the imagination, the 
 limits are prescribed beyond which these fluctua- 
 tions shall never pass. 
 
 Here it would seem that human ambition might 
 rest. Satisfied with having mastered the mysteries of 
 the system with which we are united, the mind might 
 cease its arduous struggle, and leave the wilderness of 
 fixed stars free from its intrusions and ceaseless per- 
 secutions. But this is not the effect produced by vic- 
 tory ; success but engenders new desires, and prompts 
 to more difficult enterprises. Man having obtained 
 the mastery over his own system, boldly wings his 
 flight to the star-lit vault, and resolves to number its 
 countless millions, to circumscribe its limitless extent, 
 to fathom its infinite depth, to fix the centre about 
 which this innumerable host is wheeling its silent and 
 mysterious round. 
 
 Here commences a new era. The first step in the 
 stupendous enterprise is to determine the distance of 
 some one fixed star. Here again the mind is long 
 left to struggle with difficulties which it seemed that 
 no ingenuity or skill could remove. But its efforts do 
 not go unrewarded. If it fails in the accomplishment 
 of its grand object, it is rewarded by the most brilliant 
 discoveries. The mighty law governing the planetary 
 worlds is extended to the region of the fixed stars, mo- 
 tion is there detected, orbitual motion, the revolution of 
 
INTRODUCTORY LECTURE. 35 
 
 sun about sun. The swift velocity of light is measured, 
 to become the future unit in the expression of the mighty 
 distances which remain yet to be revealed. Ever baf- 
 fled but never conquered, the mind returns again and 
 again to the attack, till finally the problem slowly 
 yields, the immeasurable gulf is passed, and the dis- 
 tance of a single star rewards the toils of half a cen- 
 tury. But what a triumph is this ? It is no less than 
 a revelation of the scale on which the universe is built. 
 The interval from sun to fixed stars, is that by which 
 the stars are separated; and a reach of distance is 
 opened up to the mind, which it only learns to con- 
 template by long continued effort. 
 
 But another startling fact is revealed in the prose- 
 cution of these profound investigations. The minute 
 examinations of the fixed stars, have changed their 
 character. For thousands of years they had been re- 
 garded as absolutely fixed among each other. This 
 proves to be mere illusion, resulting from the use of 
 means inadequate for the determination of their min- 
 ute changes. Under the scrutinizing gaze of the eye, 
 with its power increased a thousand fold, the millions 
 of shining orbs which fill the heavens, are all found to 
 be slowly moving around each other, slowly as seen 
 from our remote position, but with amazing velocity 
 when examined near at hand. 
 
 A new problem of surprising grandeur now pre- 
 sents itself. Are these motions real ? or are they due 
 to a motion in the great centre of our system ? A se- 
 ries of examinations analogous to those which divided 
 between the real and apparent motions in the planets, 
 Is commenced and prosecuted with a zeal and devotion 
 unsurpassed in the history of science. The mind rises 
 
36 STRUCTURE OF THE UNIVERSE. 
 
 to meet the sublime investigation. For a hundred 
 years it toils on; again it triumphs: the truth is reveal- 
 ed. The immobility of the sun is gone forever; our 
 last fixed point is swept from under us, and now the 
 entire universe is in motion. 
 
 With redoubled energy the mind still prosecutes the 
 inquiry, whither is the sun sweeping, and with what 
 velocity does it pursue its unknown path ? Strange 
 and incredible as it may appear, these questions are 
 answered; and in attaining this answer, the means are 
 reached to separate between the real and apparent 
 motions of the fixed stars, and to study their complex 
 changes, and to rise by slow degrees, to a complete 
 knowledge of the movements of the grand sidereal sys- 
 tem. Here we pause. Rapidly have we descended the 
 current of astronomical research, we have attained the 
 boundary of the known. We stand on the dim confines 
 of the unknown. All behind us is clear and bright and 
 perfect, all before us is shrouded in gloom and dark- 
 ness and doubt. Yet the twilight of the known flings 
 its feeble light into the domain of the unknown, and 
 we are permitted to gather some idea, not of all that 
 remains to be done, but of that which must be first ac- 
 complished. 
 
 Let us then stretch forward and propound some of 
 those questions which nature yet presents for solution, 
 but which have hitherto resisted the efforts of the hu- 
 man mind. First of all, we begin with our own sys- 
 tem. How came it to be constituted as it actually 
 exists ? All the analogies of nature forbid the idea 
 that it was thus instantly called into being by the 
 fiat of Omnipotence. Does it come, then, from some 
 primitive modification of matter, under the action of 
 
INTRODUCTORY LECTURE. 37 
 
 laws working out their results in countless millions of 
 ages? Who shall present the true cosmogony of the 
 solar system. 
 
 But this is only one unit among many millions. 
 Whence the myriads of stars ? those stupendous ag- 
 gregations into mighty clusters ? what the laws of their 
 wonderful movements, of their perpetual stability ? 
 Who will explain the periodical stars, that wax and 
 wane, like the changing moon : or still more wonder- 
 ful, reveal the mystery of those which have suddenly 
 burst on the astonished vision of man,* and have as 
 suddenly gone out forever in utter darkness. 
 
 Such are the questions which remain for the reso- 
 lution of future ages. We may not live to witness 
 these anticipated triumphs of mind over matter ; but 
 who can doubt the final result? Look backward to 
 the Chaldean shepherd, who watched the changing 
 moon from the plains of Shinar, and wondering, 
 asked if future generations would reveal those mys- 
 terious phases ? Compare his mind and knowledge 
 with those of the modern astronomer, who grasps 
 at a single glance, the past, present, and future 
 changes of an entire system. Are the heights which 
 remain to be reached, more rugged, more inaccessible^ 
 than those which have been already so triumphantly 
 scaled ? The observations recorded in Babylon three 
 thousand years ago, have reached down through the 
 long series of centuries, and are of inestimable value, 
 in the solution of some of the darkest problems with 
 which the mind has ever grappled. In like manner, 
 the records we are now making, shall descend to un- 
 born generations, and contribute to effect the triumphs 
 of genius when three thousand years shall have rolled 
 D 
 
38 STRUCTURE OF THE UNIVERSE. 
 
 away. If doubt arises as to the final resolution of 
 these profound questions, from the immense distance 
 of the objects under examination, let us call to mind 
 the fact, that the artificial eye which man has fur- 
 nished for his use, possesses a glance so piercing, 
 that no distance can hide an object from his searching 
 vision. 
 
 Should Sirius, to escape this fiery glance, dart 
 away from its sphere, and wing its flight at a velocity 
 of twelve millions of miles in every minute, for a 
 thousand years; nay, should it sweep onward at the 
 same speed for ten thousand years, this stupendous 
 distance cannot bury it from the persecuting gaze of 
 man. But if distance is to form no barrier, no termi- 
 nus to these investigations, surely there is one element 
 which no human ingenuity can overcome. The com- 
 plex movements of the planetary orbs have been 
 revealed, because they have been repeated a thousand 
 times under the eye of man, and from a comparison 
 of many revolutions, the truth has been evolved. 
 But tens of thousands of years must roll away before 
 the most swiftly moving of all the fixed stars shall 
 complete even a small fragment of its mighty orbit. 
 With motions thus shrouded, these would seem to be in 
 entire security from the inquisitive research of a being 
 whose whole sweep of existence is but a moment, 
 when compared with these vast periods. But let us not 
 judge too hastily. The same piercing vision that fol- 
 lows the retreating star to depths of space almost infi- 
 nite, is armed with a power so great, that if this same 
 star should commence to revolve around some grand 
 centre, and move so slowly that five millions of years 
 must roll away before it can complete one circuit, not 
 
INTRODUCTORY LECTURE. 39 
 
 even a single year shall pass before its motion shall be 
 detected, in ten years its velocity shall be revealed, 
 and in the life time of a single observer its mighty 
 period shall become known. * 
 
 If human genius is not to be baffled either by dis- 
 tance or time, numbers shall overwhelm it, and the 
 stars shall find their safety in their innumerable mil- 
 lions. This retreat may even fail. The watch-towers 
 of science now cover the whole earth, and the senti- 
 nels never sleep. No star or cluster or constellation, 
 can ever set. It escapes the scrutinizing gaze of one 
 astronomer, to meet the equally piercing glance of 
 another. East and west, and north and south, from 
 the watch towers of the four quarters of the globe, 
 peals the solemn mandate, onward! 
 
 Here we pause. We have closed the enunciation of 
 the great problem whose discussion and solution lie 
 before us, a problem whose solution has been in pro- 
 gress six thousand years — one which has furnished to 
 man the opportunities of his loftiest triumphs, one 
 which has taxed in every age the most vigorous efforts 
 of human genius, a problem whose successive develop- 
 ments have demonstrated the immortality of mind, 
 and whose sublime results have vindicated the wisdom 
 and have declared the glory of God. You have 
 listened to the enunciation, we now invite you to fol- 
 low us in the demonstration. And may that Almighty 
 power, which built the heavens, give to me wisdom to 
 reveal, and to you power to grasp the truths and doc- 
 trines, wrested by mind from nature in its long strug- 
 gle of sixty centuries of toil ! 
 
LECTURE II. 
 
 THE DISCOVERIES OF THE PRIMITIVE AGES. 
 
 To those who have given but little attention to the 
 science of astronomy, its truths, its predictions, its rev- 
 elations, are astonishing ; and but for their rigorous 
 verification, would be absolutely incredible. When 
 we look out upon the multitude of stars which adorn 
 the nocturnal heavens, scattered in bright profusion 
 in all directions, without law, and regardless of order 
 — when with telescopic aid, thousands are increased 
 to millions, and suns and systems and universes, rise 
 in sublime perspective, as the visual ray sweeps out- 
 ward to distances which defy the powers of arithme- 
 tic to express, how utterly futile does it seem, for the 
 mind to dare, to pierce and penetrate, to number, 
 weigh, measure and circumscribe, these innumerable 
 millions ? It is only when we remember, that from 
 the very cradle of our race, strong and powerful 
 minds, have in rapid and continuous succession, bent 
 their energies upon the solution of this grand problem, 
 that we can comprehend, how it is, that light now 
 breaks in upon us, from the very confines of the 
 universe, dimly revealing the mysterious forms, which 
 lie yet half concealed in the unfathomable gulfs of 
 space. When I reflect on the recent triumphs of 
 human genius — when I stand on the shore of that 
 d2 (41) 
 
42 STRUCTURE OF THE UNIVERSE. 
 
 mighty stream of discovery, which has grown broader 
 and deeper, as successive centuries have rolled away, 
 gathering in strength and intensity, until it has em- 
 braced the whole universe of God ; I am carried back- 
 ward through thousands of years, following this stream, 
 as it contracts towards its source, till finally its silver 
 thread is lost in the clouds and mists of antiquity. I 
 would fain stand at the very source of discovery, and 
 commune with that unknown god-like mind which 
 first conceived the grand thought, that even these 
 mysterious stars might be read, and that the bright 
 page which was nightly unfolded to the vision of man, 
 needed no interpreter of its solemn beauties, but 
 human genius. There is to my mind, no finer speci- 
 men of moral grandeur, than that presented by him 
 who first resolved to read and comprehend the heav- 
 ens. On some lofty peak he stood, in the stillness of 
 the midnight hour, with the listening stars as wit- 
 nesses of his vows, and there, conscious of his high 
 destiny, and of that of his race, resolves to commence 
 the work of ages. " Here," he exclaims, " is my 
 watch-tower, and yonder bright orbs, are henceforth 
 my solitary companions. Night after night, year 
 after year, will I watch and wait, ponder and reflect, 
 until some ray shall pierce the deep gloom which now 
 wraps the world." 
 
 Thus resolved the unknown founder of the science 
 of the stars. His name and his country are lost 
 forever. What matters this, since his works, his dis- 
 coveries, have endured for thousands of years, and 
 will endure, as long as the moon shall continue to fill 
 her silver horn, and the planets to roll and shine. 
 
 Go with me, then, in imagination, and let us stand 
 
DISCOVERIES OF THE PRIMITIVE AGES. 43 
 
 beside this primitive observer, at the close of his 
 career of nearly a thousand years, (for we must pass 
 beyond the epoch of the deluge, and seek our first 
 discoveries among those sages, whom, for their vir- 
 tues, God permitted to count their age, not by years, 
 but by centuries,) and here we shall learn the order 
 in which the secrets of the starry world slowly 
 yielded themselves, to long and persevering scrutiny. 
 And now let me unfold, in plain and simple lan- 
 guage, the train of thought, of reasoning and research, 
 which marked this primitive era of astronomical 
 science. It is true that history yields no light, and 
 tradition even fails, but such is the beautiful order in 
 the golden chain of discovery, that the bright links 
 which are known, reveal with certainty, those which 
 are buried in the voiceless past. — If then it were 
 possible to read the records of the founder of astrono- 
 my, graven on some column of granite, dug from the 
 earth, whither it had been borne by the fury of the del- 
 uge, we know now what its hieroglyphics would re- 
 veal, with a certainty scarcely less than that which 
 would be given by an actual discovery, such as we have 
 imagined. We are certain that the first discovery 
 ever recorded, as the result of human observation, was 
 on the moon. 
 
 The sun, the moon, the stars, had long continued to 
 rise, and climb the heavens, and slowly sink beneath 
 the western horizon. The spectacle of day and night, 
 was then as now, familiar to every eye ; but in gazing 
 there was no observation, and in mute wonder there 
 was no science. When the solitary observer took his 
 post, it was to watch the moon. Her extraordinary 
 phases had long fixed his attention. Whence came 
 
44 STRUCTURE OP THE UNIVERSE. 
 
 these changes ? The sun was ever round and brilliant 
 — the stars shone with undimmed splendor — while 
 the moon was ever waxing and waning, sometimes 
 a silver crescent hanging in the western sky, or full 
 orbed, walking in majesty among the stars, and 
 eclipsing their radiance, with her overwhelming splen- 
 dor. Scarcely had the second observation been made 
 upon the moon, when the observer was struck with 
 the wonderful fact, that she had left her place among 
 the fixed stars, which on the preceding night he had 
 accurately marked. Astonished, he again fixes her 
 place by certain bright stars close to her position, and 
 waits the coming of the following night. His suspi- 
 cions are confirmed — the moon is moving; and what 
 to him is far more wonderful, her motion is precisely 
 contrary to the general revolution of the heavens, from 
 east to west. With a curiosity deeply aroused, he 
 watches from night to night, to learn, whether she 
 will return upon her track; but she marches steadily 
 onward among the stars, until she sweeps the entire 
 circuit of the heavens, and returns to the point first 
 occupied, to recommence her ceaseless cycles. 
 
 An inquiry now arose, whether the changes in the 
 moon, her increase and decrease, could in any way 
 depend on her place among the fixed stars. To 
 solve this question, required a longer period. The 
 group of stars among which the new moon was first 
 seen was accurately noted, so as to be recognized at 
 the following new moon, and doubtless our primitive 
 astronomer hoped to find that in this same group 
 the silver crescent, when it should next appear, would 
 be found. But in this he was disappointed; for when 
 the moon became first faintly visible in the western 
 
DISCOVERIES OF THE PRIMITIVE AGES. 45 
 
 sky, the group of stars which had ushered her in be- 
 fore, had disappeared below the horizon, and a new 
 group had taken its place ; and thus it was discovered 
 that each successive new moon fell farther and farther 
 backward among the stars. By counting the days 
 from new moon to new moon, and those which elaps- 
 ed while the moon was passing roiand the heavens 
 from a certain fixed star to this same star again, it 
 was found, that these two periods were different; the 
 revolution from new to new occupying 29i days, 
 while the sidereal revolution, from star to star, re- 
 quired 27^ days. 
 
 This backward motion of the moon among the stars, 
 must have perplexed the early astronomers ; and for 
 a long while it was utterly impossible to decide 
 whether the motion was real or only apparent — anal- 
 ogy would lead to the conclusion that all motion must 
 be in the same direction, and as the heavens revolved 
 from east to west, it seemed impossible that the moon, 
 which manifestly participated in this general move- 
 ment, should have another and a different motion, 
 from west to east. There was one solution of this 
 mystery, and I have no doubt it was for a long while 
 accepted and believed. It was this. By giving to 
 the moon a slower motion from east to west, than the 
 general motion of the heavens, she would appear to 
 lag behind the stars, which would by their swifter ve- 
 locity pass by her, and thus occasion in her the ob- 
 served apparent motion, from west to east. We shall 
 see presently how this error was detected. 
 
 The long and accurate vigils of the moon, and the 
 necessity of recognizing her place, by the clusters or 
 groups of stars among which she was nightly found, 
 
4(5 STRUCTURE OF THE UNIVERSE 
 
 had already familiarized the eye with those along her 
 track, and even thus early the heavens began to be di- 
 vided into constellations. The eye was not long in 
 detecting the singular fact, that this stream of constel- 
 lations, lying along the moon's path, was constantly 
 flowing to the west, and one group after another ap- 
 parently dropping into the sun, or at least becoming 
 invisible, in consequence of their proximity to this 
 brilliant orb. A closer examination revealed the fact, 
 that the aspect of the whole heavens was changing 
 from month to month. Constellations which had been 
 conspicuous in the west, and whose brighter stars 
 were the first to appear as the twilight faded, were 
 found to sink lower and lower towards the horizon, till 
 they were no longer seen ; while new groups were 
 constantly appearing in the east. 
 
 These wonderful changes, so strange and inexpli- 
 cable, must have long perplexed the early student of 
 the heavens. Hitherto the stars, along the moon's 
 route, had engaged special attention ; but at length 
 certain bright and conspicuous constellations, towards 
 the north, arrested the eye: and these were watched to 
 see whether they would disappear. — Some were found 
 to dip below the western horizon, soon to re-appear 
 in the east ; while others revolving with the general 
 heavens, rose high above the horizon, swept steadily 
 round, sunk far down, but never disappeared from the 
 sight. This remarkable discovery soon led to another 
 equally important. In watching the stars in the north 
 through an entire night, they all seemed to describe 
 circles ; having a common centre, these circles grew 
 smaller and smaller as the stars approached nearer to 
 the centre of revolution, until finally one bright star 
 
DISCOVERIES OF THT PRIMITIVE AGES. 47 
 
 was found, whose position was ever fixed. — Alone un- 
 changed while all else was slowly moving. The dis- 
 covery of this remarkable star, must have been hailed 
 with uncommon delight by the primitive observer of 
 the heavens. If his deep devotion to the study of the 
 skies, had created surprise among his rude country- 
 men, when he came to point them to this never chang- 
 ing light hung up in the heavens, and explained its uses 
 in guiding their wanderings on the earth, their sur- 
 prise must have given place to admiration. Here was 
 the first valuable gift of primitive astronomical science 
 to man. 
 
 But to the astronomer this discovery opened up a 
 new field of investigation, and light began to dawn 
 on some of the most mysterious questions which had 
 long perplexed him. He had watched the constella- 
 tions near the moon's track slowly disappear in the ef- 
 fulgence of the sun, and when they were next seen, it 
 was in the east, in the early dawn, apparently emerg- 
 ing from the solar beams, having actually passed by 
 the sun. Watching and reflecting, steadily pursuing the 
 march of the northern constellations, which never en- 
 tirely disappeared, and noting the relative positions 
 of these, and those falling into the sun, it was at last 
 discovered that the entire starry heavens was slowly 
 moving forward to meet and pass by the sun, or else 
 the sun itself was actually moving backward among 
 the stars. This apparent motion had already been 
 detected in the moon, and now came the reward of 
 long and diligent perseverance. The grand discovery 
 was made, that both the sun and moon were moving 
 among the fixed stars, not apparently, but absolutely. 
 The previously received explanation of the moon's 
 
48 STRUCTURE OF THE UNIVERSE. 
 
 motion, could no longer be sustained; for the starry- 
 heavens could not at the same time so move as to pass 
 by the moon in one month, and to pass by the sun in a 
 period twelve times as great. A train of the most im- 
 portant conclusions flowed at once from this great dis- 
 covery. — The starry heavens passed beneath and 
 around the earth, — the sun and moon were wandering 
 in the same direction, but with different velocities 
 among the stars, — the constellations actually filled the 
 entire heavens above the earth and beneath the earth, 
 — the stars were invisible in the day time, not because 
 they did not exist, but because their feeble light was lost 
 in the superior brilliancy of the sun. The heavens were 
 spherical, and encompassed like a shell the entire earth, 
 and hence it was conceived that the earth itself was 
 also a globe, occupying the centre of the starry sphere. 
 
 It is impossible for us, familiar as we are at this day 
 with these important truths, to appreciate the rare merit 
 of him who by the power of his genius, first rose to their 
 knowledge and revealed them to an astonished world. 
 We delight to honor the names of Kepler, of Galileo, 
 of Newton; but here are discoveries so far back in the 
 dim past, that all trace of fheir origin is lost, which 
 vie in interest and importance with the proudest 
 achievements of any age. 
 
 With a knowledge of the sphericity of the heavens, 
 the revolution of the sun and moon, the constellations 
 of the celestial sphere, the axis of its diurnal revolu- 
 tion, astronomy began to be a science, and its future 
 progress was destined to be rapid and brilliant. A line 
 drawn from the earth's centre to the north star formed 
 the axis of the heavens, and day and night around 
 this axis all the celestial host were noiselessly pursuing 
 
DISCOVERIES OF THE PRIMITIVE AGES. 49 
 
 their never ending journies. — Thus far, the only mov- 
 ing bodies known, were the sun and moon. These 
 large and brilliant bodies, by their magnitude and 
 splendor, stood out conspicuously, from among the 
 multitude of stars, leaving these minute but beautiful 
 points of light, in one great class, unchangeable among 
 themselves, fixed in their groupings and configura- 
 tions, furnishing admirable points of reference, in 
 watching and tracing out the wanderings of the sun 
 and moon. 
 
 To follow the moon as she pursued her journey 
 among the stars was not difficult ; but to trace the 
 sun in his slower and more majestic motion, and to 
 mark accurately his track, from star to star, as he 
 heaved upward to meet the coming constellations, 
 was not so readily accomplished. Night after night, 
 as he sunk below the horizon, the attentive watcher 
 marked the bright stars near the point of setting which 
 first appeared in the evening twilight. — These grad- 
 ually sunk towards the sun on successive nights, and 
 thus was he traced from constellation to constellation, 
 until the entire circuit of the heavens was performed, 
 and he was once more attended by the same bright 
 stars, that had watched long before, his sinking in the 
 west. Here was revealed the measure of the Year. 
 The earth had been verdant with the beauties of 
 spring, — glowing with the maturity of summer, — rich 
 in the fruits of autumn, — and locked in the icy chains 
 of winter, while the sun had circled round the heavens. 
 His entrance into certain constellations marked the 
 coming seasons, and man was beginning to couple 
 his cycle of pursuits on earth with the revolutions of 
 the celestial orbs. 
 E 
 
50 STRUCTURE OF THE UNIVERSE. 
 
 While intently engaged in watching the sun as it 
 slowly heaved up to meet the constellations, some ar- 
 dent devotee to this infant science, at length marked 
 in the early twilight a certain brilliant star closely at- 
 tendant upon the sun. The relative position of these 
 two objects was noted, for a few consecutive nights, 
 when with a degree of astonishment, of which we can 
 form no conception, he discovered that this brilliant 
 star was rapidly approaching the sun, and actually 
 changing its place among the neighboring stars, — 
 night after night he gazes on this unprecedented phe- 
 nomenon, a moving star ! and on each successive night 
 he finds the wanderer coming nearer and nearer to 
 the sun. At last it disappears from sight, plunged in 
 the beams of the upheaving sun. What had become 
 of this strange wanderer ? was it lost forever ? were 
 questions which were easier asked than answered. — 
 But patient watching had revealed the fact, that when 
 a group of stars, absorbed into the sun's rays, disap- 
 peared in the west, they were next seen in the eastern 
 sky, slowly emerging from his morning beams. Might 
 it not be possible, that this wandering star would pass 
 by the sun, and re-appear in the east ? With how much 
 anxiety must this primitive discoverer have watched in 
 the morning twilight ? Day after day he sought his 
 solitary post, and marked the rising stars, slowly lift- 
 ing themselves above the eastern horizon. The gray 
 dawn came, and the sun shot forth a flood of light, the 
 stars faded and disappeared, and the watcher gives 
 over, till the coming morning. But his hopes are 
 crowned at last. Just before the sun breaks above 
 the horizon, irr the rosy east, refulgent with the com- 
 ing day, he descries the pure white silver ray of his 
 
DISCOVERIES OF THE PRIMITIVE AGES. 51 
 
 long lost wanderer. It has passed the sun, — it rises in 
 the east, — the first planet is discovered ! 
 
 With how much anxiety and interest did the delighted 
 discoverer trace the movements of his wandering star. 
 Here was a new theme for thought, for observation, for 
 investigation ; would this first planet sweep round the 
 heavens, as did the sun and moon ? w r ould it always 
 move in the same direction ? w r ould its path lie among 
 those groups of stars among which the sun and moon 
 held their course ? Encouraged by past success, he 
 rejoicingly enters on the investigations of these ques- 
 tions. For some time the planet pursues its journey 
 from the sun, leaving it farther and farther behind. 
 But directly it slackens its pace, — it actually stops in 
 its career, and the astonished observer, perhaps thinks 
 that his wandering star had again become fixed. Not 
 so, — a few days of watching dispels this idea. Slowly 
 at first, and soon more swiftly, the planet seeks again 
 the sun, moving backwards on its former path, until 
 finally its light is but just visible in the east at early 
 dawn. Again it is lost in the sun's beams for a 
 time, and contrary to all preceding analogy, when 
 next seen, its silver ray comes out pure and bright, 
 just above the setting sun. It now recedes from the 
 sun, on each successive evening increasing its dis- 
 tance, till it again reaches a point never to be passed 
 — here it stops — is stationary for a day or two, and 
 then again sinks downward to meet the sun. How 
 wonderful and inexplicable the movements of this 
 wandering star must have appeared in the early ages ! 
 oscillating backward and forward, never passing its 
 prescribed limits, and ever closely attendant upon the 
 sun. Where the sun sunk to repose, there did the 
 
52 STRUCTURE OF THE tTNIVERSE. 
 
 faithful planet sink, and where the sun rose, at the 
 same point did the wandering star make its appear- 
 ance. The number of days wan accurately noted, 
 from the stationary point in the east above the sun, to 
 the stationary point in the west above the sun, and 
 thus the period, 584 days, from station to station, be- 
 came known. 
 
 The discovery of one planet, led the way to the 
 rapid discovery of several others. If we may judge 
 of their order by their brilliancy, Jupiter was the se- 
 cond wanderer revealed among the stars. Then fol- 
 lowed Mars, and Saturn, and after a long interval 
 Mercury was detected, hovering near the sun, and im- 
 itating the curious motions of Venus. 
 
 Here the progress of planetary discovery was sud- 
 denly arrested, keen as was the vision of the old astron- 
 omer, long and patient as was his scrutiny, no depth 
 of penetration of unaided vision could stretch beyond 
 the mighty orbit of Saturn, and the search was given 
 over. — A close examination of the planets revealed 
 many important facts. Three of them, Mars, Jupiter, 
 and Saturn, were found to perform the circuit of the 
 heavens, like the sun and moon, and in the same di- 
 rection; with this remarkable difference, that while the 
 sun and moon, moved steadily and uniformly in the 
 same direction, the planets occasionally slackened 
 their pace, would then stop, move backwards on their 
 track, stop again, and finally resume their onward 
 motion. Their periods of revolution were discovered 
 by marking the time which elapsed, after setting out 
 from some brilliant and well known fixed star, until 
 they should perform the entire circuit of the heavens 
 and once more return to the same star. The times of 
 
DISCOVERIES OF THE PRIMITIVE AGES. 53 
 
 revolution were found to differ widely from each 
 other ; Mars requiring about 687 days, Jupiter 4,332 
 days, and Saturn 10,759 days, or nearly thirty of our 
 years. 
 
 The planets all pursued their journies in the heav- 
 ens, among the same constellations which marked the 
 paths of the sun and moon, and hence these groups of 
 stars concentrated the greatest amount of attention 
 among the early astronomers, and became distin- 
 guished from all the others. 
 
 Whatever light may be shed upon antiquity by 
 deciphering the hieroglyphic memorials of the past, 
 there is no hope of ever going far enough back, to 
 reach even the nation, to which we are indebted for 
 the first rudiments of the science of the stars. 
 
 Thus far in the prosecution of the study of the 
 heavens, the eye and the intellect had accomplished 
 the entire work. Rapidly as we have sketched the 
 progress of early discovery, and short as may have 
 been the period in which it was accomplished, no one 
 can fail to perceive, how vast is the difference be- 
 tween the light that thus early broke in upon the 
 mind, heralding the coming of a brighter day, and 
 the deep and universal darkness which had covered 
 the world, before the dawn of science. Encouraged 
 by the success which had thus far rewarded patient 
 toil, the mind of man pushes on its investigations 
 deeper and deeper into the domain of the mysterious 
 and unknown. 
 
 In watching the annual revolution of the sun among 
 
 the fixed stars, one remarkable peculiarity had long 
 
 been recognized. While the interval of time, from the 
 
 rising to the setting of the stars, was ever the same 
 
 e2 
 
54 DISCOVERIES OF THE PRIMITIVE AGES. 
 
 at all seasons of the year, the interval from the rising 
 to the setting of the sun, was perpetually changing, 
 passing through a cycle which required exactly one 
 year for its completion. It became manifest that 
 the sun did not prosecute its annual journey among 
 the stars, in a circle parallel with those described by 
 the stars, in their diurnal revolution. His path was 
 oblique to those circles, and while he participated in 
 their diurnal motion, he was sweeping by his annual 
 revolution round the heavens, and was at the same 
 time, by another most extraordinary movement, car- 
 ried towards the north to a certain distance, then 
 stopping, commenced a return towards the south, — 
 reached his southern limit, — again changed his direc- 
 tion, and thus oscillated from one side to the other of 
 his mean position. 
 
 These wonderful changes became the objects of 
 earnest investigation. In what curve did the sun 
 travel among the stars ? All diurnal motion was per- 
 formed in a circle, the first discovered, the simplest 
 and the most beautiful of curves : and in this curve, 
 analogy taught the early astronomers, that all celestial 
 movements must be performed. It became there- 
 fore, a matter of deep interest, to trace the sun's path 
 accurately among the stars, to mark his track, and 
 to see whether it would not prove to be a circle. 
 To accomplish this, more accurate means must be 
 adopted, than the mere watching of the stars which 
 attended the rising or setting sun. The increase 
 and decrease of the shadow of some high pointed 
 rock, to whose refreshing shade the shepherd astrono- 
 mer had repaired in the heat of noon, and beneath 
 which he had long pondered this important problem, 
 
STRUCTURE OF THE UNIVERSE. 55 
 
 first suggested the means of its resolution. — As the 
 summer came on, he remarked that the length of 
 the noon shadow of his rock, perpetually decreased 
 from day to day. As the sun became more nearly 
 vertical at noon, the shadow gave him less and 
 less shelter. Watching these noon shadows, from 
 day to day, he found them proportioned to the sun's 
 northern or southern motion, and finally the thought 
 entered his mind, that these shadows would mark 
 with certainty, the limits of the sun's motion north 
 and south, — the character of his orbit or route among 
 the stars, — the changes and duration of the seasons, 
 and the actual length of the year, which thus far had 
 been but roughly determined. To accomplish the ob- 
 servations more accurately, an area on the ground 
 was smoothed and leveled, and in its centre a verti- 
 cal pole was erected some ten or fifteen feet in length, 
 whose sharp vertex cast a well defined shadow. 
 And here we have the first astronomical instrument, 
 the gnomon, ever devised by the ingenuity of man. 
 Simple as it is, by its aid the most valuable results 
 were obtained. 
 
 The great point was to mark with accuracy the 
 length of the noon-day shadow, from month to month, 
 throughout the entire year. Four remarkable points 
 in the sun's annual track, were very soon detected 
 and marked. One of these occurred in the summer, 
 and was that point occupied by the sun on the 
 day of the shortest noon shadow. Here the sun 
 had reached his greatest northern point, and for a 
 few days the noon shadow, cast by the gnomon, 
 appeared to remain the same, and the sun stood 
 still. The noon shadows now increased slowly, for 
 
56 DISCOVERIES OF THE PRIMITIVE AGES. 
 
 six months, as the sun moved south, till a second 
 point was noted, when the noon shadow had reached 
 its greatest length. Again it became stationary, and 
 again the sun paused and stood still, before com- 
 mencing his return towards the north. These points 
 were called the summer and ivinter solstices, and oc- 
 curred at intervals of half a year. At the summer 
 solstice, the longest day occurred, while at the winter 
 solstice, the shortest day was always observed. These 
 extreme differences between the length of the day 
 and night, occasioned the determination of the other 
 two points. From the winter solstice, the noon 
 shadows decreased as the length of the day increased, 
 until finally the day and night were remarked to be 
 of equal length, and the distance to which the shadow 
 of the gnomon was thrown on that day, was ac- 
 curately fixed. If on this day the diurnal circle des- 
 cribed by the sun, could have been marked in the 
 heavens by a circle of light, sweeping from the east 
 to the west, so that the eye might rest upon and 
 retain it, and if at the same time the sun's annual 
 path among the fixed stars could have been equally 
 exhibited in the heavens, by a circle of light, these 
 two circles would have been seen to cross each other, 
 and at their point of crossing, the sun would have 
 been found. The diurnal circle was called the equa- 
 tor, the sun's path the ecliptic, and the point of in- 
 tersection was called appropriately, Ae equinox. — 
 As the sun crossed the equator in the spring and 
 autumn, these points received the names of the vernal 
 and autumnal equinoxes, and were marked with all 
 the precision which the rude means then in use 
 rendered practicable, 
 
DISCOVERIES OF THE PRIMITIVE AGES. 57 
 
 The bright circle already imagined in the heavens 
 to represent the sun's annual track among the stars, 
 passed obliquely across the equator, and the amount 
 by which these circles were inclined to each other was 
 actually measured in these early ages, with no mean 
 precision by the noon shadows of the gnomon. The 
 ray casting the shortest noon shadow, was inclined to 
 the ray forming the longest noon shadow, under an 
 angle precisely double of the inclination of the eclip- 
 tic or sun's path to the equator, and the inclination of 
 these two rays marked exactly the annual motion of 
 the sun from south to north, or from north to south. 
 A close examination of the order of increase and de- 
 crease in the length of the noon shadows cast by the 
 gnomon, demonstrated the important truth already 
 suspected, that the sun's path w r as actually a circle, 
 but inclined, as has already been shown, to the diur- 
 nal circles of the stars and to the equator. 
 
 By counting the days which elapsed from the sum- 
 mer solstice to the summer solstice again, a knowl- 
 edge of the length of the year, or period of the sun's 
 revolution, was obtained. But here again a discov- 
 ery was made which produced an embarrassment to 
 the early astronomer, which all their perseverance and 
 research never succeeded in removing. 
 
 In these primitive ages the heavenly bodies were 
 regarded with feelings little less than the reverence 
 we now bestow on the Supreme Creator. The sun es- 
 pecially, as the Lord of life and light, was regarded 
 with feelings nearly approaching to adoration, even 
 by the astronomers themselves. The idea early be- 
 came fixed, that the chief of the celestial bodies must 
 move with a uniform velocity in a circular orbit, never 
 
58 STRUCTURE OF THE UNIVERSE. 
 
 increasing or decreasing. Change being inconsistent 
 with the supreme and dignified station which was as- 
 signed to him — what then must have been the aston- 
 ishment of the primitive astronomers, who in counting 
 the days from the summer to the winter solstice, and 
 from the winter round to the summer solstice, these 
 intervals were found to be unequal. — This almost in- 
 credible result was confirmed, by remarking that the 
 shorter spaces from equinox to solstice, dividing the 
 sun's annual route, into four equal portions, were 
 passed over in unequal times. These results could 
 not be doubted, for each observation, from year to 
 year, confirmed them. They were received and re- 
 corded, but the problem was handed down to succeed- 
 ing generations for solution. 
 
 In consequence of the oblique direction of the eclip- 
 tic or sun's track, it was found difficult to retain its 
 position in the mind. To assist in the recurrence to 
 this important circle, a brazen circle was at length de- 
 vised, and fastened permanently to another brazen 
 circle of equal size, under an angle, exactly equal to 
 the inclination of the equator to the ecliptic. Circles, 
 perpendicular to the equator, and passing through the 
 solstices and equinoxes, completed the second astro- 
 nomical instrument, the sphere. Having constructed 
 this simple piece of machinery, it was mounted on an 
 axis passing through its centre, and perpendicular to 
 its equator, so as to revolve, as did the heavens, whose 
 motions it was intended to represent. Having so 
 placed the axis of rotation, that its prolongation would 
 pass through the north star, this rude sphere came to 
 play a most important part in the future investigations 
 of the heavens. Its brazen equator and ecliptic were 
 
DISCOVERIES OF THE PRIMITIVE AGES. 59 
 
 each divided into a certain number of equal parts, by 
 reference to which the motion of the heavenly bodies 
 might be followed, with far greater precision, than had 
 ever been previously obtained. 
 
 Armed with a new and more perfect instrument, the 
 astronomer resumes his great investigation. Finding 
 it now possible, to mark out the sun's path in the 
 heavens, with certainty, by means of his brazen 
 ecliptic, he discovers that the moon and planets in 
 each revolution pass across the sun's track, and spend 
 nearly an equal amount of time on the north and 
 south sides of the ecliptic. This discovery led to a 
 more accurate determination of the periods of revolu- 
 tion of the planets. The interval was noted from one 
 passage across the ecliptic to the next on the same 
 side, and these intervals marked with accuracy the 
 planetary periods. It now became possible to fix, with 
 greater certainty, the relative positions of the sun and 
 moon, and problems were once more resumed which 
 had thus far baffled every effort of human genius. 
 The phases of the moon, the very first point of inves- 
 tigation, had never yet yielded up its hidden cause, 
 and those terrific phenomena, solar and lunar eclipses, 
 which had long covered the earth with terror and dis- 
 may, w r ere wrapped in mystery, and their explanation 
 had resisted the sagacity of the most powerful and 
 gifted intellects 
 
 No one has ever witnessed the going out of the sun 
 in dim eclipse, even now when its most minute phe- 
 nomena are predicted with rigorous exactitude, with- 
 out a feeling of involuntary dismay. What then must 
 have been the effect upon the human mind in those 
 ages of the world, when the cause was unknown, and 
 
60 STRUCTURE OF THE UNIVERSE. 
 
 when these terrific exhibitions burst on earth's inhab- 
 itants unheralded and unannounced ? Here then was 
 an investigation, not prompted by curiosity alone, but 
 involving the peace and security of man in all coming- 
 ages. We cannot doubt that the causes of the solar 
 eclipse were first detected. It was observed, that no 
 eclipse of the sun ever occurred, when the moon was 
 visible. Even during a solar eclipse, when the sun's 
 light had entirely faded away, and the stars and plan- 
 ets stole gently upon the sight in the sombre and un- 
 natural twilight, the moon was sought for in vain; she 
 was never to be seen. This fact excited curiosity 
 and gave rise to a careful and critical examination of 
 the place in which the moon should be found, imme- 
 diately after a solar eclipse ; and it was soon discovered 
 that on the night following the day of eclipse, the 
 moon was seen in her crescent shape very near to the 
 sun and but a short distance from the sun's path. By 
 remarking the moon's place, next before a solar eclipse 
 and that immediately following, it was seen that at 
 the time of the occurrence of the eclipse, the moon 
 was actually passing from the west to the east side of 
 the sun's place, and finally a little calculation showed 
 that a coincidence of the sun and moon in the heav- 
 ens took place at the precise time at which the sun 
 had been eclipsed. The conclusion was irresistible, 
 and the great fact was announced to the world, that 
 the sun's light was hidden by the interposition of the dark 
 body of the moon. 
 
 Having reached this important result w T ith en- 
 tire certainty, the explanation of the moon's phases 
 followed in rapid succession. For it now became 
 manifest, that the moon shone with borrowed light, 
 
DISCOVERIES OF THE PRIMITIVE AGES. 61 
 
 and that her brilliancy came from the reflected 
 beams of the sun. This was readily demonstrated by 
 the following facts. When the moon was so situated 
 that the side next to the sun, (the illuminated one), 
 was turned from the eye of the observer, (as was the 
 case in a solar eclipse), then the moon's surface next 
 to the observer, was always found to be entirely black 
 Pursuing her journey from this critical point, the moon 
 was next seen near the sun, in the evening twilight, as 
 a slender thread of light, a very small portion of her il- 
 luminated surface being now visible. Day after day 
 this visible portion increases, until finally the moon rises 
 as the sun sets, full orbed and round,beingdirectly oppo- 
 site the sun, and turning her entire illuminated surface 
 towards the eye of the observer. By like degrees she 
 loses her light as she approaches, and finally becomes 
 invisible as she passes by the sun. From this exam- 
 ination it became evident that the moon was a globu- 
 lar body, non-luminous, and revolving in an orbit, com- 
 prehended entirely within that described by the sun, 
 and consequently, nearer to the earth than the sun. 
 Having ascertained this fact, it was concluded that 
 among all the moving heavenly bodies, the periods of 
 revolution indicated their relative distances from the 
 earth. Hence Mars was regarded as more distant 
 than the sun, Jupiter more remote than Mars, and Sat- 
 urn the most distant, as it was the slowest moving of 
 all the planets. 
 
 After reaching to a knowledge of the causes pro- 
 ducing the eclipses of the sun and the phases of the 
 moon, it remained yet to resolve the mystery of the 
 lunar eclipse. It was far more difficult to render a 
 satisfactory account of this phenomenon than either of 
 F 
 
62 STRUCTURE OF THE UNIVERSE. 
 
 the preceding. The light of the moon was not inter- 
 cepted by the interposition of any opaque body, 
 between it and the eye of the observer. No such 
 body existed, and long and perplexing was the effort 
 to explain this wonderful phenomenon. Finally it 
 was observed that all opaque bodies cast shadows, 
 in directions opposite to the source of light. Was it 
 not possible that the light of the sun, falling upon the 
 earth, might be intercepted by the earth, and thus 
 produce a shadow which might even reach as far as 
 the moon? So soon as this conjecture was made, a 
 series of examinations were commenced to confirm or 
 destroy the theory. It was at once seen that in case 
 the conjecture was true, no lunar eclipse could occur 
 except when the sun, earth, and moon, were situated 
 in the same straight line; a position which could never 
 occur, except at the full or new of the moon. It was 
 soon discovered that, it was only at the full, that lunar 
 eclipses took place, thus confirming the truth of the 
 theory, and fixing it beyond a doubt that the shadow 
 of the earth falling on the moon, was the cause of her 
 eclipse. The moon had already been shown to be 
 non-luminous, and the moment the interposition of 
 the earth, between it and its source of light, the sun, 
 cut off its light, it ceased to be visible, and passed 
 through an eclipse. The sphericity of the earth, 
 which had been analogically inferred from that of the 
 heavens, was now made absolutely certain — for it 
 was remarked, that as the moon entered the earth's 
 shadow, that the track of this dark shadow across the 
 bright surface of the moon was always circular, which 
 was quite impossible, for every position, except the 
 
DISCOVERIES OF THE PRD1ITIVE AGES. 63 
 
 earth, which cast this circular shadow, should be of 
 a globular form. 
 
 Having now attained to a clear and satisfactory 
 explanation of the two grand phenomena, solar and 
 lunar eclipses, the question naturally arose, why was 
 not the sun eclipsed in each revolution of the moon ? 
 and how happened it that the moon in the full, did 
 not always pass through the earth's shadow? An 
 examination of the moon's path among the fixed stars 
 gave to these questions a clear and positive answer. 
 It was found that the sun and moon did not perform 
 their revolutions in the same plane. The moon's 
 route among the stars crossed the sun's route under 
 a certain angle, and it thus frequently happened, that 
 at the new and full, the moon occupied some portion 
 of her orbit too remote from that of the sun to render 
 either a lunar or solar eclipse possible. 
 
 Rapidly have we traced the career of discovery. 
 The toil and watching of centuries have been con- 
 densed into a few moments of time, and questions 
 requiring ages for their solution have been asked, 
 only to be answered. In connexion with the investi- 
 gations just developed, and as a consequence of their 
 successful prosecution, the query arose whether in 
 case science had reached to a true exposition of the 
 causes producing the eclipse of the sun, was it not 
 possible to stretch forward in time, and anticipate 
 and predict the coming of these dread phenomena? 
 
 To those who have given but little attention to the 
 subject, even in our own day, with all the aids of 
 modern science, the prediction of an eclipse, seems 
 sufficiently mysterious and unintelligible. How then 
 it was possible, thousands of years ago, to accomplish 
 
64 STRUCTURE OF THE UNIVERSE. 
 
 the same great object, without any just views of the 
 structure of the system, seems utterly incredible. 
 Follow me, then, while I attempt to reveal the train 
 of reasoning which led to the prediction of the first 
 eclipse of the sun, the most daring prophecy ever 
 made by human genius. Follow in imagination, 
 this bold interrogator of the skies to his solitary moun- 
 tain summit — withdrawn from the world — surrounded 
 by his mysterious circles, there to watch and ponder 
 through the long nights of many — many years. But 
 hope cheers him on, and smooths his rugged pathway. 
 Dark and deep as is the problem, he sternly grap 
 pies with it, and resolves never to give over till 
 victory crowns his efforts. 
 
 He has already remarked, that the moon's track in 
 the heavens crossed the sun's, and that this point of 
 crossing was in some way intimately connected with 
 the coming of the dread eclipse. He determines to 
 watch and learn whether the point of crossing was 
 fixed, or whether the moon in each successive revolu- 
 tion, crossed the sun's path at a different point. If 
 the sun in its annual revolution could leave behind 
 him a track of fire marking his journey among the 
 stars, it is found that this same track was followed 
 from year to year, and from century to century with 
 undeviating precision. But it was soon discovered, 
 that it was far different with the moon. In case she 
 too could leave behind her a silver thread of light 
 sweeping round the heavens, in completing one revo- 
 lution, this thread would not join, but would wind 
 around among the stars in each revolution, crossing 
 the sun's fiery track at a point west of the previous 
 crossing. These points of crossing were called the 
 
DISCOVERIES OF THE PRIMITIVE AGES 65 
 
 moon's nodes. At each revolution the node occurred 
 further west, until after a cycle of about nineteen 
 years, it had circulated in the same direction entirely 
 round the ecliptic. Long and patiently did the as- 
 tronomer watch and wait, each eclipse is duly ob- 
 served, and its attendant circumstances are recorded, 
 when, at last, the darkness begins to give way and a 
 ray of light breaks in upon his mind. He finds that 
 no eclipse of the sun ever occurs unless the new 'moon 
 is in the act of crossing the suns track. Here was a 
 grand discovery. — He holds the key which he believes 
 will unlock the dread mystery, and now, with re- 
 doubled energy, he resolves to thrust it into the wards 
 and drive back the bolts. 
 
 To predict an eclipse of the sun, he must sweep 
 forward, from new moon to new moon, until he finds 
 some new moon which should occur, while the moon 
 was in the act of crossing from one side to the other 
 of the sun's track. — This certainly was possible. 
 He knew the exact period from new moon to new 
 moon, and from one crossing of the ecliptic to another. 
 With eager eye he seizes the moon's place in the 
 heavens, and her age, and rapidly computes where 
 she will be at her next change. He finds the new 
 moon occurring far from the sun's track ; he runs round 
 another revolution; the place of the new moon falls 
 closer to the sun's path, and the next yet closer, until 
 reaching forward with piercing intellectual vigor, he 
 at last, finds a new moon which occurs precisely at 
 the computed time of her passage across the sun's 
 track. Here he makes his stand, and on the day 
 of the occurrence of that new moon, he announ- 
 ces to the startled inhabitants of the world, that the 
 f2 
 
66 STRUCTURE OF THE UNIVERSE. 
 
 sun shall expire in dark eclipse — Bold prediction ! — 
 Mysterious prophet ! with what scorn must the un- 
 thinking world have received this solemn declaration. 
 How slowly do the moons roll away, and with what 
 intense anxiety does the stern philosopher await the 
 coming of that day which should crown him with 
 victory, or dash him to the ground in ruin and disgrace. 
 Time to him moves on leaden wings ; day after day, 
 and at last hour after hour, roll heavily away. The 
 last night is gone — the moon has disappeared from 
 his eagle gaze in her approach to the sun, and the 
 dawn of the eventful day breaks in beauty on a slum- 
 bering world. 
 
 This daring man, stern in his faith, climbs alone to 
 to his rocky home, and greets the sun as he rises and 
 mounts the heavens, scattering brightness and glory 
 in his path. Beneath him is spread out the popu- 
 lous city, already teeming with life and activity. The 
 busy morning hum rises on the still air and reaches 
 the watching place of the solitary astronomer. The 
 thousands below him, unconscious of his intense anx- 
 iety, buoyant with life, joyously pursue their rounds 
 of business, their cycles of amusement. The sun 
 slowly climbs the heavens, round and bright and full 
 orbed. The lone tenant of the mountain-top almost 
 begins to waver in the sternness of his faith, as the 
 morning hours roll away. But the time of his triumph, 
 long delayed, at length begins to dawn ; a pale and 
 sickly hue creeps over the face of nature. The sun 
 has reached his highest point, but his splendor is dim- 
 med, his light is feeble. At last it comes ! — Blackness 
 is eating away his round disc, — onward with slow but 
 steady pace, the dark veil moves, blacker than a thous- 
 
DISCOVERIES OF THE PRIMITIVE AGES. 67 
 
 and nights, — the gloom deepens, — the ghastly hue of 
 death covers the universe, — the last ray is gone, and 
 horror reigns. A wail of terror fills the murky air, — 
 the clangor of brazen trumpets resounds, — an agony 
 of despair dashes the stricken millions to the ground, 
 while that lone man, erect on his rocky summit, with 
 arms outstretched to heaven, pours forth the grateful 
 gushings of his heart to God, who had crowned his 
 efforts with triumphant victory. Search the records 
 of our race, and point me, if you can, to a scene more 
 grand, more beautiful. It is to me the proudest vic- 
 tory that genius ever won. It was the conquering of 
 nature, of ignorance, of superstition, of terror, all at a 
 single blow, and that blow struck by a single arm. — 
 And now do you demand the name of this wonderful 
 man ! Alas ! what a lesson of the instability of earthly 
 fame are we taught in this simple recital. — He who 
 had raised himself immeasurably above his race, — who 
 must have been regarded by his fellows as little less 
 than a god, who had inscribed his fame on the very 
 heavens, and had written it in the sun, with a " pen 
 of iron, and the point of a diamond," even this one 
 has perished from the earth — name, age, country, are 
 all swept into oblivion, but his proud achievement 
 stands. The monument reared to his honor stands, 
 and although the touch of time has effaced the letter- 
 ing of his name, it is powerless, and cannot destroy 
 the fruits of his victory. 
 
 A thousand years roll by : the astronomer stands on 
 the watch tower of old Babylon, and writes for pos- 
 terity the records of an eclipse ; this record escapes 
 destruction, and is safely wafted down the stream of 
 time. A thousand years roll away : the old astrono- 
 
68 STRUCTURE OF THE UNIVERSE. 
 
 mer, surrounded by the fierce, but wondering Arab, 
 again writes, and marks the day which witnesses the 
 sun's decay. A thousand years roll heavily away : 
 once more the astronomer writes from amidst the gay 
 throng that crowds the brightest capital of Europe. 
 Record is compared with record, date with date, rev- 
 olution with revolution, the past and present are link- 
 ed together, — another struggle commences, and another 
 victory is won. Little did the Babylonian dream, that 
 he was observing for one who after the lapse of 3000 
 years, should rest upon this very record, the success- 
 ful resolution of one of nature's darkest mysteries. 
 
 We have now reached the boundary where the 
 stream of discovery, which we have been tracing 
 through the clouds and mists of antiquity, begins to 
 emerge into the twilight of tradition, soon to flow on 
 in the clear light of a history that shall never 
 die. Henceforth our task will be more pleasing, be- 
 cause more certain ; and we invite you to follow us 
 as we attempt to exhibit the coming struggles and 
 future triumphs of the student of the skies. 
 
LECTURE III. 
 
 THEORIES FOR THE EXPLANATION OF THE MOTIONS OF 
 THE HEAVENLY BODIES. 
 
 If in tracing the career of astronomy in the primi- 
 tive ages of the world, we have been left to pursue 
 our way dimly, through cloud and darkness, — if re- 
 grets rise up, that time has swept into oblivion the 
 names and country of the early discoverers, in one re- 
 flection there is some compensation — while the bright 
 and enduring truths which they wrested from nature 
 have descended to us, their errors, whatever they 
 may have been, are forever buried with their names 
 and their persons. We are almost led to believe that 
 those errors were few and transient, and that the 
 mind, as yet undazzled by its triumphs, questioned 
 nature, with that humility and quiet perseverance, 
 which could bring no response but truth. 
 
 In pursuing the consequences flowing from the pre- 
 diction of an eclipse, several remarkable results were 
 reached, which we proceed to unfold. It will be re- 
 collected, that to produce either solar or lunar eclip- 
 ses, the new or full moon must be in the act of cross- 
 ing the sun's annual track. This point of crossing, 
 called the rrwortsnode, became therefore an object of the 
 deepest interest. Long and careful scrutiny revealed 
 the fact of its movement around the ecliptic, in a period 
 
 (69) 
 
70 STRUCTURE OF THE UNIVERSE. 
 
 of eighteen years and eleven days, during which time 
 there occur 223 new moons, or 223 full moons. If then, 
 a new moon falls on the sun's track to produce a solar 
 eclipse to-day, at the expiration of 223 lunations, 
 again will the new moon fall on the ecliptic, and an 
 eclipse will surely take place. Suppose then that all 
 the eclipses, which occur within this remarkable pe- 
 riod of 223 lunations, are carefully observed, and the 
 days on which they fall recorded, on each and every 
 one of these days, during the next period of 223 luna- 
 tions, eclipses may be expected, and their coming fore- 
 told. 
 
 This wonderful period of eighteen years and eleven 
 days, or 223 lunations, was known to the Chaldeans, 
 and by its use eclipses were predicted, more than 3000 
 years ago. It is likewise found among the Hindus, 
 the Chinese, and the Egyptians, nations widely sepa- 
 rated on the earth's surface, and suggesting the idea 
 that it had its origin among a people even anterior 
 to the Chaldeans. It is now known by the name of 
 the Zaros, or Chaldean period. 
 
 Let it not be supposed that the application of the 
 Zaros to the prediction of eclipses, can in any way 
 supersede modern methods. — While antiquity conten- 
 ted itself with announcing the day on which the dark 
 body of the moon should hide the sun, modern science 
 points to the exact second on the dial, which shall 
 mark the first delicate contact of the moon's dark 
 edge with the brilliant disk of the sun. 
 
 It would be a matter of great interest to fix the 
 epoch of primitive discovery. Though this is impossi- 
 ble, its high antiquity is attested by a few facts, to 
 which we will briefly advert. We find among all the 
 
MOTIONS OF THE HEAVENLY BODIES. 71 
 
 ancient nations, Chaldeans, Persians, Hindus, Chinese, 
 and Egyptians, that the seven days of the week were in 
 universal use, and what was far more remarkable, each 
 of these nations named the days of the week after the 
 seven planets, numbering the sun and moon among 
 the planets. It is moreover found, that the order of 
 naming is not that of the distance, velocity or brilliancy 
 of the planets, and neither does the first day of the 
 week coincide among the different nations ; but the 
 order once commenced is invariably preserved by all. 
 If we compute the probability of such a coincidence 
 resulting by accident, we shall find the chances mil- 
 lions to one against it. We are therefore forced to 
 the conclusion, that the planets were discovered, and 
 the seven days of the week devised and named, by 
 some primitive nation, from whom the tradition de- 
 scended imperfectly, to succeeding generations. 
 
 A remarkable discovery, made in the remote ages 
 of the world, throws some farther light on the era of 
 the primitive astronomical researches. — The release of 
 the earth from the icy fetters of winter, the return of 
 spring, and the revivification of nature, is a period 
 hailed with uncommon delight, in all ages of the 
 world. To be able to anticipate its coming, from 
 some astronomical phenomenon, was an object of ear- 
 nest investigation by the ancients. 
 
 It was found that the sun's entrance into the equi- 
 nox, reducing to equality the length of the day and 
 night, always heralded the coming of the spring. 
 Hence to mark the equinoctial point among the fixed 
 stars, and to note the place of some brilliant star 
 whose appearance in the early morning dawn, would 
 announce the sun's approach to the equator, was early 
 
72 STRUCTURE OF THE UNIVERSE. 
 
 accomplished with all possible accuracy. This star 
 once selected, it was believed that it would remain 
 forever in its place. 
 
 The sun's path among the fixed stars had been 
 watched with success, and it seemed to remain abso- 
 lutely unchanged, and hence the points in which it 
 crossed the equator, for a long while were looked 
 upon as fixed and immovable. And indeed centuries 
 must pass away before any change could become sen- 
 sible to the naked eye and its rude instrumental aux- 
 iliaries. But a time arrives at last when the bright 
 star which for more than five hundred years had, with 
 its morning ray announced the season of flowers, is 
 lost. It has failed to give its warning — spring has 
 come, the forests bud, the flowers bloom, but the star 
 which once gave promise, and whose ray had been 
 hailed with so much delight by many generations, is 
 no longer found. The hoary patriarch recalls the 
 long experience of a hundred years, and now per- 
 ceives, that each succeeding spring had followed more 
 and more rapidly after the appearance of the sentinel 
 star. Each year the interval from the first appear- 
 ance of the star" in the early dawn, up to the equality 
 of day and night, had grown less and less, and now the 
 equinox came, but the star remained invisible, and 
 did not emerge from the sun's beams until the equinox 
 had passed. 
 
 Long and deeply were these facts pondered and 
 weighed. — At length truth dawned, and the discovery 
 broke upon the unwilling mind, that the sun's path 
 among the fixed stars was actually changing, and that his 
 point of crossing the equator was slowly moving back- 
 wards towards the west and leaving the stars behind. 
 
MOTIONS OF THE HEAVENLY BODIES. 73 
 
 The same motion, only greatly more rapid, had been re- 
 cognized in the shifting of the moon's node and in the 
 rapid motion of the points at which her track crossed 
 the equator. The retrograde motion of the equinoc- 
 tial points, caused the sun to reach these points 
 earlier than it would have done had they remained 
 fixed, and hence arose the precession of the equinoxes 
 
 This discovery justly ranks among the most import- 
 ant achieved by antiquity. Its explanation was in- 
 finitely above the reach of human effort at that early 
 day; but to have detected the fact, and to have mark- 
 ed a motion so slow and shrouded, gives evidence of 
 a closeness of observation worthy of the highest ad- 
 miration. It will be seen hereafter, that the human 
 mind has reached to a full knowledge of the causes 
 producing the retrograde movement of the equinoxes 
 among the stars. Its rate of motion has been deter- 
 mined, and its vast period of nearly twenty-six thou- 
 sand years has been fixed. Once revealed, the slow 
 movement of the equinox, makes it a fitting hour 
 hand, on the dial of the heavens, with which to meas- 
 ure the revolutions of ages. As the sun's path h.-s 
 been divided into twelve constellations, each filling 
 the twelfth part of the entire circuit of the heavens for 
 the equinox to pass the twelfth part of the dial' or 
 from one constellation to the next, will require a pe- 
 riod of more than two thousand years. Since the as- 
 tronomer first noted the position of this hour hand on 
 the dial of the stars, but one of its mighty hours of two 
 thousand years, has rolled away. In case any record 
 could be found, any chiselled block of granite, exhibit- 
 ing the place of the equinox among the stars, at its 
 date no matter if ten thousand years had elapsed 
 
74 STEUCTURE OF THE UNIVERSE. 
 
 we can reach back with certainty and fix the epoch 
 of the record. 
 
 No such monument has ever been found; but there 
 are occasional notices of astronomical phenomena, 
 found among the Greek and Roman poets, which at 
 least give color to conjecture. Virgil informs us that 
 " the White Bull opens with his golden horns the year." 
 
 " Candidus auratis aperit cum cornibu3 annum, 
 Taurus." 
 
 This statement we know is not true, if applied to 
 the age in which the poet wrote, and seems to be the 
 quotation of an ancient tradition. If this conjecture 
 be true, this tradition must have been carried down 
 the stream of time for more than two thousand years, 
 to reach the age in which the poet wrote. Although 
 these conjectures are vague and uncertain, the fre- 
 quent allusions to the constellations of the zodiac, in 
 the old Hebrew Scriptures, and in the works of all 
 ancient writers, sufficiently attest the extreme an- 
 tiquity of these arbitrary groupings of the stars. 
 
 In taking leave of the primitive ages of astronomy, 
 and in entering on that portion of the career of 
 research and discovery whose history has been pre- 
 served, let us pause for a moment and consider the 
 position occupied by the human mind at this remark 
 able epoch. 
 
 Thus far the eye had done its work faithfully. 
 Through long and patient watching, it had revealed 
 the facts, from which reason had wrought out her 
 great results. The stars grouped into constellations, 
 glittered in the blue concave of a mighty sphere, 
 whose centre was occupied by the earth. Within this 
 hollow sphere, sun, moon and planets, kept their 
 
MOTIONS OF THE HEAVENLY BODIES. 75 
 
 appointed courses, and performed their ceaseless joui*- 
 nies. Their wanderings had been traced, — their path- 
 way in the heavens was known, — their periods de- 
 termined, — the inclinations of their orbits fixed. So 
 accurately had the eye followed the sun and moon, 
 that it had learned to anticipate their relative posi- 
 tions, their oppositions and conjunctions, till reaching 
 forward, it had robbed the dread eclipse of its terrors, 
 and had learned to hail its coming with delight. The 
 pathway of the sun and moon among the stars had 
 been scanned and studied, until their slowest changes 
 had been marked and measured. 
 
 Such were the rich fruits of diligence and persever- 
 ance which descended from the remote nations of 
 antiquity. With the advantage of these great dis- 
 coveries, and the experience of preceding ages, it is 
 natural to expect rapid progress, when science found 
 its home among the bold, subtle, and inquisitive 
 Greeks. He who entertains this expectation will 
 meet with disappointment. Not that investigations 
 were less constantly or perseveringly conducted, — not 
 that less perfect means were employed, or less power- 
 ful talent consecrated to the work ; but because a point 
 had been reached of exceeding difficulty. The era 
 of discovery from mere inspection was rapidly draw- 
 ing to a close. It was an easy matter to count the 
 days from full moon to full moon, to watch a planet 
 as it circled the heavens, from a fixed star until it re- 
 turned to the same star again, to mark its stopping, 
 its reversed motion, and its onward goings ; but it was 
 a far different matter to rise to a knowledge of the 
 causes of these stations and retrogradations, and to 
 render a clear and satisfactory account of them. The 
 
76 STRUCTURE OF THE UNIVERSE. 
 
 problem now presented, was to combine all the facts 
 treasured by antiquity, all the movements exhibited 
 in the heavens, and reduce them to simplicity and 
 harmony. The Greek philosophers, from Plato down 
 to the extinction of the. last school of philosophy, 
 recognized this to be the true problem, and essayed 
 its solution, with an energy and pertinacity worthy 
 of the highest admiration. 
 
 Let us now examine the causes which arrested the 
 progress ot astronomical discovery and held back the 
 mind for a period of more than two thousand years. 
 Surrounded as we are by the full blaze of truth, ac- 
 customed to the simplicity and beauty which now 
 reign every where in the heavens, we find it next to 
 impossible to realize the true position of those brave 
 minds, which, enveloped in darkness, deceived by the 
 senses, fettered by prejudice, struggled on and finally 
 won the victory, whose fruits we enjoy. 
 
 The most careful and philosophical examination of 
 the heavens seemed to lead to the admitted truth, that 
 the earth was the centre of all celestial motion. In 
 the configuration of the bright stars there was no 
 change. From age to age, from century to century, 
 immovably fixed in their relative positions, they had 
 performed their diurnal revolutions around the earth. 
 They were ever of the same magnitude, of the same 
 brilliancy. How impossible w r as this, on any hypothe- 
 sis, except that of the fixed central position of the 
 earth. Leaving the fixed stars, an examination of the 
 motions of the sun and moon — their nearly uniform 
 velocity — their invariable diameters in all portions of 
 their orbits, demonstrated the central position of the 
 earth with reference to them. To shake a faith thus 
 
MOTIONS OF THE HEAVENLY BODIES. 7? 
 
 firmly fixed, sustained by the evidence of the senses, 
 consonant with every feeling of the mind, accordant 
 with fact and reason, required a depth of research, 
 and the development of new truths, only to be revealed 
 after centuries of observation. 
 
 Every effort, then, to explain the celestial phenom- 
 ena, started with the undoubted fact, that the earth 
 was the centre of all motion. Thus far, the mind had 
 not reached the idea of apparent motion. If the moon 
 moved, so equally did the sun. There was exactly 
 the same amount of evidence to demonstrate the 
 reality of the one motion, as the other ; neither were 
 doubted. It would have been unphilosophical to reject 
 the one, without rejecting the other. 
 
 The centre of motion once determined, the nature 
 of the curve described was so obviously presented to 
 the eye, that it seemed impossible to hesitate for one 
 moment. The circle was the only regular curve 
 known to the ancients. Its simplicity, its beauty and 
 perfection, would have induced its selection, even had 
 there been a multitude of curves from which to choose* 
 Its curvature was ever the same. It had neither be- 
 ginning nor end. It was the symbol of eternity, and 
 admirably shadowed forth the eternity of the motions 
 to which it gave form. As if these considerations 
 had required confirmation, every star and planet, the 
 sun and moon, all described circles, in their diurnal 
 revolution, and it seemed impossible to doubt that their 
 orbitual motions were performed in the same beauti- 
 ful curve. In truth, observation confirmed this con- 
 jecture ; and the orbits of all the moving bodies, when 
 projected on the concave heavens, were circles. That 
 this curve, then, should have been adopted without 
 g2 
 
78 STRUCTURE OF THE UNIVERSE. 
 
 doubt or hesitation, is not to be wondered at. It came 
 therefore, to be a fixed principle, that in all hypothe- 
 ses devised to explain the phenomena of the heavens, 
 circular motion and circular orbits, alone could be 
 employed. 
 
 To these great principles, of the central position of 
 the earth, and the circular orbits, we must add that of 
 the earth's immobility. This doctrine was undoubt- 
 edly sustained by the evidence of all the senses which 
 could give testimony. No one had seen it move, — 
 had heard it move — had felt it move. How was it 
 possible to doubt the evidence of the eye, the touch, 
 the ear ? Here, then, was another incontrovertible 
 fact, which even the most skeptical could not doubt, 
 and which laid at the foundation of all effort to re- 
 solve the problem under examination. 
 
 With a full knowledge and appreciation of these 
 facts, we are prepared to enter upon an examination 
 of the career of astronomy, up to the time when all 
 darkness disappeared before the dawning of a day 
 which should never end. The early Greek philoso- 
 phers, little fitted by nature for close and laborious 
 observation, rather chose to gather in travel the wis- 
 dom which was garnered up in the temples, and 
 among the priests of Egypt, and India. Returning to 
 their native country, they theorised on the facts they 
 had learned, and taught doctrines, which found their 
 only support in trains of fanciful or specious reason- 
 ing. Thus we find Pythagoras mingling the great 
 discoveries of antiquity with theories the most vague 
 and visionary. While gleams of truth flash occasion- 
 ally through the darkness of his doctrines, they seem 
 but fortunate guesses. His views were sustained by 
 
MOTIONS OF THE HEAVENLY BODIES. 79 
 
 no solid argument, and rapidly sunk into forgetful- 
 ness. This philosopher is said to have fixed the sun 
 in the centre of his planetary system, and to have 
 taught the revolution of the earth in an orbit ; but to 
 sustain this bold conjecture, the only reason assign- 
 ed, was, that fire which composes the sun, was more 
 dignified than earth, and hence should hold the more 
 dignified position in the centre. We are not surprised 
 that Hipparchus and Ptolemy, the true astronomers 
 among the Greeks, should have rejected a doctrine 
 sustained by so futile and absurd a reason. Nicetas, 
 a follower of Pythagoras, is said to have gone farther 
 than his master, and to have adopted the idea that 
 the revolution of the heavens, was an appearance 
 produced by an actual rotation of the earth on an axis, 
 once in twenty-four hours. This extraordinary and 
 almost prophetic announcement, unfortunately was 
 not sustained by any solid argument. It was regarded 
 as a vain dream, and soon was lost in oblivion. 
 
 A crowd of theoretic philosophers filled for a long 
 time the schools of Gree-ce, contributing little to 
 science, and diverting the mind from the only train 
 of research which could lead to any true results. At 
 length a philosopher arose who restored investigation 
 to its legitimate channel. Hipparchus, abandoning, 
 for the present, all vain effort to explain the phe- 
 nomena of the heavens, gave himself up to close, 
 continuous, and accurate observation. He began with 
 the movements of the sum in his annual orbit. By 
 the construction of superior brazen circles, he meas- 
 ured the daily motion of the sun during the entire 
 year. He confirmed the discovery of the ancients, 
 of the irregular or unequal progress of this luminary, 
 
80 STRUCTURE OF THE UNIVERSE. 
 
 and fixed that point in the sun's orbit where it moved 
 with greatest velocity. Year after year, did this devo- 
 ted astronomer follow the sun, until finally he discov- 
 ered that the point on the orbit, where its motion was 
 swiftest, did not remain fixed, but was advancing in 
 each revolution, at a very slow rate along the orbit. 
 Having thus demonstrated and characterised the ir- 
 regularity of the sun's motion, he directed his atten- 
 tion to minute examinations of the moon, and reached 
 results precisely similar. From these discoveries, it 
 became manifest, that in case the motions of the sun 
 and moon were circular and uniform, the earth did 
 not occupy the exact centres of their orbits ; for on 
 this hypothesis any irregularity of motion would have 
 been impossible. Here was a point gained. The 
 exact central position of the earth was disproved in 
 two instances, and even the amount of its eccentri- 
 city, or distance from the true centre, determined. 
 Retaining the circular and uniform motion of the 
 sun and moon, the discovered irregularities were tol- 
 erably well represented by the eccentric position 
 of the earth, from whose surface these motions were 
 measured. 
 
 While pursuing these important researches, Hip- 
 parchus resolved upon a work of extraordinary diffi- 
 culty, which had never before been attempted, and 
 which fully attests the grandeur and sagacity of his 
 views. This enterprise was nothing less than num- 
 bering the stars and fixing their positions in the heav- 
 ens. This he actually accomplished, and his cata- 
 logue of 1081 of the principal stars, is perhaps the 
 richest treasure which the Greek school has transmit- 
 ted to posterity. We cannot too much admire the 
 
MOTIONS OF THE HEAVENLY BODIES. 81 
 
 disinterested devotion to science, which prompted this 
 great undertaking, and the firmness of purpose which 
 sustained the solitary observer, through long years of 
 toil. It was a work for posterity, and could yield to 
 its author no reward during his life. Conscious of 
 this, his resolution never faltered, and grateful pos- 
 terity crowns his memory with the well-earned title 
 of Father of Astronomy. The noble example thus 
 set by Hipparchus, was not lost on Ptolemy, justly the 
 most distinguished among his immediate successors. 
 An ardent student, a close observer, a patient and 
 candid reasoner, Ptolemy collected and digested the 
 discoveries and theories of his predecessors, and trans- 
 mitted them, in connection with his own, successfully 
 to posterity. Rejecting the absurd doctrine of the 
 solid crystal spheres of Eudoxus, and the unsustained 
 notions of Pythagoras, this bold Greek undertook the 
 resolution of the great problem, which Plato had long 
 before presented, and to accomplish which, so many 
 unsuccessful efforts had been made. 
 
 After a careful examination of all the facts and 
 discoveries, which the world then possessed, adding 
 his own extensive observations, Ptolemy promulged 
 a system which bears his name, and which endured 
 for more than fourteen hundred years. He fixed the 
 earth as the great centre, about which the sun, the 
 moon, the planets, and the starry heavens, revolved. 
 Retaining the doctrine of uniform circular motion, he 
 accounted for the irregularity in the movements of the 
 sun and moon by the eccentric position of the earth 
 in their orbits. — To explain the anomalous movement 
 of the planets, he devised the system of cycles and 
 epicycles. Every planet moved uniformly in the cir- 
 
82 STRUCTURE OF THE UNIVERSE. 
 
 cumference of a small circle, whose centre moved 
 uniformly in the circumference of a large circle, near 
 whose centre the earth was located. By this ingenious 
 theory, it was shown that a planet moving in the cir- 
 cumference of its small circle might appear to retro- 
 grade, to become stationary, and finally to advance 
 among the fixed stars. Thus were all the phenomena 
 known to the Greek astronomer, so satisfactorily ac- 
 counted for, that it even became possible from this 
 singular theory, to compute tables of the planetary 
 motions, from which their places could be predicted 
 with such precision, that the error, if any existed, es- 
 caped detection by the rude instruments then in use. 
 
 While the explanation of the celestial phenomena 
 had constituted the principal object of the Greek as- 
 tronomers, some rude efforts were commenced to de- 
 termine the magnitude of the earth, and the relative 
 distances of the sun and moon. The process adopted 
 by Eratosthenes, two thousand years ago, to deter- 
 mine the circumference of the earth, and its diameter, 
 is essentially the same now employed by modern 
 science. The results reached by the Greek astrono- 
 mer, owing to an ignorance of the exact value of his 
 unit, are lost to the world. 
 
 When astronomy was banished from Greece, it 
 found a home among the Arabs. When darkness and 
 gloom wrapped the earth through ten long centuries, 
 and human knowledge languished, and art died, and 
 genius slumbered, it is a remarkable fact, that astron- 
 omy during that long period of ignorance, instead of 
 being lost, was actually slowly advancing, and when 
 the dawn of learning once more broke on Europe, the 
 astronomy of the Greeks, improved by the Arabs *xnd 
 
MOTIONS OF THE HEAVENLY BODIES. 83 
 
 the Persians, was preserved in the great work oi 
 Ptolemy, and transmitted to posterity. 
 
 It is true that no change had been wrought in the 
 Greek theory, but observations had been multiplied 
 and slow changes measured, which prepared the way 
 for the discoveries which were soon to succeed. On 
 the revival of learning in Europe, the literature and 
 science of the Greeks and Romans rapidly spread, and 
 gained an astonishing ascendancy over the human 
 mind. Indeed, theirs was the only science, the only 
 wisdom. Time honored, and venerable with age, the 
 philosophy of Aristotle, the geometry of Euclid, and 
 the astronomy of Ptolemy, filled the colleges and uni- 
 versities, and fastened itself upon the age, with a te- 
 nacity, which permitted no one to question or doubt, 
 and which seemed to defy all further progress. — Such 
 was the state of science and the world, when Coper- 
 nicus consecrated his genius to the examination of the 
 heavens. 
 
 To a mind singularly bold and penetrating, Coper- 
 nicus united habits of profound study and severe ob- 
 servation. Deeply read in the received doctrines of 
 science, he examined with the keenest interest, every 
 hint which the philosophers of antiquity had left on 
 record concerning the system of nature. For more 
 than thirty years he watched, with unceasing per- 
 severance, the movements of the heavenly bodies. 
 By the construction of superior instruments, he com- 
 pared the observed places of the sun, moon and plan- 
 ets, with their positions computed from the best ta- 
 bles founded on the theory of Ptolemy. The hy- 
 pothesis of uniform circular motion, had originally 
 oeen adopted, to preserve the simplicity of nature, 
 
84 STRUCTURE OF THE UNIVERSE. 
 
 and with true philosophy. But as one irregularity 
 after another had been discovered in the movements 
 of the heavenly bodies, each of which must be ex- 
 plained on the circular hypothesis, one circle had 
 been successively added to another, eccentrics and 
 epicycles, equants and differents, until to preserve 
 simplicity, the system had grown to the most ex- 
 travagant complexity. The primitive idea of sim- 
 plicity was a just one, founded in nature, and adopt- 
 ed in reason. But after thirty years of vain effort to 
 harmonize the phenomena of the heavens with the 
 theory of Ptolemy, after entangling himself in a maze 
 of complexity in his effort to preserve simplicity, Co- 
 pernicus was at last driven to doubt, and doubt soon 
 grew into disbelief. By a close exami nation of the mo- 
 tions of Mercury and Venus, he found that these planets 
 always accompanied the sun, participated in its move- 
 ments, and never receded from it except to limited 
 distances. The uniformity of their oscillations, from 
 the one side to the other of the sun, suggested their 
 revolution about that luminary, in orbits, whose planes 
 passed nearly through the eye of the observer. The 
 Egyptians had reached to this doctrine, had commu- 
 nicated it to Pythagoras, who taught it to his country- 
 men, nearly two thousand years before the time of 
 Copernicus. 
 
 If then simplicity imperiously demanded the aban- 
 donment of the earth as the great centre of motion, 
 in the search for a new centre, a multitude of circum- 
 stances pointed to the sun. It was the largest and 
 most brilliant of all the heavenly bodies. It gave 
 light to the moon and planets. It gave life to the 
 earth and its inhabitants. It was certainly accom- 
 
MOTIONS OF THE HEAVENLY BODIES. 85 
 
 panied by two satellites, and above all, it was so 
 related to the earth, that if motion in the one was 
 abandoned, it must instantly and without a moment's 
 hesitation, be transferred to the other. Long did the 
 philosopher hesitate, perplexed with doubts, surroun- 
 ded by prejudice, embarrassed with difficulties, but 
 finally rising superior to every consideration save 
 truth, he quitted the earth, swept boldly through 
 space, and planted himself upon the sun. With an 
 imagination endowed with the most extraordinary 
 tenacity, he carried with him all the phenomena of 
 the heavens, which were so familiar to his eye, while 
 viewed from the earth. A long train of investigation 
 was now before him. He commences with his now 
 distant earth. Its immobility is gone — he beholds it 
 sweeping round the heavens in the precise track once 
 followed by the sun. The same constellations mark 
 its career, the same periodic time, the same inequali- 
 ties of motion; all that the sun has lost the earth has 
 gained. 
 
 Thus far the change had been without results. He 
 now gives his attention to the planets. Here a most 
 beautiful scene broke upon his senses. The complex 
 wanderings of the planets, their stations, their retro- 
 grade motions, all disappeared, and he beheld them 
 sweeping harmoniously around him. The earth, de- 
 prived of her immobility, started in her orbit, joined 
 her sister planets, and gave perfection to the system. 
 The oscillations of Mercury and Venus were convert- 
 ed into regular revolutions, still holding their places 
 nearest to the sun ; then came the earth, next Mars, 
 and Jupiter, and last of all Saturn away in the dis- 
 tance, slowly pursuing his mighty orbit. All were 
 H 
 
86 STRUCTURE OF THE UNIVERSE. 
 
 moving in the same direction, their paths filling the 
 same belt of the heavens. 
 
 Charmed with this beautiful scene, the philosopher 
 turns to an examination of the moon. Was she, too, 
 destined to take her place among the planets. A short 
 investigation revealed her true character. She could 
 not be a planet revolving about the sun interior to the 
 earth's orbit, for if so she would have imitated the os- 
 cillations of Mercury and Venus. — She was not a 
 planet revolving around the sun, exterior to the orbit 
 of the earth, for in that case she must have imitated 
 the stations and retrogradations of Mars, Jupiter, and 
 Saturn. The invariability of her diameter as seen 
 from the earth, joined to these considerations, estab- 
 lished the fact of her secondary character, and like a 
 favorite minister who accompanies his dethroned mon- 
 arch in his exile, so did the faithful moon cling to the 
 earth and follow it in its wanderings through space. 
 
 Such is the beautiful system wrought out by the 
 great Polish philosopher. Far from perfect, it was 
 founded in truth, and although improvement might and 
 must come, revolution could never shake its firm foun- 
 dation. — While the more prominent irregularities in 
 the planetary motions were removed by constituting 
 the sun the centre of motion, there yet remained an 
 increase and decrease in the orbitual velocities of all 
 the planets, now including the earth among the num- 
 ber, which were inexplicable. The planets did not 
 revolve, then, in circles whose exact centre was occu- 
 pied by the sun. The moon's orbit was not a cir- 
 cle, whose exact centre was the earth ; and to ex- 
 plain these unfortunate irregularities, Copernicus, 
 clinging to circular motion, as the world had done for 
 
MOTIONS OF THE HEAVENLY BODIES. w -7 
 
 2000 year?, was driven to adopt the same expedients 
 which characterized the theories of Ptolemy : the ec- 
 centric and epicycle were fastened upon the new sys- 
 tem of astronomy. Yet another difficulty embarrassed 
 the mind of Copernicus. In giving to the earth a ro- 
 tation on its axis once in twenty-four hours, he ex- 
 plained the apparent revolution of the starry heavens. 
 This axis of rotation, it was readily seen, must ever re- 
 main parallel to itself in the annual revolution of the 
 earth in its orbit. Being in this way carried round 
 such a vast circumference, the prolongation of the axis 
 ought to pierce the northern heavens in a series of 
 points which would form a curve so large as not to 
 escape detection. But no such curve appeared, the 
 north pole of the heavens, scrutinized with the most 
 delicate instruments, preserved its position, immovably 
 throughout the entire revolution of the earth in its 
 orbit, and to escape from this difficulty there was no 
 alternative but to admit that the distance of the 
 sphere of the fixed stars was so great that the diameter 
 of the earth's orbit, equal to 200,000,000 of miles, 
 was absolutely nothing, when compared with that 
 mighty distance. 
 
 Under these circumstances, it is not wonderful that 
 Copernicus should have promulged his system with 
 extreme diffidence and only after long delay ; indeed 
 his great work, setting forth his doctrines, was never 
 read by its author in print, and only reached him in 
 time to cheer his dying moments. 
 
 Vse cannot then be surprised, that the new system 
 was received with doubt and distrust, or rather that it 
 was for a long while absolutely rejected. — The pro- 
 gress of truth is ever slow, while error moves with 
 
88 STRUCTURE OF THE UNIVERSE. 
 
 rapid pace. The reason is obvious. — Error is seized 
 by a class of minds, which asks no evidence ; while 
 the searchers for truth, adopt it only after the most 
 deliberate examination. 
 
 But the revolution had been commenced. A few 
 bold minds were struck with the simplicity and 
 beauty of the conjectures of Copernicus ; and when the 
 exigencies of the age demand genius, it seems to rise 
 spontaneously. The mind had persevered in a sys- 
 tem founded in reason, and which nothing short of this 
 very perseverance could have demonstrated to be er- 
 roneous. Like the traveler, who is uncertain which 
 of two roads to take, he reflects, reasons, and decides, 
 and even if his choice be a wrong one, it would be folly 
 to stop before fully convinced that he had chosen 
 erroneously. 
 
 But the mind is once again in the path of truth; and 
 after wandering twenty long centuries in darkness, 
 which grew deeper and deeper, the change from dark- 
 ness to light gives vigor to its movements, and its 
 future achievements are destined to be rapid and 
 glorious. 
 
 Here let us pause for a moment, on the boundary 
 which divides ancient from modern science, and 
 glance at the collateral circumstances which were 
 found to modify and retard the investigations which 
 had commenced. The old doctrines of philosophy and 
 astronomy, had become intimately interwoven with 
 human society. Ptolemy, and Plato, and Aristotle, were 
 regarded with a sort of reverential awe. Even the 
 church, not following, but leading the world in this 
 profound respect for ancient philosophy, pronounced 
 the doctrines of Ptolemy in accordance with the reve 
 
MOTIONS OF THE HEAVENLY BODIES. 89 
 
 lations of scripture, and girdled them with the fires of 
 persecution, through which alone their sacredness 
 could be attacked. Thus entrenched and defended by 
 prejudice, by society and by religion, none but the most 
 daring spirit would enter the conflict against such un- 
 equal odds. Conscious of these difficulties, Coperni- 
 cus had wisely avoided collision, and gave his doc- 
 trines to the world with such caution as not to pro- 
 voke attack. But this armed neutrality could not 
 long endure. If the new doctrine were founded in 
 error, left to itself it would never advance, and would 
 soon quietly sink into oblivion. On the contrary, should 
 it prove to be based upon truth, no power could arrest 
 its progress, or stay its development. The contest 
 must come sooner or later, and demanded in those 
 who should battle for the truth the rarest qualities. 
 
 Copernicus had merely commenced the examination 
 of his bold conjecture, A life time was too short to 
 accomplish more. He had transferred the centre of 
 motion from the earth to the sun, and rested the truth 
 of his hypothesis on a diminished complexity in the 
 celestial phenomena. In case the true centre had 
 been found, it now remained to determine the exact . 
 
 ni- J 
 
 curves in which the planets revolved, the laws regu 
 lating their motion, and the nature of the bond which, 
 it was now suspected, united the planetary worlds 
 into one great system. The resolution of these pro- 
 found questions was reserved for Kepler, who has 
 without flattery been termed the legislator of the 
 heavens, and who has earned the reputation of being 
 first in fact and first in genius among modern astrono- 
 mers. He united in the most perfect manner, all the 
 qualifications of a great discoverer. Ardent, enthusi- 
 ii 2 
 
90 STRUCTURE OF THE UNIVERSE. 
 
 astic, and subtle, he pursued his investigations with 
 a keen and restless activity. Patient, laborious, and 
 determined, difficulties shrank at his approach and 
 obstacles melted before him. Unprejudiced and pious, 
 he sought for truth in the name and invoking ever 
 the guidance of the great Author of truth. If his 
 theories were not actually deduced from facts, when 
 formed, no test was too severe, and nothing short of 
 a rigid coincidence with fact could satisfy the exact- 
 ing mind of this wonderful genius. Realizing fully 
 the difficulty and importance of the researches before 
 him, once commenced, his perseverance knew no 
 limit, and the fertility of his imagination was utterly 
 inexhaustible. 
 
 Such was the man to whom the interests of science 
 at this critical juncture were committed. Having 
 adopted as an hypothesis, the central position of the 
 sun, and the revolution of the earth and planets 
 around this centre, he determined to discover the true 
 nature of the planetary orbits, and find if possible, 
 some single curve which would explain the orbitual 
 motions of the celestial bodies. To accomplish this 
 difficult enterprise, Kepler wisely determined to con- 
 fine his efforts and investigations to one single planet, 
 and Mars was selected as the subject for experiment. 
 He commenced by a rigorous comparison between the 
 observed places of the planet and those given by the 
 best tables which could be computed by the circular 
 theory. Sometimes the predicated and observed places 
 agreed well with each other, and hope whispered that 
 the true theory had been found; but pursuing the 
 planet onward in its sweep around the sun, it would 
 begin to diverge from its theoretic track, its distance 
 
MOTIONS OF THE HEAVENLY BODIES. 91 
 
 would increase until it became evident that the theory 
 was false, and must be abandoned. 
 
 Nothing daunted, the ardent philosopher consoled 
 himself with the thought, that among all possible 
 theories which the mind could frame, one had been 
 stricken from the list, and a diminished number re- 
 mained for examination. This was a new mode of 
 research, and in case the number of theories was not 
 too great, and the patience of the philosopher suffi- 
 ciently enduring, a time would come, sooner or later, 
 when success must reward his labors. Thus did 
 Kepler toil on subjecting one hypothesis after another 
 to the ordeal of rigid experiment, until no less than 
 nineteen had been tested with the utmost severity, 
 and all were rejected. Eight years of incessant labor 
 had been devoted to this examination. He had ex- 
 hausted every combination of circular motion which 
 the fertility of his imagination could suggest. They 
 had all utterly failed. — The charm was ended, and he 
 finally broke away from the fascination of this beau- 
 tiful curve, which for five thousand years had so be- 
 wildered the human mind, and boldly pronounced it 
 impossible to explain the planetary motions with any 
 circular hypothesis. This at least was a great nega- 
 tive triumph. If he had not found the curve in which 
 the planets revolved, he had found what it could not 
 be, and released from all future embarrassment from 
 eccentrics and epicycles, he now pursued a lofty and 
 independent train of investigation. 
 
 Leaving forever the circle, the next simplest curve 
 is called the ellipse, an oval figure, which when but 
 little flattened very nearly resembles the circle in form, 
 but enjoys very different properties. All diameters of 
 
92 STRUCTURE OF THE UNIVERSE. 
 
 a circle are equal. The diameters of an ellipse are 
 unequal. The centre of the circle is equally distant 
 from all points on the circumference. No such point 
 exists in the ellipse ; but two curious points are found 
 on its longest diameter, possessing the remarkable 
 property of having the sum of the lines joining them 
 with any point of the curve constantly equal to the 
 longest diameter. Each of these points is called a 
 focus. This beautiful curve, with its singular proper- 
 ties, had been discovered by the Greek mathemati- 
 cians ; but not remarking its use in nature, it had 
 hitherto been regarded only as an object of amusing 
 speculation. To this curve did Kepler apply, when 
 driven from the circular hypothesis, and again com- 
 menced his system of forming hypotheses, and hunting 
 them down, as he termed his scrutinizing process. As 
 in the circular hypothesis the sun had at first been lo- 
 cated in the centre, so in commencing the elliptic theory 
 the centre of the longest diameter was made the cen- 
 tre of motion. Buoyant with hope, the astronomer 
 sets out to follow the planet around its elliptic orbit ; 
 but although for a short distance its movements were 
 well represented, it finally broke away from the elliptic 
 track, and bid defiance to the central hypothesis. But 
 Kepler was not in the least disheartened with this 
 first effort — He now shifts the sun to the focus of the 
 ellipse, constructs his orbit, starts once more on the 
 track of the planet, watches it as it sweeps onward 
 around the sun, the elliptic orbit holds it as it moves, 
 farther and still farther. — Half its revolution is per- 
 formed and there is no diverging, onward it flies, — the 
 goal is won. — Triumph crowns the philosopher, the 
 orbit is found ! 
 
<*, 
 
 JO/ MOTIONS OF THE HEAVENLY BODIES. 93 
 
 Thus was accomplished one of the most important 
 discoveries which the mind had ever reached. The 
 elliptic orbit of Mars, rapidly led to those of the other 
 planets, and to that of the moon, and Kepler pro- 
 claimed to the world his first great law, in the follow- 
 ing language : Planets revolve in elliptic orbits about the 
 sun, which occupies the common focus of all these orbits. 
 
 This law swept forever from the heavens and from 
 astronomy those complications which had stood the 
 test of centuries, nay of thousands of years. Their 
 mysterious power was paralyzed by this single touch 
 of the enchanter's wand, and they fled from the skies. 
 The circle was as simple and beautiful as ever, but its 
 divine character was gone, and the gods or angels 
 who had so long held their abodes in the planets, were 
 exiled from their homes. — The dawn of modern science 
 broke in beauty on the world. 
 
 Kepler having been so signally rewarded by this 
 great discovery, now turned his attention to an inves- 
 tigation of the first importance, one indeed which was 
 indispensably necessary to render his first discovery 
 available. As the planets were now known to re- 
 volve in ellipses, and as their motion was found by 
 observation to be unequal in different parts of their 
 orbits, it became a matter of the first consequence to 
 ascertain some simple law, regulating the orbitual 
 motion, and by means of which a planet might be 
 readily followed, and its places computed. To detect 
 this law, in whose existence Kepler seems to have 
 entertained the most unwavering faith, a figure 
 was drawn representing the orbit of Mars, the sun 
 occupying one of the foci of the curve. — On the cir- 
 cumference of this curve the places of the planets were 
 
94 STRUCTURE OF THE UNIVERSE. 
 
 marked down as observation had determined them ; 
 and here commenced a series of examinations which 
 finally led to the knowledge of the second great law 
 of the planetary motions, which may be thus an- 
 nounced. If aline be drawn from the centre of the sun, to 
 any planet, this line as it is carried forward by the planet, 
 icill sweep over equal areas in equal portions of time. — 
 This law accorded in the most perfect manner with 
 fact, and gave at once the power of following, and 
 from the mean motion, computing the place of any 
 planet ; a triumph which all the complexity of older 
 systems had failed ever to accomplish. 
 
 Any other mind less adventurous than that of Kep- 
 ler, might have been satisfied with these two great dis- 
 coveries. The precise curves described by the planets 
 and a law regulating their motions in their orbits, 
 sufficed to render all the phenomena of the heavenly 
 bodies not only explicable, but susceptible of accurate 
 prediction. — There seemed nothing more to be added. 
 — Kepler did not think so. He conceived the idea 
 that the solar system was not a mere assemblage of iso- 
 lated planets revolving about a common centre, but a 
 great associated system, in which some common bond 
 of union existed, which once found, would present the 
 solar system in a new and true light. 
 
 This bond he believed existed in some hidden rela- 
 tion between the times occupied by the planets in de- 
 scribing their orbits, and their distances from the sun. 
 In the history of this remarkable research, we are pre- 
 sented with one of the brightest examples of the 
 fruits of perseverance. If some superior power, some 
 spirit from a brighter world, had revealed to the mind 
 of Kepler, the actual existence of some relation be- 
 
d 
 
 MOTIONS OF THE HEAVENLY BODIES. 95 
 
 tween y the planet's periods and distances, and had 
 proposed to him to discover this hidden law, there 
 would have been a definite object before the astrono- 
 mer, and to have persevered in the pursuit of this 
 object, would have been within the limits of proba- 
 bility, even if a lifetime were exhausted in fruitless 
 efforts. But to excite in his own mind a faith suffi- 
 ciently strong in the existence of a law of which there 
 existed not the slightest evidence, and to have perse- 
 vered in its research for seventeen long years of labo- 
 rious effort, seems almost incredible. 
 
 There is an immense difference between the pursuit 
 which resulted in the discovery of the first two laws 
 of Kepler, and the third one. In seeking for the curve 
 described by the planets, it was looking for that, which 
 must have an existence; and in tracing the law of a 
 planet's motion, it was absolutely impossible to follow 
 a planet, or predict its positions, without such a law 
 But in seeking for a bond of union among the planet- 
 ary periods and distances, it was a search for that, 
 which it was believed had no existence, except in the 
 wild imagination of this extraordinary philosopher. 
 The history of mind scarcely furnishes an example in 
 any degree parallel, if we except perhaps the heroic 
 fortitude which marked the career of Columbus. — -Yet 
 even the great Genoese was in possession of solid 
 facts on which to base his reasoning. He saw evi- 
 dences of the existence of another hemisphere, which 
 the superficial could never realize. Kepler, more bold, 
 more grand, more sublime, dreamed of nothing less than 
 a brotherhood of worlds, a mighty and magnificent 
 scheme of vast revolving orbs. Should success crown 
 his efforts, the most brilliant results would follow. 
 
96 STRUCTURE OF THE UNIVERSE. 
 
 The distance of a single planet from the sun once ob- 
 tained, and the periodic time of all being known, the 
 distances might then be found for each individual in 
 the entire system, without even directing an instru- 
 ment to the heavens. Here then was a prize to 
 reach which no time, or pains, or labor could be mis- 
 applied. Its return would be, a hundred fold. 
 
 But where was the prize to be sought? Even ad- 
 mitting that some common bond did bind the circling 
 worlds into one harmonious system, did it exist in 
 some hidden relation between their periods of revolu- 
 tions, their distances, their magnitudes, their densi- 
 ties ? or was it to be sought in some analogy between 
 the distances and periodic times ? After long and de- 
 liberately pondering this great problem, Kepler de- 
 cided that the strongest probability suggested that 
 the distances of the planets, and their periods of rev- 
 olution, would in some way contain the mysterious 
 bond of union. Here then did this daring mind con- 
 centrate its energies ; and his purpose once fixed, he 
 marches steadily forward in his research with a cour- 
 age which no defeat could daunt, and a perseverance 
 which knew no limit but success. 
 
 Before announcing the final result, let me explain 
 two terms employed in its statement. The square of 
 /my quantity results by multiplying it by itself. The 
 cube comes from multiplying the square by the number. 
 The square of a planet's period, or the cube of its dis- 
 tance, are known the moment we know the period, 
 and distance, by applying the simple rules of arith- 
 metic. After Kepler had exhausted all simple rela- 
 tions between the periods and distances of the planets, 
 in no degree shaken in his lofty faith, he proceeded to 
 
MOTIONS OF THE HEAVENLY BODIES. 91 
 
 try all possible relations between the squares of the 
 periods and distances; but with as little success, 
 Nothing daunted, he proceeded to investigate the pos- 
 sible relations between the cubes of the periods and 
 distances. Here again he was foiled; no law exhibited 
 itself. — He returned ever fresh to the attack, and now 
 commenced a series of trials involving the relations 
 between the simple periods and the squares of the 
 distances. Here a ray of hope broke in upon his 
 dim and darkened path. 
 
 No actual relation existed, yet there was a very 
 distant approximation, enough to excite hope. — lie 
 then tried simple multiples of the periods and the 
 squares of the distances — all in vain. He finally 
 abandoned the simple periods and distances, and rose 
 to an examination of the relations between the squares 
 of these same quantities. — Gaining nothing here, he 
 rose still higher, to the cubes of the periods and dis- 
 tances ; — no success, until finally he tried the propor- 
 tion existing between the squares of the periods in 
 which the planets perform their revolutions and the 
 cubes of their distances from the sun. — Here was the 
 grand secret, but, alas ! in making his numerical com- 
 putations, an error in the work vitiated the results, 
 and with the greatest discovery which the mind ever 
 achieved in his very grasp, the heart-sick and toil- 
 worn philosopher turned away almost in despair from 
 his endless research. 
 
 Months rolled round, and yet his mind with a sort of 
 keen instinct, would recur again and again to this last 
 hypothesis. Guided by some kind angel or spirit whose 
 sympathy had been touched by the unwearied zeal of 
 the mortal, he returned to his former computations, 
 I 
 
98 STRUCTURE OF THE UNIVERSE. 
 
 and with a heaving breast, and throbbing heart, he 
 detects the numerical error in his work, and com- 
 mences anew. The square of Jupiter's period is to 
 the square of Saturn's period as the cube of Jupiter's 
 distance is to some fourth term, which Kepler hoped 
 and prayed might prove to be the cube of Saturn's 
 distance. With trembling hand, he sweeps through 
 the maze of figures ; the fourth term is obtained ; 
 he compares it with the cube of Saturn's distance. — 
 They are the same ! — He could scarcely believe his 
 own senses. He feared some demon mocked him.— 
 He ran over the work again and again — He tried the 
 proportion, the square of Jupiter's period to the square 
 of Mars' period as the cube of Jupiter's distance to a 
 fourth term, which he found to be the cube of the dis- 
 tance of Mars. — Till finally full conviction burst upon 
 his mind: he had won the goal, the struggle of seven- 
 teen long years was ended, God was vindicated, and 
 the philosopher in the wild excitement of his glorious 
 triumph, exclaims : 
 
 " Nothing holds me. I will indulge my sacred fury ! 
 If you forgive me I rejoice ; if you are angry I can 
 bear it. The die is cast. The book is written, to be 
 read either now, or by posterity, I care not which. 
 — It may well wait a century for a reader, since God 
 has waited six thousand years for an observer ! " 
 
 More than two hundred years have rolled away 
 since Kepler announced his great discoveries . Science 
 has marched forward with swift and resistless energy. 
 The secrets of the universe have been yielded up under 
 the inquisitorial investigations of god-like intellect. 
 The domain of the mind has been extended wider and 
 wider. One planet after another has been added to 
 
MOTIONS OF THE HEAVENLY BODIES. 99 
 
 our system ; even the profound abyss which separates 
 us from the fixed stars has been passed, and thou- 
 sands of rolling suns have been descried, swiftly flying 
 or majestically sweeping through the thronged regions 
 of space. But the laws of Kepler bind them all, — 
 satellite and primary — planet and sun — sun and sys- 
 tem — all with one accord, proclaim in silent majesty, 
 the triumph of the hero philosopher. 
 
LECTURE IV, 
 
 DISCOVERY OF THE GREAT LAWS OF MOTION AND 
 GRAVITATION. 
 
 The remarkable discoveries which had rewarded 
 the researches of Kepler, confirmed in the most per- 
 fect manner the doctrines of Copernicus, flowing as 
 they did from his prominent hypothesis, the central 
 position of the sun. Having reached to the true laws 
 of the planetary motions, the whole current of astro- 
 nomical research was changed. New methods were 
 demanded, and more delicate means of observation 
 must be brought into use before the data could be 
 furnished for new discoveries. Henceforward as- 
 tronomy could only advance by the aid of kindred 
 sciences. Mathematics, optics, and above all, me- 
 chanical philosophy, were to become the instruments 
 of future conquests. 
 
 The philosophy of Aristotle, though very far from 
 deserving it, wielded quite as extensive an influence 
 over the age, as did the astronomy of Ptolemy. It 
 appears, indeed, that the followers of Aristotle re- 
 garded their master as absolutely infallible, and gave 
 to his doctrines a credence so firm, that even the 
 clearest experiments, the most undeniable evidence 
 of the senses were sooner to be doubted than the doc- 
 trines of the divine Greek. To attack and destroy a 
 i2 (ioi) 
 
102 STRUCTURE OF THE UNIVERSE. 
 
 system so deeply rooted in the prejudices of the age, 
 required a mind of extraordinary courage and power, 
 a mind deeply imbued with the love of truth, quick in 
 its perceptions, logical in argument, and firm in the 
 hour of trial. 
 
 Such a mind was that of the great Florentine phi- 
 losopher, Galileo Galilei, the senior, friend, and con- 
 temporary of Kepler. Indeed the exigencies of the 
 age seem to have given birth to three men, whose 
 peculiar constitutions fitted them for separate spheres, 
 each of the highest order, each in some measure in- 
 dependent, and yet all combining in the accomplish- 
 ment of the great scientific revolution. While Tycho, 
 the noble Dane, immured within the narrow limits of 
 his little island, watching from his sentinel towers 
 the motions of the stars, noting with patient and 
 laborious continuity, the revolutions of the sun, moon 
 and planets, was accumulating the materials which 
 were to furnish the keen and inquisitive mind of 
 Kepler with the means of achieving his great tri- 
 umphs — Galileo, with a giant hand, was shaking to 
 their foundations the philosophical theories of Aris- 
 totle, and startling the world with his grand mechani- 
 cal discoveries. But for the observations of Tycho, 
 Kepler's laws could not have been revealed; — but for 
 the magic tube of Galileo, these laws had been the 
 ne plus of astronomical science. Thus do we witness 
 the rare spectacle of three exalted intellects, contem 
 poraneously putting forth their diverse talents in the 
 accomplishment of one grand object. The Dane, the 
 German, and the Italian, divided by language and by 
 country, united in the pursuit of science and of truth. 
 
 Called to Pisa to discharge the duties of a philo- 
 
LAWS OF MOTION AND GRAVITATION. 103 
 
 sophical teacher, Galileo was not long in detecting 
 the extravagant philosophical errors of Aristotle, 
 which had been implicitly received for more than 
 twenty centuries. He continued to teach the text of 
 his old master, but it was only to expose its unsound 
 and false philosophy to his wondering and incredu- 
 lous pupils. A desecration so monstrous, could not 
 long escape exposure and punishment. Indeed the 
 Florentine made no secret of his teachings. The 
 Aristotelians made common cause against the young 
 philosophical heretic, and he was warned to desist 
 from his heresy. Galileo gave for answer to his 
 opponents, that he was ready to relinquish his new 
 views the moment they were shown by experiment to 
 be false ; on the other hand, he demanded of them 
 equal candor, and proposed to refer the matter in con- 
 troversy to the tribunal of experiment. 
 
 Aristotle, in discussing the laws of falling bodies, 
 affirmed the principle, that the velocity acquired by 
 any falling body, was in the direct proportion of its 
 weight; and if two bodies of unequal weight com- 
 menced their descent from the same height, at the 
 same moment, the heavier would move as many times 
 swifter than the lighter, as its weight exceeded 
 that of the smaller body. Galileo doubted the truth 
 of this principle, and on subjecting it to the test of 
 experiment, he saw instantly that its variation from 
 fact was wide as it could be. The obvious character 
 of this experiment, its freedom from all chances of 
 deception, and the importance of the principle in- 
 volved, induced the young philosopher to select it as 
 the test, and to challenge his opponents to a public 
 demonstration of the truth or falsehood of their old 
 
104 STRUCTURE OF THE UNIVERSE. 
 
 system of philosophy. — The challenge was accepted. 
 The leaning tower of Pisa presented the most conveni- 
 ent position for the performance of these experiments, 
 on which Galileo so confidently relied for triumphant 
 demonstration of the error of Aristotle ; and thither on 
 the appointed day the disputants repaired, each party 
 perhaps with equal confidence. It was a great crisis 
 in the history of human knowledge. On the one side, 
 stood the assembled wisdom of the universities, re- 
 vered for age and for science, venerable, dignified, 
 united and commanding. Around them thronged the 
 multitude, and about them clustered the associations 
 of centuries. On the other, there stood an obscure 
 young man, with no retinue of followers, without 
 reputation or influence, or station. But his courage 
 was equal to the occasion ; confident in the power of 
 truth, his form is erect, and his eye sparkles with 
 excitement. 
 
 But the hour of trial arrives. The balls to be em- 
 ployed in the experiments are carefully weighed and 
 scrutinized to detect deception. The parties are satis- 
 fied. The one ball is exactly twice the weight of the 
 other. The followers of Aristotle maintain that when 
 the balls are dropped from the top of the tower, the 
 heavy one will reach the ground in exactly half the 
 time employed by the lighter ball. Galileo asserts that 
 the weights of the balls do not affect their velocities, 
 and that the times of descent will be equal ; and here 
 the disputants join issue. — The balls are conveyed to 
 the summit of the lofty tower. The crowd assembles 
 round the base — the signal is given — the balls are 
 dropped at the same instant, and swift descending, at 
 the same moment they strike the earth. Again and 
 
LAWS OV MOTION AND GRAVITATION. 105 
 
 again is the experiment repeated, with uniform re- 
 sults. Galileo's triumph was complete. Not a shadow 
 of doubt remained ; but far from receiving, as he 
 had hoped, the warm congratulations of honest con- 
 viction — private interest, the loss of place, and the 
 mortification of confessing false teaching, proved too 
 strong for the candor of his adversaries. — They clung 
 to their former opinions with the tenacity of despair, 
 and assailed the now proud and haughty Galileo with 
 the bitter feelings of disappointment and hate. 
 
 The war was now openly declared, and waged with 
 a fierceness which seems to have excited the mind of 
 the young philosopher to the most extraordinary 
 efforts. Driven from Pisa, by the numbers and influ- 
 ence of his enemies, no suffering or danger could drive 
 from his mind the great truths which his researches 
 by experiment were constantly revealing. His spirit 
 was unbroken, and in retiring from the unequal con- 
 test, he hurled back defiance into the face of his con- 
 quered, though triumphant persecutors. 
 
 The mechanical investigations of Galileo, conducted 
 with clearness and precision, soon led to the most 
 important discoveries. He detected the law of falling 
 bodies, and showed that the spaces described were 
 proportional to the squares of the times ; that is, if a 
 body fell ten feet in one second of time, it would fall 
 four times as far in two seconds, nine times as far in 
 three seconds, and so on for any number of seconds. 
 He studied with success the subject of the composi- 
 tion of forces, and demonstrated this remarkable pro- 
 position, which lies at the very foundation of all 
 modern mechanical philosophy. It may be thus stated. 
 If a body receive an impulse, which singly would 
 
106 STRUCTURE OF THE UNIVERSE. 
 
 cause it to move thirty feet in a second, on the line of 
 the direction of the impulse, and at the same instant 
 another impulse be communicated in a different direc- 
 tion from the first, and which if acting alone would 
 cause the body to move on the line of direction of the 
 second impulse forty feet in one second, under the 
 joint action of these two impulses the body will move 
 in a direction easily determined from those of the 
 impulsive forces, and will fly with a velocity of fifty 
 feet in the first second of time. 
 
 Such is the universal prevalence of this beautiful 
 proposition, that no falling, flying, or moving body, 
 whether it be the rifle ball, the cannon shot, or the 
 circling planet, is free from its imperious sway. 
 Strike the knowledge of this great truth from ex- 
 istence, and the magnificent structure which modern 
 science has reared, falls in ruins at a single blow. 
 It is founded in the simple but invariable laws of 
 motion, and while these endure, this elegant dis- 
 covery of the Florentine philosopher will remain as 
 a monument to his sagacity and penetration. 
 
 Possessed of such rare qualities for philosophic 
 research, so free from prejudice, and withal, so can- 
 did, we cannot but inquire with interest, how the 
 mind of Galileo stood affected towards the new 
 astronomical doctrines of Copernicus. He had early 
 adopted and taught the Ptolemaic system, and his con- 
 version is so remarkable, and is so characteristic of 
 the man, that it cannot be omitted. A disciple of 
 Copernicus visited the city of Galileo's residence, and 
 delivered several public lectures to crowded audi 
 ences, on the new doctrines. Galileo, regarding the 
 whole subject as a species of solemn folly, would not 
 
LAWS OF MOTION AND GRAVITATION. 107 
 
 attend. Subsequently, however, in conversing with 
 one who had adopted these new doctrines, the Coper- 
 nican sustained his views with such a show of rea- 
 son that Galileo now regretted that he had heedlessly 
 lost the opportunity of attending the lectures. To 
 make amends, he sought every opportunity to con- 
 verse with the Copernicans, and remarking that they, 
 like himself, had all once been Ptolemaists, and chat 
 from the doctrines of Copernicus no one had ever 
 subsequently become a follower of the old philosophy, 
 he resolved to examine the subject with the most 
 serious attention. The result may be readily antici- 
 pated; the conversion was sudden and thorough, the 
 old astronomy was abandoned, and the new convert 
 became the great champion by whose ardor, and 
 unconquerable zeal, the strongholds of antiquated 
 systems were to be destroyed and a new and truthful 
 one founded. 
 
 Thus far the career of Galileo in science had been 
 successful and brilliant. He was rapidly rising in 
 reputation and influence, when a fortunate accident 
 revealed to the world, the application of a principle 
 in optics fraught with consequences, which it is im- 
 possible to estimate. Galileo was informed that 
 Jansen, of Holland, had contrived an instrument pos- 
 sessing the extraordinary property of causing distant 
 objects, viewed through it, to appear as distinctly as 
 when brought near to the eye. The extensive knowl- 
 edge which Galileo possessed of optics, immediately 
 gave him the command of the important principle on 
 which the new instrument had been constructed. He 
 saw at once the high value of such an instrument in 
 
108 STRUCTURE OF THE UNIVERSE. 
 
 his astronomical researches, and with his own hands 
 commenced its construction. 
 
 After incredible pains, he finally succeeded in con- 
 structing a telescope, by whose aid, the power of the 
 eye was increased thirty fold. It is impossible to con- 
 ceive the intense interest with which the philosopher 
 directed for the first time his wonderful tube to the 
 inspection of the heavens. When we reflect that 
 with the aid of this magical instrument the observer 
 was about to sweep out through space, and to ap- 
 proach the moon, and planets, and stars, to within a 
 distance only one-thirtieth of their actual distance ; 
 that their size was to increase thirty fold, and their 
 distinctness in the same ratio, it is not surprising that 
 these wonders should have excited the most extrava- 
 gant enthusiasm. — Galileo commenced by an exami- 
 nation of the moon. Here he beheld, to his inexpres- 
 sible delight, the varieties of her surface clearly 
 defined, her deep cavities, her lofty mountains, her 
 extensive plains, were distinctly revealed to his aston- 
 ished vision. Having satisfied himself of the reality 
 of these inequalities of the moon's surface, by watch- 
 ing the decreasing shadows of the mountains, as the 
 sun rose higher and higher on the moon, he turned 
 his telescope to an examination of the planets. These 
 objects, w r hich the human eye had never before beheld 
 other than brilliant stars, now appeared round and 
 clear and sharp, like the sun and the mobn to unaided 
 vision. On the 8th January, 1610, the telescope was 
 for the first time directed to the examination of the 
 planet Jupiter. Its disk was clearly visible, of a pure 
 and silver white, crossed near the centre by a series 
 of dark streaks or belts. Near the planet, Galileo 
 
LAWS OF MOTION AND GRAVITATION. 109 
 
 remarked three bright stars which were invisible to the 
 naked eye. He carelessly noted their position with 
 reference to the planet, for he believed them to be 
 fixed stars, and of no special interest, except to point 
 out the change in Jupiter's place. On the following 
 night, " induced," as he says, " by he knew not what 
 cause," he again directed his attention to the same 
 planet. The three bright stars of the preceding even- 
 ing were still within the field of his telescope, but their 
 positions with reference to each other were entirely 
 changed, and such was the change, that the orbitual mo- 
 tion of Jupiter could in no way account for it. Aston- 
 ished and perplexed, the eager astronomer awaits the 
 coming of the following night to resolve this mysterious 
 exhibition. Clouds disappoint his hopes, and he is 
 obliged to curb his impatience. — The fourth night was 
 fair, the examination was resumed, and again the 
 bright attendants of Jupiter had changed — his suspi- 
 cions were confirmed — he no longer hesitated, and 
 pronounced these bright stars to be moons, revolving 
 about the great planet as their centre of motion. A few 
 nights perfected the discovery; the fourth satellite was 
 detected, and this astounding discovery was an- 
 nounced to the world. 
 
 No revelation could have been more important or 
 more opportune than that of the satellites of Jupiter. 
 The advocates of the Copernican theory hailed it with 
 intense delight; while the sturdy followers of Ptolemy 
 stoutly maintained the utter absurdity of such pre- 
 tended discoveries, and urged as a sort of unanswera- 
 ble argument, that as there were but seven openings 
 in the head — two ears, two eyes, two nostrils and the 
 mouth, there could be in the heavens but seven planets. 
 K 
 
110 STRUCTURE OF THE UNIVERSE. 
 
 The more rational, however, saw the earth, by this 
 discovery, robbed of its pretended dignity. It com- 
 manded the attendance of but one moon, while Jupiter 
 received the homage of no less than four bright attend- 
 ants. The delighted Copernicans saw in Jupiter as a 
 central orb and in the orderly revolution of his satel- 
 lites, a miniature^of the sun and his planets, hung up 
 in the heavens, and there placed to demonstrate to all 
 coming generations, the truth of the new doctrines. 
 
 Another discovery soon followed, which it is said 
 the sagacity of Copernicus foresaw would sooner or 
 later be revealed to human vision. It had been urged 
 by the Ptolemaists, that in case Venus revolved about 
 the sun, as was asserted by Copernicus, and reflected 
 to us the light of that luminary, then must she imitate 
 exactly the phases of the moon; when on the side oppo- 
 site to the sun, turning towards us her illuminated hem- 
 isphere she ought to appear round like the moon, while 
 the crescent shape should appear on reaching the 
 point in her revolution which placed her between the 
 sun and the eye of the observer. As these changes 
 were invisible to the naked eye, the objection was 
 urged with a force which no argument could meet. 
 Indeed it was unanswerable, and in case the telescope 
 should fail to reveal these changes in Venus, the fate 
 of the Copernican theory was forever sealed. 
 
 The position of Venus in her orbit was computed — 
 the crescent phase due to that position determined — 
 the telescope applied, and the eye was greeted with 
 an exquisite miniature of the new moon. There 
 was the planet, and there was the crescent shape 
 Jong predicted by Copernicus, received by him and 
 his followers as a matter of faith, now become a 
 
LAWS OF MOTION AND GRAVITATtON. Ill 
 
 matter of sight. The doctrines of Copernicus thus 
 received not only confirmation, but so far as Venus 
 was concerned, a proof so positive that no skepticism 
 could resist. It is not my design to follow the dis- 
 coveries of the Florentine philosopher among the 
 planetary orbs. These w T ill be resumed hereafter, 
 when we come to examine more particularly the 
 physical constitution of the planets. I have merely 
 adverted to those discoveries, which became spe- 
 cially important in the discussions between the par- 
 tizans of the old and new astronomy. 
 
 Admitting the doctrines of Copernicus, and uniting 
 to them the great discoveries of Kepler, let us exam- 
 ine the qpndition of astronomical science, ascertain 
 precisely the point the mind had reached, and the na- 
 ture of the investigations which next demanded its 
 attention. From the first of Keplers laws, the figure 
 of the planetary orbits became known, and the mag- 
 nitude of the ellipse described by any planet was easily 
 determined. By observing the greatest and least dis- 
 tances of any planet from the sun, the sum of these 
 distances gave the longer axis of the orbit ; and know- 
 ing this important line, and the focus, it became a 
 simple matter to construct the entire orbit. The line 
 joining the planet with the sun, while the planet oc- 
 cupied its shortest or perihelion distance, gave the 
 position of the axis of the orbit in space, and its plane 
 being determined by its inclination to that of the 
 ecliptic, nothing remained to fix in space the figure, 
 magnitude and position of the planetary orbits. The 
 next point was to pursue and predict the move- 
 ments of these revolving bodies. This was readily 
 accomplished. A series of observations soon revealed 
 
112 STRUCTURE OF THE UNIVERSE. 
 
 the time occupied by any planet in performing one 
 complete revolution in its elliptic orbit. Knowing 
 thus the periodic time, and the position of the planet 
 in its orbit at any given epoch, the second law of 
 Kepler furnished the key to its future movements ; its 
 velocity in all parts of its orbit became known, and 
 the mind swift and true followed the flying world in 
 its rapid flight through space. It even went further; 
 anticipated its changes, and predicted its positions, 
 with a degree of certainty only limited by the accu- 
 racy with which the elements of its orbit had been 
 determined. 
 
 The third of Kepler's laws, exhibiting the proportion 
 between the periodic times and the mean distances of 
 the planets from the sun, united all these isolated and 
 wandering orbs into one great family. Their periods 
 of revolution were readily determined by observation, 
 and an accurate determination of the distance from 
 the sun of a single planet in the group, gave at once 
 the distances of all the remaining ones. The increased 
 accuracy of the means of observation w r ould render 
 more perfect each successive measure of the earth's 
 distance from the sun, and it seemed now that the 
 mind might stop and rest from its arduous toil ; that 
 scarcely any thing remained to be done. The solar 
 system was* conquered, and the fixed stars defied the 
 utmost efforts of human power. 
 
 How widely does this view differ from the true 
 one. In fact, the true investigation had not even 
 commenced. A height had indeed been gained, from 
 whence alone the true nature of the next great prob- 
 lem became visible, and standing upon this eminence 
 the mind boldly propounds the following questions: — 
 
LAWS OF MOTION AND GRAVITATION. 113 
 
 Why should the orbits of the planets and satellites be 
 ellipses, rather than any other curve ? What power 
 compelled them to pursue their prescribed paths with 
 undeviating accuracy ? What cause produced their 
 accelerated motion when coming round to those parts 
 of their orbits nearer to the sun ? What power held 
 planet and satellite steady in their swift career, pro- 
 ducing the most exquisite harmony of motion, and a 
 uniformity of results as steady as the march of time ? 
 
 Here I may be asked, do not such questions border 
 on presumption ? Are not such inquisitorial exami- 
 nations touching on the domain of God's inscrutable 
 providences, and would it not be wiser to stop and 
 rest satisfied with the answer to all these questions, 
 that God, who built the universe, governs and sustains 
 it by his power and wisdom ? Doubtless this answer 
 is true, and in its truth man humbly finds his highest 
 encouragement to attempt the resolution of the sub- 
 lime questions already propounded for examination. 
 Let us admit that the divine will produces all motion, 
 speeds the earth in its rapid flight about the sun, 
 guides the planets and their revolving moons, and 
 poises the sun himself in empty space, as the great 
 centre of life and light and heat to his attendant 
 worlds. Is it not reasonable to believe that the will 
 of the Omnipotent is exerted according to some uni- 
 form system, that this system is law, and that this 
 law is within the reach of man ? To encourage this 
 view the simple laws of motion had been already 
 revealed, and as these must exert a controlling influ- 
 ence in our future examinations, we proceed to un- 
 fold them. 
 
 First, then, it was discovered that if any body, 
 k2 
 
114 STRUCTURE OF THE UNIVERSE. 
 
 situated in space and free to move, receive an impulse 
 capable of giving it a velocity of ten feet in the first 
 second of time, or any other velocity, it will move off 
 in the direction of the impulse for ever in a straight 
 line, and with undiminished and unchanged velocity. 
 The intensity of the primitive impulse determines the 
 velocity of the body which receives it, and the one is 
 precisely proportioned to the other. Again, in case a 
 moving body while pursuing its flight receives an im- 
 pulse in a direction different from its primitive one, its 
 new direction and velocity will be determined by the 
 direction and intensity of the new impulse, according 
 to the principle discovered by Galileo, and already 
 explained. Lastly, in every revolving body a dispo- 
 sition is generated to fly from the centre of rotation. 
 The body seems urged by some invisible force from 
 the centre, and if the velocity be sufficiently in- 
 creased, no matter how strong the bond which unites 
 it to the centre, it will, in the end, be severed, and 
 the body, freed from its centre, darts away in a 
 straight line tangent to its former circle of revolu- 
 tion. This power, which urges revolving bodies from 
 the centre of motion, is called the centrifugal force, 
 and is proportioned to the squares of the velocity of 
 the revolving body. Hence a cord sufficiently strong 
 to hold a heavy ball revolving round a fixed centre 
 at the rate of fifty feet in a second, would require to 
 have its strength increased four fold, to hold the same 
 ball, if its velocity should be doubled. 
 
 These simple laws, derived from a rigorous exami- 
 nation of those moving bodies, subject to man's closer 
 scrutiny, extend their sway through the remotest re- 
 gions of space. Are these laws necessary qualities 
 
LAWS OF MOTION AND GRAVITATION. 115 
 
 of matter? Why should a body, darting away under 
 the action of some impulsive force, pursue forever its 
 undeviating direction, with undiminished velocity ? — 
 This effect cannot arise from any necessary property 
 or quality of matter. The law might have been dif- 
 ferent — the direction of the moving body might have 
 slowly varied — the velocity might have increased or 
 decreased in any proportion, and yet the flying body, 
 so far as we can understand, have retained all its 
 physical qualities and properties. No — Divine wis- 
 dom has selected these simple and beautiful laws 
 from among a multitude, either of which might have 
 been chosen. Stretching forward, therefore, to the 
 examination of the force by which the planets are 
 retained in their orbits, was it not reasonable to 
 expect, that some law might be found, governing 
 the application of that mysterious power, and in 
 some way proportioned to the mass of the moving 
 body, and to the orbit which it described in wheeling 
 around the sun. That they were held by some invisi- 
 ble power to their centre of motion, was manifest 
 from the fact that the centrifugal force, generated by 
 the rapidity of their revolution, would have hurled 
 them away from the sun, if not opposed and counter- 
 poised by some equivalent power lodged in the great 
 centre of the planetary orbs. Here was an object 
 worthy the highest ambition of the human mind. — 
 No matter what might be the nature of this force, 
 whether it should reside in the sun, or in the planet, 
 or in both — whether it should prove to be a property 
 of matter, or the mere uniform manifestation of the 
 Omnipotent will ; the discovery of its law of action 
 would give to the mind the power of penetrating the 
 
116 STRUCTURE OF THE UNIVERSE. 
 
 darkest recesses of nature, and of rising to a knowl- 
 edge of the profoundest secrets of the universe. 
 
 Such is the nature of the investigation propounded 
 to the powerful intellect of Newton. This eminent 
 philosopher, justly regarded as the most extraordinary 
 genius that ever lived, neither originated the question 
 which he undertook to discuss, nor divined the law 
 of force which he proposed to demonstrate. When 
 Kepler had closed the investigations which led to the 
 discovery of his three great laws, his sagacity at once 
 suggested to his mind the existence of some central 
 force, by whose power the planetary movements were 
 controlled. He had watched the moon circling around 
 the earth, he had scrutinized the ocean tide, whose 
 crested wave seemed to rise and follow the move- 
 ments of the moon, until he boldly announced that 
 some invisible bond, some inscrutable power, united 
 the one to the other. He even reached the conclu- 
 sion, that this unknown force resided in the moon — 
 that by its power the waters were heaved from their 
 beds, and caused to follow the moon and imitate its 
 motions. Doubtless the solid earth itself felt this 
 mysterious power, and swayed to its influence ; but in 
 consequence of the immobility of its particles, its 
 effects had, thus far, escaped detection. Thus once 
 started on the track, Kepler pursued the speculation. 
 He attributed a similar power to the sun, and exten- 
 ded its controlling influence to the planets. He went 
 yet farther, and conjectured that the law of this un- 
 known force was such that it diminished as the squares 
 of the distances at which it operated increased. That 
 is, if the intensity of the power which it exerted on 
 a planet where the distance was one hundred millions 
 
LAWS OF MOTION AND GRAVITATION. 117 
 
 of miles from the sun, be counted as unity, removing 
 the planet to double the distance, or to two hundred 
 millions of miles, the sun's influence over it would be 
 reduced to one-fourth of its former value. 
 
 With Kepler this wonderful conjecture always re- 
 mained without proof. He had placed it on record, 
 and succeeding philosophers had treated it with 
 greater or less seriousness, according to the esti- 
 mate which they placed upon the sagacity of its 
 author. Even if Kepler, himself, had attempted the 
 demonstration of this principle — the data were as 
 yet wanting, which would have rendered its accom- 
 plishment possible. The period intervening between 
 the time of Kepler and Newton had not been left 
 unimproved. Descartes had revealed the law of 
 centrifugal force, and by one of those extraordinary 
 strokes of genius — occurring once in an age — had 
 fastened the irresistible power of analysis upon 
 geometry, which had given to the mind a force and 
 rapidity in the investigation of the figure of curves 
 and curvilinear motion, which had quadrupled its 
 capacity. By repeated efforts, a more accurate knowl- 
 edge had been obtained of the circumference and 
 diameter of our earth, and through this the distance 
 of the moon from the earth in the successive points 
 of its orbit had been approximated with still greater 
 precision. 
 
 With these advantages, Newton gave the energies 
 of his mind to the demonstration of that principle 
 which had existed with Kepler as a mere conjecture. 
 
 Before proceeding to develop the train of reason- 
 ing pursued by the great English astronomer, permit 
 me first to prepare the way by a simple and per- 
 
118 STRUCTURE OF THE UNIVERSE. 
 
 spicuous exhibition of the method employed in deter- 
 mining the diameter of the earth and the distance of 
 the moon ; two elements which figure conspicuously 
 in the demonstration about to be made, and without a 
 knowledge of which it would have been impossible to 
 proceed. We commence with a determination of the 
 diameter of the earth. 
 
 If an observer should start from any point on the 
 surface of the earth in the northern hemisphere, and 
 fixing his eye upon the north pole of the heavens, 
 should travel directly towards that point, all the stars 
 in the north would appear to rise higher above the 
 horizon as he advanced in his journey. The star 
 which occupied the point immediately above his 
 head when he started, would appear gradually to de- 
 cline towards the south. If it were possible to travel 
 on the same great circle of the earth entirely around 
 its circumference, the zenith star would appear to 
 pursue an opposite route in the heavens, and would 
 return to its primitive position only on the return of 
 the observer to his point of starting. This, however, 
 is not possible. What the observer can accomplish, 
 is this. He may travel north until his zenith star 
 shall appear to have moved south by one degree, or 
 the three hundred and sixtieth part of the circumfer- 
 ence of the heavens ; then will he have passed over 
 the three hundred and sixtieth part of the entire cir- 
 cumference of the earth ; all these parts are of equal 
 length, — he measures the one over which he has 
 passed — multiplies its value by three hundred and 
 sixty, and the result gives him the circumference of 
 the earth, from which the diameter is readily deduced 
 by the well-known proportion which exists between 
 
LAWS OF MOTION AND GRAVITATION. 119 
 
 these lilies. By this simple method, the diameter of 
 the earth being determined, its radius is known, and 
 we are prepared to explain the process by which the 
 moon's distance may be found. 
 
 Let us locate, in imagination, two observers at 
 distant points on the same great circle of the earth, 
 each prepared to measure the angular distance at which 
 the moon appears from the zenith point of each sta- 
 tion ; but the zenith of any place is the point in which 
 the earth's radius prolonged reaches the heavens, — 
 the angular distance of the moon from the zenith will 
 exhibit precisely the inclination of the visual ray 
 drawn to the moon's centre with the earth's radius 
 drawn to the place of observation ; the zenith dis- 
 tances being observed at each station, the observers 
 knowing that part of the great circle of the earth by 
 which their stations are separated, come together, 
 compare observations, and construct a figure composed 
 of four lines. Two of these are the radii of the earth 
 drawn to the points of observation. These may be 
 laid down under their proper angle, — drawing from 
 their extremities two lines, forming with the radii, an- 
 gles equal to the moon's measured zenith distances. 
 These represent the visual rays drawn to the moon; 
 they meet in a point which determines their length, 
 and if the figure be constructed accurately, it will be 
 found that either of these lines is about sixty times 
 longer than the radius of the earth, or the moon's dis- 
 tance is about 240,000 miles. 
 
 We now return to the examination of the great 
 question of a central force, and to the discovery of its 
 law of action. Allow me in the out-set to explain, 
 with extreme simplicity, the assumed law, whose 
 
120 STRUCTURE OF THE UNIVKRSE. 
 
 truth or falsehood it was required to demonstrate. If 
 any force resided in the sun which could resist the 
 centrifugal force of the planets, or in any primary to 
 resist the centrifugal force of the revolving satellite, 
 it was conjectured that this force would decrease in 
 proportion as the square of the distance increased. 
 In other language, if the planets were arranged at 
 the following distances from the sun, the forces exert- 
 ed upon them would be represented by the second 
 series, thus : 
 
 Distances, 12 3 4 5 6 &c, 
 
 Forces, 1 | | : • tV 2V A &c - 
 
 The measure of the intensity of any force of attrac- 
 tion situated at the centre of the earth or sun, is 
 accurately represented by the velocity it is capable of 
 imparting to a falling body in any unit of time. Ex- 
 periment shows that that power which causes a heavy 
 body to fall to the earth's surface, is capable of im- 
 pressing upon it a motion of about 16 feet in the first 
 second of time after its fall commences. In case the 
 force diminishes, as we remove the falling body 
 farther from the centre of attraction, the law of 
 diminution would manifest itself in the diminished 
 amount of motion communicated to the falling body. 
 Now if Newton could have carried a heavy body 
 upward, above the earth, until he should gain a height 
 above its surface of four thousand miles, he would 
 then be twice as far from the centre as when at the 
 surface of the earth. Dropping the heavy body, and 
 measuring accurately the distance through which it 
 passes in the first second of time, in case he finds 
 this to be one-fourth of 16 feet, the distance fallen 
 through by the same body in the same time, at the 
 
LAWS OF MOTION AND GRAVITATION. 121 
 
 distance of 4000 miles from the earth's centre, the 
 result would have confirmed the law which conjecture 
 had assigned as the law of nature. Could he have 
 mounted one unit higher, gaining an altitude of 8000 
 miles above the earth's surface, or three units from 
 the centre, here repeating his experiment, in case the 
 space passed through by the falling body is now one- 
 ninth of 16 feet, it would yet farther confirm the truth 
 of the conjectured law. Thus, could he have increased 
 his altitude by one unit or radius of the earth after 
 another, repeating his experiment as each new unit 
 was added to his elevation, finding in every instance 
 the law of diminution fulfilled by the falling body, all 
 doubt as to the truth of the law would have been 
 removed, and its foundation in nature would have 
 justly flowed from such a series of experiments. 
 
 Here, then, is precisely what must be accomplished 
 to demonstrate the assumed law of gravitation. But 
 since these altitudes of 4000 and 8000 miles could not 
 be reached, might not some change in the distance 
 passed over by a heavy falling body, be noticed and 
 measured, if removed from a valley to the top of the 
 highest mountain? Alas ! the increased distance from 
 the centre of the earth, gained by ascending the loftiest 
 mountain on its surface, is almost inappreciable, 
 when compared with the entire distance, four thou- 
 sand miles. Even if the mountain were ten miles 
 high, the two elevations at which the experiment 
 might then be performed, would be 4000 miles and 
 4010 miles, and the diminished velocity would not be 
 appreciable, even with the most delicate tests, much 
 less could it be relied on to demonstrate the truth or 
 falsehood of a great principle. Here, then, the mind 
 L 
 
122 STRUCTURE OF THE UNIVERSE. 
 
 was brought to a full stop ; and for a long time it 
 seemed impossible that the philosopher should con- 
 quer the difficulties which rose up in his path, and 
 defied his further advance. Finding it impossible 
 to perform any satisfactory experiment on the earth's 
 surface, the daring mind of Newton conceived the 
 idea of employing the moon itself as the falling body, 
 and of testing the truth of his great theory by its fall 
 towards the earth. But could he reach out his hand, 
 grasp the revolving moon, stop it in its orbit, drop it 
 to the earth, and measure its descent in the first sec- 
 ond of time? No — this was impossible. The moon 
 could not be arrested in its career ; but is this neces- 
 sary ? Is not the moon, in one sense, constantly fall- 
 ing towards the earth ? Newton asserted this to be 
 true, and thus did he prove it. 
 
 Stand upon the earth, and stretching outward into 
 space 240,000 miles, there let the moon be located, 
 poised and fixed in space, on a point of its present 
 orbit. There let us suppose it to receive an impulse in 
 a direction perpendicular to the line which joins it 
 with the earth. By the first law of motion, being 
 free to move, it will sweep off in a straight line, tan- 
 gent to its present orbit, and will pass over a space 
 in the first second of time, proportioned to the inten- 
 sity of the impulse received. Mark that space, and 
 bring the moon back to its primitive position. Now 
 drop it towards the earth, and as it descends freely 
 under the earth's attraction, mark the space through 
 which it falls in the first second of time. This being 
 known, bring back the moon once again to its starting 
 point. Now combine the impulsive force first given, 
 with that power which caused the moon, when left 
 
LAWS OF MOTION AND GRAVITATION. 123 
 
 free to move, to fall to the earth. Let them both act 
 at once : the impulse is given, the moon darts off in 
 a straight line, but is instantly seized by the earth's 
 attraction, which drags it from its rectilineal path, 
 and the two contending forces, ever struggling, neither 
 conquering, exercise a divided empire over the 
 moon ; onward she moves, obedient to the impulsive 
 force, bent to her orbit by the action of the earth's 
 attraction. Now the amount by which it is deflected 
 in one second of time, from the straight line it would 
 have pursued, is the amount precisely, by which it falls 
 to the earth. 
 
 If thus far I have been successful, what remains 
 can readily be accomplished. Newton easily compu- 
 ted, from the known velocity of the moon in its orbit, 
 and from the radius of that orbit, the space through 
 which the moon actually fell towards the earth in one 
 second of time. He next computed the space through 
 which a heavy body would fall towards the earth's 
 surface, if removed from the earth to a distance equal 
 to that of the moon. Now in case these two quantities 
 should prove to be exactly equal, the truth of the 
 demonstration would be complete ; the moon did fall 
 through the space required by the assumed law, and 
 in this event the law must be the law of nature. For 
 seventeen long years did this incomparable philoso- 
 pher, rivaling the example of the immortal Kepler, 
 toil on in this most difficult enterprise. He finally 
 reaches the result ; the two quantities are found and 
 compared, but alas ! the computed distance through 
 which the moon must fall, in case the law of gravita- 
 tion were true, differed from the observed distance 
 through which it actually fell, by a sixth part of its 
 
124 STRUCTURE OF THE UNIVERSE. 
 
 value. Any less scrupulous, any less philosophic 
 mind, would have been content with this near approx- 
 imation, and would have announced the discovery to 
 the world. Not so with Newton. Nothing short of 
 the most rigorous accuracy could satisfy his consci- 
 entious regard for truth. His manuscripts are laid 
 aside, and the pursuit for the present abandoned. 
 
 Months roll by. Occasionally he returns to his 
 computations, runs over the figures, hoping to detect 
 some numerical error ; but all is right, and he turns 
 away. At length, while attending a meeting of the 
 Royal Society in London, he learns that Picard had just 
 closed a more accurate measurement of the diameter 
 of the earth. This was one of the important quanti- 
 ties which entered into his investigation. He returns 
 home, — and with impatient curiosity spreads before 
 him his old computations — the new value of the earth's 
 diameter is substituted — he dashes onward through 
 the maze of figures— he sees them shaping their 
 values towards the long sought result — the excitement 
 was more than even his great mind could bear — he- 
 resigns to a friend — the work is completed, the results 
 compared — they are exactly equal ! The victory is 
 won, — he had seized the golden key which unlocks 
 the mysteries of the universe, and he held it with a 
 giant's grasp ! 
 
 There never can come another such moment as the 
 one we have described, in the history of any mortal. 
 There are no such conquests remaining to be made. 
 Standing upon the giddy height he had gained, 
 Newton's piercing gaze swept forward through 
 coming centuries, and saw the stream of discovery 
 flowing from his newly discovered law, slowly increas- 
 
LAWS OF MOTION AND GRAVITATION. 125 
 
 ing, spreading on the right hand and on the left, 
 growing broader, and deeper, and stronger, encircling 
 in its flow planet after planet, sun after gun, system 
 after system, until the universe of matter was encom- 
 passed in its mighty movement. He could not live to 
 accomplish but a small portion of this great work. — 
 Rapidly did he extend his theory of gravitation to the 
 planets and their satellites. Each accorded perfectly 
 with the law, and rising as the inquiry was pursued, 
 he at length announced this grand prevailing law : 
 
 Every particle of matter in the universe attracts every 
 other particle of matter with a force or power directly 
 proportioned to the quantity of matter in each, and decreas 
 ing as the squares of the distances which separate the 
 particles increase. 
 
 Having reached this wonderful generalization, 
 Newton now propounded this important inquiry. 
 " To determine the nature of the curve which a body 
 would describe in its revolution about a fixed centre, 
 to which it was attracted by a force proportional to 
 the mass of the attracting body, and decreasing with 
 the distance according to the law of gravitation." 
 
 His profound knowledge of the higher mathematics, 
 which he had greatly improved, gave to him aston- 
 ishing facilities for the resolution of this great problem. 
 He hoped and believed that when the expression 
 should be reached, which would reveal the nature of 
 the curve sought, that it would be the mathemat- 
 ical language descriptive of the properties of the 
 ellipse. This was the curve in which Kepler had 
 demonstrated that the planets revolved, and a confirm- 
 ation of the law of gravitation required that the ellipse 
 l 2 
 
126 STRUCTURE OF THE UNIVERSE. 
 
 should be the curve described by the revolving body, 
 on the conditions announced in the problem. 
 
 There happens to be a remarkable class of curves, 
 discovered by the Greek mathematicians, called the 
 conic sections; thus named, because they can all be 
 formed by cutting a cone in certain directions. The 
 figure of a cone with a circle for its base, and converg- 
 ing to a point, is familiar to all. Cut this cone 
 perpendicular to its axis, remove the part cut, and 
 the line on the surface round the cone will be found 
 to be a circle. Cut it again, oblique to the axis, then 
 the line of division of the two parts will be an ellipse. 
 Cut again so that the knife may pass downward 
 parallel to the slope of the cone, and in this case 
 your section is a parabola. Make a last cut parallel 
 to the axis of the cone, and the curve now obtained 
 is the hyperbola. 
 
 When Newton reached the algebraic expression 
 which, when interpreted, would reveal the proper- 
 ties of the curve sought and which he had hoped 
 would prove to be the ellipse — he was surprised to 
 find that it did not look familiar to his eye. He ex- 
 amined it closely — it was not the equation of the 
 ellipse, and yet it resembled it in some particulars. 
 What was his astonishment to find, on a complete 
 examination, that the mathematical expression, which 
 he had reached, expressing the nature of the curve 
 described by the revolving body, was the general 
 algebraic expression embracing all the conic sections. 
 Here is a most wonderful revelation. Is it possi- 
 ble that under the law of gravitation, the heavenly 
 bodies may revolve in any or either of these curves ? 
 Observation responds to the inquiry. The planets 
 
LAWS OF MOTION AND GRAVITATION. 127 
 
 were found to revolve in ellipses; the satellites of 
 Jupiter in circles; and those strange, anomalous, out- 
 lawed bodies, the comets, whose motions hitherto 
 had defied all investigation, take their place in the 
 new and now perfect system, sweeping round the sun 
 in parabolic and hyperbolic orbits. 
 
 Thus were these four beautiful curves, having a 
 common origin, possessed of certain common proper- 
 ties, yet diverse in character, mingling in close prox- 
 imity, and gliding imperceptibly into each other, sud- 
 denly transferred to the heavens, to become the orbits 
 of countless worlds. For nearly twenty centuries, 
 they had been the objects of curious speculation to 
 the mathematician ; henceforward they were to be 
 given up to the hands of the astronomer, the power- 
 ful instrument of his future conquests among the 
 planetary and cometary worlds. 
 
 The three great laws of Kepler, to which he had 
 risen with such incredible toil and labor, were now 
 found to flow as simple consequences of the law of 
 gravitation. It is impossible to convey the slightest 
 idea, in discussions so devoid of mathematics, of the 
 incredible change which had thus suddenly been 
 wrought in the mode of investigation. I never have 
 closed Newton's investigation, by which he deduces 
 the nature of the curve, described by a body revolving 
 around a fixed centre, under the law of gravitation, 
 bearing with it consequences so simple yet so wonder- 
 ful, without feelings of the most intense admiration. I 
 can convey no adequate idea of the difference of the 
 methods employed by Kepler and Newton, in reach- 
 ing the three laws of planetary motion. J see Kep- 
 ler in the condition of one on whom the fates have 
 
128 STRUCTURE OF THE UNIVERSE. 
 
 fixed the task of rolling a huge stone up some rug- 
 ged mountain side, to its destined level, within a few 
 feet of the summit. He toils on manfully, heav- 
 ing and struggling, day and night, in storm and in 
 darkness, never quitting his hold, lest he may lose 
 what he has gained. If the ascent be too steep and 
 rocky, he diverges to the right, then to the left, wind- 
 ing his heavy way zigzag up the mountain side. — 
 Years glide by— -he grows gray in his toil, but he never 
 falters — onward and upward he still heaves the heavy 
 weight — his goal is in sight, he renews his efforts, the 
 last struggle is over — he has finished his task — the 
 goal is won. 
 
 Such was Kepler's method of reaching his laws. 
 Now for Newton's. He stands, not at the base 
 of the mountain, with its long, ascending rocky sides, 
 but on the top. He starts his heavy stone, it rolls of 
 itself over, slowly over, and once again, and falls qui- 
 etly to its place. Let me not be misunderstood in 
 this strange comparison, as detracting in the smallest 
 degree from the just fame that is due to Kepler. But 
 for his sublime discoveries, Newton could never have 
 reached the mountain summit, on which he so proudly 
 stood. Standing there, he never forgot by whose 
 assistance he had reached the lofty point, and ever 
 recognized, in the most public manner, his deep 
 indebtedness to the immortal Kepler. 
 
 A few words with reference to the rigorous appli- 
 cation of Kepler's laws in nature, will close this dis- 
 cussion. The first law, announcing the revolution of 
 the planets in elliptic orbits, was now made general, 
 and recognised the revolution of the heavenly bodies 
 
LAWS OF MOTION AND GRAVITATION. 129 
 
 in conic sections : the circle, ellipse, parabola and 
 hyperbola. 
 
 The second law, fixing the equality of the spaces 
 passed in equal times, by the lines joining the planets 
 to the sun as these were carried round in their elliptic 
 orbits, now became applicable to all bodies revolving 
 about a fixed centre, in any curve, and according to 
 any law. 
 
 The third law, recognising the proportion between 
 the squares of the periodic times and the cubes of 
 the mean distances of the planets, was extended to 
 the satellites, and to the comets ; modified slightly in 
 the case of the larger planets, by taking into account 
 their masses or quantities of matter. 
 
 Here we close the era of research by observation. 
 The mind has gained its last grand object. The era 
 of physical astronomy dawns ; new and wonderful 
 scenes open, and to the contemplation of these, we 
 shall soon invite your attention. 
 
LECTURE V. 
 
 UNIVERSAL GRAVITATION APPLIED TO THE EXPLANATION 
 OF THE PHENOMENA OF THE SOLAR SYSTEM. 
 
 The progress of the mind, in its efforts to reach a 
 satisfactory explanation of the movements of the 
 heavenly bodies, previous to the discovery of univer- 
 sal gravitation, had been made independent of any 
 guiding law. The mind had been feeling its way 
 slowly and laboriously, guiding its direction by atten- 
 tively watching the celestial phenomena, and relying 
 for its success exclusively on the accuracy and num- 
 ber of its observations. Each discovery made was 
 isolated, and although it prepared the way for the 
 succeeding ones, it did not in any sense involve them 
 as necessary consequences. By the discovery of the 
 great law of universal gravitation, a perfect and 
 entire revolution had been made in the science of 
 astronomy. A new department was now added, 
 which, previous to the knowledge of this law, could 
 have no existence. In this branch of astronomy, the 
 process of investigation being inverted, the mind de- 
 scends from one great law to an examination of its 
 consequences, tracing these in their modified and 
 diversified influences to their final limits. Observa- 
 tion is now employed to verify discovery, and not 
 as the basis on which, and without which, discovery 
 cannot be made. 
 
 ( 131 ) 
 
132 STRUCTURE OF THE UNIVERSE. 
 
 The era of physical astronomy is, therefore, the 
 great era in the history of the science. It involves 
 the resolution of the most wonderful problems — it 
 calls into use the most refined and powerful mathe- 
 matical analysis, and demands the application of the 
 most ingenious and delicate instruments in seeking for 
 the data by means of which its theory may be rendered 
 practically applicable to the problems of nature. 
 The mechanical philosopher in his closet may con- 
 struct his imaginary system. In its centre he locates 
 a sun, containing a certain mass of matter. — At any 
 convenient distance from this sun he locates a planet, 
 whose weight he assumes. To this planet he gives 
 an impulse, whose intensity and direction are assumed. 
 The moment these data are fixed, and the impulse 
 given to the imaginary planet — no matter in what 
 kind of an orbit it may dart away, whether circular, 
 elliptical, parabolic, or hyperbolic — the laws of motion 
 and gravitation asserting their empire, the planet is 
 followed by the mathematician, with a certainty and 
 accuracy defying all escape. He assigns its orbit in 
 the heavens — the velocity of its movement — the pe- 
 riod of its revolution. In short, in a single line, he 
 writes out its history with perfect accuracy for a mil- 
 lion years. 
 
 If, now, to this simple system of a great central sun 
 and one solitary planet, the physical astronomer add 
 a third body, a moon, to the planet, he assumes its 
 weight, the intensity and direction of the impulsive 
 force starting it in its career, and now his system be- 
 comes more complex. Strike the sun out of exist- 
 ence, fix the planet, and the process of binding the 
 satellite in mathematical fetters is precisely similar 
 
UNIVERSAL GRAVITATION. 133 
 
 to that by which the movements of the planet were 
 prescribed around the sun before the existence of the 
 satellite. But now, with these three bodies the train of 
 investigation becomes more intricate and involved. 
 While the planet alone circulated around the sun, 
 such is the undeviating accuracy with which it will 
 forever pursue its path around the sun, that if it w T ere 
 possible to hang up in space along its route golden 
 rings, whose diameter would just permit the flying 
 planet to pass, millions of revolutions will nevei 
 mark the slightest change. The rings once passed 
 and then fixed, will mark forever the pathway of the 
 solitary planet. But the moment a moon is given to 
 this flying world, in that instant its motion is changed — 
 it is swayed from its original fixed orbit — it no longer 
 passes through the golden rings, and although the 
 physical astronomer may write out in his analytic 
 symbols the future history of his planet and moon, 
 these expressions are no longer marked w r ith the sim- 
 plicity w T hich obtained in those which recorded the 
 history of the single planet. While solitary, all 
 changes were effected by the planet in one single 
 revolution, and these were repeated in the same pre- 
 cise order in each successive revolution. Now, with 
 the satellite added, there are changes introduced run- 
 ning through many revolutions, and requiring for 
 their complete compensation vast periods of time. 
 Indeed, the inquiry arises, whether this system of a 
 central sun, with a planet and its satellite revolving 
 about it, can be so constituted that the changes 
 which the planet and its moon mutually produce on 
 each other's movements, may not go on, constantly 
 accumulating in the same direction, until all features 
 M 
 
134 STRUCTURE OF THE UNIVERSE. 
 
 of the original orbits of both may be destroyed, both 
 worlds being finally precipitated on the sun, or driven 
 farther and farther from this luminary, until they 
 are lost in infinite space. This inquiry, in a more 
 extended form, will be examined hereafter. We pro- 
 ceed to build up our imaginary system. Thus far, 
 we have regarded our planet and its satellite as mere 
 material heavy points. In case we give to them mag- 
 nitude and rotation on an axis, the velocity of rota- 
 tion will determine the figure of the planet and of its 
 satellite. These figures will deviate from the exact 
 spherical form, and this change of figure will sensibly 
 affect the stability of the axis of rotation, and will 
 introduce a series of subordinate movements, each of 
 which must become the subject of research ; and to 
 write out the future history of the system, these mi- 
 nute and concealed changes must likewise receive 
 their mathematical expression. 
 
 Having thus thoroughly mastered all the phenom- 
 ena of this system of three bodies, the astronomer 
 now adds another planet, whose mass is assumed, to- 
 gether with the direction and intensity of its primi- 
 tive impulse. Its orbit is now computed, subject to 
 the greatly predominant influence of the sun, but sen- 
 sibly affected by the quantity of matter in the old 
 planet and its satellite, which prevents it from form- 
 ing a fixed and unchangeable orbit in space. Again 
 he is obliged to return to an examination of his first 
 planet and its moon, for these, again break away from 
 their previous routes, and in consequence of the ac- 
 tion of the second planet, assume new orbits, and are 
 subjected to periodical fluctuations, which demand 
 critical examination, and without a knowledge of 
 
UNIVERSAL GRAVITATION. 135 
 
 which no truthful history of the planetary system can. 
 be written. To the second planet let us now add 
 several satellites, each of which has its mass as- 
 signed, and the direction and intensity of the impul- 
 sive force by which they are projected in their orbits. 
 Here, then, is a subordinate system demanding a 
 complete examination. The satellites mutually af- 
 fect each other's motions, and each is subjected to the 
 influence of the primitive planet and its moon. Again 
 does the physical astronomer review his entire inves- 
 tigation. The addition of these satellites to his second 
 planet has introduced changes in all the previous 
 bodies of the system, which must now be computed, 
 to keep up with the growing complexity. This task is 
 at last accomplished. All the changes are accurately 
 represented. Analysis has mastered the system, and 
 the history of its changes are written out for hun- 
 dreds and thousands of years. 
 
 A third planet, w r ith its satellite, is now added. 
 This new subordinate system is discussed, and its op 
 eration on all the previous planets and satellites com- 
 puted, and after incredible pains, the astronomer once 
 more masters the entire group, and follows them all 
 with unerring precision, through cycles of changes 
 comprehending thousands or even millions of years. 
 
 Thus does the difficulty of grasping the system in- 
 crease in a high ratio by the addition of every new 
 planet and satellite, till finally the last one is placed 
 in its orbit, and the system is complete, so far as 
 planets and satellites are concerned. Through this 
 complicated system now cause thousands of comets to 
 move in eccentric orbits, coming in from every quarter 
 of the heavens, plunging downwards towards the sun, 
 
136 STRUCTURE OF THE UNIVERSE. 
 
 sweeping with incredible velocity around this central 
 luminary, and receding into space to vast distances, 
 either to be lost forever, or to return after long peri 
 ods to revisit our system. These wandering bodies 
 must be traced and tracked, their orbits fixed, their 
 periods determined, their influence on the planets and 
 satellites, and that exerted by these on the comets, 
 must be computed and determined; then, and not till 
 then, does the physical astronomer reach to a full 
 knowledge of this now almost infinitely complex 
 system. 
 
 In this imaginary problem it will be observed that 
 certain quantities were invariably assumed before the 
 discussion could proceed. The mass of the sun — the 
 mass of each planet and satellite — the intensity and 
 direction of the primitive impulse given to each planet 
 and satellite — these quantities are supposed to be 
 known. If, now, the astronomer has actually ac- 
 complished the resolution of the imaginary problem, 
 and has obtained analytic expressions which write 
 out and reveal the future history of his assumed 
 planets and satellites, as they revolve around his as- 
 sumed sun, if in these expressions he should substi- 
 tute the actual quantities which exist in the solar 
 system for those assumed, his expressions would then 
 give the history of the solar system for coming ages, 
 and by reverse action would reveal its past history 
 with equal certainty. 
 
 Before we can, therefore, bring the power of analy- 
 sis to bear on the resolution of the grand problem 
 of nature, we must interrogate the heavens, and ob- 
 tain the absolute weight of our sun, of each planet, 
 and of every satellite. Next we require the intensity 
 
UNIVERSAL GRAVITATION. 137 
 
 and direction of the impulsive force which projected 
 each planet and satellite in its orbit, and which would 
 have fixed forever the magnitude and position of that 
 orbit, in case no disturbing causes had operated to 
 modify the action of the primitive impulse. 
 
 Having thus attempted to exhibit, at a single view, 
 the general outlines of the great problem of the solar 
 system, we propose now to return to the examination 
 of a system composed of three bodies ; and to fix our 
 ideas, w r e assume the sun, earth, and moon. In case 
 the earth existed alone, the elliptic orbit described in 
 its first revolution around the sun would remain un- 
 changed forever, and having pursued it, and marked 
 its changes of velocity in the different parts of its 
 orbit for a single revolution, this would be repeated 
 for millions of years. But let us now give to the 
 earth its satellite, the moon, and setting out from its 
 perihelion, or nearest distance from the sun, let us 
 endeavor to follow these two bodies as they sweep 
 together through space, and mark particularly the 
 effect produced on the moon's orbit by the disturbing 
 influence of the sun. To give to the problem greater 
 simplicity, let us conceive the plane of the moon's 
 orbit to coincide with the earth's. The law of gravi- 
 tation which gives to every attracting body a power 
 over the attracted one, gravity increasing as the dis- 
 tance decreases, it will be perceived that when the 
 earth and moon are nearest to the sun, whatever in- 
 fluence the sun possesses to embarrass or disturb the 
 motions of the moon about the earth, will here be ex- 
 ercised with the greatest effect. But since the sun is 
 exterior to the moon's orbit, its tendency will be to 
 draw the moon away from the earth, and cause her 
 m 2 
 
138 STRUCTURE OF THE UNIVERSE. 
 
 to describe around her primary a larger orbit, in a 
 longer period of revolution than would have been 
 employed in case no sun existed, and the moon was 
 given up to the exclusive control of the earth. 
 
 Starting the planet on its annual journey, as it 
 recedes from the sun in passing from its nearest to its 
 most remote distance, or from perihelion to aphelion 
 the moon is gradually removed from the disturbing 
 influence of the sun; it is subjected more exclusively 
 to the earth's attraction ; its distance from the earth 
 grows less, and the periodic time becomes shorter. 
 These changes continue in the same order until the 
 earth reaches its aphelion. There the moon's orbit 
 is a minimum, and its motion is swiftest. In passing 
 from the aphelion to the perihelion, the earth is con- 
 stantly approaching the sun, and as the sun's influ- 
 ence on the moon increases as its distance diminishes, 
 its orbit will now expand by slow degrees, and the 
 periodic time will diminish until on reaching the peri- 
 helion, in case the figure of the earth's orbit remains 
 unchanged, the moon's periodic time will be restored 
 to its primitive value, and all the effects resulting 
 from the elliptic figure of the earth's orbit will have 
 been entirely effaced. 
 
 Thus far we have directed our attention exclusively 
 to the changes in the distance of the moon and its 
 periodic time. But the moon's orbit is elliptical, as 
 well as the earth's, and it is manifest that the sun's 
 influence will operate to change not only the magni- 
 tude of this orbit, but will in like manner produce a 
 change in the position of the moon's perigee, or nearest 
 point of distance from the earth. If the earth were 
 stationary, and the moon revolved around it, passing 
 
UNIVERSAL GRAVITATION. 139 
 
 between it and the sun, and then coming round so as 
 to be beyond the earth with respect to this luminary, 
 although the moon's orbit would be sensibly affected 
 by the sun's attraction, yet this having exerted itself 
 during one revolution of the moon, all its effects 
 would be repeated in the same order during the next 
 revolution, and the relative positions of the sun and 
 earth remaining the same, the moon would come 
 finally to have a fixed orbit, and its principal lines or 
 axes would never change. But this is not the case 
 of nature. — The earth swiftly turning in its orbit, and 
 bearing with it its revolving satellite, by the time the 
 moon has completed a revolution, the sun and earth 
 have entirely changed their relative positions, and 
 the moon cannot reach its perigee, or nearest distance 
 from the earth, at the same point as in the preceding 
 revolution. 
 
 By an attentive examination of this problem, it is 
 found that the tendency is to cause the moon to reach 
 its perigee earlier than it would do if not dhsfairbed, 
 and in this way the perigee of a fixed orbit appears 
 to advance to meet the coming moon, and in the end . 
 to continue advancing until it actually revolves en- 
 tirely round in a period which observation determines 
 to be about nine years. 
 
 It is not my intention to enter into a detailed ex- 
 amination of all the effects resulting from the sun's 
 disturbing power on the moon's motions ; neither shall 
 I attempt to exhibit all the effects produced by the 
 moon on the earth. — This would require a train of 
 investigation too elaborate and intricate to comport 
 with my present purposes. My object is simply to 
 show that changes must arise from the mutual and 
 
140 STRUCTURE OF THE UNIVERSE. 
 
 reciprocal action of these three bodies, which the 
 theory of gravitation must explain, and the telescope 
 point out, before it be possible to obtain a perfect 
 knowledge of these bodies. 
 
 The exact estimation of these changes can never 
 be made until we shall have learned the relative 
 masses of matter contained in the sun, earth, and 
 moon. In other language, we must know how many- 
 moons it would require to weigh as much as the 
 earth, and how many earths would form a weight 
 equal to that of the sun. 
 
 But is it possible that man, situated upon our planet, 
 237,000 miles from the moon, and 95,000,000 of miles 
 from the sun, can actually weigh these worlds against 
 each other, and determine their relative masses of 
 matter ? Even this has been accomplished, and I shall 
 now proceed to explain how the earth may be weighed 
 against the sun. Dropping a heavy body at the earth's 
 surface, the velocity impressed on it in the first second 
 of time will measure the weight of the earth in one 
 sense. If it were possible to take the same body to 
 the sun, drop it, and measure the velocity acquired by 
 the falling body in the first second of time, the rela- 
 tive distances passed through at the sun and at the 
 earth by the same body in the same time, would 
 show exactly the relative weight of the sun and 
 earth, for their capacity to communicate velocity are 
 exactly proportioned to their masses. Now, although 
 this experiment cannot be performed in the exact 
 terms announced, yet as we have already shown, the 
 moon is constantly dropping towards the earth, and 
 the earth is as constantly dropping towards the sun. 
 Now in case we measure the amount by which the 
 
UNIVERSAL GRAVITATION. 141 
 
 moon is deflected from a straight line in one second 
 of time, this measures the intensity of the earth's 
 power. But the amount by which the earth is de- 
 flected from a right line by the central power of 
 the sun in one second, is easily measured from a 
 knowledge of its period and the magnitude of its or- 
 bit. Executing these calculations, it is found that the 
 sun's effect on the earth is rather more than twice as 
 great as the earth's effect on the moon, and in case 
 these effects were produced at equal distances, then 
 would the sun be shown to contain rather more than 
 twice as much matter as is found in the earth. But 
 the sun produces its effect at a distance 400 times 
 greater than that at which the earth acts on the 
 moon : hence, as the force diminishes as the square 
 of the distance increases, a sun acting at twice the 
 distance at which the earth acts, must be four times 
 heavier to produce an equal effect ; at three times 
 the distance, it must be nine times heavier, and at 
 four times the distance, sixteen times heavier ; — at 
 400 times the distance, 160,000 times heavier than the 
 earth. Thus do we find that in case the sun's action 
 on the earth were exactly equal to the earth's action 
 on the moon, in consequence of the great distance at 
 which it operates, its weight would be equal to that 
 of 160,000 earths. But its actual effect is rather 
 more than double that of the earth on the moon, and 
 hence we find it contains rather more than double 
 160,000 earths, or exactly 354,936 times the quantity 
 of matter contained in the earth. 
 
 This enormous mass of the sun is confirmed by 
 an examination of its actual dimensions. An object 
 with an apparent diameter equal to that of the sun, 
 
142 STRUCTURE OF THE UNIVERSE. 
 
 and at a distance of 95,000,000 of miles, must have a 
 real diameter of 883,000 miles, a quantity so great 
 that if the sun's centre were placed at the earth's 
 centre, its vast circumference would give ample room 
 for the moon to circulate within its surface, leaving 
 as great a space between the moon's orbit and the 
 sun's surface as now exists between the moon and 
 earth. 
 
 It is this immense magnitude of the sun, when 
 compared with the planets and their satellites, which 
 renders the orbits of the planets comparatively unal- 
 terable. It is true that these bodies mutually affect 
 each other, but these effects are comparatively slight, 
 and astronomers regard them as perturbations, or mere 
 disturbances of the original elliptic motion. Hence 
 ve find the magnitude and position of the earth's 
 elliptic orbit remain without any very sensible varia- 
 tion for two or three revolutions ; but the slight 
 disturbance experienced at each revolution, constantly 
 accumulating in the same direction in a long series 
 of years, occasions changes that cannot be lost sight 
 of, and which, by a reflex influence, become in some 
 instances exceedingly important in their practical 
 applications. 
 
 As it will be impossible to treat fully the complex 
 subject of perturbation, I will call your attention to 
 a few points about which cluster peculiar interest, in 
 consequence of their great difficulty, and the almost 
 infinite reach of analysis displayed in their success- 
 ful examination. 
 
 I have already explained how it is that the disturb- 
 ing influence of the sun occasions a constant fluctua- 
 tion in the periodic time of the moon, accelerating it 
 
UNIVERSAL GRAVITATION. 143 
 
 as the earth moves from perihelion to aphelion, and 
 again retarding it from aphelion to perihelion. If, 
 now, we take a large number of revolutions of the 
 moon, say a thousand, add them all up, and divide by 
 one thousand, we obtain a mean period of revolution, 
 which, in case the earth's orbit remains invariable, 
 will never change, but will be constantly the same 
 for thousands of years. By such an examination 
 during the last century, the mean motion of the moon 
 was obtained with great precision. But on a com- 
 parison of eclipses recorded by the Babylonians with 
 each other, it was discovered that the moon in those 
 early ages required a longer time to perform her mean 
 revolution than in modern times. A like comparison 
 of the Babylonian eclipses with those recorded in the 
 middle ages by the Arabian astronomers, confirmed 
 this wonderful discovery, which was yet farther sub- 
 stantiated by comparing the Arabian eclipses with 
 those observed in modern times. It thus became 
 manifest that, to all appearance at least, the moon's 
 mean motion was growing swifter and swifter from 
 century to century ; that it was approaching closer 
 and still closer to the earth, and if no limit to this 
 change was ever to be fixed, sooner or later the final 
 catastrophe must come, and the moon be precipitated 
 on the body of the earth, and the system be destroyed. 
 An effort was made to account for this acceleration 
 of the moon, on the theory of gravitation ; but for a 
 long time there seemed to be no possibility of ren- 
 dering a satisfactory explanation of the phenomena, 
 far less of prescribing the limits which should cir- 
 cumscribe the changes. Some, to escape from the 
 difficulty, rejected entirely the ancient eclipses, and 
 
144 STRUCTURE OF THE UNIVERSE. 
 
 boldly cut the knot, by pronouncing the acceleration 
 as impossible, and without any foundation in fact. — 
 Others admitted the fact, but finding it impossible to 
 account for it on the hypothesis of gravitation, con- 
 ceived the idea that the moon was moving in some 
 ethereal fluid capable of resisting its motion, and pro- 
 ducing a diminution in its periodic time of revolution. 
 That acceleration should be the effect of resistance, may 
 seem to some very strange, but a little reflection will 
 render the subject clear. In case the moon's orbitual 
 motion is resisted, then the centrifugal force, which 
 depends on the velocity, becomes diminished, and the 
 central power of the earth draws the moon closer to 
 itself, decreases the magnitude of its orbit, and in 
 like manner reduces the time of accomplishing one 
 revolution about the earth. 
 
 Finding no better solution of the mystery, and 
 being obliged to acknowledge the fact that the mean 
 motion of the moon was becoming swifter and swifter, 
 from the action of a resisting medium, there was no 
 escape from the final consequences ; and it was by 
 some believed that the elements of decay existed, that 
 the doom of the system was fixed, and although thou- 
 sands, possibly millions, of years might roll away 
 before the fatal day, yet it must come, slowly, but 
 surely as the march of time. Such was the condition 
 of the problem when Laplace gave the powers of his 
 giant intellect to the resolution of this mysterious 
 subject. The consequences involved gave to it an 
 unspeakable interest, and the world waited with keen 
 anxiety to learn the result of the investigations of this 
 great geometer. Long and difficult was the struggle 
 — slow and laborious the task of devising and tracing 
 
UNIVERSAL GRAVITATION. 145 
 
 out the secret causes of this inscrutable phenomenon. 
 The planets are weighed and poised against the 
 earth, their effects computed on its orbit, the final re- 
 sult of these effects determined, and the reflex influ- 
 ence on the moon's motion computed with the most 
 extraordinary precision. Under the searching ex- 
 amination of Laplace's potent analysis, nature is 
 conquered, the mystery is resolved, the law of gravi- 
 tation is vindicated — the system is stable, and shall 
 endure through periods whose limits God alone, and 
 not man, shall prescribe. 
 
 Follow me in a simple explanation of this most re- 
 markable discovery. It has already been stated, that 
 in case the earth's orbit could remain unchanged, that 
 the mean period of the moon, as derived from a thou- 
 sand of its revolutions, w^ould be constant, and would 
 endure without the slightest change for millions of 
 years. But this permanency of the earth's orbit does 
 not exist. — Laplace discovered that under the joint 
 action of all the planets, the figure of the earth's 
 orbit was slowly changing ; that while its longer axis 
 remained invariable, that its shape was gradually be- 
 coming more and more nearly circular. At the end 
 of a vast period, its ellipficity would be destroyed, 
 and the earth would sweep around the sun in an orbit 
 precisely circular. Attaining this limit, a reversed 
 action commences — the elliptic form is resumed by 
 slow degrees — the eccentricity increases from age to 
 age — until, at the end of millions of years, a second 
 limit is reached. The motion is again reversed — the 
 orbit again opens out, approaches its circular form, 
 and thus vibrates backwards and forwards in millions 
 N 
 
146 STRUCTURE OF THE UNIVERSE. 
 
 of years, like some mighty pendulum beating the 
 slowly ebbing seconds of eternity ! 
 
 But do you demand how this change in the figure 
 of the earth's orbit can affect the moon's mean mo- 
 tion? The explanation is easy. Were it possible to 
 seize the earth and hurl it to an infinite distance from 
 the sun, its satellite, now released from the disturbing 
 influence of this great central mass, would yield itself 
 up implicitly to the earth's control. It would be 
 drawn closer to its centre of motion, and its orbit 
 being thus diminished, its periodic time would be 
 shorter, or its motion would be accelerated or made 
 swifter than it now is. This is an exaggerated hy- 
 pothesis, to render more clear the effect produced by 
 removing the earth farther from the sun. Now the 
 change from the elliptical to the circular form, which 
 has been progressing for thousands of years, in the 
 earth's orbit, is, so far as it goes, carrying the earth at 
 each revolution a little farther from the sun, releasing 
 in this way the moon, by slow degrees, from the dis- 
 turbing influence of that body ; giving to the earth a 
 more exclusive control over the movements of its satel- 
 lite, and thus increasing the velocity of the moon in 
 its orbit from age to age. But will this acceleration 
 ever reach a limit ? Never, until the earth's orbit 
 becomes an exact circle, at the end of millions of 
 years. Then, indeed, does the process change. At 
 every succeeding revolution of the earth in its orbit, 
 its ellipticity returns — its distance from the sun dimin- 
 ishes — the moon is again subjected more and more to 
 the action of the sun, is drawn farther and farther 
 from the earth, and its periodic time slowly increases. 
 Thus is acceleration changed into retardation, and at 
 
UNIVERSAL GRAVITATION. 147 
 
 the end of one of these mighty cycles, consisting of 
 millions of years, an exact compensation is effected, 
 and the moon's motion having gone through all its 
 changes, once more resumes its original value. 
 
 I can never contemplate this wonderful revolution 
 without feelings of profound admiration. Such is the 
 extreme slowness of this change in the moon's mean 
 motion, that in the period of three thousand years 
 she has got only four of her diameters in advance of 
 the position she would have occupied in case no change 
 whatever had been going on. Here, then, is a cycle 
 of changes extending backward to its least limit mil- 
 lions of years, and extending forward to its greatest 
 limit tens of millions of years, detected and measured 
 by man, the existence of whose race on our globe has 
 scarcely been an infinitesimal portion of the vast pe- 
 riod required for the full accomplishment of this entire 
 series of changes. 
 
 May it not, then, be truly said, that man is in some 
 sense immortal, even here on earth. What is time to 
 him, who embraces changes in swiftly revolving worlds, 
 requiring countless ages for their completion, within 
 the limits of an expression so condensed that it may 
 be written in a single line ? Does he not live in the 
 past and in the future, as absolutely as in the present ? 
 Indeed, the present is nothing — it is the past and 
 future which make up existence. 
 
 In the example of the moon's acceleration just ex- 
 plained, we must not fail to notice a most remarkable 
 fact. It is this: — The slow change in the figure of 
 the earth's orbit, occasioned by the joint action of all 
 the planets, and upon which depends the acceleration 
 of the moon's mean motion, is so disguised, that but 
 
148 STRUCTURE OF THE UNIVERSE. 
 
 for its reflex influence on the moon, the probability is 
 tt would have escaped detection for thousands of 
 years. The direct effect is almost insensible, but 
 being indirectly propagated to the moon, it is dis- 
 played in a greatly exaggerated manner — is in this 
 way detected, and finally, after incredible pains, 
 traced to its origin, and demonstrates in the most 
 beautiful manner the prevalence of the great law of 
 universal gravitation. 
 
 Since the general adoption of this law, the human 
 mind has been, in not a few instances, disposed to 
 abandon its universality, and seek for a solution of 
 some intricate problem, by which it was perplexed, in 
 some change or modification of the law ; but in no 
 instance has the effort to fly from the law been suc- 
 cessful. No matter how long and intricate the ex- 
 amination, how far the mind might be carried from 
 this great law, in the end it must come back and 
 acknowledge its universal empire over our entire 
 system. 
 
 It has already been remarked, that one of the effects 
 of the sun's disturbing influence exerted on the moon, 
 was to occasion a change in the position of its 
 perigee, causing it to complete an entire revolution in 
 the heavens in about nine years. The theory of gravi- 
 tation gave a very satisfactory account of this phe- 
 nomenon generally ; but when Sir Isaac Newton under- 
 took the theoretic computation of the rapidity with 
 which the moon's perigee should move, he found, to 
 his astonishment, that no more than one half of the 
 observed motion of the perigee was obtained from 
 theory. In other language, in case the law of gravi- 
 tation be true, Newton found that the moon's perigee 
 
UNIVERSAL GRAVITATION. l4*> 
 
 ought to require eighteen years to perform its revolu- 
 tion in the heavens, while observation showed that 
 the revolution was actually performed in one half of 
 this period. This great philosopher exhausted all his 
 skill and power in the vain effort to overcome this dif- 
 ficulty. He died, leaving the problem unresolved, 
 bequeathing it to his successors, as a research worthy 
 of their utmost efforts.. 
 
 Astronomers did not fail to recognize the high 
 claims of this investigation. Gravitation was once 
 more endangered. The most elaborate computations 
 were made, and the results obtained by Newton were 
 so invariably verified by each successive computer, 
 that it seemed utterly impossible to avoid the conclu- 
 sion ; — they were absolutely accurate, and that the 
 theory of gravitation must be modified in its applica- 
 tion to this peculiar phenomenon. At length the 
 problem was taken up by the distinguished astrono- 
 mer Clairaut. After repeating, in the most accurate 
 manner, the extensive computations of his predeces- 
 sors, reaching invariably the same results, he finally 
 abandoned the law of gravitation in despair, pro- 
 nounced it incapable of explaining the phenomenon, 
 and undertook to frame a theory which should be in 
 accordance with the facts. 
 
 This startling declaration of Clairaut excited the 
 greatest interest. An abandonment of the theory of 
 gravitation was nothing less than returning once 
 more to the original chaos which had reigned in the 
 planetary worlds, and of commencing again the reso- 
 lution of the great problem which it had long been 
 hoped was entirely within the grasp of the human 
 intellect. In this dilemma, when the physical astrono- 
 n 2 
 
150 STRUCTURE OF THE UNIVERSE. 
 
 mer had abandoned the law of gravitation in despair, 
 and the legitimate defenders of the theory were mute, 
 an advocate arose where one was least to be ex- 
 pected. Buffon, the eminent naturalist and meta- 
 physician, boldly attacked the new theory of Clairaut, 
 pronounced it impossible, and defended the law of 
 gravitation by a train of general reasoning, which the 
 astronomer felt almost disposed to treat with ridicule. 
 What should a naturalist know of such matters ? was 
 rather contemptuously asked by the astronomer. It 
 is true he knew but little, yet his attack on Clairaut 
 had the effect to induce the now irritated astronomer 
 to return to his computations, with a view to over- 
 whelm his adversary. He now determined to rest 
 satisfied with nothing short of absolute perfection. — 
 A certain series which had been reached by every 
 computer, and the value of whose terms had been re- 
 garded as decreasing by a certain law, until they 
 finally became inappreciable, from their extreme mi- 
 nuteness, and therefore might, without sensible error, 
 be rejected, was found, on a more careful examina- 
 tion, to undergo a most remarkable change in its 
 character. It was true that the value of its terms did 
 decrease till they became exceedingly small ; but so 
 far from becoming absolutely nothing, on reaching a 
 certain value, the decrease became changed into in- 
 crease — the sum of the series expressing the velocity 
 of the moon's perigee was in this way actually 
 doubled, and Clairaut found, to his inexpressible as- 
 tonishment, that the investigation which had been 
 commenced with the intention of forever destroying 
 the universality of the law of gravitation, resulted in 
 
UNIVERSAL GRAVITATION. 151 
 
 his own defeat, and in the perfect and triumphant 
 establishment of this great law. 
 
 Thus far, in our examinations of the moon and 
 earth, we have regarded their orbits as lying in the 
 same plane, an hypothesis which greatly simplifies the 
 complexity of their motions. This, however, is not 
 the case of nature. The moon revolves in an orbit 
 whose plane is inclined under an angle of about four 
 degrees to the plane of the ecliptic. During half of 
 its journey, it lies above the plane of the earth's 
 orbit, while the remaining part of its route is per- 
 formed below the ecliptic. Thus does the moon, at 
 each revolution, pass through the ecliptic at two 
 points, called the nodes, which points, being joined by 
 a straight line, gives us the intersection of the plane 
 of the moon's orbit with that of the earth. This line 
 of intersection, called the line of the nodes, but for 
 the disturbing influence of external causes, would re- 
 main fixed in the heavens. But we know it to be 
 constantly fluctuating, and in the end performing an 
 entire revolution. The exact amount of this change 
 has been made the subject of accurate examination, 
 and the law of its movement has been found to result 
 precisely from the law of gravitation. Not only is 
 the line of intersection of the plane of the moon's 
 orbit with that of the earth constantly changing, 
 but theory, as well as observation, has ascertained 
 that a series of changes are equally progressing in 
 the angles of inclination of these two planes. The 
 limits are narrow, but the oscillations are unceasing, 
 complicating more and more the relative motions of 
 these two remarkable bodies. 
 
 In the physical examination of the revolution of 
 
i52 STRUCTURE OF THE UNIVERSE. 
 
 the planetary orbs by the application of the law of 
 gravitation, the general features of the investigation 
 are greatly simplified by the fact that the planets and 
 satellites may be regarded as spherical bodies, and 
 may in general be treated as though their entire mass 
 were condensed into a material heavy point, situated 
 at their centre. While this statement is true in its 
 broader application to the theory of planetary pertur- 
 bations, or even in the theory of the sun's action on 
 the planets, especially the more distant ones, it is by 
 no means to be admitted, when we come to a critical 
 examination of the figures of the planets, and the 
 influence exerted by these figures on their near 
 satellites. 
 
 In case the earth had been created an exact sphere, 
 and had been projected in its orbit without any rota- 
 tion on an axis, then would its globular figure have 
 remained without sensible change. But as it revolves 
 swiftly on its axis, the laws of motion and gravita- 
 tion come in to modify the figure of the earth, and to 
 change it from an exact spherical figure to one which 
 is flattened at the poles and protuberant at the equa- 
 tor. Newton's sagacity detected this result as a 
 necessary consequence of the action of gravitation, 
 and he actually computed the figure of the earth from 
 theory, long before any observation or measurement 
 had created a suspicion that its form was other than 
 spherical. The truly wonderful train of consequences 
 flowing from the spheroidal form of the earth gives to 
 this subject a high interest, and demands as close an 
 examination of its principal features as the nature of 
 our investigations will permit. 
 
 Give to the earth, then, an exactly spherical form, 
 
UNIVERSAL GRAVITATION. 153 
 
 and a diameter of 8000 miles, with a rotation on an 
 axis once in twenty-four hours, and let us critically 
 examine the consequences. A particle of matter 
 situated on the equator is 4,000 miles from the earth's 
 axis, and since it passes over the circumference of a 
 circle whose radius is 4,000 miles, it will move with 
 a velocity of about one thousand miles an hour. As 
 we recede from the equator towards the poles, either 
 north or south, the particles revolve at the extremities 
 of radii constantly growing shorter and shorter, until 
 finally at the exact pole there is no motion whatever. 
 But in every revolving body, a centrifugal force is 
 generated — a tendency or disposition to fly from the 
 axis of rotation in a plane perpendicular to this axis. 
 
 Such is the power of this centrifugal force, that if 
 it were possible to make the earth rotate seventeen 
 times in twenty-fours, instead of once, bodies at the 
 equator would be lifted up by the centrifugal force, 
 and the attraction of gravitation would be counter- 
 poised, if not absolutely overcome. ' The force of 
 gravity exerts its power in directions passing nearly 
 through the centre of the earth, while the centrifugal 
 force is always exerted in a direction perpendicular 
 to the axis of rotation. The consequence is manifest, 
 that these two forces cannot counterpoise each other, 
 except in their action on particles situated on the 
 equator of the revolving body. Let us consider the 
 condition of a particle situated any where between 
 the equator and the pole, and free to move under 
 the joint action of these two forces. 
 
 In order that such a particle may be held in equili- 
 brium, the two forces must act on the same straight 
 line, and in opposite directions. This is not the case 
 
154 STRUCTURE OF THE UNIVERSE. 
 
 in question, for gravity draws the particle to the 
 centre of the earth, while the centrifugal force urges 
 it from the axis in a plane perpendicular to that axis. 
 The direction of these two forces is inclined under 
 an angle which is nothing at the equator, and in- 
 creases from the equator to the poles. But the effect 
 produced by the centrifugal force may always be ob- 
 tained by the joint action of two forces, the one 
 directed to the centre of the earth, the other tangent 
 to the earth's surface. Substituting these two forces 
 for the centrifugal force, we perceive that the partial 
 force directed towards the earth's centre is destroyed 
 by gravitation, while the tangential force exerts its 
 full power to move the particle towards the equator 
 of the earth. 
 
 This being understood, it is manifest that as parti- 
 cles are coming constantly from both poles towards 
 the equator, that a change of figure in the earth must 
 be effected. It becomes protuberant at the equator, 
 and is flattened at the poles. 
 
 The question now arises, whether there be any 
 limit to this change of figure. In case the velocity of 
 rotation continues undiminished, is there not reason 
 to fear that the earth will grow more and more pro- 
 tuberant at the equator, heaping up the matter higher 
 and higher, till the figure of the earth be destroyed, 
 and its surface rendered uninhabitable ? Theory has 
 answered this important question ; and it has been 
 fully demonstrated that the figure of the earth cannot 
 pass a limit, which it has even now actually attained, 
 and its present form will not change, from the action 
 of the centrifugal force, in millions of years. A 
 condition of equilibrium has been attained, and all 
 
UNIVERSAL GRAVITATION. 155 
 
 further change is at an end. Indeed, if' we examine 
 carefully the subject, we may readily perceive, from 
 the nature of the forces, and the conditions of the 
 problem, that such a result might have been antici- 
 pated. As the earth grows more protuberant, chang- 
 ing from the spherical form, the particles must be 
 heaved up the side of this elevated ridge w T hich belts 
 the earth around the equatorial regions, and finally 
 the resistance they meet from the elevation they are 
 obliged to overcome, is quite equal to the moving 
 force, and the two destroy each other. This point 
 attained, equilibrium ensues, and further change be- 
 comes impossible. 
 
 Such is the beautiful order of nature, such the ad- 
 mirable arrangement for stability and perpetuity, 
 every where manifested, that the thought constantly 
 comes to the mind that divine wisdom alone could 
 have framed so admirable a system. 
 
 But the question may here arise, is this a mere 
 theoretic result? Has observation confirmed the 
 theoretic figure? I answer that observations, the 
 most numerous and diversified, have all united their 
 harmonious testimony to the truth of these beautiful 
 results. In executing exact measures of the degrees 
 of a meridian passing through the poles round the 
 earth, the length of the degree is found to increase 
 from the equator towards the poles, showing that the 
 curvature is more flattened as we recede from the 
 equator. But a more delicate proof is found in the 
 vibrations of the pendulum. A pendulum of a given 
 length will vibrate with a velocity precisely propor- 
 tioned to the intensity of the force of gravity which 
 operates on it. But the intensity of gravity decreases 
 
156 STRUCTURE OF THE UNIVERSE. 
 
 as the square of the distance from the centre increases; 
 so that it is manifest that the force of gravity is less 
 at the equator than at the poles, in case the surface 
 at the equator is farther from the centre than at the 
 poles, which is the fact asserted by theory. 
 
 This being understood, we are prepared to deter- 
 mine the exact figure of the earth, by transporting a 
 pendulum of given length from the equator to differ- 
 ent latitudes north and south. — The number of vibra- 
 tions in one hour being accurately counted at the 
 equator, as we recede north or south, will determine 
 with certainty whether we are approaching to, or 
 going farther from the earth's centre. These experi- 
 ments have actually been performed, and with the 
 most satisfactory results. The number of vibrations 
 in an hour increases the farther we go north or south, 
 and in a ratio giving the strongest confirmation to the 
 truth of the earth's figure derived from the theoretic 
 investigations — each combining to show that the 
 polar diameter of the earth is but 7,898 miles, while 
 the equatorial diameter is 7,924 miles, producing a 
 sort of ridge or belt around the equatorial regions, 
 rising about thirteen miles above the general spherical 
 surface described about the polar axis as a diameter. 
 
 More than two thousand years have passed away 
 since a discovery was made, showing that the sun's 
 path among the fixed stars was slowly changing. — 
 The point at which it crossed the equatorial line, and 
 which for ages had been regarded as fixed, was finally 
 detected to have a slow retrograde motion, producing 
 the precession of the equinoxes. The fact was received, 
 but, no depth of penetration, no stretch of intellectual 
 vigor could divine the cause of this inexplicable 
 
UNIVERSAL GRAVITATION. 157 
 
 change. Another fact was revealed about the same 
 time. It was found by attentive examination, that 
 the north pole of the heavens, the point in which the 
 prolongation of the earth's axis pierces the celestial 
 sphere, was actually changing, by slow degrees, its 
 place among the fixed stars. The bright star which, 
 in former ages, had marked the place of the pole, and 
 whose circle of diurnal revolution was scarcely to be 
 perceived from its smallness, as centuries slowly 
 glided by, was increasing its distance from the pole, 
 gradually describing around it a circle of greater 
 radius. An attentive examination of the stars near 
 the pole soon demonstrated the fact, that it was an 
 actual motion of the pole, and not of the stars in its 
 neighborhood. 
 
 Now, incredible as this statement may appear, 
 modern science has traced these phenomena, the revo- 
 lution of the equinoctial point, and the movement of 
 the north pole of the heavens, to a common origin, 
 and has demonstrated, in the clearest manner, that 
 they are both consequences of the spheroidal figure 
 of the earth, which we have just examined. It is not 
 my design to enter into an elaborate investigation of 
 this wonderful subject, but, in accordance with the 
 plan already announced, I cannot leave you with a 
 mere announcement of a truth so startling, without 
 some effort to explain how this may be. The subject 
 is difficult, but favored by your close attention, I do 
 not despair of rendering it approximately intelligible. 
 
 Let us conceive the earth's axis to be a solid bar 
 of iron driven through the centre of the earth, com- 
 ing out at the poles, and extending indefinitely to- 
 wards the sphere of the fixed stars. JNow turn this 
 O 
 
158 STRUCTURE OF THE UNIVERSE. 
 
 axis up until it stands perpendicular to the plane of 
 the orbit in which the earth revolves around the sun. 
 Then do the equator and ecliptic exactly coincide, and 
 if the fixed stars are at a distance nearly infinite, the 
 point in which the earth's axis prolonged pierces the 
 heavens will appear stationary, so far as the revolu- 
 tion of the earth in its orbit is concerned. Now if 
 this iron axle could be grasped by some giant hand, 
 and drawn away from its upright or perpendicular 
 position, the solid earth would turn with it, and the 
 equator, ceasing to coincide with the ecliptic or plane 
 of the earth's orbit, comes to be inclined to it, under 
 an angle precisely equal to the angle through which 
 the axis has been inclined. It is thus seen that no 
 change can be wrought on the position of the axis, 
 that does not involve a corresponding change in the 
 whole earth, and especially in the plane of the equa- 
 tor, which must ever remain perpendicular to the axis 
 in all its positions. 
 
 The reverse of this proposition is equally manifest. 
 If the solid earth be seized at the equator, and be turned 
 up or down, the axis will participate in this movement, 
 and its change will exhibit itself in the changed posi- 
 tion of the point in which it meets the celestial sphere. 
 One step more, and the difficulty is surmounted. — 
 Conceive a flat wheel of wood floating on still water. 
 Through its centre pass an axle which stands perpen- 
 dicular to the surface of the wheel and water. So 
 long as the wheel floats level, the axle stands erect, 
 but in case the north half of the wheel is tilted down 
 under the water, the south half at the same time rising 
 out of the water, the axis will tilt towards the north. 
 Bring the wheel again to its level position. Now 
 
UNIVERSAL GRAVITATION. 159 
 
 plunge the eastern portion of the wheel below the 
 surface. — The axis now is tilted towards the east. — 
 The experiment is simple, and shows that, in case 
 the successive portions of the wheel be submerged, 
 the axis will always be tilted towards the point which 
 goes under first. To reverse the experiment: in case 
 we take hold of the axle and turn it east, it sinks the 
 eastern half of the wheel below the surface of the 
 water, while the western half is raised out of it, and 
 then in case we make the upper extremity of the 
 axis follow round the circumference of a circle whose 
 surface is parallel to that of the water, and whose 
 centre is exactly above the centre of the wheel, it 
 will be seen that, as the axle moves round, successive 
 portions of the wheel are submerged, until finally the 
 w r ater line will have divided the wheel into all its 
 successive halves, and will have successively coincided 
 with every possible diameter of the wheel. 
 
 Now for the application. The level surface of the 
 water is the level plane of the earth's orbit, the 
 wheel is the earth's equator, and the axle is the 
 earth's axis of rotation. One-half of the equator is 
 constantly submerged below the plane of the ecliptic 
 — the other half rises above it. But the water line, 
 or the intersection of these two planes, the equinoc- 
 tial line, cannot remain fixed in the same line. A 
 power does seize the equator and plunge successive 
 halves of it beneath the plane of the ecliptic, chang- 
 ing perpetually the water line, until finally each half 
 in succession, into which all its diameters can be di- 
 vided, are sunk below the surface, or plane of the 
 ecliptic, thus causing the earth's axis to tilt over to- 
 wards the portions successively submerged, until it 
 
160 STRUCTURE OF THE UNIVERSE. 
 
 finally sweeps entirely round and comes to resume 
 its first position. 
 
 But do you now demand what power seizes the 
 earth's protuberant equator, and tilts it successively 
 towards every point of the compass? I answer, that 
 the power is lodged in the sun and moon, and it is 
 their combined action which works out these wonder- 
 ful results. In case the sun and moon were so situated 
 as always to be in the plane of the earth's equator, 
 then they would have no power to change the position 
 of the equator. But we know that they are not in 
 this plane, except when passing through it, and are 
 found sometimes on the north and sometimes on the 
 south side of it. Wherever either of them may be, 
 the nearest half of the redundant matter about the 
 earth's equator will be more forcibly attracted than 
 the remote half, and the equator will be tilted towords 
 the attracting body, and the axis of the earth will fol- 
 low the movement of the equator to which it is firmly 
 fixed. 
 
 Thus does the earth's whole solid mass sway to the 
 motion of the ring of matter heaped up around the 
 equator, delicately and beautifully sensitive to all the 
 changes in the relative places of the sun and moon. 
 Neither the earth nor its axis are ever, for one mo- 
 ment, released from the action of these remote bodies. 
 However slight the effects, however varied in action, 
 oscillating to every point within certain prescribed 
 limits, the stability is preserved, and the final effect is 
 a small retrograde motion of the equinox at the end 
 of every year, and a slight change in the place of the 
 pole of the heavens. 
 
 But there is no isolated matter in the universe. — 
 
UNIVERSAL GRAVITATION. 161 
 
 Every particle of matter attracts every other particle 
 of matter, and it is impossible for the sun and moon 
 to exert any influence on the equatorial ring of mat- 
 ter which belongs to our globe, without feeling, in 
 their turn, the reaction of this ring on themselves. — 
 The remote and ponderous sun may, in consequence 
 of its vast size and distance, escape from any effect 
 capable of being detected by observation. But this is 
 not the case with the moon. Her proximity to the 
 earth and diminutive mass, render her peculiarly 
 sensitive to the influence of the redundant matter at 
 the earth's equator, and as her attraction tilts the 
 plane of the earth's equator, so does the equatorial 
 ring tilt the plane of the moon's orbit. These effects 
 have been accurately observed and measured, and 
 strange to relate, their exact values have exhibited 
 the figure which belongs to the earth with far greater 
 precision than can be obtained from measures on its 
 surface. We may even go farther, for such is the in- 
 timate relationship between the earth and its attend- 
 ant satellite, that there is scarcely a question can be 
 asked with reference to the one, that is not answered 
 by the other. 
 
 If we demand the weight of the earth when com- 
 pared with the sun, the moon answers. If the excess 
 of the equatorial diameter of the earth over the polar 
 be required, the moon answers. If the homogenity of 
 the interior of the solid earth be required, the moon 
 replies. If the thickness of the earth's crust is sought 
 for, question the moon, and the answ r er comes. If 
 you w r ould know the sun's distance from the earth, 
 ask the moon. If the permanency of the axis of rota- 
 tion be required, ask the moon, and she alone yields 
 o2 
 
162 STRUCTURE OF THE UNIVERSE. 
 
 a satisfactory reply. Finally, if curiosity leads us to 
 inquire whether the length of the day and night, the 
 revolution of the earth on its axis, be uniform, or 
 whether it may not have changed by a single second 
 in a thousand years, we go to the moon for an an- 
 swer, and in each and every instance her replies to 
 all these profound and mysterious questions are clear 
 and satisfactory. How wonderful the structure of the 
 universe ! How gigantic the power of the human 
 intellect ! If all the stars of heaven were struck 
 from existence ; if every planet and satellite which 
 the eye and the telescope descry, inside and beyond 
 the earth's orbit, were swept away forever, and the 
 sun, earth and moon alone remained for the study of 
 man, and as evidences of the being and wisdom of 
 God, in the exquisite adjustments of this system, in the 
 reciprocal influences of its three bodies, in their vast 
 cycles of configuration, in their relative masses, mag- 
 nitudes, distances, motions, and perturbations, there 
 would remain themes sufficient for the exercise of the 
 most exalted genius, and proof of the being of God, 
 so clear and positive, that no sane mind could com- 
 prehend it and disbelieve. 
 
LECTURE VI. 
 
 THE STABILITY OF THE PLANETARY SYSTEM. 
 
 When, by the application of a single great law, the 
 mind had succeeded in resolving the difficult problems 
 presented by the motions of the earth and its satel- 
 lite, the moon, it rose to the examination of the higher 
 and more complicated questions of the stability of 
 the entire system of planets, satellites, and comets, 
 which are found to pursue their courses round the 
 sun. The number of bodies involved in this investi- 
 gation, their magnitudes and vast periods of revolu- 
 tion, their great distances from the observer, and the 
 exceeding delicacy of the required observations, com- 
 bined with the high interest which attaches itself to 
 the final result, have united to render this investiga- 
 tion the most wonderful which has ever employed the 
 energies of the human mind. 
 
 To comprehend the dignity and importance of this 
 great subject, let us rapidly survey the system, and 
 moving outward to its known boundaries, mark the 
 number and variety of worlds involved in the investi- 
 gation. Beginning, then, at the great centre, the 
 grand controlling orb, the sun, we find its magnitude 
 such as greatly to exceed the combined masses of all 
 its attendant planets. Indeed, if these could all be 
 arranged in a straight line on the same side of the 
 sun, so that their joint effect might be exerted on that 
 body, the centre of gravity of the entire system thus 
 
 (163) 
 
164 STRUCTURE OF THE UNIVERSE. 
 
 located, would scarcely fall beyond the limits of the 
 sun's surface. At a mean distance of 36,000,000 of 
 miles from the sun we meet the nearest planet, Mer- 
 cury, revolving in an orbit of considerable eccentricity, 
 and completing its circuit around the sun in a period 
 of about eighty-eight of our days. This world has 
 a diameter of only 3,140 miles, and is the smallest 
 of the old planets. Pursuing our journey, at a dis- 
 tance of 68,000,000 of miles from the sun, we cross 
 the orbit of the planet Venus. Her magnitude is 
 nearly equal to that of the earth. Her diameter is 
 7,700 miles, and the length of her year is nearly 225 
 of our days. The next planet we meet is the earth, 
 whose mean distance from the sun is 95,000,000 of 
 miles. The peculiarities which mark its movements, 
 and those of its satellite, have been already discussed. 
 Leaving the earth, and continuing our journey out- 
 ward, we cross the orbit of Mars, at a mean distance 
 from the sun of 142,000,000 of miles. This planet is 
 4,100 miles in diameter, and performs its revolution 
 around the sun in about 687 days, in an orbit but 
 little inclined to the plane of the ecliptic. Its features, 
 as we shall see hereafter, are more nearly like those 
 of the earth than any other planet. Beyond the 
 orbit of Mars, and at a mean distance from the sun 
 of about 250,000,000 of miles, we encounter a group 
 of small planets, eight in number, presenting an 
 anomaly in the system, and entirely different from 
 anything elsewhere to be found. These little planets 
 are called asteroids. Their orbits are, in general, 
 more eccentric, and more inclined to the ecliptic, than 
 those of the other planets ; but the most remarkable 
 fact is this : — that their orbits are so nearly equal in 
 
STABILITY OF THE PLANETARY SYSTEM. 165 
 
 size, that when projected on a common plane, they 
 are not enclosed, the one within the other, but actually 
 cross each other. 
 
 We shall return to an examination of these won- 
 derful objects hereafter. At a mean distance of 
 485,000,000 of miles from the sun, we cross the orbit 
 of Jupiter, the largest and most magnificent of all the 
 planets. His diameter is nearly 90,000 miles. He is 
 attended by four moons, and performs his revolution 
 round the sun in a period of nearly twelve years. — 
 Leaving this vast world, and continuing our journey 
 to a distance of 890,000,000 of miles from the sun, 
 we cross the orbit of Saturn, the most wonderful of 
 all the planets. His diameter is 76,068 miles, and he 
 sweeps round the sun in a period of nearly twenty-nine 
 and a half years. He is surrounded by several broad 
 concentric rings, and is accompanied by no fewer than 
 seven satellites or moons. The interplanetary spaces 
 we perceive are rapidly increasing. The orbit of 
 Uranus is crossed at a mean distance from the sun of 
 1,800,000,000 of miles. His diameter is 35,000 miles, 
 and his period of revolution amounts to rather more 
 than eighty-four of our years. He is attended by six 
 moons, and pursues his journey at a slower rate than 
 any of the interior planets. Leaving this planet, we 
 reach the known boundary of the planetary system, 
 at a distance of about 3,000,000,000 of miles from 
 the sun. Here revolves the last discovered planet, 
 Neptune, attended by one, probably by two mcons, 
 and completing his vast circuit about the sun in a 
 period of one hundred and sixty-four of our years. — 
 His diameter is eight times greater than the earth's, 
 and he contains an amount of matter sufficient to 
 
166 STRUCTURE OF THE UNIVERSE. 
 
 form one hundred and twenty-five worlds such as 
 ours. 
 
 Here we reach the known limit of the planetary 
 worlds, and standing at this remote point and looking 
 back towards the sun, the keenest vision of man could 
 not descry more than one solitary planet along the line 
 we have traversed. The distance is so great, that 
 even Saturn and Jupiter are utterly invisible, and the 
 sun himself has shrunk to be scarcely greater than a 
 fixed star. 
 
 There are certain great characteristics which dis- 
 tinguish this entire scheme of worlds. They are all 
 nearly globular — they all revolve on axes — their orbits 
 are all nearly circular — they all revolve in the same 
 direction around the sun — the planes of their orbits 
 are but slightly inclined to each other, and their moons 
 follow the same general laws. With a knowledge of 
 these general facts, it is proposed to trace the recip- 
 rocal influences of all these revolving worlds, and to 
 learn, if it be possible, whether this vast scheme has 
 been so constructed as to endure while time shall 
 last, or whether the elements of its final dissolution 
 are not contained within itself, either causing the 
 planets, one by one, to drop into the sun, or to recede 
 from this great centre, released from its influence, to 
 pursue their lawless orbits through unknown regions 
 of space. 
 
 Before proceeding to the investigation of the great 
 problem of the stability of the universe, let us examine 
 how far the law of gravitation extends its influence 
 over the bodies which are united in the solar system. 
 A broad and distinct line must be drawn between 
 those phenomena, for which gravitation must render 
 
STABILITY OF THE PLANETARY SYSTEM. 16^ 
 
 a satisfactory account, and those other phenomena, 
 for which it is in no wise responsible. In the solar 
 system we find, for example, that all the planets re- 
 volve in the same direction around the sun, in orbits 
 slightly elliptical, and in planes but little inclined to 
 each other. Neither of these three peculiarities is in 
 anyway traceable to the law of gravitation. 
 
 Start a planet in its career, and, no matter what be 
 the eccentricity of its orbit, the direction of its move- 
 ment, or the inclination of the plane in which it pur- 
 sues its journey, once projected, it falls under the 
 empire of gravitation, and ever after, this law is ac- 
 countable for all its movements. We are not, there- 
 fore, to regard the remarkable constitution of the 
 solar system as a result of any of the known laws of 
 nature. 
 
 If the sun were created, and the planetary worlds 
 formed and placed at the disposal of a being possessed 
 of less than infinite wisdom, and he were required so 
 to locate them in space, and to project them in orbits, 
 such that their revolutions should be eternal, even 
 with the assistance of the known laws of motion and 
 gravitation, this finite being w r ould fail to construct 
 his required system. 
 
 Let it be remembered, that each and every one of 
 these bodies exerts an influence upon all the others. 
 There is no isolated object in the system. Planet 
 sways planet, and satellite bends the orbit of satellite, 
 until the primitive curves described, lose the simplicity 
 of their character, and perturbations arise, which may 
 end in absolute destruction. There is no chance 
 work in the construction of our mighty system. Every 
 planet has been weighed and poised, and placed pre- 
 
168 STRUCTURE OF THE UNIVERSE. 
 
 cisely where it should be. If it were possible to drag 
 Jupiter from its orbit, and cause him to change places 
 with the planet Venus, this interchange of orbits 
 would be fatal to the stability of the entire system. 
 In contemplating the delicacy and complexity of the 
 adjustment of the planetary worlds, the mind cannot 
 fail to recognize the fact that, in all this intricate 
 balancing, there is a higher object to be gained than 
 the mere perpetuity of the system. 
 
 If stability had been the sole object, it might have 
 been gained by a far simpler arrangement. If God 
 had so constituted matter that he sun might have 
 attracted the planets, while th^se should exert no in- 
 fluence over each other — that the planets might have 
 attracted their satellites, while these were free from 
 their reciprocal influences — then, indeed, a system 
 would have been formed, whose movements would 
 have been eternal, and whose stability would have 
 been independent of the relative positions of the 
 worlds, and the character of their orbits. Give to 
 them but space enough in which to perform their rev- 
 olutions around the sun, so that no collisions might 
 occur, freed from this only danger, every planet, and 
 every satellite, will pursue the same undeviating 
 track throughout the ceaseless ages of eternity. 
 
 If this statement be true, it may be demanded, why 
 such a system was not adopted. It is impossible for 
 us to assign all the reasons which led to the adoption 
 of the present complicated system. Of one thing, 
 however, we are certain : — If God designed that in 
 the heavens his glory and his wisdom should be de- 
 clared, and that in the study of his mighty works, his 
 intelligent creatures should rise higher and higher to- 
 
STABILITY OF THE PLANETARY SYSTEM. 169 
 
 wards his eternal throne, then, indeed, has the present 
 system been admirably constituted for the accomplish- 
 ment of this grand design. To have acquired a 
 knowledge of a system constituted of independent 
 planets, free from all mutual perturbations, would 
 have required scarcely no effort to the mind, when 
 compared with that put forth in the investigation of 
 the present complex construction of the planetary 
 system. The mind would have lost the opportunity 
 of achieving its greatest triumphs, while the evidence 
 of infinite wisdom displayed in the arrangement and 
 counterpoising of the present system would have been 
 lost forever. There is one other thought which here 
 suggests itself with so much farce that I cannot turn 
 away from it. We speak of gravitation as some in- 
 herent quality or property oi matter, as though mat- 
 ter could not exist in case it were deprived of this 
 quality. This is, however, a false idea. Matter might 
 have existed independent of any quality which should 
 cause distant globes to influence each other. — 
 This force called gravitation, even admitting that it 
 must have an existence, no special law of its action 
 could have forced itself on matter to the exclusion of 
 all other laws. Why does this force diminish as the 
 square of the distance at which it operates, increases ? 
 There are almost an infinite number of laws, accord- 
 ing to which an attraction might have exerted itself, 
 but there is no one which would have rendered the 
 planets fit abodes for sentient beings, such as now 
 dwell on them, and which would at the same time 
 have guaranteed the perpetuity of the system. Ad- 
 mitting, then, that matter cannot be matter, without 
 exerting some influence on all other matter, (which 
 P 
 
170 STRUCTURE OF THE UNIVERSE. 
 
 I am unwi ling to admit), in the selection of the law 
 of the inverse square of the distance, there is the 
 strongest evidence of design. 
 
 If we rise above the law of gravitation to the Great 
 Author of nature, and regard the laws of motion and 
 of gravitation as nothing more than the uniform ex- 
 pressions of his will, we perceive at once the impos- 
 sibility of constructing the universe in such manner 
 that the sun should attract the planets, without these 
 attracting each other ; or that the planets should at- 
 tract their satellites without, in turn, being recipro- 
 cally influenced by their satellites ; for this would be 
 equivalent to saying that the will of the same Al- 
 mighty Being should exert itself, and not exert itself, 
 at the same moment, which is impossible. As there 
 is but one God, so there is but one kind of matter, 
 governed by one law, applied by infinite wisdom to 
 the formation of suns and systems without number, 
 crowding the illimitable regions of space, all moving 
 harmoniously, fulfilling their high destiny, and all sus- 
 tained by the single arm of divine Omnipotence. 
 
 We now proceed to an examination of the great 
 question, Is the system of worlds by which we are 
 surrounded, and of which our earth and its moon form 
 a part, so constructed that, under the operation of the 
 known laws of nature, it shall forever endure, without 
 ever passing certain narrow limits of change, which 
 do not in any way involve its stability ? 
 
 It is well known that the planets revolve in ellip- 
 tical orbits of small eccentricity — that under the action 
 of the primitive impulse by which they were projected 
 in their orbits, they would have moved off in a straight 
 line, with a velocity proportioned to the intensity of 
 
STABILITY OF THE PLANETARY SYSTEM. 171 
 
 the impulse, and which would have endured forever ; 
 but being seized by the central attraction of the sun, 
 at the moment of starting in their career, the joint 
 action of these two forces, bends the planet from its 
 straight direction, and cause it to commence a curvi 
 linear path, w r hich carries it round the sun. 
 
 The question which first presents itself isthis : — If 
 the central force lodged in the sun has the power to 
 cause a planet to diverge from the straight line in 
 which, but for this, it would have moved — if it draw 
 it into a curved path, will not this central force, which 
 is ever active, finally overcome, entirely, the impul- 
 sive force originally given to the planet, draw it closer 
 and closer to the sun in each successive revolution, in 
 a spiral orbit, until, finally, the planet shall fall into 
 the sun, and be destroyed forever? This question 
 arises independent of the extraneous influence which 
 the planets exert over each other. It refers to a soli- 
 tary globe revolving around the sun, under the influ- 
 ence of a central force which varies its action as does 
 the law r of gravitation. The problem has been sub- 
 mitted to the most rigorous mathematical examina- 
 tion, and a result has been obtained which settles 
 the question in the most absolute manner. The 
 amount by which the central force, in a moment of 
 time, overcomes the effect produced by the primitive 
 impulse, is a quantity infinitely small, and of the second 
 order. If it were found to be infinitely small in each 
 moment of time, then might it accumulate so that, at 
 the end of a vast period, it might become finite and 
 appreciable. But because it is of the second order of 
 infinitely small quantities, before it can become an infi- 
 nitely small quantity of the first order, a period equal 
 
172 STRUCTURE OF THE UNIVERSE. 
 
 to infinite ages must roll by, and to make a finite ap- 
 preciable quantity out of this, an infinite cycle of 
 years must roll round an infinite number of times ! 
 
 Such is the answer given by analysis to this wonder- 
 ful question. "Is there no change ?" demands the 
 astronomer. " Yes," answers the all-seeing analysis. 
 " When Mil it become appreciable ? n asks the astron- 
 omer. "At the end of a period infinitely long, repeated 
 an infinite number of times," is the reply. 
 
 Having settled this important question, it remains 
 now to examine whether the mutual attractions of 
 the planets on each other may not, in the end, change 
 permanently the form of their orbits, and lead, ulti- 
 mately, to the destruction of the system. To com- 
 prehend more readily the nature of the examination, 
 let us review the points involved in the permanency 
 of our orbit. 
 
 Take, for example, our own planet, the earth. It 
 now revolves in an elliptic orbit, whose magnitude is 
 determined by the length of its longer axis, and by 
 its eccentricity. These elements are readily deduced 
 from observation. If it were possible to construct 
 this orbit of some material, like wire, which would 
 permit us to take it up and locate it in space at will, 
 to enable us to give it the position now occupied by 
 the actual orbit of the earth, we must first carry 
 its focus to the sun's centre ; we must then turn its 
 longer axis around this centre as a fixed point, until 
 the nearest vertex of the wire orbit shall fall upon 
 that point of the earth's orbit which is at this time 
 nearest to the sun. Having accomplished this, the 
 axes will coincide in their entire length, and to make 
 the orbits coincident, we must revolve the artificial 
 
STABILITY OF THE PLANETARY SYSTEM. 1?3 
 
 one around the now common axis, until its plane shall 
 fall upon the actual orbit of the earth. 
 
 If, now, change should ever come, in the absolute 
 coincidence of these two orbits, regarding the iron one 
 as fixed and permanent, the orbit of nature may vary 
 from it in any one or all of the following way^ :— 
 First. The natural orbit, all other things remaining 
 the same, may leave the fixed orbit by a variation of 
 eccentricity :— that is, it may become more or less 
 nearly circular. Second. The planes of the orbits re- 
 maining coincident, the curves may separate from 
 each other, in consequence of an angular movement 
 of the longer axis of the natural orbit, by means of 
 which the vertex of the natural curve shall be carried 
 to the right or to the left of the vertex of the fixed 
 one. Third. While these causes are operating to pro- 
 duce change, an increase of deviation may be occa- 
 sioned by the fact that the two planes may become 
 inclined to each other, thus causing the natural orbit 
 to lie partly above and partly below the fixed one.— 
 These, then, are the several ways in which the orbits 
 of the planets may change; and to settle the question 
 of stability, we must ascertain whether these changes 
 actually exist, and whether any of them, in case they 
 do exist, and are progressing constantly in the same 
 direction, will ever prove fatal to the permanency of 
 the system, finally accomplishing its absolute destruc- 
 tion, or rendering it unfit for the sustentation of that 
 life which now exists upon the planet. 
 
 By a close examination of this great subject, both 
 theoretically and practically, it is found that the sys- 
 tem is so constituted, that not a single planet or satel- 
 lite revolves in an orbit absolutely invariable. Theorv 
 p 2 
 
174 STRUCTURE OF THE UNIVERSE. 
 
 demonstrates that such changes must exist, and ob- 
 servation confirms this great truth, by showing that 
 they actually do exist. 
 
 Draw, in imagination, a straight line from the sun's 
 centre, through the perihelion, or nearest point to the 
 sun of the earth's orbit, and let it be extended to the 
 outermost limits of the entire system. On this locate 
 the perihelion points of the orbits of all the planets, 
 and in these points fix the planets themselves. They 
 are now all on the same side of the sun, the longer 
 axes of their orbits are in the same direction, and 
 they are all located at their nearest distance from the 
 sun, or in perihelion. The planes of the orbits are 
 inclined to each other under their proper angles, and 
 they all intersect in a common line of nodes passing 
 through the sun's centre. Now give the entire group 
 of planets their primitive impulse, and at the same 
 instant they start in their respective orbits round the 
 sun. Now, in case no perturbations existed, the peri- 
 helion points, the inclinations, and the lines of nodes, 
 would remain fixed forever, and although millions of 
 years might pass away before the planets would again 
 resume their primitive position with reference to each 
 other, yet the time would come when a final restora- 
 tion would be effected. 
 
 At the end of 164 years, Neptune will have com- 
 pleted its revolution round the sun, and will return to 
 its starting point. All the other planets will have 
 performed several revolutions, but each, on reaching 
 the point of departure, will find the perihelion of its 
 orbit changed in position, the inclination altered, and 
 the line of nodes shifted. These changes continue 
 until the longer axes of the orbits, which once coin- 
 
STABILITY OF THE PLANETARY SYSTEM. 175 
 
 cided, radiate from the sun in all directions. The 
 lines of nodes, once common, now diverge under all 
 angles, the inclinations increasing or decreasing, and 
 even the figures of the orbits undergoing constant 
 mutation ; and the grand question arises, whether 
 these changes, no matter how slow, are ever to con- 
 tinue progressing in the same direction, until all the 
 original features of the system shall be effaced, and 
 the possibility of return to the primitive condition 
 destroyed forever. 
 
 Such a problem would seem to be far too deep and 
 complicated ever to be grasped by the human intel- 
 lect. It is true that no single mind was able to ac- 
 complish its complete solution, but the advance made 
 by one has been steadily increased by another, until, 
 finally, not a question remains unanswered. The so- 
 lution is complete, yielding results of the most won- 
 derful character. 
 
 We shall examine this great problem in detail, and 
 commence with the figure of the orbit of any planet, 
 our earth, for example. 
 
 The amount of heat received from the sun by the 
 earth depends, other things being the same, on the 
 minor axis of its ecliptic orbit. Any change in the 
 eccentricity operates directly to increase or decrease 
 the shorter axis, and consequently to increase or de 
 crease the mean annual amount of heat received 
 from the sun. Now we know that animal and vege- 
 table life is adjusted in such way that it requires al- 
 most exact uniformity in the mean annual amount of 
 heat which it shall enjoy. An increase or decrease 
 of two or three degrees in temperature would make 
 an entire revolution in the animals and plants belong- 
 
.76 SfRUCTURE OF THE UNIVERSE. 
 
 ing to the region experiencing such a change. If, 
 then, it be true that the eccentricity of the earth's 
 orbit is actually changing, under the combined action 
 of the other planets, may this change continue so far 
 as to subvert the order of nature on its surface ? — 
 This question has been answered in the most satis- 
 factory manner. 
 
 It is found that the greater axes of the planetary 
 orbits are subjected to slight and temporary varia- 
 tions, returning, in comparatively short periods, to 
 their primitive values. This important fact guaran- 
 tees the permanency of the periodic times, so that it 
 becomes possible to deduce, with the utmost precision 
 the periodic times of the planets, from the mean of a 
 large number of revolutions. That of the earth is 
 now so accurately known, and so absolutely invaria- 
 ble, that we know what it w T ill be a million of years 
 hence, should the system remain as it now is, as per- 
 fectly as at the present moment. But neither of these 
 elements secures the stability of the eccentricity, or 
 of the minor axis. Lagrange, however, demonstrated 
 a relation between the masses of the planets, their 
 major axes and eccentricities, such, that while the 
 masses remain constant, and the axes invariable, the 
 eccentricity can only vary its value through extremely 
 narrow limits. These limits have been assigned, be- 
 yond which the change can never pass, and within 
 these narrow bounds we find the orbits of all the 
 planets slowly vibrating backward and forward, in 
 periods which actually stun the imagination. 
 
 This remarkable law for the preservation of the 
 system would not hold in any other organization. It, 
 demands orbits nearly circular, with planes nearly co- 
 
STABILITY OF THE PLANETARY SYSTEM. 177 
 
 incident, with periodic times related as are those of 
 the planets, and the planets themselves located as 
 they actually are. No interchange of orbits is admis- 
 sible ; but, constituted as the system now is, the per- 
 petuity is absolutely certain, so far as the change of 
 eccentricity is concerned. 
 
 Let us now examine the changes which affect the 
 position of the major axis in its own plane. The 
 perihelion of every orbit is found to be slowly advanc- 
 ing, Nor is this advance ever to be changed into a 
 retrograde motion. The movement is ever progres- 
 sive in the same direction, and the perihelion points of 
 all the orbits are slowly sweeping round the sun. — 
 That of the earth's orbit accomplishes its revolution 
 in one hundred and eleven thousand years ! How won- 
 derful the fact, that such discoveries should be made 
 by man, whose entire life is but a minute fraction of 
 these vast periods of time ! 
 
 Owing to a retrograde motion in the vernal equi 
 nox. carrying it around in the opposite direction in 
 25,868 years, the perihelion and equinox pass each 
 other once in 20.984 years. Knowing their relative 
 positions at this moment, and their rates of motion, 
 it is easy to compute the time of their coincidence. 
 Their last coincidence took place 4.089 years before 
 the Christian era, or about the epoch usually assigned 
 for the creation of man. The effect of the coinci- 
 dence of the perihelion with the vernal equinox, is to 
 cause an exact equality in the length of spring and 
 summer, compared with autumn and winter. In other 
 language, the sun will occupy exactly half a year in 
 passing from the vernal to the autumnal equinox, and 
 
178 STRUCTURE OF THE UNIVERSE. 
 
 the 3ther half in moving from the autumnal to the 
 vernal equinox. 
 
 At present, the line of equinoxes divides the earth's 
 elliptic orbit into two unequal portions. The smaller 
 part is passed over in the fall and winter, causing the 
 earth to be nearer the sun at this season than in sum- 
 mer, and making a difference in the length of the two 
 principal seasons, summer and winter, of some seven- 
 teen and a half days. This inequality, which is now 
 in favor of summer, will eventually be destroyed, and 
 the time will come when the earth will be farthest 
 from the sun during the winter, and nearest in the 
 summer. But at the end of a great cycle of more 
 than 20,000 years, all the changes will have been 
 gone through, and, in this respect, a complete com- 
 pensation and restoration will have been effected. 
 
 This epoch of subordinate restoration will find the 
 perihelion of the earth's orbit located in space far 
 distant from the point primitively occupied. Five of 
 these grand revolutions of 20,984 years must roll 
 round before the slow movement of the perihelion 
 shall bring it back to its starting point. 110,000 
 years will then restore the axis of the earth's orbit, 
 and the equinoctial line, nearly to their relative po- 
 sitions to each other, and to the same region of abso- 
 lute space occupied at the beginning of this grand 
 cycle. 
 
 Jf, now, we direct our attention to the other planets, 
 we find their perihelion points all slowly advancing 
 in the same direction. That of the orbit of Jupiter 
 performs its revolution round the sun in 186,207 
 years, while the perihelion of Mercury's orbit occu- 
 pies more than 200,000 years in completing its circuit 
 
STABILITY OF THE PLANETARY SYSTEM. 179 
 
 round the sun. To effect a complete restoration of 
 the planetary orbits to their original position, with 
 reference to their perihelion points, will require a 
 grand compound cycle, amounting to millions of 
 years. Yet the time will come when all the orbits 
 will come again to their primitive positions, to start 
 once more on their ceaseless journeys. 
 
 In the changes of the eccentricities, it will be re- 
 membered, the stability of the system was involved. 
 Should these changes be ever progressive, no matter 
 how slowly, a time would finally come when the 
 original figure of the orbit would be destroyed, the 
 planet either falling into the sun, or sweeping away 
 into unknown regions of space. But a limit is as- 
 signed, beyond which the change can never pass. — 
 Some of the planetary orbits are becoming more cir- 
 cular, others growing more elliptical; but all have their 
 limits fixed. The earth's orbit, for example, should 
 the present rate of decrease of eccentricity continue, 
 in about half a million of years w T ill become an exact 
 circle. There the progressive motion of the changes 
 stops, and it slowly commences to recover its ellipticity. 
 This is not the case with the motions of the perihelia. 
 Their positions are in no way involved in the well 
 being of a planet, or in its capacity to sustain the 
 life which exists on its surface ; and since the stability 
 of the system is not endangered by progressive 
 change, it ever continues in the same direction, until 
 the final restoration is effected, by an entire revolu- 
 tion about the sun. 
 
 Let us now examine the inclinations of the plane- 
 tary orbits. Here it is found that there is no guaran- 
 tee for the stability of the system, provided the angles 
 
ISO STRUCTURE OF THE UNIVERSE. 
 
 under which the orbits of the planets are inclined to 
 each other do not remain nearly th^ same forever. — 
 If changes are found to exist, by which the inclina- 
 tions are made to increase, without stopping and re- 
 turning to their primitive condition, then is the perpe- 
 tuity of the system rendered impossible. Its fair 
 proportions must slowly wear away, the harmony 
 which now prevails be destroyed, and chaos must 
 come again. 
 
 Commencing again with the earth, we find that, 
 from the earliest ages, the inclination of the earth's 
 equator to the ecliptic has been decreasing. Since 
 the measure of Eratosthenes, 2,078 years ago, the de- 
 crease has amounted to about 23' 44", or about half a 
 second every year. Should the decrease continue, in 
 about 85,000 years the equator and ecliptic would co- 
 incide, and the order of nature would be entirely 
 changed J — perpetual spring would reign throughout 
 the year, and the seasons would be lost forever. Of 
 this, however, there is no danger. The diminution 
 will reach its limit in a comparatively short time, 
 when the decrease of inclination will change into 
 an increase, and thus slowly rocking backwards and 
 forwards in thousands of years, the seasons shall ever 
 preserve their appointed places, and seed time and 
 harvest shall never fail. These changes of inclina- 
 tion are principally due to the perturbations of Venus, 
 and arising from configurations, will be ultimately 
 entirely compensated. 
 
 The angles under which the planetary orbits are 
 inclined to each other are in a constant state of mu- 
 tation. The orbit of Jupiter at this time forms an 
 angle with the ecliptic of 4,731 seconds, and this 
 
STABILITY OF THE PLANETARY SYSTEM. 181 
 
 angle is decreasing at such a rate that, in about 20,000 
 years the planes would actually coincide. This would 
 not affect the well being of the planets or the sta- 
 bility of the system, but should the same change now 
 continue, the angle between the orbits might finally 
 come to fix them even at right angles to each other, 
 and a subversion of the present system would result. 
 
 A profound investigation of the problem of the 
 planetary inclinations, accomplished by Lagrange, re- 
 sulted in the demonstration of a relation between the 
 masses of the planets, the principal axes of their 
 orbits, and the inclinations, such that, although the 
 angles of inclination may vary, the limits are narrow 7 , 
 and they are all found slowly to oscillate about their 
 mean positions, never passing the prescribed limits, 
 and securing, in this particular, the perpetuity of the 
 system. 
 
 Here, again, we are presented with the remarkable 
 fact, that whenever mutation involves stability, this 
 mutation is of a compensatory character, always re- 
 turning upon itself, and, in the long run, correcting 
 its own effects. If all this mighty system w r as organ- 
 ized by chance, how happens it that the angular 
 motions of the perihelia of the planetary orbits are 
 ever progressive, while the angular motions of the 
 planes of the orbits are vibrating? Design, positive 
 and conspicuous, is written all over the system, in 
 characters from which there is no escape. 
 
 We now proceed to an examination of the lines in 
 which the planes of the planetary orbits cut each 
 other, or the lines in which they intersect a fixed 
 plane. These are called the lines of nodes. They all 
 pass through the sun's centre, and, in case they ever 
 
 Q 
 
182 STRUCTURE OF THE UNIVERSE. 
 
 were coincident, they now radiate from a common 
 point in all directions. 
 
 Here is an element in no degree involving in its 
 value the stability of the system, and from analogy 
 we already begin to anticipate that its changes, what- 
 ever they may be, will probably progress always in 
 the same direction. This is actually the case. The 
 nodes o^ the planetary orbits are all slowly retrograd- 
 ing on a fixed plane, and in vast periods, amounting 
 to thousands of years, accomplish revolutions, which, 
 in the end, return them to their primitive positions. 
 
 Thus are we led to the following results. Of the 
 two elements which fix the magnitude of the plane- 
 tary orbits, the principal axes, and the eccentricity, the 
 axes remain invariable, while the eccentricity oscil- 
 lates between narrow and fixed limits. In the long 
 run, therefore, the magnitudes of the orbits are 
 preserved. 
 
 Of the three elements which give position to the 
 planetary orbits, viz : the place of the perihelion, the 
 lines of nodes, and the inclinations, the two first ever 
 vary in the same direction, and accomplish their res- 
 toration at the end of vast periods of revolution, 
 while the inclinations vibrate between narrow and 
 prescribed limits. 
 
 One more point, and we close this wonderful inves- 
 tigation. The last question which presents itself is 
 this : — May not the periodic times of the planets be 
 so adjusted to each, as that the results of certain con- 
 figurations may be ever repeated without any com- 
 pensation, and thus, by perpetual accumulation, finally 
 effect a destruction of the system? 
 
 If the periodic times of two neighboring planets 
 
STABILITY OF THE PLANETARY SYSTEM. 183 
 
 were exact multiples of the same quantity, or if the 
 one was double the other, or in any exact ratio, then 
 the contingency would arise, above alluded to, and 
 there would be perturbations which would remain 
 uncompensated. A near approach to this condition 
 of things actually exists in the system, and gave 
 great trouble to geometers. It was found, on com- 
 paring observations, that the mean periods of Jupiter 
 and Saturn were not constant — that one was on the 
 decrease, while the other was on the increase. This 
 discovery seemed to disprove the great demonstration 
 which had fixed as invariable the major axes of 
 the planetary orbits, and guaranteed the stability of 
 the mean motions. It was not until after Laplace 
 had instituted a long and laborious research, that the 
 phenomenon was traced to its true origin, and was 
 found to arise from the near commensurability of the 
 periodic times of Jupiter and Saturn — five of Jupiter's 
 periods being nearly equal to two of Saturn's. In 
 case the equality were exact, it is plain that if the 
 two planets set out from the same straight line drawn 
 from the sun, at the end of a cycle of five of Jupiter's 
 periods, or two of Saturn's, they would be again found 
 in the same relative positions, and whatever effect the 
 one planet had exerted over the other would again be 
 repeated under the same precise circumstances. Hence 
 would arise derangements which would progress in 
 the same direction, and eventually lead to permanent 
 derangement of the system. 
 
 But it happens that five of Jupiter's periods are not 
 exactly equal to two of Saturn's, and in this want of 
 equality safety is found. The difference is such, 
 that the point of conjunction of the planets does not 
 
184 STRUCTURE OF THE UNIVERSE. 
 
 fall at the same points of their orbits, but at the end 
 of each cycle is in advance by a few degrees. Thus 
 the conjunction slowly works round the orbits of the 
 planets, and, in the end, the effect produced on one 
 side of the orbit is compensated for on the other, and a 
 mean period of revolution comes out for both planets, 
 which is invariable. In the case of Jupiter and Sat- 
 urn, the entire compensation is not effected until after 
 a period of nearly a thousand years. 
 
 A similar inequality is found to exist between the 
 earth and Venus, with a period much shorter, and 
 producing results much less easily observed. In no 
 instance do we find the periods of any two planets 
 in an exact ratio. They are all incommensurable 
 with each other, and in this peculiar arrangement 
 we find the stability of the entire system is secured. 
 
 So far, then, as the organization of the great plan 
 etary system is concerned, we do not find within 
 itself the elements of its own destruction. Mutation 
 and change are everywhere found — all is in motion — 
 orbits expanding or contracting — their planes rocking 
 up and down — their perihelia and nodes sweeping in 
 opposite directions round the sun, — but the limits of 
 all these changes are fixed ; — these limits can never 
 be passed, and at the end of a vast period, amounting 
 to many millions of years, the entire range of fluctua- 
 tion will have been accomplished, the entire system, 
 planets, orbits, inclinations, eccentricities, perihelia, 
 and nodes, will have regained their original values 
 and places, and the great bell of eternity will have 
 then sounded one. 
 
 Having reached the grand conclusion of the sta- 
 bility of the system of Dlanets, in their reciprocal in- 
 
STABILITY OF THE PLANETARY SYSTEM. 185 
 
 fluences, and that no element of destruction is found 
 in the organization, we propose next to inquire 
 whether the same features are stamped on the sub- 
 ordinate groups composing the planetary system. — 
 As our limits will not permit us to enter into a full 
 examination of all the subordinate groups, we shall 
 confine our remarks to our own earth and its satellite, 
 Jupiter and his satellites, and to Saturn, his rings and 
 moons. We shall, in this examination, find it practi- 
 cable to answer, to some extent, the inquiry as to 
 whether either of these systems has received any 
 shock from external causes. We know nothing as 
 to the future, and can, in this particular, only form 
 our conjectures as to what is to be, from what has 
 been. 
 
 We commence our inquiry by an examination of 
 two questions, viz : — Is the velocity of rotation of the 
 earth on its axis absolutely invariable ? Has the re- 
 lation between the earth and moon ever been dis- 
 turbed by any external cause ? There is nothing so 
 important to the well being of our planet and its in- 
 habitants as absolute invariability in the period of its 
 axical rotation. The sidereal day is the great unit 
 of measure for time, and is of the highest consequence 
 in all astronomical investigations. If causes are 
 operating, either to increase or decrease the velocity 
 of rotation, a time will come when the earth will 
 cease to rotate, or else acquire so great a velocity as 
 to destroy its figure, and, in the end, scatter its parti- 
 cles in space. 
 
 It is difficult to ascertain from theory a perfectly 
 satisfactory answer to the question of the invariable 
 velocity of rotation of the earth, but Laplace has 
 a 2 
 
186 STRUCTURE OF THE UNIVERSE. 
 
 demonstrated that the length of the day has not va- 
 ried by the hundredth of one second during the last 
 two thousand years — that is, the length of the day is 
 neither greater nor less than it was two thousand 
 years ago by the hundredth of a second. The reason- 
 ing leading to this remarkable result is simple, and 
 may be readily comprehended by all. Two thousand 
 years ago, the duration of the moon's period of revo- 
 lution around the earth was accurately determined, 
 and was expressed in days and parts of a day. The 
 measure of the same period has been accomplished 
 in our own time, and is expressed in days and parts 
 of a day. Now all the causes operating to change 
 the moon's period of revolution are known, and may 
 be applied. When this is done, it is found that the 
 moon's period now and two thousand years ago, agree 
 precisely, being accomplished in the same number of 
 days and parts of a day — which would be impossible, 
 if the unit of measure, the day, had varied ever so 
 slightly. 
 
 The extraordinary relation existing between the 
 moon's period in her orbit and the time occupied in 
 her axical rotation, gives us the opportunity of ascer- 
 taining whether our system has received any external 
 shock. These two periods are so accurately adjusted, 
 that in all respects an exact equality exists. The 
 moon ever turns the same hemisphere to the earth, 
 and ever will, unless some external cause should 
 arise to disturb the perfect harmony which now reigns. 
 It is not my purpose to explain why it is that this 
 phenomenon exists. I merely desire to state, that 
 this delicate balancing of periods furnishes an admi- 
 rable evidence that, for several thousands of years, at 
 
STABILITY OF THE PLANETARY SYSTEM. 187 
 
 least, no shock has been received by the earth and it3 
 satellite. Steadily have they moved in their orbits, 
 subject only to the influence of causes originating in 
 the constitution of the mighty system of which they 
 constitute a part. 
 
 Moving out to a more complex system, we find in 
 the remarkable arrangement of the satellites of Jupi- 
 ter, a delicate test for the action of sudden and extra- 
 neous causes. Here we find the periodic times of the 
 satellites so related, that a thousand periods of the 
 first, added to two thousand periods of the third, will 
 be precisely equal to three thousand periods of the 
 second. This delicate balancing of periods would be 
 destroyed by the action of any external shock, such 
 as might be experienced from the collision of a comet 
 sweeping through the system. Thus far, we know 
 that no disturbance has entered, and a knowledge of 
 facts will now pass down to posterity, which will give 
 the means of ascertaining exactly the influence of 
 all disturbing causes which do not form a part of the 
 great system. 
 
 The last subordinate group, and the most extraor- 
 dinary one to which I will at this time direct your 
 attention, is that of Saturn and his rings. Here we 
 find a delicacy of adjustment and equilibrium far ex- 
 ceeding any thing yet exhibited in our examinations. 
 This great planet is surrounded certainly by two, 
 probably by three, immense rings, which are formed 
 of solid matter, in all respects like that constituting 
 the central body. These wonderful appendages are 
 nowhere else to be found, throughout the entire solar 
 system, at least with certainty. Their existence has 
 elsewhere been suspected, but around Saturn they are 
 
je88 STRUCTURE OF THE UNIVERSE. 
 
 seen with a perfection and distinctness which defies 
 all scepticism as to their actual existence. The di- 
 ameter of the outer ring is no less than 176,000 miles. 
 Its breadth is 21,000 miles, while its thickness does not 
 exceed one hundred miles. The inner ring is separa- 
 ted from the outer one by a space of about 1,800 miles, 
 — its breadth 34,000 miles, its inner edge being about 
 20,000 miles from the surface of the planet. — Its thick- 
 ness is the same as that of the outer ring. These ex- 
 traordinary objects are rotating in the same direction 
 as the planet, and with a velocity so great that objects 
 on the exterior edge of the outer ring are carried 
 through space with the amazing velocity of nearly 
 50,000 miles an hour, or nearly fifty times more 
 swiftly than the objects on the earth's equator. 
 
 What power of adjustment can secure the stability 
 of these stupendous rings ? No solid bond fastens 
 them to the planet — isolated in space, they hold their 
 places, and revolving with incredible velocity around 
 an imaginary axis, they accompany their planet in 
 its mighty orbit round the sun. Such is the exceed- 
 ing delicacy with which this system is adjusted, that, 
 the slightest external cause once deranging the equili- 
 brium, no readjustment would be effected. The rings 
 would be thrown on the body of the planet, and the 
 system would be destroyed. 
 
 To understand the extraordinary character of this 
 system, we will explain a little more fully the three 
 different kinds of equilibrium. The first is called an 
 equilibrium of instability, and is exemplified in the 
 effort to balance a rod on the tip of the finger. The 
 slightest deviation from the exact vertical, increases 
 itself constantly, until the equilibrium is destroyed. — 
 
STABILITY OF THE PLANETARY SYSTEM. 159 
 
 In case the same rod be balanced on its centre on the 
 finger, it presents an example' of an equilibrium of 
 indifference ; that is. if it be swayed slightly to the one 
 side or the other, there is no tendency to restore itself, 
 or to increase its deviation. — It remains indifferent to 
 any change. Take the same rod, and suspend it like 
 a pendulum. Z^ow cause it to deviate from the ver- 
 tical to the right or left, and it returns of itself to the 
 condition of equilibrium. This is an equilibrium of 
 stability. We have already seen that this is the kind 
 of equilibrium which exists in the planetary system. 
 There are constant deviations, but a perpetual effort 
 is making to restore the object to its primitive 
 condition. 
 
 Now in case the rings of Saturn are homogeneous, 
 equally thick, and exactly concentric with the planet, 
 their equilibrium is one of instability. The smallest 
 derangement would find no restorative power, and 
 would even perpetuate and increase itself, until the 
 system is destroyed. For a long time it was believed 
 that the rings were equally thick, and concentric with 
 the planet, but when it was discovered that such fea- 
 tures would produce an equilibrium of instability, and 
 that there existed no guarantee for the permanency 
 of this exquisite system, an analytic examination was 
 made, which led to this singular result, viz : — To 
 change the equilibrium of instability into one of sta- 
 bility, all that is necessary is to make the ring thicker 
 or denser in some parts than in others, and to cause 
 its centre of position to be without the centre of the 
 planet, and to perform around that centre a revolution 
 in a minute orbit. Finding these conditions analyti- 
 cally, it now became a matter of deep interest to as- 
 
190 STRUCTURE OF THE UNIVERSE. 
 
 certain whether these conditions actually existed in 
 nature. The occasional disappearance of the ring, in 
 consequence of its edge being presented to the eye of 
 the observer, gave a capital opportunity of determin. 
 ing whether it was of uniform thickness. On these 
 rare occasions, in the most powerful telescopes, the 
 ring remains visible edgewise, and looks like a slen- 
 der fibre of silver light drawn across the diameter of 
 the planet. In the gradual wasting away of the two 
 extremities of the ring, it has been remarked, that the 
 one remains visible longer than the other. As the ring 
 is swiftly revolving, neither extremity can, in any 
 sense, be regarded as fixed, and hence sometimes the 
 one, sometimes the other, fades first from the sight. 
 An exactly uniform thickness in the ring would ren- 
 der such a phenomenon impossible, and hence we 
 conclude, that the first condition of stability is ful- 
 filled, — the rings are not equally thick throughout. 
 
 The micrometer was now applied to detect an ec- 
 centricity in the central point of the ring. Recent 
 examinations by Struve and Bessel have settled this 
 question in the most satisfactory manner. The centre 
 of the ring does not coincide with that of the planet, 
 and it is actually performing a revolution around the 
 centre of the planet in a minute orbit, thus forming 
 the second delicate condition of equilibrium. The 
 analogy of the great system is unbroken in the sub- 
 ordinate one. For more than two hundred years 
 have these wonderful circles of light whirled in their 
 rapid career under the eye of man, and freed from 
 all external action, they are so poised that millions 
 of years shall in nowise affect their beautiful organi- 
 zation. Their, graceful figures and beautiful light 
 
STABILITY OF THE PLANETARY SYSTEM. 191 
 
 shall greet the eyes of the student of the heavens 
 when ten thousand years shall have rolled away. 
 
 Thus do we find that God has built the heavens in 
 wisdom, to declare his glory, and to show forth his 
 handy-work. There are no iron tracks, with bars and 
 bolts, to hold the planets in their orbits. Freely in 
 space they move, ever changing, but never changed ; 
 poised and balancing; swaying and swayed ; disturb- 
 ing and disturbed, onward they fly, fulfilling with un- 
 erring certainty their mighty cycles. The entire 
 system forms one grand complicated piece of celestial 
 machinery ; — circle within circle ; wheel within wheel ; 
 cycle within cycle ; — revolutions so swift as to be 
 completed in a few hours ; movements so slow that 
 their mighty periods are only counted by millions of 
 years. Are we to believe that the Divine Architect 
 constructed this admirably adjusted system to wear 
 out, and to fall in ruins, even before one single revolu- 
 tion of its complex scheme of wheels had been per- 
 formed? No. — I see the mighty orbits of the planets 
 slowly rocking to and fro, their figures expanding and 
 contracting, their axes revolving in their vast periods; 
 but stability is there. Every change shall wear 
 away, and after sweeping through the grand cycle of 
 cycles, the whole system shall return to its primitive 
 condition of perfection and beauty. 
 
LECTURE VII. 
 
 THE DISCOVERY OF NEW PLANETS. 
 
 In the earliest ages of the world, the keen vision 
 of the old astronomers had detected the princi- 
 pal members of the planetary system. Even Mer- 
 cury, which habitually hovers near the sun, and whose 
 light is almost constantly lost in the superior bril- 
 liancy of that luminary, did not escape the eagle 
 glance of the primitive students of the stars. For 
 many thousand years no suspicion arose in the mind, 
 as to the existence of other planets, belonging to the 
 great scheme, and which had remained invisible from 
 their immense distance or their minute dimensions. — 
 Indeed the grand investigations which have recently 
 engaged our attention, the mutation of the planetary 
 orbits, their perpetual oscillations and final restora- 
 tion^ the equilibrium of the whole system, had been 
 prosecuted and completed before the mind gave itself 
 seriously to the contemplation of invisible worlds. 
 
 The singularly inquisitive genius of Kepler, over 
 whom analogy seems to have ever played the tyrant, 
 in an examination of the interplanetary spaces, find- 
 ing these to increase with regularity in proceeding 
 outward from the sun, until reaching the space be- 
 tween Mars and Jupiter, which was out of all pro- 
 portion too great, conceived the idea that an invisible 
 planet revolved in this space, and thus completed the 
 
 R (193) 
 
194 STRUCTURE OF THE UNIVERSE. 
 
 harmony of the system. The space from the orbit of 
 Mercury to that of Venus is 31,000,000 of miles ; from 
 the orbit of Venus to that of the earth is 27,000,000 of 
 miles ; from the earth's orbit to that of Mars is 50,- 
 000,000 of miles, but between the orbit of Mars and 
 that of Jupiter, there exists the enormous interval of 
 859,000,000 of miles. The order is again resumed 
 between the orbits of Jupiter and Saturn, and from 
 these slender data Kepler boldly predicted that a time 
 would come when a planet would be found interme- 
 diate between the orbits of Mars and Jupiter, whose 
 discovery would establish a regular progression in 
 the interplanetary spaces. For nearly two hundred 
 years this daring speculation was regarded as one of 
 the wild dreams of a great, but visionary mind. 
 
 Towards the close of the eighteenth century, when 
 the planetary orbs had been studied with great care, 
 and a comparatively accurate knowledge of their per- 
 turbations had been reached, certain unexplained ir- 
 regularities gave rise to the suspicion that the move- 
 ments of Saturn might be disturbed by the action of 
 an unknown planet revolving in a vast orbit, remote 
 from, and far beyond that of Saturn. These specula- 
 tions led to no serious results, and it was only by a 
 fortunate accident that, on the 13th of March, 1781, 
 Sir William Herschel noticed a small star of remarka- 
 ble appearance, which happened to fall in the field 
 of his telescope. On applying a greater magnifying 
 power, the strange star showed unequivocal symptoms 
 of increased dimensions. Its position among the 
 neighboring stars was noticed with care, and by an 
 examination on the following evening, the stranger 
 was found to have sensibly changed position. A few 
 
DISCOVERY OF NEW PLANETS. 195 
 
 nights sufficed to establish the fact that the newly dis- 
 covered body was actually a wandering star, and no; 
 for a moment dreaming of the discovery of a new 
 planet, Herschel announced to the world that he had 
 found a remarkable comet. Efforts were made to ob- 
 tain the orbit of the stranger, on the hypothesis, that 
 like those of all the then known comets, it was ex- 
 tremely elongated. Maskelyn and Lexell soon reached 
 the conclusion that no eccentric orbit could possibly 
 represent the motions of the newly discovered star 
 and on a close and diligent examination, it was a r . 
 last discovered to be a primary planet, revolving in 
 an orbit nearly circular, and almost coincident with 
 the plane of the ecliptic. Its motion was progressive, 
 like the other planets, and its vast orbit was only 
 completed at the end of eighty-four of our years. It a 
 distance from the sun was found to be no less than 
 1,800,000,000 of miles, and its dimensions such that out 
 of it might be formed more than eighty worlds as 
 large as the earth. 
 
 This great discovery excited the highest interest in 
 the astronomical w r orld. From the earliest ages, the 
 mighty orbit of Saturn had been regarded as forming 
 the boundary of the vast scheme of planets depend- 
 ant on the sun. Its slow and majestic motion, it- 
 great period and distance, and the wonderful mag- 
 nificence of its rings and moons, seemed to render it 
 a fitting object to guard the frontiers of the mighty 
 system with which it was associated. But the su- 
 premacy of Saturn was now gone forever, and its 
 sentinel position was usurped by Uranus, whose 
 grand orbit expanded to twice their original dimen- 
 sions the boundaries of the solar system. Far sweep- 
 
106 STRUCTURE OF THE UNIVERSE. 
 
 ing in the depths of space, this new world pursued 
 its solemn journey, flinging back the light of its 
 parent orb, steadily obedient to the great law of 
 universal gravitation, wnich held the old planets true 
 to their changing orbits. 
 
 Another unit in the number of interplanetary spaces 
 was thus given, and the law which might possibly 
 regulate the distances ot the planets from the sun 
 was sought after with an interest and perseverance 
 which could not long fail of its reward. No exact 
 progression was indeed discovered, but the following 
 remarkable empirical law was detected by Prof. Bode : 
 Write the series 3 b 12 24 48 96 192, &c. 
 Add to each term 4444444 4 
 The sums are 4 7 10 16 28 52 100 196. 
 
 Now if 10 be assumed as the earth's distance from 
 the sun, the other terms of the series will represent 
 very nearly the distances of the planets, thus : 
 
 4 7 10 16 28 52 100 196 
 
 Mercury, Venus, Earth, Mars, — , Jup., Saturn, Uranus. 
 The fifth term in the series is blank, and falls exactly 
 in the enormous interval which exists between the 
 orbits of Mars and Jupiter, precisely where Kepler 
 had predicted a new planet would be found. As early 
 as 1784, three years after the discovery of Uranus, 
 Baron de Zach, struck w T ith the remarkable law of 
 Bode, even went so far as to compute the probable 
 distance and period of the now generally suspected 
 planet. The impression that a new world would 
 soon be added to the system grew deeper and stronger 
 in the minds of astronomers, until finally, in 1800, at 
 a meeting held at Lilienthal, by six distinguished ob- 
 servers, the subject was discussed with deep earnest- 
 
DISCOVERY OF NEW PLANETS. 197 
 
 ness, and it was finally resolved that the long sus- 
 pected, but yet undiscovered world, should be made 
 the object of strict and persevering research. The 
 range of the Zodiac was divided into twenty-four 
 parts, and distributed among an equal number of ob- 
 servers, whose duty it was to scrutinize their particu- 
 lar regions, and detect, if possible, any moving body 
 which might show itself among the fixed stars. 
 
 In case it were possible to note down, with perfect 
 precision, the relative places and magnitudes of all 
 the stars in a given region, any subsequent changes 
 which might occur would be easily recognized. In 
 other language, could a daguerreotype picture of any 
 region in the heavens be made to-night, and at the 
 end of a year another picture of the same region, 
 could be taken, by comparing the number of stars in 
 the one picture with that in the second, in ca^e any 
 one had wandered away from its place, or a stranger 
 had come to occupy a place within the limits of the 
 pictured region, it would be an easy matter to ascer- 
 tain either the lost star, or the newly arrived stranger. 
 Now, although a daguerreotype picture cannot be 
 had, yet, by observation, the exact relative positions 
 of all the visible stars may be mapped out, and a 
 picture formed, which shall become the ready means 
 of detecting future changes. 
 
 Such was the method of examination adopted by 
 the congress of astronomers" assembled at Lilienthal, 
 in 1800. The organization was made.- — Baron de 
 Zach was elected president, and Schroeter was chosen 
 perpetual secretary. To those who have paid but 
 little attention to the circumstances under which this 
 strange enterprise was undertaken, nothing can ap- 
 r 2 
 
198 STRUCTURE OF THE UNIVERSE. 
 
 pear more wild and chimerical. To commence a 
 prolonged research for an invisible world, one that 
 no keenness of vision could detect, and which never 
 could be revealed but by telescopic aid, a world whose 
 magnitude was so small that it would not appear so 
 large as a star of the smallest size visible to the naked 
 eye, and one which must be sought out and detected, 
 not by its planetary disc, but by its wanderings 
 among thousands of stars, which it in all respects 
 resembled, and from which it could in no wise be dis- 
 tinguished, but by its motion, seemed like a w r asting 
 of time and utter throwing away of labor and energy. 
 Piazzi, of Palermo, in Sicily, was one of the planet 
 searching association. He had already distinguished 
 himself as an eminent and accurate observer, and had 
 with indefatigable zeal constructed a most extensive 
 catalogue of the relative places of the fixed stars, 
 and thus, in some sense, anticipated a part of the la- 
 bor that the research for the suspected planet contem- 
 plated. Assisted by his own and by preceding cata- 
 logues, he entered on the great work with the energy 
 and zeal which distinguished all his great astronomi- 
 cal efforts. On the evening of the first day of the 
 year 1801, this astronomer had his attention attracted 
 by a small star in the constellation of the Bull, which 
 he took to be one recorded in the catalogue of Mayer; 
 but on examination, it was found not to occupy any 
 place either on Mayer's or his own catalogue. Yet it 
 was so small that it was an easy matter to account 
 for this fact, by its having been overlooked in preced- 
 ing explorations of the region in which it was found. 
 With intense anxiety the astronomer awaited the 
 evening of the following night, to settle the great 
 
DISCOVERY OF NEW PLACETS. 199 
 
 question whether the newly detected star was a 
 fixed or moving body. On the evening of the 2d of 
 January he repaired to his observatory, and so soon 
 as the fading twilight permitted, directed the telescope 
 to the exact point in which,, on the preceding evening, 
 his suspicious star had been located. The spot was 
 blank ! But another, which was distant 4' in right 
 ascension, and SV in declination, which, on the pre- 
 vious night had certainly been vacant, was now 
 gleaming with the bright little object which, on the 
 preceding evening, had so earnestly fixed his atten- 
 tion, and for which he was again so anxiously seek- 
 ing. Night after night he watched its retrograde mo- 
 tion, — a motion precisely such as it ought to have, in 
 case it were the long desired planet, — until, on the 
 12th, it became stationary, and then slowly commenced 
 progressing in the order of the signs. Piazzi was 
 unfortunately taken ill : his observations were sus- 
 pended, and such was the difficulty of intercommuni- 
 cation, that, although he sent intelligence of his dis- 
 covery to Bode and Orani, associates in the great 
 enterprise, the newly discovered body was already 
 lost in the rays of the sun, before it became possible 
 to renew the train of observations by which its orbit 
 might be made known. Piazzi feared to announce 
 the newly discovered body to be the suspected planet. 
 His observations were few, and he was the only per- 
 son in the world who had seen it. Bode no sooner 
 received the intelligence of its discovery, than he at 
 once pronounced it to be the long sought planet, and 
 from the scant}' materials furnished by Piazzi. Oibers, 
 Burkhart, and Gauss, all computed the elements of its 
 orbit, settled the great fact that it was a superior 
 
200 STRUCTURE OF THE UNIVERSE. 
 
 planet, and that its orbit was included between those 
 of Mars and Jupiter. Some doubt, however, yet 
 rested on the subject, and the disengagement of the 
 planet from the beams of the sun was awaited with 
 the deepest interest. 
 
 Several months passed away. Every eye and every 
 telescope was directed to the region in the heavens 
 where the new planet was expected to be found. The 
 most scrutinizing search was made for its rediscovery, 
 but without any success. But for the high reputation 
 of Piazzi, his well known accuracy and honesty, 
 doubts would have arisen as to whether he had not 
 been self-deceived, or was intentionally deceiving 
 others. The subject became of deeper and deeper in- 
 terest. The world began to sneer at a science which 
 could find a body in the heavens, and then forever lose 
 it. We must remember that Piazzi had followed it 
 through only about 4° out of 360° of its orbit, and 
 on this narrow basis a research was to be instituted, 
 having for its object the determination of the exact 
 position which the lost planet must occupy. Gauss, 
 then comparatively a young man, and little known as 
 a computer, had conceived a new method of deter- 
 mining the orbits of comets, from a very few and very 
 closely consecutive observations. Here was an ad- 
 mirable opportunity of giving a practical proof of 
 the power of his new method. The long and intri- 
 cate calculation was finished, the place of the lost 
 planet determined, the telescope was directed to the 
 spot, and lo ! the beautiful little orb flashed once more 
 on the eager gaze of the youthful astronomer. For 
 one entire year had the planet been sought in vain, 
 and but for the powerful analysis of Gauss, nothing 
 
DISCOVERY OF NEW PLANETS. 201 
 
 but years of persevering toil could have wiped away 
 the reproach which rested on astronomy. 
 
 A sufficient number of observations were soon 
 made to reveal the orbitual elements of the planet ; 
 now named Ceres. It was found, in all respects, to 
 harmonize in its movements with the older planets, 
 and its orbit filled precisely the blank in the strange 
 empirical law discovered by Bode. The period and 
 distance hypothetically computed from that law six- 
 teen years before, by Baron de Zach, were verified in 
 the most remarkable manner by the actual period and 
 distance of Ceres. Order and beauty now reigned in 
 the planetary system, and a most signal victory had 
 crowned the efforts of astronomical science. 
 
 The only remarkable difference between the new 
 planet and the old ones, consisted in its minute size, 
 the great obliquity of its orbit, and the dense atmos- 
 phere by which it appears to be surrounded. Its di- 
 ameter is so small as to render its measure next to 
 impossible, and the best practical astronomers differ 
 widely in their results. Sir William Herschel makes 
 its diameter only 163 miles, while Schroeter cannot 
 make it less than ten times that quantity. The mean 
 of these two extremes is probably near the truth. — 
 No satellites have been found in attendance on this 
 minute planet, although Sir William Herschel sus- 
 pected the existence of two at one time, a suspicion 
 which subsequent observations have not confirmed. 
 
 The beautiful order established in the solar system 
 by the discovery of Ceres was a subject of the highest 
 gratification to the whole astronomical world, and 
 especially to those who had been instrumental in 
 reaching this remarkable result. An opportunity had 
 
202 STRUCTURE OF THE UNIVERSE. 
 
 scarcely presented itself for the expression of delight 
 occasioned by this announcement, before all interested 
 were startled by a declaration from Dr. Olbers, of 
 Bremen, that he had found another planet on the 
 evening of the 28th of March, 1802, with a mean 
 distance and periodic time almost identical with those 
 of Ceres. This discovery broke through all the analo 
 gies of the solar system, and presented the wonder- 
 ful anomaly of two planets revolving in such close 
 proximity, that their orbits, projected on the plane of 
 the ecliptic, actually intersected each other. 
 
 The new planet was called Pallas, and is of a mag- 
 nitude about equal to that of Ceres. Its orbit is 
 greatly inclined to the plane of the ecliptic, and its 
 eccentricity is very considerable. The existence of 
 these small planets, in such near proximity, for a long 
 while perplexed astronomers. At length Olbers sug- 
 gested that these minute bodies might be the frag- 
 ments of a great world, rent asunder by some internal 
 convulsion of sufficient power to produce the terrific 
 result, but of a nature entirely beyond the boundary 
 of conjecture. 
 
 Extraordinary as this hypothesis may appear, the 
 results to which it led are not less remarkable. If a 
 world of large size had been actually burst into frag- 
 ments, it is easy to perceive that these fragments, all 
 darting away in the orbits due to their impulsive forces, 
 would start from the same point, and hence would 
 return at different intervals indeed, but would all 
 again pass through the point of space occupied by 
 the parent orb when the convulsion occurred. Hav- 
 ing found two of these fragmentary worlds, the point 
 of intersection of their orbits would indicate the re- 
 
DISCOVERY OF NEW PLANETS. 203 
 
 gion through which the other fragments might be 
 expected to pass, and in which they might possibly 
 be discovered. So reasonable did the views of Olbers 
 appear, that his suggestions were immediately acted 
 upon by himself and several distinguished observers, 
 and on the 2d of September, 1804, Mr. Harding, of 
 Lilienthal, while scrutinizing the very region indicated 
 by Olbers, detected a star of the eighth magnitude, 
 which seemed to be a stranger, and was soon recog- 
 nized to be another small planet, fully agreeing, in 
 all its essential characteristics, with the theory of 
 Olbers. The new world was named Juno, and is re- 
 markable for the eccentricity of its orbit. Its diame- 
 ter has not been well determined, owing to its minute 
 size. This discovery gave to the theory of Olbers the 
 air of reality, and finding the nodes of the three frag- 
 ments to lie in the opposite constellations Cetus and 
 Virgo, he prosecuted his researches in these regions 
 with redoubled energy and zeal. 
 
 His efforts were not long without their reward. On 
 the 29th of March, 1807, he detected the fourth of his 
 fragments in the constellation Virgo, and very near 
 the point through which he had, for four years, been 
 waiting to see it pass. This was a most wonderful 
 discovery, and almost fixed the stamp of truth upon 
 the most extraordinary theory which had ever been 
 promulgated. This new asteroid was named Vesta 
 and for nearly forty years, the examinations which 
 were conducted revealed no new fragment, and it be- 
 gan to be regarded as positively ascertained, that all 
 the small bodies revolving in this region had been re- 
 vealed to the eye. 
 
 But on the 8th day of Dec, 1845, Mr. Hencke, of 
 
204 STRUCTURE OF THE UNIVERSE. 
 
 Dreisen announced to the world the discovery of an- 
 other asteroid, which was named Astrea. Before two 
 years had rolled round, the same indefatigable ob- 
 server discovered a sixth member in this wonderful 
 group, which was called Hebe. His success induced 
 other observers to undertake a similar examination, 
 and in a very short time the researches of Mr. Hind, 
 of London, were rewarded by the discovery of a 
 seventh and eighth asteroid, which were named Iris 
 and Flora. 
 
 Thus have we no less than *eight of these minute 
 worlds, revolving in orbits so nearly equal, that for 
 weeks and months these miniature orbs may sweep 
 along in space, almost within hail of each other. Let 
 us now return to an examination of the hypothesis 
 of Olbers, that these are the fragments of a world of 
 large size, which once occupied an orbit intermediate 
 between those of Mars and Jupiter. 
 
 If any internal convulsion could burst a world and 
 separate its fragments, it is readily seen that the frag- 
 ments of largest mass would move in orbits more 
 nearly coincident with that of the original planet, 
 while the smaller fragments would revolve in orbits 
 greatly inclined to the primitive one. This condition 
 is wonderfully fulfilled among the asteroids. The 
 larger planets, Ceres and Vesta, revolve in orbits 
 with small inclinations to the ecliptic, while the 
 smaller objects are in some instances found to move 
 in planes with very great inclinations. The force 
 necessary to burst a planet, and to give to its frag- 
 ments certain orbits, has been computed by Lagrange, 
 and he finds that in case any fragment is projected 
 with an initial velocity one hundred and twenty-one 
 
DISCOVERY OF NEW PLANETS. 205 
 
 times greater than that of a cannon ball, it would 
 become a direct comet, with a parabolic orbit, while a 
 primitive velocity one hundred and fifty-six times 
 greater than that of a cannon ball would cause the 
 fragments to revolve with a retrograde motion in the 
 curve of a parabola. Any less powerful force would 
 cause the fragment to revolve in ellipses ; and it is 
 probable that the force which operated to produce the 
 asteroids was not more than twenty or thirty times 
 greater than that of a cannon ball. Although the 
 theory of Olbers has received new accessions of 
 strength from the discovery of every new asteroid, it 
 would be wrong to regard it as one of the demon- 
 strated truths of astronomy. In the mean time, pow- 
 erful efforts are making to scour the heavens, and a 
 method of observation has been proffered to the Acad- 
 emy of sciences, of Paris, by which all the visible 
 fragments may be discovered within a period of four 
 years. Should this plan, which contemplates a di- 
 vision of the heavens among different astronomers, be 
 adopted, volunteers have already presented them- 
 selves, and the most interesting results may be 
 anticipated. 
 
 From this curious branch of astronomical inquiry 
 we turn to one of still deeper interest. In the exam- 
 inations for new planets, thus far, the telescope has 
 been the sole instrument of research. Conjectures 
 based upon analogical reasoning, it is true, guided 
 the instrumental examinations, but the mind had 
 never dared to rise to the effort of reasoning its way 
 analytically to the exact position of an unknown 
 body. It has been reserved for our own day to pro- 
 duce the most remarkable and the boldest theorizing 
 S 
 
206 STRUCTURE OF THE UNIVERSE. 
 
 which has ever marked the career of astronomical 
 science. — I refer to the analytic effort to trace out the 
 orbit, define the distance, and weigh the mass of an 
 unknown planet as far beyond the extremest known 
 planet as it is from the sun. 
 
 I am fully aware of the difficulties by which I am 
 surrounded, when I invite your attention to this com- 
 plex and intricate subject; and I know how utterly 
 impossible it is, in a popular effort, to do any kind of 
 justice to the intricate and involved reasoning of the 
 great geometers, who have not only rendered them- 
 selves, but the age in which we live, illustrious by 
 their efforts to resolve this, the grandest problem 
 which has ever been presented for human genius. — 
 Trusting to your close attention, I shall attempt to 
 exhibit some faint outline of the train of reasoning 
 and the kind of research employed in rescuing an un- 
 known world from the viewless regions of space in 
 which it has been tracing its unknown orbit for ages 
 commensurate with the existence of the great system 
 of orbs of which it constitutes a part. 
 
 After the discovery of the planet Uranus, by Sir 
 William Herschel, geometers were not long in fitting 
 it with an orbit which represented in the outset, with 
 accuracy, its early movements. With this orbit it 
 became possible to trace its career backwards, and 
 to define its position among the fixed stars for fifty 
 or one hundred years previous to the date of its dis- 
 covery. This was actually done, with the hope of 
 finding that the place of the planet had been observed 
 and recorded by some astronomer, who ranked it 
 among the fixed stars. This hope was not disap- 
 pointed. The planet, believed to be a fixed star, had 
 
DISCOVERY OF, NEW PLANETS. 207 
 
 been seen and observed no less than nineteen differ- 
 ent times, by four different observers, through a period 
 running back nearly one hundred years previous to 
 the discovery of its planetary character by Herschel. 
 These remote observations were of the greatest value 
 as data for the determination of the elements of its 
 elliptic orbit, and for the computation of the mean 
 places, which might serve to predict its position in 
 coming years. 
 
 A distinguished astronomer, M. Bouvard, of the 
 Paris Academy of Sciences, about thirty years ago, 
 undertook the analytic investigation of the movements 
 of Uranus, and a computation of exact tables. He 
 was met, however, by difficulties which, in the state 
 of knowledge as it then existed, with reference to 
 this planet, were absolutely insurmountable. He 
 found it quite impossible to obtain any orbit which 
 w r ould pass through the places of the planet deter- 
 mined after its discovery, and through those positions 
 which had been fixed previous to that epoch. In this 
 dilemma it became necessary to reject the old obser- 
 vations as less reliable than the new ones, and the 
 learned computer leaves the problem for posterity to 
 resolve, carefully abstaining from any absolute de- 
 cision in the case. 
 
 His orbit, based upon the new or modern observa- 
 tions, and his tables being computed, it was hoped 
 that the theoretic places of the planet would there- 
 after coincide with the observed places, and that all 
 discrepancies which might not be fairly chargeable to 
 errors of observation, would be removed. In this ex- 
 pectation, however, the astronomical world was dis- 
 appointed ; and while the tables of Bouvard failed 
 
208 STRUCTURE OF THE UNIVERSE. 
 
 absolutely to represent the ancient observations, in a 
 few years they were but little more truthful in giving 
 the positions actually filled by the planet under the 
 telescope. The discrepancies between the theoretic 
 and actual places of the planet began to attract at- 
 tention many years since. As early as 1838, Mr. 
 Airy, Astronomer Royal of England, on a compari- 
 son of his own observations with the tables, found 
 that the planet was out of its computed track, by a 
 distance as great as the moon's distance from the 
 earth, and that it w r as actually describing an orbit 
 greater than that pointed out by theory. It seemed 
 that this remote body was breaking away from the 
 sun's control, or that it was operated on by some un- 
 known body' deep sunk in space, and which thus far 
 had escaped the scrutinizing gaze of man. 
 
 These deviations became so palpable as to attract 
 general attention, and various conjectures were made 
 with reference to their probable cause. Some were 
 disposed to regard the law of gravitation as some- 
 what relaxed in its rigorous application to this remote 
 body ; others thought the deviation attributable to 
 the action of some large comet, which might sway 
 the ph A et from its course; while a third set of philos- 
 ophers conjectured the existence of a large satellite 
 revolving about Uranus, and from whose attraction 
 the planet was caused to swerve from the computed 
 orbit. These conjectures were not sustained by any 
 show of reasoning, and were of no scientific value. 
 
 Such was the condition of the problem when it was 
 undertaken by a young French astronomer, not quite 
 unknown to fame in his own country, but compara- 
 tively at the beginning of his scientific career. The 
 
DISCOVERY OF NEW PLANETS. 209 
 
 friend of Arago, Leverrier's Cometary Investigations, 
 and more especially Jiis researches of the motions of 
 Mercury, had gained for him the confidence of this 
 distinguished savant, and Arago urged on his young 
 associate the importance of the great problem pre- 
 sented in the perturbations of Uranus, and induced 
 him to abandon other investigations, and concentrate 
 all the energies of his genius on this profound and 
 complex investigation. 
 
 The extraordinary powers of Leverrier as a mathe- 
 matical astronomer had been so successfully displayed 
 in his researches of the motions of Mercury, that it 
 deserves a passing notice. The old tables of this 
 planet, Leverrier believed to be defective. He there- 
 fore set about a thorough examination of its entire 
 theory, and after a rigid scrutiny, deduced a new set 
 of tables, from which the places of the planet might 
 be predicted with greater precision. 
 
 The transit of Mercury across the sun's disc, 
 which occurred on the 8th day of May, 1845, pre- 
 sented an admirable opportunity to test the truth of 
 the new theory of the young astronomer. Most un- 
 happily for his hopes, all observations in Pp "s were 
 rendered impossible by the clouds, which cove ed the 
 heavens during the entire day on which the transit 
 took place. While the computer was sadly disap- 
 pointed, I wavS more fortunate, for a pure and trans- 
 parent atmosphere favored this, the first astronomical 
 observation I ever made. A slight reference to this 
 occurrence may be pardoned. For three years I had 
 been toiling to complete a most difficult and labori- 
 ous enterprise, the erection of an astronomical ob- 
 servatory of the first class, in a country where none 
 s 2 " 
 
210 STRUCTURE OF THE UNIVERSE. 
 
 had ever existed. Amid difficulties and perplexities 
 which none can ever know, the work had moved on, 
 and at length I had the high satisfaction of seeing 
 mounted one of the largest and most perfect instru- 
 ments in the world. I had arranged and adjusted its 
 complex machinery — had computed the exact point 
 on the sun's disc where the planet ought to make its 
 first contact — had determined the instant of contact 
 by the old tables, and by the new ones of Leverrier, 
 and with feelings which must be experienced to be 
 realized, five minutes before the computed time of 
 contact, I took my post at the telescope to watch the 
 coming of the expected planet. After waiting what 
 seemed almost an age, I called to my friend how much 
 time was yet to pass, and found but one single min- 
 ute out of five had rolled heavily away. The watch 
 was again resumed. Long and patiently did I hold 
 my place, but again was forced to call out, how speeds 
 the time? and was answered that there was yet want- 
 ing two minutes of the computed time of contact. — 
 With steadfast eye, and a throbbing heart, the vigil 
 was resumed, and after waiting what seemed an age, 
 I caught the dark break which the black body of the 
 planet made on the bright disc of the sun. Now ! I 
 exclaimed ; and within sixteen seconds of the computed 
 time did the planet touch the solar disc, at the precise 
 point at which theory had indicated the first contact 
 would occur. 
 
 The planet was followed across the disc of the sun, 
 round and sharp, and black, and every observation 
 confirmed the superior accuracy of the new tables of 
 Leverrier. While the old tables were out fully a min- 
 ute and a half in the various contacts, those of Le- 
 
DISCOVERY OF NEW PLANETS. 211 
 
 verrier were in error by only about sixteen seconds as 
 a mean. 
 
 The great success of this investigation encouraged 
 the young astronomer to accept the difficult task 
 which Arago proposed for his accomplishment, and 
 he earnestly set about preparing the way for a full 
 discussion of the grand problem of the perturbations 
 of Uranus. The importance of the subject demanded 
 the greatest caution, and having determined to rely 
 solely on his own efforts, he at once rejected all that 
 had been previously done, and commenced the prob- 
 lem at the very beginning. New analytic theories 
 were formed; elaborate investigations of the planets 
 Jupiter and Saturn, as disturbing bodies, were made, 
 and an entire clearing up of all possible causes of 
 disturbance in the known bodies of the system was 
 laboriously and successfully accomplished, and the in- 
 defatigable mathematician finally reached a point 
 where he could say, here are residual perturbations 
 which are not to be accounted for by any known exist- 
 ing body, and their explanation is to be sought beyond 
 the present ascertained limits of the solar system. 
 
 As early as the 10th of November, 1845, M. Lever- 
 rier presented a memoir to the Royal Academy of* 
 Sciences in Paris, in which he determined the exact 
 perturbations of Jupiter and Saturn on Uranus. This 
 was followed by a memoir, read before the academy 
 on the 1st of June, 1846, in which he demonstrates 
 that it is impossible to render an exact account of the 
 perturbations of Uranus in any other way than by 
 admitting the existence of a new planet exterior to the 
 orbit of Uranus, and whose heliocentric longitude he 
 fixes at 325° on the 1st of January, 1847. On the 
 
212 STRUCTURE OF THE UNIVERSE. 
 
 30th of August, 1846, a third memoir was presented 
 to the academy, in which the elements of the orbit of 
 the unknown planet are fixed, together with its mass 
 and actual position, with greater accuracy, giving on 
 the 1st of January, 1847, 326° 32' for its heliocentric 
 longitude. Finally, on the 5th of October, 1847, a fourth 
 memoir was read, relative to the determination of the 
 plane of the orbit of the constructive planet. 
 
 It is quite impossible to convey, in popular form, 
 the least idea of the profound analytic reasoning em- 
 ployed by M. Leverrier in this wonderful investiga- 
 tion. None but the rarest genius would have dared 
 to reach out 1,800,000,000 of miles into unknown re- 
 gions of space, to feci for a planet which had displaced 
 Uranus by an amount only about equal to four times 
 the apparent diameter of the planet Jupiter, as seen 
 with the naked eye — a quantity so small that no eye, 
 however keen and piercing, without telescopic aid, 
 could ever have detected it. Yet from this minute 
 basis was the magnificent superstructure to be reared 
 which should eventually direct the telescope to the 
 place of a new and distant world. To many minds, 
 the resolution of such a problem may appear utterly 
 beyond the powers of human genius, and without 
 one ray of light to illumine the midnight darkness 
 which surrounds it to them, they are disposed to re- 
 ject the entire subject. An attentive examination of 
 the following train of reasoning may at least demon- 
 strate that the problem is not quite so hopeless as it 
 would at first appear. 
 
 It was not necessary to extend researches to all 
 quarters of the heavens indifferently, in an effort 
 to find the unknown body. All the planets revolve 
 
DISCOVERY OF NEW PLANETS. 213 
 
 in planes nearly coincident with the plane of 
 the earth's orbit, and more especially do the distant 
 ones. Jupiter and Saturn and Uranus revolve in or- 
 bits but little inclined to the plane of the ecliptic. — 
 Hence, it was fair to conjecture that the new planet, 
 should it ever be found, would not violate this gen- 
 eral law, and a search for it was properly limited to 
 a narrow belt near the plane of the earth's orbit. — 
 The limits of research were thus brought dow T n to a 
 narrow zone, sweeping around the entire heavens in- 
 deed, but insignificant in extent, when compared with 
 the whole celestial sphere. 
 
 The next point of examination was the probable 
 distance of the unknown planet. Here, again, anal- 
 ogy came to the aid of Leverrier. The empirical 
 law of Bode, already explained in a former lecture, 
 showed that the remote planets increased their dis- 
 tances by a very simple law. Saturn was twice as 
 remote as Jupiter ; Uranus was at double the distance 
 of Saturn, and it was fair to conclude that the un- 
 known planet would be about twice as far from the 
 sun as Uranus. As a first approximation, then, its 
 distance was fixed at about 3,600,000,000 of miles 
 from the sun. Kepler's law, regulating the ratio be- 
 tween the distances and periods of the planets, gave 
 at once the time of revolution of the new planet, in 
 case its distance had been correctly assumed. In the 
 next place, it was fair to conclude that the orbit of 
 the new planet, like those of Jupiter, Saturn, and 
 Uranus, would not differ greatly from a circle. These 
 conjectures were, in some degree, confirmed by a very 
 simple train of reasoning with reference to the dis- 
 tance of the disturbing body. If it revolved in an 
 
214 STRUCTURE OF THE UNIVERSE. 
 
 orbit very near to that of Uranus, then its effect on 
 Uranus ought to be excessive, when compared with 
 its influence on Saturn, which was found not to be 
 the case. Again, if it revolved in an orbit very far 
 beyond the limit assigned above, its effect on Uranus 
 and Saturn would be very nearly the same, which 
 was not verified by examination. 
 
 Having thus roughly fixed limits for the orbit of the 
 unknown body, the work of the mathematician now 
 commences, having for its grand object the determin- 
 ation of the true places of the planet sought at some 
 given epoch, and such an orbit as will represent the 
 perturbations of Uranus in the most perfect manner. 
 To exhibit, in some faint degree, the difficulty of this 
 investigation, let us conceive that up to the 1st of 
 January, 1800, the solar system had consisted only of 
 the known bodies, the sun, planets, satellites, and 
 comets. The orbits of all the planets are accurately 
 ascertained, and their reciprocal influences computed 
 and known. The outermost planet, Uranus, revolves 
 in its vast orbit obedient to the great law of gravita- 
 tion, acknowledging the predominant influence of the 
 sun, and swaying more or less to the action of the 
 nearest planets, Saturn and Jupiter. Its predicted 
 and observed places coincide, and its movement is 
 followed with confidence and exactitude. 
 
 With a full and perfect knowledge of the orbit of 
 Uranus, let a new planet be created and projected in 
 a vast orbit exterior to, and remote from the orbit of 
 Uranus. The new body thus added to the system 
 would instantly derange the motions of Uranus, caus- 
 ing it to recede from the sun, and increasing its mean 
 period of revolution. In this case, the total effect of 
 
DISCOVERY OF NEW PLANETS. 215 
 
 the new planet on Uranus would be perturbation, and 
 it would not be quite impossible, even for one not 
 skilled in the higher mathematics, to see how the ac- 
 tion of the newly created planet on the movements 
 of the old one might actually reveal approximately 
 the position of the disturbing body. It is manifest 
 that when the two planets are in conjunction, or on a 
 right line passing through them and the sun, that at 
 this configuration the new planet would exert its 
 greatest power to drag the old one outward from the 
 sun, and if it could be found at what point of its orbit 
 the old planet actually receded to its greatest distance 
 from the sun, in the same direction, nearly, must the 
 disturbing body have been situated at that time. In 
 this way, we perceive, one place of the new planet 
 might be approximately found, and from its periodic 
 time it would be possible to trace it backward or for- 
 ward in its orbit, for the present supposed to be 
 circular. 
 
 The problem here presented is certainly sufficiently 
 difficult, yet its complexity is very far from being 
 equal to that presented in nature, and with which the 
 French geometer found himself obliged to grapple. — 
 Although unknown, the new planet did exist, and for 
 ages had silently pursued its unknown orbit round 
 the sun. Its influence on Uranus had been ever ac- 
 tive, and when the observations on Uranus were 
 made, and its places determined, from which its ellip- 
 tic elements were to be derived, these very places 
 were in part dependent on the action of the invisible 
 disturber, and hence a portion of its influence would 
 be darkly concealed in the orbit of Uranus ; and to 
 divide the entire effect of the new planet on the old 
 
216 STRUCTURE OF THE UNIVERSE. 
 
 one correctly between the disguised portion and that 
 producing real perturbation, was attended with the 
 greatest difficulty, and could only be reached by adopt- 
 ing certain positive hypotheses. Surrounded by all 
 these difficulties, Leverrier worked on, and with con- 
 summate art, so constructed his analytical machinery 
 as to meet and master every difficulty ; and he finally 
 announces to the world the figure of the orbit of his 
 imaginary planet, its distance, period of revolution, 
 and even the mass of matter it contains. 
 
 These important communications were made to the 
 French Academy of Sciences, on the 31st of August, 
 1846. On the 18th of the following month, M. Lever- 
 rier wrote to his friend M. Galle, of Berlin, requesting 
 him to direct his telescope to that point in the heavens 
 which his computations had revealed as the one occu- 
 pied by the constructive planet. The request was 
 readily complied with, and on the very first evening 
 of examination, a star of the eighth magnitude was 
 discovered, which was evidently a stranger in that 
 region, as it was not found on an accurate map of the 
 heavens including all stars of that magnitude. The 
 following evening was awaited with the deepest in- 
 terest, to decide, by the actual motion of the suspected 
 star, whether indeed it was the planet so wonderfully 
 revealed by the analysis of Leverrier. The night 
 came on. Again was the telescope directed to the 
 star in question, when lo ! it had moved from its for- 
 mer place, in a direction and with a velocity almost 
 precisely accordant with the theory of the French 
 geometer ! The triumph was perfect — the planet was 
 actually found. The new T s of its discovery flew in 
 
DISCOVERY OF NEW PLANETS. 217 
 
 every direction, and filled the world with astonishment 
 and admiration. 
 
 The exceeding accuracy with which its place had 
 been predicted, coming within less than one degree of 
 its actual position, gave to M. Leverrier the highest 
 confidence in the perfection of his analysis, and filled 
 with astonishment the oldest and most learned as- 
 tronomers. If scepticism had existed with reference 
 to the possible solution of so complex a problem — if 
 the theory of Leverrier had been regarded as a beau- 
 tiful speculation, ingenious and plausible, but vain in 
 its practical application, — the actual discovery of the 
 planet silenced all cavil, and put to flight every lin- 
 gering doubt. 
 
 As if anything were wanting, to give a more posi- 
 tive character to the computations of Leverrier, it 
 was now found that a young English mathematician, 
 Mr. Adams, of Cambridge, had actually accomplished 
 the resolution of precisely the same problem, and had 
 reached results almost identical with those of the 
 French geometer. This astonishing coincidence on 
 the part of two computers unknown to each other, 
 each starting from the same data, pursuing indepen- 
 dent trains of reasoning, and arriving at the same re- 
 sults, confirmed, as it would seem, in the fullest man- 
 ner, the accuracy of the resolution which had been 
 obtained. 
 
 On learning that Leverrier had communicated to 
 the Academy of Sciences, in August, 1846, his final 
 results, T wrote immediately, requesting the computed 
 place of his planet, with such directions as would 
 best guide me in a search which I desired to make for 
 it with the great refracting telescope of the Cincin- 
 
218 STRUCTURE OF THE UNIVERSE. 
 
 nati Observatory. But before my letter reached its 
 destination, the planet had been found, and the news 
 of its discovery soon reached the United States. It 
 was almost impossible for me to credit the statement 
 and I was almost disposed to believe that the pre- 
 diction of the planet's position had been mistaken for 
 its actual discovery. With these conflicting doubts, I 
 waited for the coming of night with a degree of anx- 
 iety and excitement which may be readily imagined. 
 I had no star chart to guide me in my search for the 
 planet ; — I had no meridian instrument with which to 
 detect it by its motion ; but I was not without hope 
 that the power of our great telescope might be suf- 
 ficient to select, at once, the planet from among the 
 fixed stars, by the magnitude of its disc. 
 
 As soon as the twilight disappeared, the instrument 
 was directed to the point in the heavens where the 
 planet had been found. I took my place at the finder, 
 or small telescope attached to the larger one, and my 
 assistant was seated at the great instrument. 
 
 On placing my eye to the finder, four stars of the 
 eighth magnitude occupied its field. One of them 
 was brought into the field of the large telescope, and 
 critically examined by my assistant, and rejected. A 
 second star was in like manner examined, and re- 
 jected. A third star, rather smaller and whiter than 
 either of the others, was now brought to the centre 
 of the field of the great telescope, when my assistant 
 exclaimed, "there it is! there is the planet! with a 
 disc as round, bright and beautiful as that of Jupiter !" 
 There, indeed, was the planet, throwing its light back 
 to us from the enormous distance of more than 3,000,- 
 000,000 of miles, and yet so clear and distinct, that 
 
DISCOVERY OF NEW PLANETS. 219 
 
 in a few minutes, its diameter was measured, and its 
 magnitude computed. 
 
 It is not my intention to follow, critically, the his- 
 tory of this wonderful discovery, yet there are some 
 facts so remarkable that it would be wrong to pass 
 them in silence. From the moment the planet was 
 detected in Berlin, it has been observed by all the 
 best instruments in the world, with a view of ascer- 
 taining how accurately theory had assigned the ele- 
 ments of its orbit. In consequence of its very slow 
 motion, it became a matter of the utmost importance 
 to obtain, if possible, some remote observation made 
 by an astronomer who might have entered the place 
 of the planet in his catalogue as a fixed star. Mr. 
 Adams, of England, led the way in the computation 
 of the elements of the orbit of the new planet, from 
 actual observation, and was followed by many other 
 computers, among them our countryman S. C. Walker, 
 then of the Washington Observatory. 
 
 Having obtained an approximate orbit, Mr. Walker 
 computed backwards the places of the new planet for 
 more than fifty years, and then examined the late 
 catalogues, in the hope of finding its place on some of 
 them as a fixed star. Among recent catalogues there 
 was no success, but in an examination of Lalande's 
 catalogue, he found an observation on a star of the 
 eighth magnitude, made May the 10th, 1795, which 
 was so near the place which his computation assigned 
 the planet at the same date, that he was led to sus- 
 pect that this star might indeed prove to be the new 
 planet. In case his conjecture were true, on turning 
 the telescope to the place occupied by the star, it 
 would be found blank, as its planetary motion would 
 
220 STRUCTURE OF THE UNIVERSE. 
 
 have removed it very far from the place which it oc- 
 cupied more than fifty years before. The experiment 
 having been made, no star could be found, and strong 
 evidence was thus presented that Mr. Walker had 
 actually found an observation of the new planet, giv- 
 ing its position in 1795 ; but in consequence of the 
 great discrepancy between the period of M. Leverrier 
 and that which would result from a reliance on this 
 observation of the new planet Neptune, Mr. Walker's 
 discovery was at first received with great hesitation. 
 A greater doubt was thrown over the matter from 
 the fact that Lalande had marked the observation as 
 uncertain, and it was only by reference to the original 
 manuscripts preserved in the Royal Observatory of 
 Paris that the doubts could be removed. 
 
 The discovery of Mr. Walker was subsequently 
 made by Mr. Petersen, of Altona, and the results of 
 these astronomers reached Paris on the same day. A 
 committee was at once appointed to examine the 
 original manuscript of Lalande, when a most remark- 
 able discovery was made. This astronomer had ob- 
 served a star of the eighth magnitude on the evening 
 of the 8th of May, 1795, and on the evening of the 
 10th, not finding the star as laid down, but observing 
 one of the same magnitude very near the former 
 place, he rejects the observation of the 8th of May as 
 inaccurate, and enters the observation of the 10th, 
 marking it doubtful. 
 
 On close examination, this star proves to be the 
 planet Neptune, and by this discovery we are placed 
 in possession of observations which render it possible 
 to determine the elliptic elements of the new planet 
 with great precision. These differ so greatly from 
 
DISCOVERY OF NEW PLANETS. 221 
 
 those announced by Leverrier and Adams previous to 
 the discovery, that Prof. Pierce, of Cambridge, Mass., 
 pronounces it impossible so to extend fairly the lim- 
 its of Leverrier's analysis as to embrace the planet 
 Neptune ; and that, although its mass, as determined 
 from the elongations of its satellite, renders it possi- 
 ble to account for all the perturbations of Uranus by 
 its action, in the most surprising manner, yet, in the 
 opinion of Prof. Pierce, it is not the planet to which 
 geometrical analysis directed the telescope. Lever- 
 rier rejects absolutely the result reached by the Amer- 
 ican geometer, and claims Neptune to be the planet 
 of his theory, in the strictest and most legitimate 
 sense. 
 
 Time and observation will settle the differences of 
 these distinguished geometers, and truth being the 
 grand object of all research, its discovery will be 
 hailed with equal enthusiasm by both of the dispu- 
 tants. In any event, the profound analytic research 
 of Leverrier is an ever-during monument to his 
 genius, and his name is forever associated with the 
 most wonderful discovery that ever marked the career 
 of astronomical science. 
 
 t2 
 
LECTURE VIII. 
 
 THE COMETARY WORLDS. 
 
 The wonderful characteristics which mark the flight 
 of comets through space; the suddenness with which 
 they blaze forth ; their exceeding velocity, and. their 
 terrific appearance ; their eccentric motions, sweeping 
 towards the sun from all regions and in all directions, 
 have rendered these bodies objects of terror and dread 
 in all ages of the world. While the planets pursue 
 an undeviating course round the sun, in orbits nearly 
 circular, and almost coincident with the plane of the 
 earth's orbit, all revolving harmoniously in the same 
 direction, the comets perform their revolutions in 
 orbits of every possible eccentricity, confined to no 
 particular plane, and moving indifferently in accord- 
 ance with, or opposed to, the general motion of the 
 planets. They come up from below the plane of the 
 ecliptic, or plunge downwards towards the sun from 
 above, sweep swiftly round this their great centre, 
 and with incredible velocity wing their flight far into 
 the fathomless regions of space, in some cases never 
 again to reappear to human vision. 
 
 In the early ages of the world, superstition regarded 
 these wandering fiery worlds with awe, and looked 
 upon them as omens of pestilence and war; and in- 
 deed, even in modern times, no eye can look upon the 
 fiery train spread out for millions of miles athwart 
 
 ( 223 ) 
 
224 STRUCTURE OF THE UNIVERSE. 
 
 the sky, and watch the eccentric motions of these 
 anomalous objects, without a feeling of dread. The 
 movements of the planets inspire confidence. They 
 are ever visible, and true to their appointed times, 
 while the comet, erratic in its course, bursts suddenly 
 and unannounced upon the sight, and no science can 
 predict in the outset its uncertain track — w T hether it 
 may plunge into the sun, or dash against one of the 
 planetary systems, or even come into collision with 
 our own earth, is equally uncertain, until after a suf- 
 ficient number of observations shall have been made 
 to render the computation of the elements of its orbit 
 possible. 
 
 Previous to the discovery of the law of universal 
 gravitation, comets were looked upon as anomalous 
 bodies, of whose motions it was quite impossible to 
 take any account. By some philosophers they were 
 regarded as meteors kindled into a blaze in the earth's 
 atmosphere, and when once extinguished they were 
 lost forever. Others looked upon them as permanent 
 bodies, revolving in orbits far above the moon, and 
 reappearing at the end of long but certain intervals. 
 When, however, it was discovered that, under the in- 
 fluence of gravitation, any revolving world might de- 
 scribe either of the four curves, the circle, ellipse, para- 
 bola or hyperbola, it at once became manifest that the 
 eccentric movements of the comets might be perfectly 
 represented by giving to them orbits of the parabolic 
 or hyperbolic form, the sun being located in the focus 
 of the curve. According to this theory, the comet 
 would become visible in its approach to its perihelion, 
 or nearest distance from the sun, — would here blaze 
 with uncommon splendor, and in its recess to the re- 
 
THE COMETARY WORLDS. 225 
 
 mote parts of its orbit, would gradually fade from the 
 sight, relaxing its speed, and performing a large pro- 
 portion of its vast curve far beyond the reach of hu- 
 man vision. 
 
 Such was the theory of Newton, and such were the 
 fair deductions from the great law of nature which he 
 had revealed to the world. He awaited with deep 
 interest the appearance of some brilliant comet, w T hose 
 career he might trace, in the full confidence that ob- 
 servation would confirm the truth of his bold hypothe- 
 sis. Fortunately, his impatience was soon gratified. 
 In the year 1680 a most wonderful comet made its 
 appearance, which, by its splendor and swiftness, ex- 
 cited the deepest interest throughout the world. It 
 came from the regions of space immediately above 
 the ecliptic, and plunging downwards with amazing 
 velocity, in a direction almost perpendicular to this 
 plane, it appeared to direct its flight in such manner 
 that it must inevitably plunge directly into the sun. 
 This was not, however, the case. Increasing its ve- 
 locity as it approached the sun, it swept round this 
 body with the speed of a million of miles an hour 
 approaching the sun to within a distance of its sur- 
 face of a sixth part of the sun's radius. It then 
 commenced its recess, throwing off a train of light 
 which extended to the enormous distance of 100,000,- 
 000 of miles. With the swiftness of thought almost, 
 it swept away from the sun, and was gradually lost 
 in the distant regions of space whence it came, and 
 has never since been seen. Such were the general 
 characteristics of the body to whose rapid motions 
 Newton attempted to apply the law of universal 
 gravitation. 
 
226 STRUCTURE OF THE UNIVERSE. 
 
 Its positions were marked with all the accuracy 
 which the instruments then in use permitted, and it 
 was found that a parabolic curve could be constructed 
 which would embrace all the places of the comet. — 
 The great eccentricity of its orbit, and its vast period, 
 amounting to nearly six hundred years, gave to the 
 comet great interest, but rendered it an unfit object 
 for successful analytic researche. The great English 
 astronomer, Halley, had studied it with the closest 
 care, and with a rigid application of Newton's theory, 
 he reached results quite as satisfactory as the circum- 
 stances of the case rendered possible. 
 
 Fortunately, in 1682, another comet made its ap- 
 pearance, to the study of which Halley devoted him- 
 self with a zeal and success which has justly stamped 
 his name on this remarkable body ; and as our limits 
 forbid an extensive investigation of the history and 
 theory of comets, I propose to examine this one with 
 that degree of detail which may convey some idea of 
 the limits of human knowledge in this complicated 
 department of science. 
 
 At the suggestion of Newton, Halley had searched 
 all ancient and modern records, for the purpose of 
 rescuing any historical details touching the appearance 
 and aspect of comets, from the primitive ages down to 
 his own time. On the appearance of the comet of 
 1682, he observed its positions with great care, and 
 with wonderful pains computed the elements of its 
 orbit. He found it moving in a plane but little in- 
 clined to the ecliptic, and in an ellipse of very great 
 elongation. In its aphelion, it receded from the sun 
 to the enormous distance of 3,400,000,000 of miles. — 
 He discovered that the nature of its orbit was suck 
 
THE COMETARY WORLDS. 227 
 
 as to warrant the belief that the comet would return 
 at regular intervals of about seventy-five years, and 
 recurring to his historical table of comets, he found it 
 possible to trace it back with certainty several hun- 
 dred years, and with probability even to the time of 
 the birth of Mithridates, one hundred and thirty years 
 before Christ. At this, its first recorded appearance, 
 its magnitude must have been far beyond anything 
 subsequently seen, as its splendor is said to have sur- 
 passed that of the sun. 
 
 In the years 248, 324, and 399 of the Christian era, 
 remarkable comets are recorded to have appeared, 
 and the equality of interval corresponds well with Hal- 
 ley's comet. In the year 1006, it presented a frightful 
 aspect, exhibiting an immense curved tail in the form 
 of a scythe. In 1456, its appearance spread conster- 
 nation through all Europe, and led to most extrava- 
 gant acts on the part of the reigning pontiff, who 
 actually instituted a form of prayer against the bale- 
 ful influence of the comet, and thus increased the 
 terrors of the ignorant and superstitious. The comet 
 appeared with certainty in 1531, and again in 1607, 
 and from an examination of all the facts, and with full 
 confidence in his computations, Halley ventured the 
 bold prediction that this same comet would reappear 
 about the close of 1758, or the beginning of 1759. 
 
 This was certainly the most extraordinary predic- 
 tion ever made, and the distinguished philosopher, 
 knowing that he could not live to witness the verifica- 
 tion of this prophetic announcement, expresses the 
 hope that when the comet shall return, true to his 
 computed period, posterity will do him the justice to 
 remember that this first prediction was made by an 
 
228 STRUCTURE OF THE UNIVERSE. 
 
 Englishman. In the age when these investigations 
 were made, the theory of comets was in its infancy, 
 and it is believed by those competent to form a just 
 opinion, that Halley was the only man living who 
 could have computed the orbit of his comet. 
 
 As the period approached for the verification of this 
 extraordinary announcement, the greatest interest was 
 manifested among astronomers, and efforts were made 
 to predict its coming with greater accuracy, by com- 
 puting the disturbing effects of the larger planets 
 within the sphere of whose influence the comet might 
 pass. This was a new and difficult branch of astro- 
 nomical science, and it would be impossible to convey 
 the least idea of the enormous labor which was gone 
 through by Clairaut and Lalande, in computing the 
 perturbations of this comet through a period of two 
 revolutions, or one hundred and fifty years. 
 
 " During six months," says Lalande, " we calculated 
 from morning till night, sometimes even at meals, — 
 the consequence of which was that I contracted an 
 illness which changed my constitution during the re- 
 mainder of my life. The assistance rendered by 
 Madame Lepaute was such, that without her we never 
 should have dared to undertake the enormous labor, 
 in which it was necessary to calculate the distance 
 of each of the two planets, Jupiter and Saturn, from 
 the comet, separately for every degree, for one hun- 
 dred and fifty years." 
 
 Amid all these difficulties, the computers toiled on, 
 until finally, the period coming on rapidly for the 
 comet's return, they were forced to neglect some mi- 
 nor irregularities, and Clairaut announced that the 
 comet would be retarded one hundred days by the in- 
 
THE C0METARY WORLDS. 229 
 
 fluence of Saturn, and five hundred and eighteen days 
 by the action of Jupiter ; — he therefore fixed its peri- 
 helion passage for the 13th of April. 1759, stating, at 
 the same time, that the result might be inaccurate by 
 some thirty days either way, in consequence of being 
 pressed for time, and his having neglected certain 
 small perturbations. 
 
 These results were presented to the Academy of 
 Sciences on the 14th of November, 1758, and on the 
 25th of the following December, George Palitch, an 
 amateur peasant astronomer, caught the first glimpse 
 of the long expected wanderer, which, after an ab- 
 sence of three-quarters of a century, once more re- 
 turned to crown with triumph the great English as- 
 tronomer who first foretold its period, and the eminent 
 French mathematicians who had actually computed 
 its perihelion passage, to within nineteen days, in 
 seventy-six years ! 
 
 Here, then, was a new world added to the solar 
 system, linked to the sun by the immutable law of 
 gravitation; sweeping out into space to the amazing 
 distance of 3,800,000,000 of miles ; lost to the gaze 
 of the most powerful telescope, and yet traced by the 
 human mind through its vast and hidden career, with 
 an accuracy and precision from which there was no 
 escape. The very small error of nineteen days in 
 Clairaut's computation strikes us with astonishment, 
 when we remember the imperfect state of analytical 
 science at that day, and the fact that two planets, 
 Uranus and Neptune, which have since been dis- 
 covered., were then not even suspected to have any 
 existence. 
 
 The magnificent display which had marked some 
 
230 STRUCTURE OF THE UNIVERSE. 
 
 of the early returns of Halley's comet, and which 
 produced such consternation among all classes, the 
 educated as well as the ignorant, were not presented 
 during its appearance in 1758. This was owing, in 
 part, to the unfavorable position of the earth in its 
 orbit at the time of the comet's perihelion passage. — 
 The vast trains of light which are sometimes seen to 
 accompany comets, are only displayed in their ap- 
 proach to the sun. They attain their greatest splen- 
 dor while the comet is in the act of passing its peri- 
 helion, and as it recedes into space, the tail fades 
 away, from two causes — an actual diminution from 
 condensation, and an apparent decrease on account 
 of increased distance. 
 
 As the comet, when near the sun, moves with in- 
 creased velocity, it occupies, in general, only a short 
 period in passing through the limits of distance from 
 the sun w r ithin which any train of light is developed. 
 It may happen that at one return of the same comet, 
 the earth may occupy a point in her orbit, during its 
 perihelion passage, which may be very near to the 
 comet, and thus afford an opportunity of witnessing 
 its appearance at a short distance ; while, on the 
 next return, the earth being at a remote part of its 
 orbit w 7 hile the comet is passing the sun, it may be 
 seen only w r ith great difficulty, or even become quite 
 invisible. If, therefore, astronomers were obliged to 
 depend upon a uniform physical appearance of 
 comets at their successive returns, to determine their 
 identity, there would scarcely be the slightest chance 
 of ever recognizing even a single one among the 
 many thousands w 7 hich are sweeping through the re. 
 gions of space. 
 
THE COMETARY WORLDS. 231 
 
 The interval from 1759 to 1835, when Halley's 
 comet ought to make its next appearance, had wit- 
 nessed extraordinary changes in astronomy. The 
 methods for computing planetary perturbations had 
 been greatly improved ; the planet Uranus had been 
 added to the system, and more accurate masses of the 
 larger planets, especially of Saturn, had been ob- 
 tained. Twenty-five years before the close of the 
 comet's period, its return commenced to interest as- 
 tronomers, and prizes were offered by two academies 
 for the most perfect theory of this remarkable body. 
 Baron Damoiseau and M. Pontecoulant were the suc- 
 cessful competitors for the two prizes, although sev- 
 eral other astronomers undertook and completed the 
 task of computing the planetary perturbations. Al- 
 though the computers differed slightly in the time of 
 the perihelion passage, the difference was due to the 
 imperfection of the data employed, rather than to any 
 defect in the methods of computation. 
 
 For the expected return in 1835, not only was the 
 perihelion passage computed, but the exact route of 
 the comet among the fixed stars was wrought out 
 with surprising accuracy, and the precise point to- 
 wards which the telescope must be directed at the 
 time when the comet would first attain the limits of 
 visibility. Strange and almost incredible as it must 
 appear, guided by these predictions, M. Dumouchel, 
 director of the observatory of the Roman College, on 
 the evening of the 5th of August, 1835, fixed his tel- 
 escope in the position indicated by computation, and, 
 on placing his eye to the tube, lo ! the comet ap- 
 peared, as a faint and almost invisible stain of light 
 on the deep blue of the heavens. 
 
232 STRUCTURE OF THE UNIVERSE. 
 
 Again did science triumph, in the most remarkable 
 manner, and the computed orbit of the comet was 
 followed by it with the most surprising accuracy. — 
 The perihelion passage was predicted to within nine 
 days of its actual occurrence, a most astonishing ap- 
 proximation to the truth, when it is remembered that 
 this body, far as it penetrates into space, never, even at 
 the remotest point of its orbit, escapes from the sen- 
 sible influence of the planet Jupiter. Moreover, at 
 that time, the new planet, Neptune, was unknown, 
 and its influence over the comet could not be taken 
 into account. 
 
 It is interesting to remark the confidence with 
 which astronomers relied on Halley's comet for infor- 
 mation relative to those bodies, which inhabited the 
 regions of space exterior to the known limits of the 
 solar system. It was urged by every computer that 
 the orbit of this comet would one day come to be so 
 perfectly known, that the perturbations due to the 
 recognized bodies of the solar system might be com- 
 puted with such precision, that the residual perturba- 
 tions might be pronounced to be the effect of un- 
 known planets or comets circulating in the distant 
 regions of space. This conjecture has been realized, 
 although by different means, and a planet is now 
 added to our system, which revolves in an orbit so 
 vast as to circumscribe within its limits the entire 
 sweep of the comet ; and as the orbits of Neptune 
 and Halley's comet are inclined under an angle of 
 only 15° or 16°, a time will come when the perturba- 
 tions experienced by the comet when at its aphelion, 
 from Neptune's influence, may be so great that, but 
 for the fortunate discovery of the cause, would have 
 
THE COMETARY WORLDS. 233 
 
 falsified, in the most unaccountable manner, the pre- 
 dictions of the comet's return by future astronomers. 
 During its late return, the finest telescopes in the 
 world were employed in a critical examination of the 
 physical condition of Halley's comet. Elaborate 
 drawings have been made by M. Struve, the dis- 
 tinguished director of the Imperial Observatory at 
 Pulkova, Russia, with the grand refracting telescope 
 under his charge, and also by Sir John Herschel, 
 at the Cape of Good Hope, with a twenty feet reflec- 
 tor of superior power. To these beautiful drawings 
 reference w T ill be made hereafter. 
 
 The most wonderful changes in the magnitude and 
 figure of the comet were observed to take place from 
 night to night, and almost perceptible from hour to 
 hour under the eye of the observer. The nucleus 
 was sometimes seen sharp and strongly condensed, 
 with more or less nebulous light around it. Some- 
 times a luminous crescent became distinctly visible 
 near the nucleus, giving to the comet a most extra- 
 ordinary appearance. At one time M. Struve saw 
 the comet attended by two delicately shaped appen- 
 dages of light of a most graceful form, the one pre- 
 ceding, the other following the nucleus of the comet. 
 At other times it was seen to be surrounded by a sort 
 of semi-circular veil, which, extending backwards, 
 was lost in a double train of light, which flung itself 
 out to a vast distance from the body of the comet. 
 
 Leaving, for the present, the consideration of the 
 physical constitution of these eccentric bodies, we 
 proceed to the examination of a remarkable object 
 which bears the name of Encke's comet, in conse- 
 quence of the discovery by this learned astronomer 
 t: 2 
 
234 STRUCTURE OF THE UNIVERSE. 
 
 that its orbit was elliptical, and its period of revolu- 
 tion so short as to fall fairly within the limits of per- 
 petual examination. 
 
 In 1818, a comet was discovered by Pons, not at all 
 remarkable for its magnitude, for it was even invisible 
 to the naked eye, but when the attempt was made to 
 represent its places by a parabolic orbit, which had 
 thus far been invariably applied to the comets, it was 
 found impossible to assign any elongated orbit which 
 would embrace the observed positions of the comet. 
 After a very elaborate investigation, Professor Encke 
 at length reached the conclusion that the orbit was 
 not a parabola, but an ellipse of comparatively small 
 dimensions, and that this comet was actually revolv- 
 ing around the sun in a period of about three years. 
 This discovery excited a great deal of interest, for it 
 was the first in which a short period had been detect- 
 ed, and efforts were at once made to identify the new 
 member of the solar system in its preceding revolu- 
 tions. Olbers determined its identity with a comet 
 which appeared in 1795, and subsequently ascertained 
 that another, which had been observed but twice in 
 1786, and from which observations no elements could 
 be computed, could be no other than the new comet 
 of that period. In this way, observations on this in- 
 teresting object were obtained, stretching through 
 some thirty-three years, or about ten of its revolu- 
 tions. This extended series of observations furnished 
 the data for a critical examination of the elements of 
 the comet's orbit, and Prof. Encke, having discussed 
 them with elaborate care, reached the astonishing 
 conclusion that the magnitude of the orbit was grad- 
 ually diminishing, the periodic time growing shorter 
 
THE COMET ARY WORLDS. 235 
 
 from revolution to revolution, and that the comet was 
 certainly falling nearer and nearer to the sun ! 
 
 To account for this extraordinary phenomenon, the 
 learned astronomer, having exhausted all causes 
 known to exist in the solar system, finally, with much 
 hesitation, announced the theory of the comet's motion 
 in a resisting medium. The existence of such a me- 
 dium was in direct opposition to all the received doc- 
 trines of astronomy, and the absolute necessity for its 
 use in this instance was looked upon by astronomers 
 with feelings of strong distrust. But Encke argued 
 that such a medium might exist, of such exceeding te- 
 nuity as not sensibly to affect the movements of the 
 ponderous planets, while a filmy mass of vapor, such 
 as this comet undoubtedly was, might be very sensibly 
 retarded in its original velocity, which would diminish 
 continually the centrifugal force, and give to the cen- 
 tral attraction of the sun a constantly increasing 
 power, which would produce precisely the phenom- 
 ena exhibited by the comet. 
 
 With these views, Encke predicted the reappear 
 ance of the comet in 1822. In consequence of its 
 great southern declination at that period, it escaped 
 all the European observers, and was only seen at 
 Paramatta, by Rumker. The approach to the sun 
 was in some degree confirmed by these observations, 
 but it was impossible to reconcile all the observations 
 with the hypothesis of a medium of given density. — 
 The return in 1825 was not favorable for deciding the 
 question, which had now become one of the deepest 
 interest. 
 
 Its reappearance in 1828-9 was awaited with great 
 anxiety by the friends and opponents of the new 
 
236 STRUCTURE OF THE UNIVERSE. 
 
 theory. The comet came round, and passed its peri- 
 helion approximately in accordance with the predic- 
 tions, but the discrepancies from 1819 up to 1829, 
 with any theory, were so great, as to give much per- 
 plexity to those engaged in the computations. After 
 long and patient examination, the cause of this diffi- 
 culty was finally detected. The plane of the comet's 
 orbit makes but a small angle with the orbit of Jupi- 
 ter, and when the comet is in aphelion, or farthest 
 from the sun, it always approaches very near to the 
 path described by the planet. 
 
 A time may then come when Jupiter shall be in the 
 act of passing that part of its orbit very near to the 
 aphelion point of the cometary ellipse, while the 
 comet occupies its aphelion, bringing these bodies 
 into close proximity, and producing excessive pertur- 
 bations in the movements of this almost spiritual 
 mass. Such, indeed, was the configuration between 
 the returns of 1819 and 1829, on which occasion the 
 comet was delayed in its return to its aphelion by 
 nearly nine days, by the powerful attraction of Jupi- 
 ter. Under these circumstances, any error in the as- 
 sumed mass of the planet would exhibit itself in an 
 exaggerated form in the perturbations of the comet. 
 But it was believed in the outset of this investigation, 
 that the mass of Jupiter, employed by Laplace in 
 his theory of the planets, and computed by Bouvard, 
 could be relied on as accurate. Indeed, Laplace had 
 applied the calculus of probabilities, and had found 
 that there was but one chance out of eleven millions 
 that the mass he had adopted could be in error by the 
 one hundredth part of its value. 
 
 Suspicion, however, having been aroused with ref- 
 
THE COMETARY WORLDS. 237 
 
 crence to the mass of Jupiter, efforts were at once 
 commenced to sift thoroughly the matter, and three 
 different computers of high reputation undertook the 
 determination of Jupiter's mass by different processes. 
 Encke obtained a mass from the perturbations of the 
 small planet Vesta, ]\icolai from the perturbations of 
 Juno, and Airy reexamined the original measures of 
 the elongations of Jupiter's satellite, made new meas- 
 ures, and thus obtained new data for the resolution 
 of the problem of Jupiter's mass. The results ob- 
 tained by the three astronomers agreed in a most re- 
 markable manner, and proved incontestably that La- 
 place's value of the mass of this planet was in error 
 more than four times the hundredth part of its value, 
 and that, instead of requiring 1,070 globes of the mag- 
 nitude of Jupiter to balance the sun, only 1,049 were 
 necessary. 
 
 With the new mass of Jupiter it seemed possible, 
 by admitting a resisting medium, to account for all 
 the perturbations of Encke's comet, and for a time 
 this theory seemed to receive greater consideration 
 from distinguished men. The appearance of Halley's 
 comet in 1835 again threw great doubt over the sub- 
 ject, for it was found impossible to reconcile the move- 
 ments of the two comets with any assumed density 
 of a resisting medium. Some have been disposed to 
 adopt the idea that the revolution of the planets, for 
 ages, in the same direction, in this supposed ethereal 
 fluid, has impressed upon it a certain amount of mo- 
 tion in the same direction, and that those comets 
 which chance to revolve with the current will be 
 found to be operated upon differently from those 
 
238 STRUCTURE OF THE UNIVERSE. 
 
 which may happen to come into our system in a di- 
 rection opposed to the current. 
 
 I confess, frankly, that my own mind has always 
 revolted against the doctrine of a resisting fluid. — 
 There are so many ways in which the single phenom- 
 enon of the gradual approach of Encke's comet to 
 the sun may be accounted for, without resorting to an 
 hypothesis which involves the entire destruction of 
 the planetary system, whose perpetuity has been so 
 effectually provided for by the great Architect of the 
 universe, that it would require the most unequivocal 
 testimony to secure the full consent of my own mind 
 to the adoption of this remarkable theory. It is 
 proper, however, to say, that it has long been received 
 with favor by men to whose judgment I am generally 
 disposed to yield with implicit confidence. 
 
 Leaving the further consideration of this subject 
 for the present, we proceed to the examination of an- 
 other comet of short period, which has excited great 
 attention, especially in its recent return. As early as 
 1805, Prof. Gauss, in computing the elements of the 
 orbits of the comets of that year, found one which 
 seemed to complete its revolution in about six years. 
 This comet, however, was lost sight of, and it was 
 not until 1826 that M. Biela discovered the same comet 
 on its return to its perihelion. This discovery appears 
 to have been the result of computation, but how far 
 the investigation was carried, I have never been able 
 to learn. 
 
 The same object was also discovered by M. Gam- 
 bart about the same time, who, on fixing its elements, 
 found that it performed its revolution about the sun 
 in an ellipse, with a period of six and three-quarter 
 
THE C0METARY WORLDS. 239 
 
 years. This comet, like Encke's, is only to be seen 
 with the telescope. It presents no solid, or even well 
 defined nucleus, and appears to be a mere vapory 
 mass, of exceeding tenuity. Taking into account 
 the disturbing influence of Jupiter, the returns of 
 Biela's comet, as predicted, agreed well with observa- 
 tion, and gave confidence in the theory on which the 
 predictions were founded. 
 
 The return in 1832 excited the liveliest interest 
 throughout the civilized world, in consequence of the 
 fact that it was discovered from computation, that on 
 the night of the 29th of October, this comet would 
 pass a little within the earth's orbit, and those unac- 
 quainted with the subject received the impression 
 from this announcement, that the earth and comet 
 would come into collision, producing the most terrific 
 consequences. Such was the consternation excited, 
 throughout the city of Paris especially, that the Acad- 
 emy of Sciences found it necessary to give to the sub- 
 ject their serious attention, and finally gave the mat- 
 ter in charge to M. Arago, who produced an elaborate 
 report on the subject of comets generally, which 
 served to calm the popular apprehension, and has 
 proved to be a valuable addition to our knowledge on 
 this difficult subject. 
 
 In this report, M. Arago showed that the comet 
 would indeed cross the earth's track at the time pre- 
 dicted, but at the moment of crossing, the earth would 
 be some fifty-five millions of miles distant from the 
 point occupied by the comet, and could not experience 
 the slightest possible influence from such a body, at 
 such a distance. 
 
 If the comet had been delayed in its approach for 
 
240 STRUCTURE OF THE UNIVERSE. 
 
 thirty days, by any disturbing cause, then, indeed, the 
 earth and comet would have filled at the same time 
 the point where their orbits intersect, and the dreaded 
 collision would have taken place. The consequences 
 of such a shock it is impossible to conjecture, but 
 reasoning from the known physical condition of the 
 comet, none of the terrible disasters so generally an- 
 ticipated would have occurred. The exceeding rarity 
 of the matter composing this body may be inferred 
 from the statements of Sir John Herschel. " It 
 passed," says he, " over a small cluster of most minute- 
 stars of the 16th and 17th magnitude; and when on 
 the cluster presented the appearance of a nebula re- 
 solvable, and partly resolved, the stars of the cluster 
 being visible through the comet. A more striking 
 proof could not have been offered of the extreme 
 translucency of the matter of which the comet con- 
 sists. The most trifling fog would have effaced this 
 group of stars, yet they continued visible through a 
 thickness of cometic matter which, calculating on its 
 distance and apparent diameter, must have exceeded 
 50,000 miles, at least towards its central parts. That 
 any star of the cluster was centrally covered, is indeed 
 more than I can assert ; but the general bulk of the 
 comet might be said to have passed centrally over 
 the group" 
 
 Such is the nature of the body from whose contact 
 the ignorant apprehended the most fearful convul- 
 sions. Olbers, who studied the subject with great 
 care, was disposed to think that in case the earth had 
 passed directly through the comet, no inconvenience 
 would have occurred, and no change beyond a slight 
 influence on the climate would have been experienced 
 
THE COMETARY WORLDS. 241 
 
 It is useless to speculate with reference to the 
 probable consequences of a collision, which there is 
 scarcely one chance in millions can ever occur. — 
 Science has as yet discovered no guarantee for any 
 planet against the possible shock of a comet ; but an 
 examination of the delicate adjustments of our own 
 system, and those of Jupiter and Saturn, would seem 
 to indicate to us that in all past time no derangement 
 has ever occurred from such a cause. 
 
 The last return of Biela's^comet was marked by a 
 phenomenon unexampled, so far as I know, in the his- 
 tory of these wandering bodies. True to the predic- 
 tions of Santini, the comet first became visible on 
 the evening of the 26th of November, 1845, and in 
 the precise point which had been assigned by theory. 
 DeVico, the director of the observatory at Rome, was 
 the first to catch a glimpse of the expected comet. — 
 Nothing remarkable in its appearance was noticed, 
 until about the 29th of December, when Mr. E. C. 
 Herrick, of New Haven, pointed out to several friends 
 what he regarded to be a sort of anomalous tail, but 
 shooting out from the head of the comet in a direction 
 entirely at variance with the usually received theory, 
 that the tail is always opposite to the sun. In this 
 supposed tail a kind of knot was noticed, brighter and 
 more condensed than any other part. Owing to in- 
 sufficient optical power, the true character of the 
 phenomenon was not fairly detected by Mr. Herrick. 
 
 On the night of the 12th of January, 1848, Lieut, 
 Maury, in charge of the observatory at Washington 
 City, discovered that what had hitherto appeared as a 
 single body, was actually composed of two distinct and 
 separate comets This most extraordinary fact was 
 
242 STRUCTURE OF THE UNIVERSE. 
 
 immediately announced, and the double character 
 was observed at all the principal observatories in 
 Europe and the United States. There can be no 
 doubt whatever as to the reality of the appearance. 
 The comet actually became double, and the two parts 
 bound together by some inscrutable bond, continued 
 their swift journey through space, pursuing almost 
 exactly the route predicted for the single comet. 
 
 From measures obtained by Prof. Challis, of Cam- 
 bridge, England, on the 23d of January, 1846, the 
 two comets were separated from each other by a dis- 
 tance equal to about one-thirteenth the apparent di- 
 ameter of the sun. On the 28th of the same month, 
 Sir John Herschel records the following notices : — 
 " The comet was evidently double, consisting of two 
 distinct nebulae, a larger and a smaller one, both 
 round, or nearly so, — the one in advance faint and 
 small, and not much brighter in the middle ; the one 
 which followed nearly three times as bright, and one 
 and a half times larger in diameter, and a good deal 
 brighter in the middle, with an approach to a stellar 
 point." 
 
 On the evening of the 9th of February, having re- 
 turned to the observatory at Cincinnati, after an ab- 
 sence of more than two months, I had an opportunity 
 of beholding, for the first time, these wonderful ob- 
 jects, with the twelve inch refractor. The moon was 
 nearly full, and yet the comets were distinctly visible, 
 both included within the limits of the field of view 
 of the instrument, and separated from each other by 
 a distance equal to about the eighth part of the sun's 
 diameter. The preceding comet was evidently the 
 brighter of the two 
 
THE COMB! iRY WORLDS. 243 
 
 Clouds prevented a continuous examination of the 
 comets from night to night, but on the evening of the 
 21st of February, I was surprised to find a remarka- 
 ble change in the relative brilliancy of the two parts. 
 On that evening the following comet was very deci- 
 dedly brighter than its companion, and from observa- 
 tions made elsewhere, the change of relative bright- 
 ness seems to have been effected about the 13th or 
 14th of February. The change was observed by 
 Prof. Encke, of Berlin, as early as the 14th. On the 
 evening of the 21st of February, both comets exhib- 
 ited distinct trains of light, extending from the sun, 
 and in directions parallel to each other. The centre 
 of the nucleus of each comet was brighter than the 
 surrounding portions, but there was no stellar point 
 visible. The nebulosity of the two points did not 
 intermingle. 
 
 The distance between the comets increased from 
 day to day, until, on the 25th of February, they were 
 separated by an amount equal to 445 seconds of arc 
 or between a fourth and fifth part of the sun's diame- 
 ter. A part of the increase of distance was only 
 apparent, arising from the approach of the comets to 
 the earth, but the comets were actually receding from 
 each other while pursuing their rapid flight through 
 space. 
 
 Neither did the line joining the central points of the 
 comets remain parallel to itself. From the 23d of 
 January to the 11th of February, this line shifted its 
 position by an amount of angular motion equal to 8° 
 as is shown by a comparison of the measures of 
 Chalhs and Encke. By the 21st of February, this 
 angular motion had bf en nearly destroyed by a retro- 
 
244 STRUCTURE OF THE UNIVERSE. 
 
 grade movement, and thus the comets were seen tc 
 oscillate about each other, according to some mysteri- 
 ous law which has never been revealed. Such is a 
 bri )f sketch of the phenomena presented by Biela's 
 comet in its late return. Its next appearance will be 
 looked for with deep interest, to confirm or destroy 
 certain theories which have been propounded to ex- 
 plain its duplex character. 
 
 While the periods of the comets which we have 
 thus far considered are comparatively short, those of 
 others which have visited our system have been ascer- 
 tained to extend to many thousands of years. The 
 great comet of 1811, one of the most brilliant of 
 modern times, in consequence of its remaining visible 
 for nearly ten months, gave ample opportunity for the 
 investigation of the elements of its orbit. After a 
 careful investigation, M. Argelander fixes its period 
 of revolution at 2,888 years. Bessel had examined 
 the same subject previously, and probably with less 
 attention, but obtained a period even greater than 
 Argelander's, amounting to 3,383 years. 
 
 The comet of 1807 also occupied the attention of 
 Bessel. A long series of observations furnished the 
 data for computing its elements. The periodic time 
 was fixed at 1,543 years. These computations are 
 necessarily only approximate. The difficulty of ob- 
 taining accurately the periodic time increases with 
 the length of the period, and all that can be done is 
 to fix al limit below which it cannot fall. These vast 
 periods give to us the means of learning somewhat 
 of the great distance to which these objects penetrate 
 into space. The comet of 1811, having a period 
 probably three thousand times greater than that of 
 
THE COMETARY WORLDS. 245 
 
 2>ur earth, must revolve at a mean distance from the 
 sun of more than 80,000,000,000 of miles, and in con- 
 sequence of its very near approach to the sun at its 
 perihelion, its greatest distance cannot fall below 
 160,000,000,000 of miles ! 
 
 Great as this distance is, it is perfectly certain that 
 there are many comets which revolve in orbits far 
 more extensive than the one described by the comet 
 of 1811. Indeed, there seems to be no limit to the 
 distance to which these bodies may sweep outward 
 from the sun; and their return depends simply on the 
 fact whether they recede so far as to fall within the 
 attractive influence of some other sun, towards which 
 they begin to urge their flight, and through whose sys- 
 tem of planets they carry the same apprehensions of 
 danger which have been caused in our own. 
 
 In reflecting on these singular objects, we are led to 
 inquire what they are, whence their origin, and by what 
 laws are the vast trains of light which occasionally 
 distinguish them developed ? Arago divides comets 
 into three classes, with reference to their physical con- 
 stitution. He thinks they occasionally appear round, 
 and with well defined planetary discs, showing them 
 to be soild opaque bodies, in all respects resembling 
 planets, and only differing from these in the great ec- 
 centricity of their orbits. In confirmation of this 
 opinion, he asserts that comets have been seen to 
 transit the sun, and when passing between this lumi- 
 nary and the eye of the spectator, they appear round 
 and black, like the planets Mercury and Venus, when 
 seen under the same circumstances. An example of 
 this kind occurred on the 18th of November, 1826, 
 when the transit of a comet across the sun was wit- 
 v 2 
 
246 STRUCTURE OF THE UNIVERSE. 
 
 nessed by two persons, widely separated from each 
 other. 
 
 A second class of comets comprehends those in 
 which there is a nucleus, but devoid of opacity, per- 
 mitting the light to penetrate through even that por- 
 tion which may possibly be solid. The third class, 
 and that by far the. most numerous, comprehends 
 those comets destitute, entirely, of any solid nucleus, 
 consisting of matter so attenuated as to compare 
 fairly with nothing of which we have any knowledge 
 on the earth's surface. The comets named for Encke 
 and Biela appear to belong to this class ; and even 
 Halley's comet, according to the opinion of Sir John 
 Herschel, seems, at its last return, to have been en- 
 tirely turned into vapor in its perihelion passage. 
 
 No theory, with the exception of Laplace's nebular 
 hypothesis, has ever been framed to explain the ori- 
 gin of these wandering bodies. This is not the place 
 to enter into a full development of this subject. — A 
 few hints only can be given. Laplace, following up 
 the speculation of Sir William Herschel, applied the 
 theory of that astronomer to the formation of the 
 solar system, comprehending the comets, as well as 
 the planets and their satellites. This theory supposes 
 that the original chaotic condition of the matter of 
 all suns and worlds was nebulous, like the matter 
 composing the tails of comets. Under the laws of 
 gravitation, this nebulous fluid, scattered throughout 
 all space, commences to condense towards certain 
 centres. The particles moving towards these central 
 points, not meeting with equal velocities, and in op- 
 posite directions, a motion of rotation is generated in 
 
THE COMETARY WORLDS. 247 
 
 the entire fluid mass, which, in figure, approximates 
 the spherical form. 
 
 The spherical figure once formed, and rotation com- 
 menced, it is not difficult to conceive how a system 
 of planets might be produced from this rotating mass, 
 corresponding, in nearly all respects, to the charac- 
 teristics which distinguish the planets belonging to 
 . our own system. If, by radiation of heat, this nebu- 
 lous mass should gradually contract in size, then a 
 well known law of rotating bodies would insure an 
 increased velocity of rotation. This might continue 
 until the centrifugal force, which increases rapidly 
 w r ith the velocity of the revolving body, would finally 
 come to be superior to the force of gravity at the 
 equator, and from this region a belt of nebulous fluid 
 would thus be detached, in the form of a ring, which 
 would be left in space by the shrinking away of the 
 central globe. The ring thus left would generally 
 coalesce into a globular form, and thus would present 
 a planet with an orbit nearly, if not quite circular, 
 lying in a plane nearly coincident with the plane of 
 the equator of the central body, and revolving in its 
 orbit in the same direction in which the central globe 
 rotates on its axis. 
 
 As the globe gradually contracts, its velocity of ro- 
 tation continually increasing, another ring of matter 
 may be thrown off, and another planet formed, and 
 so on, until the cohesion of the particles of the cen- 
 tral mass may finally be able to resist any further 
 change, and the process ceases. 
 
 The planetary masses, while in the act of cooling 
 and condensing, may produce satellites in the same 
 manner, and by the operation of the same laws by 
 
248 STRUCTURE OF THE UNIVERSE. 
 
 which they were themselves formed. Strange and 
 fanciful as this speculation may appear, there are 
 many facts which tend strongly to give it more than 
 probability. It accounts for all the great features of 
 the solar system, which, in its organization, presents 
 the most indubitable evidence that it has resulted 
 from the operation of some great law. 
 
 The sun rotates on an axis in the same direction 
 in w^hich the planets revolve in their orbits ; the 
 planets all rotate on their axes in the same direction ; 
 they all circulate around the sun in orbits nearly circu- 
 lar, in the same direction, and in planes nearly coinci- 
 dent with the plane of the sun's equator. The satel- 
 lites of all the planets, with one single exception, 
 revolve in orbits nearly circular, but little inclined to 
 the equators of their primaries, and in the same direc- 
 tion as the planets. So far as their rotation on axes 
 has been ascertained, they follow the general law. — 
 In one instance alone we find the rings of matter 
 have solidified in cooling, without breaking up or be- 
 coming globular bodies. This is found in the rings 
 of Saturn, which present the very characteristics 
 which would flow from their formation according to 
 the preceding theory. They are flat and thin, and re 
 volve on an axis nearly, if not exactly, coincident 
 with the axis of their planetf. Their stability, as we 
 have seen, is guaranteed by conditions of wonderful 
 complexity and delicacy, and the adjustment of the 
 rings to the planet, (humanly speaking), would seem 
 to be impossible after the formation of the planet. — 
 At least it is beyond our power to conceive how this 
 could be accomplished by any law of which we have 
 
THE COMETARY WORLDS. 249 
 
 any knowledge, and we must refer their structure at 
 once to the fiat of Omnipotence. 
 
 Granting the formation of a single sun by the neb- 
 ular theory, and we account at once for the formation 
 of all other suns and systems throughout all space ; 
 and according to the advocates of this theory, the 
 comets have their origin in masses of nebulous mat- 
 ter occupying positions intermediate between two or 
 more great centres, and held nearly in equilibrio, 
 until, finally, the attraction of some one centre pre- 
 dominates, and this uncondensed filmy mass com- 
 mences slowly to descend towards its controlling orb. 
 This theory would seem to be sustained, so far as a 
 single truth can sustain any theory, by the fact that 
 the comets come into our system from all possible di- 
 rections, and pursue their courses around the sun 
 either in accordance with, or opposed to, the direction 
 in which the planets circulate. Their uncondensed 
 or nebulous condition results from the feeble central 
 attraction which must necessarily exist in bodies com- 
 posed of such small quantities of matter. Moreover, 
 in some cases at least, there is reason to believe, that 
 in their perihelion passage they are entirely dissipa- 
 ted into vapor by the power of the sun's heat, and 
 may thus revolve for ages, going through alternate 
 changes of solidification and evaporation. 
 
 But whence come the enormous trains of light 
 which sometimes attend these wandering bodies ? — 
 The last return of Halley's comet has furnished the 
 data for the positive illustration of this mysterious 
 subject. Sir John Herschel, after a careful and most 
 elaborate examination of all the physical character- 
 istics of this comet, comes to the conclusion that the 
 
250 STRUCTURE OF THE UNIVERSE. 
 
 figure of the comet, envelope and tail, could not be a 
 figure of equilibrium under the law of gravitation. 
 He is therefore compelled to bring in a repulsive force 
 to explain the phenomena. 
 
 I cannot do better than to quote his own language 
 in this bold introduction of a new power. — " Nor let 
 any one be startled at the assumption of such a re- 
 pulsive force as here supposed. Let it be borne in 
 mind that we are dealing (in the tails of comets) with 
 phenomena utterly incompatible with our ordinary 
 notions of gravitating matter. If they be material in 
 that ordinary received sense which assigns to them 
 only inertia and attractive gravitation, where,! would 
 ask, is the force which can carry them round in the 
 perihelion passage of the nucleus, in a direction point- 
 ing continually from the sun, in the manner of a rigid 
 rod, swept round by some strong directive power, and 
 in contravention to all the laws of planetary motion, 
 which would require a slower angular motion of the 
 more remote particles, such as no attraction to the 
 nucleus could give them, be it ever so intense ? The 
 tail of the comet of 1680, in five days after its peri- 
 helion passage, extended far beyond the earth's orbit ? 
 having, in that brief interval, shifted its angular posi- 
 tion nearly 150°. Where can we find, in its gravita- 
 tion either to the sun, or to the nucleus, any cause for 
 this extravagant sweep ? 
 
 " But again, where are we to look (if only gravity 
 be admitted) for any reasonable account of its pro- 
 jection outward from the sun, putting its angular mo- 
 tion out of the question ? Newton calculated that the 
 matter composing its upper extremity quitted the nu- 
 
THE COMET ARY WORLDS. 251 
 
 cleus only two days previous to its arriving at this 
 enormous distance." 
 
 Herschel argues the inadequacy of gravitation to 
 account for these wonderful phenomena. The velo- 
 city with which the matter composing the tail shot 
 forth from the head of the comet, from the sun, was 
 far greater than that which the sun could impress on 
 a body falling to it, even from an infinite distance. — 
 An energy of a different kind from gravitation, and 
 far more powerful, must exist, to produce such re- 
 sults. If, then, we are forced to the admission that a 
 power exists in the sun capable of repelling matter 
 of a certain quality existing in comets, a way is 
 opened for the explanation of some of the most diffi- 
 cult problems with which the mind has been obliged 
 to contend. 
 
 The diminution of the periodic time of Encke's 
 comet has led some astronomers to adopt the idea of 
 the existence of a resisting medium. But in case the 
 sun possesses the power of repelling the matter of 
 comets in their perihelion passage, a part of the mat- 
 ter thus repelled may be driven entirely beyond the 
 attractive influence of the nucleus, and be irrecovera- 
 bly lost. In this case, a diminution of mass would 
 inevitably involve a like diminution of periodic time, 
 a contraction of the orbit, and all the phenomena 
 presented by this mysterious object. Herschel even 
 thinks it possible, on this theory, to account for the 
 separation of Biela's comet into two distinct objects, 
 and it appears to me that it presents the most reason- 
 able explanation of the luminous appearance seen at 
 certain seasons of the year, called the zodiacal light. — 
 This phenomenon appears to be a ring of nebulous 
 
252 STRUCTURE OF THE UNIVERSE. 
 
 matter surrounding the sun, and some of whose par- 
 ticles are sustained at a much greater distance than 
 could be accounted for by gravitation. Admitting the 
 repulsive power already adverted to, there is no diffi- 
 culty in understanding how this nebulous ring may be 
 sustained at a vast distance from the sun. 
 
 Here we freely admit that we enter the confines of 
 the unknown. We have left the solid ground of truth 
 and certainty, and are pushing our investigations into 
 the dim twilight of the invisible and uncertain. But 
 as antiquity predicted- that the time would come when 
 the comets would be traced in their career, their pe- 
 riods revealed, and their orbits ascertained, so we may 
 confidently hope that, at no very distant day, all the 
 mysteries which hang around these chaotic worlds will 
 be fully revealed, and a knowledge of their physical 
 condition shall reward the long study and deep re- 
 search of the human mind. 
 
LECTURE IX. 
 
 THE SCALE ON WHICH THE UNIVERSE IS BUILT. 
 
 Thus far our attention has been directed to an ex- 
 amination of the achievements of the human mind 
 within the limits of our own peculiar system. We 
 have swept outward from the sun through the plane- 
 tary worlds, until we have reached the frontier limits 
 of this mighty family. Standing upon the latest found 
 of all the planets, at a distance of more than 3,000,- 
 000,000 of miles from the sun, we are able to look 
 backwards, and examine the worlds and systems 
 which are all embraced within the vast circumference 
 of Neptune's orbit. An occasional comet, overleap- 
 ing this mighty boundary, and flying swiftly past us, 
 buries itself in the great abyss of space, to return 
 after its " long journey of a thousand years," and re- 
 port to the inhabitants of earth the influences which 
 have swayed its movements in the invisible regions 
 whither it speeds its flight. 
 
 The magnificence and complexity of the great sys- 
 tem of planets and satellites and comets which con- 
 stitute the sun's retinue ; the immense magnitude of 
 some of these globes ; their periods of revolution, and 
 reciprocal action, would seem to furnish a sufficient 
 exercise, not only for the highest intellectual efforts, 
 but for the entire energy which the human mind can 
 exert. But the whole of this stupendous scheme, as 
 
 W (263 ; 
 
254 STRUCTURE OF THE UNIVERSE. 
 
 we shall soon see, is but an infinitesimal portion of 
 the universe of God, one unit among the unnumbered 
 millions which fill the crowded regions of space. — 
 Standing at the verge of the planetary system, we 
 find ourselves surrounded by a multitude of shining 
 orbs, some radiant with splendor, others faintly gleam- 
 ing with beauty. The smallest telescopic aid suffices 
 to increase their number in an incredible degree, 
 while with the full power of the grand instruments 
 now in use, the scenes presented in the starry heavens 
 become actually so magnificent as to stun the imagi- 
 nation and overwhelm the reason. Worlds and sys- 
 tems, and schemes and clusters, and universes, rise in 
 sublime perspective, fading away in the unfathomable 
 regions of space, until even thought itself fails in its 
 efforts to plunge across the gulf by which we are sepa- 
 rated from these wonderful objects. 
 
 In our measurements within the limits of the solar 
 system, the radius of the earth's orbit has sufficed for 
 a unit with which to exhibit the distances of the plan- 
 ets and comets. Great as is this unit, measuring no 
 less than 95,000,000 of miles, we shall soon find it 
 far too minute and insignificant to serve in our re- 
 searches with reference to the grand scale of the visi- 
 ble universe. To obtain comprehensible ideas with 
 reference to the interstellar spaces, we shall be obliged 
 to call to our aid a unit, not exactly of distance, but 
 of velocity ; and before entering on the full exhibition 
 of the main object of this lecture, permit me to direct 
 your attention to a remarkable discovery, by which 
 the important fact has been revealed, that light does 
 not pass instantly from a luminous body to any re- 
 mote object on which it may fall, but with a progres- 
 
SCALE OX WHICH THE UNIVERSE IS BUILT. 255 
 
 sive motion, whose actual velocity has been ascer- 
 tained. The important bearing of this discovery will 
 become apparent as we advance in our examination 
 of the sidereal heavens. 
 
 After the motions of the four moons of Jupiter had 
 been sufficiently observed to construct tables of their 
 movements, with a view to predict their eclipses, 
 some unaccountable phenomena presented them- 
 selves, which, for a long time, baffled all efforts to 
 explain them. It should be remembered, that the 
 orbit of Jupiter encloses that of the earth, and when 
 the two planets happen to be on the same side of the 
 sun, and in a straight line passing through that orb, 
 they are then at their least distance from each other, 
 and are said to be in conjunction. Now suppose Ju- 
 piter to remain stationary, at the end of half a year 
 the earth will have reached the opposite point of her 
 orbit, and will now be more distant from Jupiter by 
 an amount equal to the diameter of her orbit, or 
 nearly 200,000,000 of miles. Retaining carefully 
 these positions in the mind, we shall follow the facts 
 about to be presented with the greatest ease. 
 
 It was found that those eclipses of Jupiter's satel- 
 lites, which occurred while the earth and planet were 
 at their least distance from each other, always came 
 on sooner than the time predicted by the tables ; while, 
 on the contrary, those which took place when the 
 planets were most remote from each other, occurred 
 later than the computed time. A still more extended 
 examination of these remarkable phenomena demon- 
 strated the fact, that the discrepancies depended evi- 
 dently on the absolute increase and decrease of dis- 
 tance which marked the relative position of the plan- 
 
256 STRUCTURE OF THE UNIVERSE. 
 
 ets in their revolutions around the sun. For a long 
 time, no explanation of these undeniable truths could 
 be found, until the mystery was finally solved by 
 Roemer, a Danish astronomer, who, with admirable 
 sagacity, traced these irregularities to their true 
 source, and found that they arose from the fact th&t 
 light traveled through space with a finite and meas- 
 urable velocity. 
 
 The explanation is simple. When Jupiter and the 
 earth are at their least distance from each other, the 
 stream of light flowing from the satellite of the great 
 planet traverses a shorter space to reach the eye of 
 the observer on the earth, by nearly 200,000,000 of 
 miles, than when the planets are most remote from 
 each other. In case, therefore, this stream is in any 
 way cut off, it will run out sooner in the first than in 
 the second position, by the time required to pass over 
 the diameter of the earth's orbit. The stream of light 
 is actually shorter, by 200,000,000 of miles, in the 
 first than in the second position of the planets. 
 
 Now the satellites of Jupiter receive their light 
 from the sun ; — they reflect this light to the ea*rth, and 
 when the body of their primary is interposed between 
 them and their source of light, they are eclipsed ; their 
 light is cut off ; its flow is interrupted ; and when the 
 stream of light starting from them at the instant the 
 supply is cut off shall have run out, then, and not till 
 then, does the satellite become invisible. This ex- 
 planation accounted for all the phenomena in the 
 most beautiful manner; 
 
 The tables had been constructed from the mean of 
 a great number of observed eclipses. Hence, those 
 which took place while Jupiter and the eartb were 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 257 
 
 near to each other, would happen earlier than pre- 
 diction ; while those taking place when the planets 
 were at their greatest distance, would occur later than 
 the time given by the tables. But the velocity with 
 which this mysterious, subtle, intangible substance 
 called light, flew through the regions of space, as de- 
 termined by this wonderful theory, was so great as to 
 startle the minds of even its strongest advocates, and 
 to demand the most positive testimony to induce the 
 belief of those disposed to scepticism. It was found 
 to traverse a distance equal to the entire diameter of 
 the earth's orbit, or 190,000,000 of miles, in about 16 
 minutes ! — giving a velocity of 12,000,000 of miles 
 per minute, or 192,000 miles in each second of time ! 
 
 It is not our purpose to enter into any investi- 
 gation as to the true theory of light, whether it be an 
 actual emanation from a luminous body of material 
 particles, or whether it be a mere vibratory or undu- 
 lating motion produced by luminous bodies on some 
 ethereal medium. My only object, at this time, is to 
 assert the undoubted fact, that in case a luminous 
 body were to be suddenly called into being, and located 
 in space at the distance of 12,000,000 of miles from 
 the eye of an observer, who was on the look-out for 
 its light, this light would not reach him until one minute 
 after the creation of the object; and should it sud- 
 denly be struck from existence, the same observer 
 would behold it for one minute after the extinction. 
 
 Should any mind revolt from these statements — 
 should the difficulty of the investigation, and the in- 
 credible velocity of light, demand higher and better 
 evidence, before full faith can be given to the theory, 
 1 can only say that this evidence shall be given before 
 w 2 
 
258 STRUCTURE OF THE UNIVERSE. 
 
 we close this discussion, and with a fullness and 
 clearness which shall set all doubts at defiance. 
 
 I now proceed to an examination of the great 
 problem of the parallax of the fixed stars, a problem 
 which has taxed the ingenuity of the greatest minds, 
 and which has called into requisition the most admi- 
 rable skill for a period of more than 300 years. A 
 familiar explanation of the nature of this problem 
 may prepare the way for a rapid sketch of the various 
 means which have been employed in its solution. If 
 it were possible to measure on the earth's surface a 
 base line of a thousand miles in length, by locating 
 an observer at each extremity of this base, with in- 
 struments suitable to -fix the moon's place among the 
 fixed stars, the telescopes of those two observers, di- 
 rected to the moon's centre at the same instant, would 
 incline towards each other, and the visual ray from 
 each of those instruments would meet at the moon's 
 centre, and form an angle with each other. This an- 
 gle, or opening of the visual rays, is called the parallax 
 and in case the object under examination were a fixed 
 star, then would the angle in question be called the 
 parallax of the fixed star. 
 
 It is readily seen that when the length of the base 
 is known, and the parallactic angle measured, then 
 the length of the visual ray may be at once deter- 
 mined, and the distance of the object is made known 
 by the simplest rules of geometry. Parallax, then, in 
 general, is the apparent change in the place of an ob- 
 ject, occasioned by the real change in the place of the 
 spectator. 
 
 The whirling of the trees of a forest, produced by 
 the rapid speed of the beholder along a railway, is a 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 259 
 
 parallactic motion, and becomes less and less percep- 
 tible as the velocity of the spectator diminishes, or as 
 the distance of the seemingly moving object becomes 
 greater. To measure the distance of the fixed stars 
 is then equivalent to determining the amount of par- 
 allactic change in their relative positions, occasioned 
 by the actual change of the positions from which they 
 may be viewed by a spectator on the earth's surface. 
 
 With the sun and moon and planets, a base line 
 equal to the earth's diameter, or about 8,000 miles, 
 has sufficed to produce a sensible and measurable 
 parallax ; but when we extend our visual rays to a 
 fixed star, from the extremities of this base, their di- 
 rections, to our senses, are absolutely parallel, or, in 
 other language, the parallax arising from such a base 
 is perfectly insensible. This first effort indicates, at 
 once, the vast distance of the objects under examina- 
 tion ; for such is the accuracy with which minute 
 spaces are now divided, that parallax may be de- 
 tected in case the object is even 160,000 times farther 
 distant than the length of the base line. 
 
 When the orbitual motion of the earth was first 
 propounded by Copernicus, and it was asserted to 
 revolve in an ellipse of nearly 600,000,000 of miles in 
 circumference, and with a motion so swift that it 
 passed over no less than 68,000 miles in every hour 
 of time, the opponents of these startling doctrines ex- 
 claimed No ! this is impossible ; for if we are sweep- 
 ing around the sun in this vast orbit, and with this 
 amazing velocity, then ought the fixed stars to whirl 
 round each other, as do the forest trees to the trav- 
 eler flying swiftly by them. 
 
 But the stars of heaven do not move. Seen from 
 
280 STRUCTURE OF THE UNIVERSE. 
 
 any point, and at any time, their places are ever the 
 same, — fixed, immutable, eternal, — the bright and liv- 
 ing witnesses of the extravagance and absurdity of 
 this new and impossible theory. To this reasoning, 
 which was well founded, and without sophistry, the 
 Copernicans could only reply, that such was the enor- 
 mous distance of the sphere of the fixed stars, that no 
 perceptible change was occasioned by the revolution 
 of the earth in its orbit. But this was mere assertion, 
 and the opponents met the statement by this very 
 plain exhibition of the case. — You who believe in the 
 doctrines of Copernicus assert that the earth revolves 
 on an axis, which, as it sweeps round the sun, re- 
 mains ever parallel to itself. This axis prolonged 
 meets the celestial sphere in a point called the north 
 pole. Now as the earth describes an orbit of nearly 
 200,000,000 of miles in diameter, its axis prolonged will 
 cut out of the sphere of the heavens a curve of equal 
 dimensions, and the pole will appear to revolve and 
 successively fill every point of this celestial curve in 
 the course of the year. Now the north pole does not 
 revolve in any such curve; it is ever fixed, and your 
 theory is false. The Copernican could only reply 
 that all the premises were true, but that the conclu- 
 sion was false. The pole of the heavens did revolve 
 in just such a curve as stated, but such was the dis- 
 tance of the sphere of the fixed stars, that this curve 
 of 200,000,000 of miles in diameter was reduced to 
 an invisible point! 
 
 Three hundred years have rolled away since this 
 controversy began. The struggle has been long and 
 arduous. The mind, baffled in one direction, has di- 
 rected its energies in another — failing in one mcde of 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 261 
 
 research, it devises another, and thus struggling on* 
 ward for three long centuries, it at length triumphs. 
 The facts are developed, and the truth of the grand 
 theory of Copernicus is vindicated and established, 
 and the accuracy of these incredible statements is 
 proved in the clearest manner. 
 
 As this discussion exhibits, clearly and beautifully, 
 the progressive advances of human genius, I shall 
 be pardoned for entering, at some length, into an 
 examination of the various attempts which have 
 been made to resolve the problem of the parallax of 
 the fixed stars. Indeed, the distance of the nearest 
 fixed star is to become the unit of measure with which 
 we are to traverse the innumerable worlds and sys- 
 tems by which we are surrounded, and on the accu- 
 racy with which it shall be determined will depend 
 the correctness of the survey which we are soon to 
 make. 
 
 Failing entirely in obtaining any parallactic angle 
 with a base line of 8,000 miles in length, the earth 
 was employed to transport the observer from the first 
 point of observation to a distance of 190,000,000 of 
 miles, there again to erect his telescope, and to send 
 up his second visual ray to the far distant star, in the 
 hope of finding a parallactic angle with a base of 
 such enormous extent. 
 
 Permit me to illustrate the nature of this investi- 
 gation. Suppose from the centre of a plane a solid 
 granite rock, deep sunk and immoveable, rears its 
 head far above the mists and impurities which float 
 in the lower air. Ascending to the summit, the as- 
 tronomer hews out some rough peak into the form of 
 a vertical shaft. To this solid shaft he bolts the me* 
 
262 STRUCTURE OF THE UNIVERSE. 
 
 tallic plates which shall bear his telescope. The in- 
 strument is of a size and power commensurate with 
 the grand objects which it is required to accomplish. 
 Placed in a position such that its axis shall be exactly- 
 vertical, it is screw-bolted and iron-bound to the solid 
 rock with fastenings which shall hold it from year to 
 year, fixed and immoveable as its rocky base. 
 
 To give more perfect precision to his work, the as- 
 tronomer places in the focus of his eye-piece two 
 delicate lines made from the spider's web, of a mi- 
 nuteness almost mathematical, which, by crossing at 
 right angles, form a point of the utmost precision ex- 
 actly in the axis of the telescope. These are in like 
 manner fixed immoveably in their places, and now 
 the machinery is prepared with which the observa- 
 tions are to be conducted. 
 
 Suppose the observations to commence to-night. — 
 On placing the eye to the telescope, and looking di- 
 rectly up to the zenith, a star enters the field of the 
 instrument, and borne along by the diurnal motion of 
 the heavens, advances towards the central point de- 
 termined by the intersection of the spider's lines. In 
 passing across the field of view, its minute diameter 
 is exactly bisected by one of these delicate lines, and 
 the exact moment, to the hundredth part of a second 
 of time, is noted at which it passes the central point. 
 This observation completed with all possible pre- 
 cision, in case no change in the apparent place of the 
 star is produced by the revolution of the earth in its 
 orbit, or by any other cause, on each successive night 
 throughout the entire year the same phenomena will 
 be repeated in the same precise order. When the 
 hour comes round, the star will enter the field, thread 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 263 
 
 the spider's line, and reach the central poirt at the 
 same precise instant, night after night, even for a 
 thousand revolutions of the earth on its axis. 
 
 Such, then, is the delicate means employed in the 
 examination of the problem of the parallax of the 
 fixed stars; and nearly in this way did Bradley, the 
 great English astronomer, prosecute this intricate in- 
 vestigation. If any change in the star's place is oc- 
 casioned by the revolution of the earth in its orbit, 
 sweeping, as it does, the spectator round the circum- 
 ference of a track nearly 200,000,000 of miles in di- 
 ameter, it is easy to compute, not the amount, but the 
 direction in which these changes will be accomplished. 
 These computations were made by the astronomer, 
 and all things being prepared, he commenced the 
 series of observations which were to lead to the most 
 important results. The discovery of absolute fixity 
 in the star would be a great negative result, and any 
 changes, no matter of what kind or character, could 
 not fail to be detected. 
 
 Night after night was the astronomer found at his 
 post, and as the months rolled slowly away, he began 
 to perceive that his star, which, for a long time, 
 threaded the spider's line as it was in the act of pass- 
 ing the field of the telescope, began slowly to work 
 off from this line, at last absolutely separating itself 
 from it, and failing to reach the central point of the 
 field at the precise instant first recorded. It soon be- 
 came manifest that some cause or causes were oper- 
 ating to produce an apparent change in the place of 
 the star, but what was the astonishment of Bradley 
 to find that the changes in question could not be pro- 
 duced by parallax, for the motions detected were al- 
 
264 STRUCTURE OF THE UNIVERSE. 
 
 most precisely opposite to those which would arise 
 from this cause. 
 
 Long years of laborious examination were finally 
 rewarded with two of the most brilliant discoveries 
 ever accomplished by human skill and genius. The 
 first of these demonstrated the fact that the sun and 
 moon were so operating on the protuberant matter 
 at the earth's equator as to cause the axis of the 
 earth to oscillate or revolve in a minute orbit, nodding 
 to and fro under the influence of the configurations 
 of these two controlling bodies, and following, in the 
 most absolute manner, their relative positions. The 
 effect of this variation, called nutation, is to cause all 
 the stars to appear alternately to approach and recede 
 from the pole. — The real effect is to move the pole by 
 the same amount. 
 
 The value of this change has been determined with 
 the utmost precision, and although its entire effect 
 does not shift the pole over a greater space than the 
 fourth part of the apparent diameter of the planet 
 Jupiter, its values, as deduced by different astronomers, 
 and by different processes, scarcely differ by the frac- 
 tion of a second of space. As a specimen of the ac- 
 curacy attained in these delicate measurements, I will 
 give three values recently obtained by the Russian 
 astronomers. — M. Busch, from Bradley's observations, 
 obtains the value 9". 2320; M. Liendhal, from obser- 
 vations at Derpat, finds the value 9". 1361 ; M. Peters, 
 from right ascensions of Polaris, observed at Derpat, 
 fixes the value at 9^.2164. — The mean of the three 
 values is 9". 2231, the highest difference from which is 
 less than the tenth part of one second of arc. 
 
 Valuable as was this discovery, it was actually sur- 
 
SCALE OS WHICH THE UNIVERSE IS BUILT. 265 
 
 passed by the importance of the second, for which we 
 are in like manner indebted to Bradley. This second 
 phenomenon consisted in an apparent movement of 
 all the fixed stars in a minute orbit, which was ac- 
 complished in a year for every individual, and showed, 
 in the most absolute manner, that it depended in 
 some way on the orbitual revolution of the earth. — 
 For a long time, the true explanation of this phenom- 
 enon, which Bradley saw at once was not parallactic, 
 eluded his highest sagacity. Potent thought and per- 
 severing reflection were, however, at last triumphant, 
 and an explanation was finally reached, not only of 
 the most satisfactory kind, but involving nothing less 
 than an absolute demonstration of the orbitual mo- 
 tion of the earth, and a full confirmation of the velo- 
 city of light, whose prodigious swiftness had stag- 
 gered the faith of many anxious to credit so marvel- 
 ous a statement. 
 
 A few words will suffice to explain these phenom- 
 ena. If we admit the progressive motion of light and 
 the revolution of the earth in its orbit, it is manifest 
 that the celestial bodies will not occupy in the heavens 
 the places they appear to fill. Take, for example, 
 the planet Jupiter, and even suppose the planet to be 
 fixed. The telescope is directed to this object, and 
 the light from the planet, streaming through the axis 
 of the instrument, reaches the eye of the observer, 
 and produces the visible image of the planet. But 
 these very particles of light have occupied nearly 40 
 minutes in passing from the planet to the eye of the 
 observer. During these 40 minutes, the earth has 
 progressed in its orbit some 37,000 miles, and the 
 spectator on the earth, borne along with it, must see 
 X 
 
266 STRUCTURE OF THE UNIVERSE. 
 
 the planet, not where it actually is, but where it was 
 in appearance some forty minutes before. The same 
 effect, in kind, is produced on the places of the fixed 
 stars, and is called aberration. Understanding, now, 
 that some effect must arise from these causes, (the ve- 
 locity of light and the motion of the earth), let us 
 endeavor to render its nature clear, and the results 
 palpable. To accomplish this, we must resort to the 
 simplest means of elucidation. 
 
 Suppose a person were on the deck of a boat float- 
 ing down the current of a river at any given rate per 
 hour. As he moves steadily down the stream, he 
 catches sight of an object on the shore, through which 
 he proposes to send a rifle ball. The marksman will 
 not aim directly at the object. Why? Because he 
 knows that the rifle ball will partake of the boat's 
 motion, and will be carried down, after it leaves the 
 gun and before it reaches the mark, a distance equal 
 to the progressive motion of the boat during the time 
 of flight of the ball. To strike the mark, he must 
 therefore make this necessary allowance, and aim 
 above it the required quantity. It is readily seen that 
 the faster the boat moves, the greater will this allow- 
 ance be. 
 
 Now reverse the proposition, and suppose a rifle 
 fixed on shore, and so directed as to fire a ball down 
 the barrel of a gun on a moving boat. In case the 
 two rifles are on the same exact level, and the axes 
 of the barrels come precisely to coincide, it might be 
 supposed that if the fixed one is fired at the exact in- 
 stant the muzzles come precisely opposite to each 
 other, that the ball from the one will pass down the 
 other. But this, from a moment's reflection, is found 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 207 
 
 to be false. The fixed rifle must be fired before the 
 moving one comes opposite, and the allowance must 
 be made by knowing how long the ball requires to 
 move from the one gun to the other, and with what 
 velocity the moving piece is descending. This com 
 putation being accurately made, the ball from the 
 shore might be made to enter the muzzle of the mov- 
 ing rifle ; but while it is progressing down the barrel, 
 the barrel itself is progressing down the stream, and 
 hence, to avoid the pressure of the ball against the 
 upper side of the barrel, we must fix it in an inclined 
 position, and the bottom of the barrel must be as far 
 up stream as it will descend by the boat's motion du- 
 ring the progress of the ball down the barrel. Hence 
 we see that the direction in which the barrel of the 
 rifle which is to receive the ball is to be placed, is de- 
 ermined by the velocity of the ball, and the velocity 
 of the boat which bears the rifle. 
 
 Now for the application. The particles of light 
 coming from the fixed stars are the balls from the 
 fixed rifle. The boat corresponds to the earth sweep- 
 ing around in its orbit, and bearing with it the tube 
 of the astronomer, down whose axis the particles of 
 light must pass to reach the observer's eye. The ve- 
 locity of the earth's motion is well known, and the 
 amount by which the telescope must be inclined, to 
 cause the light to enter, has been accurately deter- 
 mined, and from these two data the velocity of the 
 light itself becomes known, and confirms, in the most 
 satisfactory manner, the previously determined value 
 of this incredible velocity, while the reality of the 
 earth's motion is absolutely necessary to render the 
 phenomena at all explicable. 
 
268 STRUCTURE OF THE UNIVERSE. 
 
 Such were the beautiful results reached by Bradley, 
 and although nothing was gained with reference to 
 the parallax, these preliminary discoveries were in 
 themselves of the highest value, and prepared the 
 way for subsequent observers, who, with better 
 means and more delicate instrumental aid, might 
 prosecute the same great investigation. 
 
 Amid the numerous and diversified researches of 
 Sir William Herschel, the problem of the parallax of 
 the fixed stars could not fail to engage his attention, 
 by its difficulty and importance. He devised a new 
 means of prosecuting this research, which seemed to 
 promise the most certain success. In his exploration 
 of the heavens with his powerful telescopes, he dis- 
 covered the curious fact that many fixed stars which, 
 to the unassisted eye, appear as single objects, under 
 the space-annihilating power of the telescope, are 
 seen to consist of two, s-ometimes of three or more, 
 individual stars, so close to each other that, to the 
 naked eye, they blend into a single object. 
 
 Herschei, in the outset, conceived that this prox- 
 imity of the stars was an accidental circumstance, 
 and that where a pair could be found, in which one 
 individual was about double the other in magnitude, 
 it might reasonably be inferred that the smaller of the 
 two w r as twice as deeply sunk in space as the larger. 
 If this hypothesis could be shown to be true, then 
 would these objects present an admirable means of 
 detecting, with the greatest accuracy, any change in 
 their relative positions, occasioned by the orbitual 
 motion of the earth. In case their proximity was 
 optical, or merely occasioned by the fact that the vis- 
 ual ray drawn to the one passed v >«*~ly through the 
 
SCALE *JI WHICH THE UNIVERSE IS BUILT. 269 
 
 other, it is manifest that, shifting greatly the position 
 of the observer, the stars might be made to open out 
 or close up on each other, or even revolve the one 
 about the other. In employing this mode of investi- 
 gation, the objects of comparison fell within the field 
 of view of the same telescope, and almost all extra- 
 neous sources of error were eliminated. 
 
 Such was the plan devised, or rather perfected by 
 Herschel, (for his predecessors had already suggested 
 it), and on the prosecution of which he entered with 
 the zeal which ever distinguished this great astrono- 
 mer. When he commenced his researches, some half 
 dozen double stars had been discovered and recorded. 
 His first duty was to increase this number as rapidly 
 as possible, and from his entire catalogue to select 
 those best adapted to his purpose. Under his pene- 
 trating glance, the number of these curious duplex 
 objects increased with astonishing rapidity, and he 
 w r as himself startled with their frequent occurrence. 
 However, with a mind fixed on his original design, he 
 selected a large number of pairs, of such relative 
 magnitudes, and in such positions, as promised 
 the most certain success. Let it be remembered 
 that many of these delicate objects were not divided 
 from each other by a space greater than the thou- 
 sandth part of the sun's diameter. 
 
 To ascertain the apparent changes in the relative 
 positions and distances of the stars composing these 
 pairs, Herschel measured, with every care, the dis- 
 tance which separated them, and took the direction 
 of the line drawn from the centre of the one to the 
 centre of the other. Variations of distance and po- 
 sition, occasioned by parallax, were easily computed 
 x 2 
 
270 STRUCTURE OF THE UNIVERSE. 
 
 in kind and character, and the great astronomer com- 
 menced and prosecuted his observations with san- 
 guine hopes of success. One thing was certain: — all 
 parallactic movements would have a period of one 
 year, since they arise from the annual revolution of 
 the earth in its orbit, and at the end of this period the 
 stars composing the double sets ought to return to the 
 position occupied at the outset. What was Herschel's 
 astonishment to find that, in many instances, the stars 
 composing these pairs were actually in motion; but 
 the movement was certainly not of a parallactic kind, 
 for it neither agreed in direction or in period with the 
 effects of parallax. Here was another grand discovery ! 
 These double stars, which were scattered throughout 
 the heavens with far greater profusion than accidental 
 optical proximity could warrant, were found to be 
 magnificent systems of revolving suns ! They were 
 united by the law of gravitation, and exhibited the 
 wonderful spectacle of stupendous globes, moving in 
 obedience to the same influences which hold the plan- 
 ets in their orbits, and guide the comets in their ec- 
 centric career. — This is not the place to enter into de- 
 tail concerning these wonderful objects. 
 
 While a new field of investigation, boundless and 
 magnificent, was opened up to the human mind; 
 while the great discoverer of these far-sweeping 
 suns was more than rewarded for his toil and labor, 
 the original object of his research was not only left 
 un attained, but the method selected with so much 
 reasonable hope of success, became utterly inapplica- 
 ble. The parallactic and absolute motions of the 
 systems of stars became so inextricably involved, that 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 271 
 
 ihb imperfect micrometrical means of Herschel could 
 not separate them. 
 
 Thus far, the efforts to obtain the distance of the 
 stars had been unavailing. — A negative solution had 
 indeed been reached. That their distance was enor- 
 mous, was made evident, from the fact that the par- 
 allax had remained insensible, even under the most 
 careful and delicate instrumental tests. Any absolute 
 solution began almost to be despaired of, when hope 
 was again revived by the magnificent refracting teles- 
 copes, for which the world was indebted to the skill and 
 genius of the celebrated Frauenhofer, of Munich. — 
 This great artist, aided by the profound science of 
 Bessel, contrived and executed an instrument of ex- 
 traordinary power, and especially adapted to the re- 
 search for the parallax of the fixed stars. 
 
 Armed with a micrometrical apparatus of wonder- 
 ful perfection, and capable of executing measures of 
 great, as well as minute distances, the telescope was 
 so arranged as to be carried forward by delicate ma- 
 chinery, with a velocity exactly equal to the diurnal 
 motion of the object under examination. — To give 
 some idea of the delicacy of the contrivances with 
 which these great telescopes have been provided, it 
 is only necessary to state that the micrometer of the 
 great Refractor of the Cincinnati observatory is capa- 
 ble of dividing an inch into 80,000 equal parts ! — 
 When mechanical ingenuity failed to construct lines 
 of mathematical minuteness, the spider lent his aid, 
 and it is with his delicate web that these measures 
 are accomplished. Two parallel spider's webs are 
 adjusted in the focus of the eye-piece of the microme- 
 ter, and when the light of a small lamp is thrown 
 
272 STRUCTURE OF THE UNIVERSE. 
 
 ■upon them, the eye, on looking through the telescope, 
 sees two minute golden wires, straight and beautiful, 
 draw^n across the centre of the field of view, and pic- 
 tured on the heavens. These are within the control 
 of the observer. He can increase or decrease their 
 distance at pleasure, and so revolve them as to bring 
 them into any position, every motion being accurately 
 measured by properly divided scales. 
 
 Suppose, then, it is desired to take the distance and 
 position of the stars forming a pair. The telescope 
 is directed to them, and they are brought to the centre 
 of the field of view. The clock work is set in action ; 
 it takes up the ponderous instrument, weighing more 
 than 2,500 pounds, and with the most astonishing 
 accuracy it bears it onward, keeping its mighty eye 
 fixed on the object under examination. The observer 
 is thus left with both hands free to make his meas- 
 ures. — He first revolves his micrometer spider's lines 
 round until one of them shall exactly pass from centre 
 to centre of the two stars. This position is noted, 
 and from it is deduced the angle formed by this line 
 with the meridian. He then revolves them a quarter 
 of the circumference, and they are then perpendicular 
 to their former position. He now separates the wires 
 until the one shall exactly bisect one star, while the 
 other wire passes through the centre of the second 
 star, reading this distance on the proper scale. He 
 has fixed, in these two observations, the position and 
 distance of the two components of the double set. — 
 Such is the precision attained in this work, that the 
 most minute motions cannot escape detection. If the 
 stars separate from each other a*t so slow a rate that 
 a million of years would be required to perform the 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 273 
 
 circuit of the heavens, their motion would be detected 
 in half a year ! 
 
 With machinery more delicate even than this, and 
 better adapted to the purpose, and of a kind some- 
 what different, Bessel once more renewed the re- 
 search after the unattainable parallax of the fixed 
 stars. His great instrument, called the heliometer, was 
 mounted as early as 1829, but a multitude of causes, 
 and some unsuccessful efforts, delayed his principal 
 operations up to August, 1837. Three great princi- 
 ples guided him in his selection of 61 in the Swan, 
 as the star on which to perform his observations.— 
 First. It was affected by a very great proper motion, a 
 characteristic which we will explain fully hereafter, 
 and which indicated it to be among the nearest of all 
 the stars. Second. Its duplex character adapted it 
 especially to the instrument he was about to employ. 
 Third. The region occupied by 61 Cygni contains a 
 number of minute stellar points, close to the double 
 star, and presenting admirable fixed points, to which 
 the relative motions of the two components of the 
 star to be measured might be referred. 
 
 With these advantages, and a magnificent instru- 
 ment, Bessel commenced his observations. He meas- 
 ured the distance from the centre of the line joining 
 the two stars, to two of the small stellar points, which 
 served him as points of reference, and this kind of 
 observation was repeated night after night, whenever 
 the stars were visible, from the middle of August, 1837 
 up to the end of September, 1838. The entire series 
 of observations was then taken and corrected for 
 every possible known error, and in case any appre- 
 
274 STRUCTURE OF THE UNIVERSE. 
 
 ciable change remained, it could only be attributed to 
 parallax. 
 
 After a most careful and elaborate investigation, a 
 variation commenced to show itself, increasing pre- 
 cisely as parallactic variation ought to increase, and 
 diminishing as it ought to diminish. The period of 
 these changes was precisely a year, and in all partic- 
 ulars, there was an exact correspondence in kind 
 with the changes which ought to be produced by par- 
 allax. But such was their minute character, that 
 Bessel hesitated. 
 
 During another year the observations were repeated 
 The same results came out, and the previous values 
 were confirmed. A third year's observations, yield- 
 ing precisely the same values, removed all doubt, and 
 the great Koeningsburgh philosopher announced to 
 the world that he had passed the impassable gulf of 
 space, and had measured the distance to the sphere 
 of the fixed stars ! But how shall I convey any ade- 
 quate idea of this stupendous distance ? Millions 
 and millions of miles serve only to confound the 
 mind. Let us employ a different kind of unit. 
 
 Light, as we have seen, travels w T ith a velocity of 
 12,000,000 of miles in every minute of time. Hence, 
 to reach us from the most remote of all the planets, 
 Neptune, whose distance from the sun is about 3,000,- 
 000,000 of miles, will require a journey of about four 
 hours ; but to wing its flight across the interval which 
 separates our sun from 61 Cygni, will require a pe- 
 riod not to be reckoned by hours, or by days, or by 
 months. Nearly ten years of time must roll away 
 before its light, flying, in every second, 192,000 miles, 
 can complete its mighty journey ! If the mind re- 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 275 
 
 volts at this conclusion; if the distance be too great 
 for comprehension ; if the scale of the universe thus 
 suggested even staggers the imagination, I can only 
 say, that all subsequent observation has confirmed, in 
 the most satisfactory manner, the accuracy of Bessel's 
 results. This great astronomer first led the way 
 across the mighty gulf which separates us from the 
 fixed stars. The distance once passed, the route has 
 become comparatively easy, and succeeding observers 
 have determined the parallax of a sufficient number 
 of stars to show that their results are entirely trust- 
 worthy. 
 
 Having now succeeded in gaining a knowledge of 
 the distance which separates our sun from its remote 
 companions, we are prepared to extend our explora- 
 tions of the universe. The question naturally arises, 
 how are the stars distributed throughout space ? — are 
 they indifferently scattered in all directions, or are 
 they grouped together into magnificent systems ? A 
 cursory examination of the starry heavens with the 
 naked eye shows us, that so far as the larger stars 
 are concerned, they do not appear to have been dis- 
 tributed in the celestial sphere according to any deter- 
 minate law ; but on applying the telescope, that lu- 
 minous zone which, under the name of the Milky Way, 
 girdles the whole heavens, is found to be composed of 
 minute stars, scattered like millions of diamond points 
 on the deep blue ground of the sky. 
 
 Sir William Herschel conceived the idea that it 
 might be possible to fathom this mighty ocean of 
 stars, and to determine its metes and bounds ■ to give 
 to it figure, and to circumscribe its limits. It will not 
 be difficult to explain, in a few words, the genera] 
 
276 STRUCTURE OF THE UNIVERSE. 
 
 outline of the plan adopted by this extraordinary man 
 in the prosecution of this wonderful undertaking. — 
 In case we admit that the stars are of equal magni- 
 tudes, and at equal distances from each other, it 
 w^ould not be difficult to ascertain how far they ex- 
 tended in any given direction, the one behind the 
 other. It is manifest, that in examining the heavens 
 with a telescope of given power and aperture, we 
 shall be able to count more stars in the field of view 
 in those regions where they are so arranged as to 
 reach farthest back into space; and in case we know 
 their absolute distance from each other, the number 
 counted in any field of view, will determine with cer- 
 tainty the length of the visual ray reaching to the 
 most remote star visible in that field. 
 
 Now, although the hypothesis that the stars are 
 of equal magnitude, and are uniformly distributed 
 through space, may not be rigorously true, yet doubt- 
 less the mean distances are not far from this hypothe- 
 sis ; and although our results may only be approxi- 
 mate, yet as such they are to be relied upon, and they 
 become the more interesting as they carry us to the 
 utmost limits of human investigation. Armed with 
 his mighty telescopes, Sir William Herschel com- 
 menced the stupendous task of sounding the heavens, 
 with the purpose of ascertaining whether the stars 
 composing the Milky Way were unfathomable, or 
 were bounded and circumscribed by definite limits. 
 
 Sweeping a circle round the heavens which cut this 
 grand stratum of stars in a direction nearly perpen- 
 dicular to its circumference, he directed his great tel- 
 escope to a certain number of points along this circle, 
 and as he moved slowly onward, counted all the stars 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 277 
 
 visible in each field of view. It was fair to conclude, 
 that wherever most stars were to be seen, there was 
 the stratum deepest. Having gone entirely around 
 the heavens, along the circumference of his circle, he 
 had sounded the depth of the stars along a section 
 of the Milky Way, and to obtain the figure of the sec- 
 tion thus cut out was not a difficult matter. 
 
 He assumed a central point on paper to represent 
 his point of observation. He then drew from this 
 point lines radiating, and in the actual directions 
 which he had given to his telescope while engaged in 
 his explorations. On each of these indefinite lines 
 he laid off a distance proportioned to the number of 
 stars counted in the field of view in the direction 
 which the line represented, and by joining these 
 points thus determined, he formed a figure which rep- 
 resented the relative depths to which he had pene- 
 trated into space ; and in case he could be certain 
 that he had gone absolutely through the stratum in 
 every instance, and had grasped every star, even 
 where the extent was most profound, the figure thus 
 constructed would represent the form of the line cut 
 from the outside boundary of the Milky Way by the 
 plane of the circle in which the explorations had been 
 made. 
 
 Did he then actually penetrate the deepest por- 
 tions, or any portion, of the Milky Way ? This was 
 now his grand question, and to its decision he gave 
 all his power and ingenuity. As a unit wherewith 
 to measure the space-penetrating power of his teles- 
 copes, he assumed the power of the human eye, and 
 knowing that stars of the sixth magnitude are within 
 the reach of the unaided eye, he concluded, from the 
 
^78 STRUCTURE OF THE UNIVERSE. 
 
 law regulating the decrease of light, that these mi- 
 nute stars were twelve times more distant than the 
 nearest or brightest stars. Now a telescope having 
 an aperture such as to concentrate twice as much 
 light as the eye, would penetrate into space twice as 
 far, or would reach stars of the twenty-fourth order 
 of distances, and so on for telescopes of all sizes. — 
 In this way he concluded that his great forty foot re- 
 flector, with a diameter of four feet, would penetrate 
 194 times as far as the naked eye, or that it would 
 still see a star of the first magnitude if it were car- 
 ried backward into space 2,328 times its present 
 distance ! 
 
 Such, then, was the computed length of the sound- 
 ing line employed in gauging these mighty depths. — 
 Suppose, then, it was required to determine whether 
 this line actually penetrated any given region of the 
 Milky Way. Even with a single telescope, a series 
 of experiments may be performed which go very far 
 to determine this great question. As the space-pene- 
 trating power of a telescope depends on the diameter 
 of its aperture, it is easy to give to the same instru- 
 ment different powers, by covering up, by circular 
 coverings, certain portions of its object glass. Take 
 circles of paste-board, or any other suitable material, 
 and in the first cut an opening one inch in diameter, 
 in the second an opening of two inches, and so on. 
 up to the diameter of the object glass. These dia- 
 phragms being successively applied to the object 
 glass, give to the telescope space-penetrating powers 
 proportioned to the diameter of the openings. 
 
 In this way Herschel prepared himself to explore 
 one of the deepest portions of the Milky Way. The 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 279 
 
 spot selected was a nebulous or hazy cloud in the 
 sword handle of Perseus, in which, to the naked eye, 
 not a solitary star was visible. I have many times 
 examined the same object, which is certainly one of 
 the most magnificent the eye ever beheld. With the 
 lowest telescopic aid, many stars are rendered visible, 
 surrounded by a hazy light, in which minute glimpse 
 points are occasionally to be seen. As the space- 
 penetrating power was increased, the bright spots of 
 light were successively resolved into groups of bril- 
 liant stars, and more nebulous haze came up from the 
 deep distance, indicating that the visual ray was not 
 long enough to fathom the mighty distance. At last 
 the full power of his grand instrument was brought 
 to bear, when a countless multitude of magnificent 
 orbs burst on the sight, like so many sparkling dia- 
 monds on the deep blue of the heavens. There was 
 no haze behind ; the telescopic ray had shot entirely 
 through the mighty distance, and the clear deep hea- 
 vens formed the back-ground of the brilliant picture. 
 Thus did Herschel penetrate to the limits of the 
 Milky Way, and send his almost illimitable sounding 
 line far beyond, into the vast abyss of space, bound- 
 less and unfathomable. And now do you inquire the 
 depth of this stupendous stratum of stars ? The an- 
 swer may be given, since we have the unit of measure 
 in the distance of stars of the first magnitude. Light, 
 with its amazing velocity, requires ten years to come 
 to us from the nearest fixed stars, and yet Sir Wil- 
 liam Herschel concluded, from the examinations he 
 had been able to make, that in some places the depth 
 of the Milky Way was such, that no less than 500 
 stars were ranged one behind the other in a line, each 
 
280 
 
 STRUCTURE OF THE UNIVERSE. 
 
 separated from the other by a distance equal to that 
 which divides our sun from the nearest fixed star. — 
 So that, for light to sweep across the diameter of this 
 vast congeries of stars, would require a period of a 
 thousand years at the rate of 12,000,000 of miles in 
 every minute of time ! 
 
 The countless millions of stars composing the 
 Milky Way appear to be arranged in the form of a 
 'flat zone or ring, or rather stratum, of irregular shape, 
 which I shall explain more fully hereafter. Its extent 
 is so great as properly to form a universe of itself. — 
 If it were possible, to-night, to wing our flight to any 
 one of the bright stars which blaze around us, sweep- 
 ing away from our own system, until planet after 
 planet fades in the distance, and finally the sun itself 
 shrinks into a mere star, alighting on a strange 
 world that circles round a new and magnificent sun, 
 which has grown and expanded in our sight, until it 
 blazes with a magnificence equal to that of our own, 
 here let us pause and look out upon the starry hea- 
 vens which now surround us. 
 
 We have passed over sixty millions of millions of 
 miles. We have reached a new system of worlds re- 
 volving about another sun, and from this remote 
 point we have a right to expect a new heavens, as 
 w r ell as a new earth on which we stand. But no. — 
 Lift up your eyes, and lo ! the old familiar constella- 
 tions are all there. Yonder blazes Orion, with its 
 rich and gorgeous belt; there comes Arcturus, and 
 yonder the Northern Bear circles his ceaseless journey 
 round the pole. All is unchanged, and the mighty 
 distance over which we have passed is but the thou- 
 sandth part of the entire diameter of this grand clus- 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 281 
 
 ter of suns and systems ; and although we have 
 swept from our sun to the nearest fixed star, and 
 have traveled a distance which light itself cannot 
 traverse in less than ten years, yet the change 
 wrought by this mighty journey, in the appearance 
 of the heavens, is no greater than would be produced 
 in the relative positions of the persons composing 
 this audience to a person near its centre, who should 
 change his seat with his immediate neighbor ! 
 
 Such, then, is the scale on which the starry heavens 
 are built. If, in examining the magnificent orbits of 
 the remoter planets, and in tracing the interminable 
 career of some of the far-sweeping comets, we feared 
 there might not be room for the accomplishment of 
 their vast orbits, our fears are now at an end. There 
 is no jostling here ; there is no interference, no per- 
 turbation of the planets of one system by the suns of 
 another. Each is isolated and independent, filling 
 the region of space assigned, and within its own 
 limits, holding on its appointed movements. 
 
 Thus far we have spoken only of the Milky Way. 
 In case it be possible to pierce its boundaries, and 
 pass through into the regions of space which lie be- 
 yond, the inquiry arises, what meets the vision there? 
 What lies beyond these mighty limits ? Does crea- 
 tion cease with this one great cluster, and is all blank 
 beyond its boundary? 
 
 Here again the telescope has given us an answer 
 When we shall have traveled outward from our own 
 sun, and passed in a straight line from star to star, 
 until we shall have left behind us in grand perspec- 
 tive a series of five hundred suns, we then stand on 
 the confines of our own great cluster of stars. All 
 v2 
 
282 STRUCTURE OF THE UNIVERSE. 
 
 behind blazes with the light of countless orbs, scat- 
 tered in wild magnificence, while all before us is deep, 
 impenetrable, unbroken darkness. No glance of hu- 
 man vision can pierce the dark profound. 
 
 But summoning the telescope to our aid, let us pur- 
 sue our mighty journey through space ; far in the dis- 
 tance we are just able to discover a faint haze of light 
 — a minute luminous cloud which comes up to meet 
 us — and towards this object we will urge our flight. 
 We leave the shining millions of our own great clus- 
 ter far behind. Its stars are shrinking and fading ; 
 its dimensions are contracting. It once filled the 
 whole heavens, and now its myriads of blazing orbs 
 could almost be grasped with a single hand. But 
 now look forward. — A new universe, of astonishing 
 grandeur, bursts on the sight. The cloud of light has 
 swelled and expanded, and its millions of suns now 
 fill the whole heavens. 
 
 We have reached the clustering of ten millions of 
 stars. Look to the right ; there is no limit ; — look to 
 the left ; there is no end. Above, below, sun rises 
 upon sun, and system on system, in endless and im- 
 measurable perspective. Here is a new universe, as 
 magnificent, as glorious as our own, — a new Milky 
 Way, whose vast diameter the flashing light would 
 not cross in a thousand years. Nor is this a solitary 
 object. Go out on a clear cold winter night, and 
 reckon the stars which strew the heavens, and count 
 their number, and for every single orb thus visible to 
 the naked eye the telescope reveals a universe, far 
 sunk in the depths of space, and scattered with vast 
 profusion over the entire surface of the heavens. 
 
 Some of these blaze with countless stars, while 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 283 
 
 others occupying the confines of visible space, bu* 
 dimly stain the blue of the sky, just perceptible with 
 the most powerful means that man can summon t< 
 the aid of his vision. These objects are called clus- 
 ters and nebulae, — clusters when near enough to per- 
 mit their individual stars to be shown by the telescope, 
 nebulae when the mingled light of all their suns and 
 systems can only be seen as a hazy cloud. 
 
 Thus have we risen in the orders of creation. We 
 commenced with a planet and its satellite ; — we rose 
 to the sun and its revolving planets, a magnificent 
 system of orbs, all united into one great family, and 
 governed by the same great law ; and we now find 
 .nillions of these suns clustered and associated to- 
 gether in the formation of distinct universes, whose 
 number, already revealed to the eye of man, is not to 
 be counted by scores or hundreds, but has risen to 
 thousands, while every increase of telescopic power 
 is adding by hundreds to their catalogue. 
 
 Let us now explain these " island universes," as 
 the Germans have aptly termed them, and attempt 
 approximately to circumscribe their limits, and meas- 
 ure their distances from us, and from each other. — 
 Sir William Herschel, to whom we are indebted for 
 this department of astronomy, conceived a plan by 
 which it was possible approximately to sound the 
 depths of space, and determine, within certain limits, 
 the distance and magnitudes of the clusters and neb- 
 ulae within the reach of his telescopes. To convey 
 some idea of his method of conducting these most 
 wonderful researches, imagine a level plane, of in- 
 definite extent, and along a straight line, separated 
 by intervals of one mile each, let posts be placed 
 
284 STRUCTURE OF THE UNIVERSE. 
 
 bearing boards on which certain words are printed in 
 letters of the same size. The words printed on the 
 nearest board, we will suppose, can just be read with 
 the naked eye. To read those on the second, teles- 
 copic aid is required, and that power which suffices to 
 enable the letters to be distinctly seen, is exactly 
 double that of the unaided eye. The telescope reveal- 
 ing the letters at the distance of three miles is three- 
 fold more powerful than the eye, and so of all the 
 others. In this way we can provide ourselves w T ith in- 
 struments whose space-penetrating power, compared 
 with that of the eye, can be readily obtained. 
 
 Now to apply these principles to the sounding of 
 the heavens. The eye, without assistance, would 
 follow and still perceive the bright star Sirius, if re- 
 moved back to twelve times its present distance. — 
 After this, as it recedes, it must be followed by the 
 telescope. Suppose, then, a nebula is discovered 
 with a telescope of low power, and it is required to 
 determine its character and distance. The astrono- 
 mer applies one power after another, until he finally 
 employs a telescope of sufficient reach to reveal the 
 separate stars of which the object is composed, which 
 shows it to be a cluster ; and since the space-pene- 
 trating power of this instrument is known, relative to 
 that of the human eye, in case the power is one hun- 
 dred times greater than that of the eye, then would 
 the cluster be located in space one hundred times far- 
 ther than the eye can reach, or twelve hundred times 
 more remote than Sirius, or at such a distance that 
 its light would only reach our earth after a journey 
 of 120,000 years ! 
 
 Such was HerschePs method of locating these ob- 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 285 
 
 jects in space. Some are so remote as to be far be- 
 yond the reach of the most powerful instruments, and 
 no telescopic aid can show them other than nebulous 
 clouds of greater or less extent. It was while pursu- 
 ing these grand investigations that Herschel was led 
 to the conclusion, that among the nebulae which were 
 visible in the heavens, there w r ere some composed of 
 chaotic matter, a hazy, luminous fluid, like that occa- 
 sionally thrown out from comets on their approach to 
 the sun. 
 
 Among these chaotic masses he discovered some in 
 which the evidences of condensation appeared mani- 
 fest, while in others he found a circular disc of light, 
 with a bright nucleus in the centre. Proceeding yet 
 farther, he found well formed stars surrounded by a 
 misty halo, which presented all the characteristics of 
 what he now conceived to be nebulous fluid. Some 
 of the unformed nebulae were of enormous extent, 
 and among those partially condensed, such as the 
 nebulae with planetary discs, many were found so 
 vast that their magnitude would fill the space occu- 
 pied by the sun and all its planets, forming a sphere 
 with a diameter of more than 6000 millions of miles. 
 Uniting these and many other facts, the great astron- 
 omer was finally brought to believe, that worlds and 
 systems of worlds might yet be in the process of for- 
 mation, by the gradual condensation of this nebulous 
 fluid, and that from this chaotic matter originally 
 came the sun and all the fixed stars which crowd the 
 heavens. This theory, extended, but not modified, in 
 the hands of Laplace, is made to account for nearly 
 all the phenomena of the solar system, and has been 
 already referred to in a former lecture. 
 
286 STRUCTURE OF THE UNIVERSE. 
 
 For a long time, this bold and sublime speculation 
 was looked upon, even by the wisest philosophers, 
 with remarkable favor. The resolution of one or two 
 nebulae, (so classed by Herschel), with the fifty- two 
 feet reflector of Lord Rosse, has induced some persons 
 to abandon the theory, and to attempt to prove its 
 utter impossibility. All that I have to say, is, that 
 Herschel only adopted the theory after he had resolv- 
 ed many hundreds of nebulae into stars ; and if there 
 ever existed a reason for accepting the truth of this 
 remarkable speculation, that reason has been scarcely 
 in any degree affected by recent discoveries. 
 
 I have examined a large number of these mysteri- 
 ous objects, floating on the deep ocean of space like 
 the faintest filmy clouds of light. No power, how- 
 ever great, of the telescope, can accomplish the slight- 
 est change in their appearance. So distant that their 
 light employs (in case they be clusters) hundreds of 
 thousands of years in reaching the eye that gazes 
 upon them, and so extensive, even when viewed from 
 such a distance, as to fill the entire field of view of 
 the telescope many times. Sirius, the brightest, and 
 probably the largest of all the fixed stars, with a di- 
 ameter of more than a million of miles, and a dis- 
 tance of only a single unit, compared with the tens of 
 thousands which divide us from some of the nebulae ; 
 and yet this vast globe, at this comparatively short 
 distance, is an inappreciable point in the field of the 
 telescope. What, then, must be the dimensions of 
 those objects, which, at so vast a distance, fill the en- 
 tire field of view even many times repeated ? 
 
 Herschel computes that the power of his great re- 
 flectoi would follow one of the large clusters if it 
 
SCALE ON WHICH THE UNIVERSE IS BUILT. 287 
 
 were plunged so deep in space that its light would re- 
 quire 350,000 years to reach us, and the great teles- 
 cope of Lord Rosse would pursue the same object 
 probably to ten times this enormous distance. 
 
 Such examinations absolutely overwhelm the mind, 
 and the wild dream of the German poet becomes a 
 sort of dreadful sublime reality : — 
 
 " God called up from dreams a man into the vesti- 
 bule of heaven, saying, ' Come thou hither, and see 
 the glory of my house.' And to the servants that 
 stood around his throne he said, f Take him, and un- 
 dress him from his robes of flesh : cleanse his vision, 
 and put a new breath into his nostrils : only touch 
 not with any change his human heart — the heart 
 that weeps and trembles.' It was done : and, with a 
 mighty angel for his guide, the man stood ready for 
 his infinite voyage ; and from the terraces of heaven, 
 without sound or farewell, at once they wheeled away 
 into endless space. Sometimes with the solemn flight 
 of angel wing they fled through Zaarrahs of darkness, 
 through wildernesses of death, that divided the worlds 
 of life ; sometimes they swept over frontiers, that 
 were quickening under prophetic motions from God. 
 Then, from a distance that is counted only in heaven, 
 light dawned for a time through a sleepy film ; by un- 
 utterable pace the light swept to them, they by unut- 
 terable pace to the light. In a moment the rushing 
 of planets was upon them : in a moment the blazing 
 of suns was around them. 
 
 " Then came eternities of twilight, that revealed, 
 but were not revealed. On the right hand and on the 
 left towered mighty constellations, that by self-repeti- 
 tions and answers from afar, that by counter-positions, 
 
288 STRUCTURE OF THE UNIVERSE. 
 
 built up triumphal gates, whose architraves, wh se 
 arch-ways — horizontal, upright — rested, rose — at alti- 
 tude by spans — that seemed ghostly from infinitude. 
 Without measure were the architraves, past number 
 were the archways, beyond memory the gates. Within 
 were stairs that scaled the eternities below ; above 
 was below — below was above, to the man stripped 
 of gravitating body : depth was swallowed up in 
 height insurmountable, height was swallowed up in 
 depth unfathomable. Suddenly, as thus they rode 
 from infinite to infinite, suddenly, as thus they tilted 
 over abysmal worlds, a mighty cry arose — that sys- 
 tems more mysterious, that worlds more billowy, — 
 other heights and other depths, — were coming, were 
 nearing, were at hand. 
 
 " Then the man sighed, and stopped, shuddered, and 
 wept. His overladened heart uttered itself in tears ; 
 and he said — ' Angel, I will go no farther. For the 
 spirit of man acheth with this infinity. Insufferable 
 is the glory of God. Let me lie down in the grave 
 and hide me from the persecution of the infinite ; for 
 end, I see, there is none.' And from all the listening 
 stars that shone around issued a choral voice, ' The 
 man speaks truly : end there is none, that ever yet 
 we heard of. 5 [ End is there none?' the angel 
 solemnly demanded : ' Is there indeed no end ? — and 
 is this the sorrow that kills you ? ' But no voice an- 
 swered, that he might answer himself. Then the 
 angel threw up his glorious hands to the heaven of 
 heavens, saying, 'End is there none to the universe 
 of God. Lo ! also there is no beginning.' " 
 
LECTURE X. 
 
 THE MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 
 
 Having reached, in the course of the preceding lec- 
 ture, to the outermost confines of the visible creation, 
 let us now return home from this survey of the " island 
 universes " which crowd the illimitable regions of 
 space, to the stars which compose our own cluster, 
 and learn how far the human mind has progressed in 
 its examination of the millions of suns which consti- 
 tute, in a more definite sense, our own Milky Way. 
 
 We have already seen that the parallax of 61 
 Cygni rewarded the laborious and extraordinary ef- 
 forts of Bessel. The example set by this great as- 
 tronomer encouraged those who followed him, and 
 while his results in this particular case have been 
 confirmed in the most astonishing manner, the dis- 
 tances of many other stars have been obtained, until 
 a sufficient amount of data has been accumulated to 
 determine the approximate distances of the spheres 
 of the fixed stars of different magnitudes. Struve es 
 timates the mean distance of stars of the first magni 
 tude to be 986,000 times the radius of the earth's 
 orbit, or so remote that their light reaches us only 
 after a journey of fifteen years and a half. Stars of 
 the second magnitude send us their light in twenty- 
 eight years, those of the third magnitude in forty- 
 three years ; while the light from stars of the ninth 
 
 Z ' 289 ) 
 
290 STRUCTURE OF THE UNIVERSE. 
 
 magnitude only reaches the eye of the observer after 
 traversing 3pace for five hundred and eighty-six years, 
 at the rate of twelve millions of miles in every min- 
 ute of time. 
 
 My range of investigation does not permit me to 
 explain, at this time, how these extraordinary conclu- 
 sions have been reached. The reasoning, however, is 
 close and clear, and the results are no doubt approxi- 
 mately correct. 
 
 Such, then, are the distances separating man from 
 the objects of his research. To have attained to a 
 knowledge of these distances even, is sufficiently 
 wonderful, but what we are about to reveal as the 
 results of human investigation among these far dis- 
 tant orbs, cannot fail to fill the mind with astonish- 
 ment, and demonstrate the great truth that " man has 
 been made but a little lower than the angels." 
 
 Before it became possible to examine with absolute 
 certainty the places of the stars, with a view to as- 
 certain their absolute fixity, many difficult preliminary 
 preparations had to be accomplished. Instruments 
 of the most perfect kind must be provided, not only 
 in their optical performances, but in their space-di- 
 viding machinery. Moreover, the places of the stars, 
 as determined by the best telescopes, must be cor- 
 rected for every possible instrumental error. The 
 two points to which the stars are referred are the 
 north pole and the vernal equinox. In case any mo- 
 tions belong to these points, their amounts and di- 
 rections must be ascertained and allowed for. Then 
 the effects of refraction, and of the abberration of 
 light, were indispensable to a perfect investigation of 
 the absolute places of the stars. 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 291 
 
 All these and many other preliminary matters hav- 
 ing been satisfactorily determined, it became possible 
 to examine, in the most critical manner, the places of 
 the stars, and to learn whether indeed, (as had been 
 supposed for thousands of years), their configura- 
 tions were eternal and unchangeable, or whether they 
 moved among themselves with a motion rendered so 
 slow by their immense distance, as hitherto to have 
 escaped the most scrutinizing watch. 
 
 Fully armed with the necessary instruments, it did 
 not require many years to determine the grand truth, 
 that among the tens of thousands of stars which fill 
 the heavens, not a solitary one, in all probability, is 
 in a state of absolute rest. Many were found to 
 move so swiftly, that their velocity was determined 
 even in a single year; while others, in consequence of 
 their enormous distance, may require centuries to de- 
 tect any appreciable change. In the outset these ex- 
 traordinary movements seemed to be directed by no 
 law — some stars were sweeping in one direction, and 
 some in another. Motion, ceaseless, eternal motion, 
 seems to be stamped on the entire universe, and 
 while the stars are pursuing their mighty orbits, we 
 cannot resist the idea that our own sun, the centre of 
 our great planetary system, itself a star, must partici- 
 pate in the general movement, and is, in all probabil- 
 ity, urging its flight, accompanied by all its planets, 
 satellites, and comets, to some unknown region of 
 space. 
 
 The revolution of the stars, the organization of the 
 grand cluster with which our sun is associated, the 
 demonstration of the sun's absolute translation through 
 space, its direction, velocity, and period, are the topics 
 
292 STRUCTURE OF THE UNIVERSE. 
 
 to which I invite your attention in the closing lecture 
 of the present course. 
 
 When forced to acknowledge the rotation of our 
 globe on its axis, and its swift orbitual motion, sur- 
 rounded by wheeling planets and flying comets, the 
 mind naturally retreats to the sun as the great im- 
 moveable centre, where it can rest and contemplate 
 these circling worlds. But even here, as we shall 
 presently see, there is no rest. The sun himself be- 
 comes a subordinate member of a grander combina- 
 tion of worlds, and, obedient to higher influence, 
 sweeps around in its unmeasured orbit. 
 
 We shall present a rapid summary of the evidences 
 of change among the fixed stars, and then proceed to 
 develop the reasoning by w r hich the direction and 
 velocity of the sun's motion in space has been 
 determined. 
 
 More than two thousand years ago, the celebrated 
 Greek astronomer, Hipparchus, was astonished by 
 the sudden bursting forth of a brilliant star in a re- 
 gion of the heavens where none had previously ex- 
 isted. Up to this time, no doubt of the immutability 
 of the starry sphere seems to have been entertained, 
 and while the philosopher gazed and wondered, he 
 resolved to execute a work from which posterity 
 might learn the changes of the celestial sphere. He 
 undertook and completed his great catalogue of the 
 places of a thousand stars, locating them with all the 
 accuracy permitted by the rude instruments then in 
 use. Subsequent observers, by comparing their own 
 determined positions of the stars with their places as 
 fixed on the catalogue of Hipparchus, could readily 
 perceive any sensible change which might occur in 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 293 
 
 their configuration, the appearance of new stars, or 
 the disappearance of those which had once existed. 
 
 The sudden breaking forth of a new star is a phe- 
 nomenon of such wonderful character that we might 
 well doubt the possibility of its occurrence, if we 
 were obliged to rely on the historical account trans- 
 mitted to us from the time of Hipparchus. But, for- 
 tunately, more than one brilliant example of the kind 
 has occurred in modern times, presenting the most 
 unequivocal evidence of the reality of this inexpli- 
 cable wonder. 
 
 In 1572, a new star of great splendor appeared 
 suddenly in the constellation Cassiopeia, occupying 
 a position which had previously been blank. This 
 star was first perceived by Schuler, of Wittemburg, 
 on the 6th of August. It was detected by Tycho, the 
 Danish astronomer, on the 11th of the following No- 
 vember, and the wonder produced by this most extra- 
 ordinary phenomenon induced him to give to the star 
 the most unremitting attention. Its magnitude in- 
 creased until it is said to have surpassed even Jupiter 
 in splendor, and finally became visible in the day 
 time. It retained its greatest magnitude but for a 
 very short time, when it commenced to diminish in 
 brilliancy, changing from white to yellow, then to 
 reddish, and finally it became faintly blue; and so di- 
 minishing by degrees, it vanished from the sight in 
 March, 1574, and has never since been seen. 
 
 In the year 1604, while the scholars of Kepler 
 were engaged in observations of Mars, Jupiter and 
 Saturn, then in close proximity to each other, having 
 been interrupted a day or two by clouds, on the re- 
 turn of fine weather, Maestlin was astonished to find 
 z 2 
 
294 STRUCTURE OF THE UNIVERSE. 
 
 near the planets then in the constellation Ophiuchus, 
 a brilliant star, which certainly had not been there a 
 few days before. This object attracted the attention 
 of all the great astronomers then living, and was par- 
 ticularly observed by Galileo and Kepler. It is said 
 to have attained a splendor equal to that of the 
 planet Venus, and from this, its greatest brilliancy, it 
 gradually declined, until, about the beginning of 1606, 
 it ceased to be visible, and no telescopic power 
 has since been able to detect any star in the place 
 once occupied by this remarkable stranger. 
 
 Although observed with the greatest care, no sensi- 
 ble parallax was ever detected in either of these ob- 
 jects, and no doubt exists as to their occupying the 
 region of the fixed stars. Many other less remarka- 
 ble examples are on record, but up to the present no 
 satisfactory explanation of this astonishing phenom- 
 enon has been given. Whether it indicates the actual 
 destruction of some magnificent system, or the revolu- 
 tion of these stars in orbits of great eccentricity, caus- 
 ing them to appear to us, like the comets, only in the 
 perihelion points of their mighty orbits, is equally un- 
 certain. One thing is certain : they present evidence 
 of change in the starry heavens, of the most startling 
 and irresistible kind. 
 
 While new stars have occasionally made their ap- 
 pearance, to astonish mankind with their brilliancy, 
 there are many well authenticated cases of the entire 
 disappearance of old stars, whose places had been 
 fixed with a degree of certainty not to be doubted. — 
 In October, 1781, Sir William Herschel observed a 
 star, No. 55 in Famsted's catalogue, in the constella- 
 tion Hercules. In 1790, the same star was observed 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 295 
 
 by the same astronomer, but since that time no search 
 has been able to detect it. The star is gone ; whether 
 never to return, it is impossible to say. A like dis- 
 appearance has occurred with reference to the stars 
 numbered 80 and 81, both of the fourth magnitude, in 
 the same constellation. In May, 1828, Sir John Her- 
 schel missed the star numbered 42 in the constella- 
 tion Virgo, which has never since been seen. Exam- 
 ples might be multiplied, but it is unnecessary. 
 
 In these cases the stars have been lost entirely ; — 
 no return has ever been marked ; and but for the dis- 
 covery of another class of remarkable objects among 
 the stars, no return would probably ever have been 
 suspected. If I could direct your attention to-night 
 to a brilliant star named Algol, in the head of Medusa, 
 and bring a powerful telescope to aid in your exam- 
 inations, this star, while you are watching it, might 
 be seen to lose its splendor, and from its rank of the 
 second magnitude to decline in brightness, until it 
 would scarcely be visible to the naked eye. Having 
 reached a certain limit, it would commence an in- 
 crease, and by slow degrees resume its original splen- 
 dor. — This decrease and increase is actually accom- 
 plished in about eight hours. Having regained its 
 usual light, it remains stationary for about two days 
 and a half, and then repeats the changes already de- 
 tailed ; and thus have its periodical fluctuations con- 
 tinued since the date of its discovery, with the most 
 astonishing regularity. The bright star marked 
 Beta, in the constellation Lyra, is known to pass 
 from the third to the fifth magnitude, and to regain its 
 light in a period of six days and nine hours. These 
 are called periodical stars, and a sufficient number 
 
296 STRUCTURE OF THE UNIVERSE. 
 
 have already been detected to present a progressively 
 increasing series of periods from two days twenty 
 hours up to four hundred and ninety-four days, and in 
 one case even many years. 
 
 Here, again, are phenomena indicative of extraor- 
 dinary activity in these remote regions of space. — - 
 No explanation of these changes has yet been given 
 in all respects satisfactory. Some have attributed 
 them to the existence of dark spots on the stars, which, 
 by rotation on an axis, periodically present them- 
 selves, and thus dim the lustre of the stars. Others 
 think the changes are due to the revolution of large 
 planets about the stars, which, by coming between 
 the eye and the star, eclipse a portion of its light ; 
 while a third class conceive the fluctuations to arise, 
 in some instances at least, from an orbitual motion of 
 the stars in orbits of excessive elongation, and so lo- 
 cated as to have their greater axes directed towards 
 our system. 
 
 It will be seen that this theory may be readily ex- 
 tended so as to embrace the new stars already refer- 
 red to, and even to account for those which have been 
 lost from their places in the heavens. Here, how- 
 ever, we enter the confines of the uncertain. Centu- 
 ries may roll away before the true explanation of 
 these astonishing changes shall be given ; but the 
 mind is on the track, and with a steady and resistless 
 movement is slowly pushing its investigations deeper 
 and still deeper into the dark unknown. 
 
 While the phenomena of the new and lost stars, 
 and the fluctuations in the light of the variable ones, 
 gave undeniable evidence of constant change in what 
 Aristotle was pleased to call the eternal and incor- 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 297 
 
 ruptible heavens, HerschePs brilliant discovery of the 
 orbitual motion of the double stars gave to the mind 
 the opportunity of determining the nature of the law 
 which sways the movements in these distant regions 
 of space. It was natural, in the first efforts to com- 
 pute the orbits of the double stars, to adopt the hy- 
 pothesis that they attracted each other by the same 
 law which prevails in the planetary system. Results 
 did not disappoint expectation. — Gravitation, which 
 Newton, in the outset of his great discovery, had 
 boldly affirmed exerted its influence wherever matter 
 existed or motion reigned, was extended, in the 
 most absolute manner, to the region of the fixed stars. 
 There, at a distance from our own system almost in- 
 conceivable, suns and systems of suns, rising in orders 
 of greater complexity, revolving with swift velocity, or 
 with slow and majestic motion, bore testimony, ample 
 and unequivocal, to the truth of the great law of 
 universal gravitation. 
 
 Every particle of matter in the universe attracts 
 every other particle of matter with a force which is 
 proportioned directly to the mass, and which decreases 
 as the square of the distance at which it operates in- 
 creases. This is no longer a bold hypothesis. The 
 double star marked Zeta, in the constellation Hercu- 
 les, has been subjected to the analysis of the com- 
 puter. The elements of its orbit have been obtained, 
 and true to its predicted period, it has actually per- 
 formed an entire revolution in a period of thirty-five 
 years. The components of the star Eta, in the 
 Northern Crown, revolve around their common centre 
 in about forty-four years. Both of these pairs have 
 completed an entire revolution since their discovery. 
 
298 STRUCTURE OF THE UNIVERSE. 
 
 Many others might be named, but my only object, at 
 present, is to exhibit the evidence which shall remove 
 all doubt as to the actual extension of the law of 
 gravitation to the fixed stars. 
 
 Let it be remembered that this department of as- 
 tronomy is yet in its infancy. Thousands of double 
 stars have been detected, and every year adds hun- 
 dreds to the list. Among these, a large proportion 
 must prove to be binary systems, varying in their 
 periods of revolution, from thirty years or less, up to 
 many thousands, perhaps millions of years. 
 
 The association of two suns naturally suggests the 
 possible union of a greater number, forming more 
 complicated systems. This idea has been verified — a 
 large number of triple systems has been discovered. 
 In a few instances quadruple sets have been found, 
 of which a remarkable example exists in the constel- 
 lation of the Harp. Here was found four suns, ar- 
 ranged in pairs of two. The components of the 
 first pair revolve around each other in about one thou- 
 sand years ; those of the second pair appear to re- 
 quire about double that period, while one pair re- 
 volves about the other in a period which, determined 
 roughly from their distance, cannot fall much below a 
 million of years ! The evidence of the physical union 
 of these four stars into one grand system rests, at 
 present, on the ascertained fact that their proper mo- 
 tions are the same. 
 
 From quadruple systems we rise, by analogy, still 
 higher, until we find hundreds, sometimes thousands, 
 of stars compacted together in so small a compass 
 that their proximity cannot be the effect of accident. 
 Look at the beautiful little cluster called the Pleiades ; 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 299 
 
 an ordinary eye may here see six or seven stars. One 
 of very great power has been known to count four- 
 teen in this group, while the telescope increases the 
 number to hundreds ; and yet the space in which they 
 are located might easily be covered by the moon. 
 
 Suppose an indifferent scattering of the stars 
 through space, and compute the chances that such a 
 number would fall together at any one point, and we 
 shall find not one chance out of millions in favor of 
 such an accident. We are therefore forced to the 
 conclusion that here is a more magnificent order, one 
 in which hundreds of suns, surrounded by their sub- 
 ordinate worlds, are all united by gravitation into 
 one grand system. This is not a solitary example. — 
 Many of these beautiful objects, comparatively close 
 to our sun, are found in the heavens, leading the 
 mind gradually up to the contemplation and examina- 
 tion of that mighty system of systems, that great 
 cluster of clusters, the Milky Way, of which all these 
 are but subordinate groupings, — vast in themselves, 
 but when compared with the whole, mere units 
 among the millions of which it is composed. 
 
 From what we have seen, it is impossible to avoid 
 the conclusion that gravitation exerts its power 
 among the myriads of shining orbs which strew the 
 Milky Way. The innumerable suns which form this 
 stupendous cluster must feel the reciprocal influence 
 of each other, and nothing short of the centrifugal 
 force arising from orbitual motion can balance this 
 universal attractive power, and give to this grand 
 system the great characteristic of stability. 
 
 Herschel succeeded, at least approximately, in sound- 
 ing the profundities of the Milky Way, and fixed the 
 
300 STRUCTURE OF THE UNIVERSE. 
 
 relative position of our own sun among the stars by 
 which it is surrounded. He found it to be located 
 not very distant from the centre of the great stratum, 
 and near the line where the principal current of stars 
 divides into two great streams, which for a time sep- 
 arate from each other, but finally reunite in a distant 
 region of the heavens. 
 
 Having accomplished thus much, this great astrono- 
 mer attempted the resolution of the grand problem 
 of the sun's movement through space. This investi- 
 gation is so lofty, so daring and utterly incomprehen- 
 sible at the first glance, that its mere announcement 
 produces little effect on the mind. Consider, for one 
 moment, what it involves. Man is located on a 
 planet almost infinitely larger than himself. This 
 planet is swiftly revolving on its axis, and in its orbit 
 round a great central luminary, the sun. The daring 
 philosopher participates in all these motions. He 
 provides himself with instruments which measure the 
 distances and positions of the almost infinitely dis- 
 tant fixed stars. These fixed stars, when subjected 
 to his critical examination, cease to be fixed, and are 
 found to be moving with astonishing velocity in all 
 directions. Among these he numbers his own sun, 
 and although borne along in the progressive motion 
 of his own great centre, he ventures to attempt the 
 determination of the fact of its actual motion, the di- 
 rection in which it moves, and the velocity with 
 which it is sweeping through space. 
 
 This problem is so wonderful that I beg your ear- 
 nest attention while the effort is made to simplify 
 the reasoning by which its resolution has been 
 accomplished. 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 301 
 
 Before the actual motions of the earth were dis- 
 covered, the sun, moon, and planets, as well as the 
 stars, appeared to move in certain directions, and with 
 certain velocities, not easily explained. The rotation 
 of the earth on its axis rendered a clear explanation 
 of the diurnal movements of the heavenly bodies, and 
 its orbitual motion around the sun explained the sun's 
 apparent annual movement among the fixed stars. — 
 Thus it is seen and readily apprehended, that in case 
 the spectator is progressing, his actual motion may 
 be transferred to distant bodies under examination, 
 and these may appear to move while he seems to be 
 at rest. 
 
 Now in case the sun is sweeping towards any 
 quarter of the heavens, it must carry with it all its 
 planets, satellites, and comets. The earth is borne 
 along in common with its companions, and the ob- 
 server on its surface will transfer his own movemen 
 through space to the distant objects which only ap- 
 pear to change their places, in consequence of his 
 own translation through space. Thus the distant 
 stars may be affected with a parallactic change, not 
 to be confounded with that produced by the revolu- 
 tion of the earth in its orbit, but occasioned by the 
 fact that while the earth revolves around the sun, she 
 is carried forward by this luminary in his journey 
 through space. As the whole system participates in 
 this motion, in case the planets are inhabited, their 
 astronomers will detect in the fixed stars the paral- 
 lactic motion due to the suits movement, and hence 
 this change among the stars may be properly termed 
 their systematic parallax. 
 
 Herschel commenced his examination of this great 
 2 A 
 
302 STRUCTURE OF THE UNIVERSE. 
 
 problem by forming a catalogue of stars situated in 
 all parts of the heavens, in which an appreciable 
 amount of proper motion had been detected and meas- 
 ured. Now in case this apparent motion of the stars 
 could be attributed to the movement of the solar sys- 
 tem through space, a close scrutiny of the directions 
 in which the stars appeared to move w r ould indicate 
 the direction in which the observer, carried along 
 with the sun, was passing through space. 
 
 In case a person is traveling on a railway, in a di- 
 rect line through a forest of trees, as he advances, all 
 objects tow r ards which he is moving will appear to 
 open out or separate from each other, while those left 
 behind will appear to close up. If, then, the astrono- 
 mer, borne along by the movement of the sun through 
 the vast forest of stars by which he is surrounded, de- 
 sires to ascertain the direction in which he is progres- 
 sing, let him search the heavens until he finds a point 
 where the stars seem to be increasing their distance 
 from each other. Should he find such a point, let 
 him confirm his suspicions by looking in the direction 
 precisely opposite and behind him, and in case he 
 finds the stars located in this region closing up on 
 each other, he may fairly conclude that he has found 
 the direction in which he is moving, and a rigid co- 
 incidence of all the phenomena would demonstrate 
 the accuracy of his conclusions. 
 
 Such was the general train of investigation adopted 
 by Herschel. After as extended an examination as 
 the data with which he was then furnished permitted, 
 he announced his belief that a part of the proper 
 motion of the fixed stars must be attributed to the 
 effect of systematic parallax, and that the solar sys- 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 303 
 
 tern was moving through space towards a point in 
 the constellation Hercules. 
 
 The announcement of this astonishing result was 
 received with hesitation and doubt by the best living 
 astronomers, and Herschel died before any confirma- 
 tion of his great theory had been obtained. After his 
 death, for nearly half a century, no mind seemed wil- 
 ling to renew the investigation. The theory fell into 
 disrepute, and was only regarded as a bold and sub- 
 lime speculation, but not founded on any well deter- 
 mined observations. 
 
 Within a few years, the problem has engaged the 
 attention of the distinguished astronomers of Russia. 
 Argelander, of Bonn, led the way, and by a train of 
 reasoning based upon extensive and accurate obser- 
 vations, has sustained and demonstrated, in the most 
 undeniable manner, not only the general truth of 
 Herschel's theory, but has even confirmed the direc- 
 tion in which that astronomer believed the solar sys- 
 tem to be moving. 
 
 Here again permit me to attempt a popular expla- 
 nation of Argelander's reasoning. Suppose a single 
 star to have its place fixed absolutely by observation 
 on the first day of the year 1700. One hundred years 
 after, its place is again determined, when it is found 
 to have shifted its position. Conceive the star to 
 have so moved as to reach the meridian earlier than 
 it formerly did. When on the meridian, its old place 
 will be behind or east of the new place, and a line 
 joining the old and new places will show the direc- 
 tion in which the star has been moving, and the dis- 
 tance between the two places will exhibit the amount 
 of motion in one hundred years. If the star do not 
 
304 STRUCTURE OF THE UNIVERSE. 
 
 move exactly north or south, its line of direction will 
 form an angle with the meridian, whose value is de- 
 termined from a comparison of the old and new 
 places o the star. 
 
 Argelander commenced by selecting five hundred 
 stars, in all regions of the heavens, whose places had 
 been well determined by preceding astronomers. — . 
 The preference was of course given to those which 
 had been longest subjected to observation. Having 
 himself determined the new places of all these stars, 
 a comparison of his own with previously observed 
 positions, determined the direction in which these 
 stars were moving, and their rates of motion. The 
 angles formed by the lines along which each star was 
 progressing, with the meridian, became known from 
 observation, and these angles we shall call the ob- 
 served angles of direction. Now it is not difficult to 
 compute the directions in which the stars would ap- 
 pear to move, if their motion be produced by the 
 movement of the solar system. 
 
 Suppose, for example, that the sun, with its plan- 
 ets, is sweeping exactly towards the north pole of the 
 heavens, then would all the stars appear to move to- 
 wards the south. Those in the equator would move 
 with the swiftest velocity from the north pole, but 
 those nearest the pole would appear to separate from 
 each other, while their recess from the pole would be 
 comparatively slight. To render this reasoning still 
 plainer, imagine this room to be pierced on every 
 side, so that an eye placed at the centre could see 
 every star in the heavens through the openings. — 
 Through each of these holes conceive iron rods to 
 pass, all meeting at a point in the centre, and all di- 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 305 
 
 rected exactly to the stars. On the outside let go den 
 balls be fixed to the extremities of these rods, to rep- 
 resent the stars. Now, grasping the extremities of 
 all these rods in the hand, urge the point where they 
 all unite towards the north pole, and watch the move- 
 ment of the balls at the outer extremities of the rods. 
 The ball corresponding to the north star will scarcely 
 seem to move, because the eye travels directly to- 
 wards it. The balls corresponding to the stars on the 
 equator, having their rods perpendicular to the direc- 
 tion of the motion of the central point, will sweep 
 swiftly towards the south. The idea once gained, 
 there is no difficulty in its application. 
 
 The visual rays drawn to the stars correspond to 
 the rods, and these rays, meeting in the eye of the 
 observer, are carried forward by the sun in its pro- 
 gression through space. I have supposed the sys- 
 tem to move due north; but in case the motion be as- 
 sumed in any other direction, it is easy to compute 
 the changes consequent. Understanding these pre- 
 liminary statements, we are prepared to follow Arge- 
 lander in his investigation. 
 
 The five hundred stars selected for examination 
 were divided into three groups, according to the 
 amount of annual proper motion. The first con- 
 tained only such stars as were seen to move with a 
 velocity not less than one second of space in a year. 
 Although this motion may appear excessively slow, 
 yet its direction in one hundred years may be deter- 
 mined with very great precision. A general examin- 
 ation of the direction in which the stars of this first 
 group appeared to move, indicated the quarter of the 
 heavens towards which the solar system must be pro- 
 2 a 2 
 
306 STRUCTURE OF THE UNIVERSE. 
 
 gressing ; and now commenced the investigation, hav- 
 ing for its object the discovery of the exact point. — ■ 
 To accomplish this, a point was assumed, and on the 
 hypothesis that it was correctly chosen, the directions 
 of the motion of all the stars composing the first 
 group were computed, and the angles formed by their 
 lines of direction with the meridian were determined. 
 
 If the motion of these stars was the effect of sys- 
 tematic parallax, and if the direction of the solar 
 movement had been accurately chosen, then would 
 the computed angles of direction agree exactly, in every 
 instance, with the observed angles of direction. The 
 comparison of these angles having been made, it was 
 easy to see the discrepancies, and by shifting the as- 
 sumed point, these differences could be reduced to 
 their minimum value. The point which gave the 
 smallest differences between the observed and com- 
 puted angles would be the one towards which the so- 
 lar system was progressing. Such was the reasoning 
 of Argelander, and such the train of investigation on 
 which he relied for the resolution of this great 
 problem. 
 
 Having closed his examinations based on the group 
 of stars with the most rapid motion, and having found 
 the point in the heavens which corresponded to their 
 motions, he proceeded to execute his calculations with 
 reference to his second group. The stars of this group 
 moved annually an amount greater than half a second 
 of space, and less than one second. The result was 
 again reached, and the direction of the solar motion 
 thus derived, agreed, in a remarkable manner, with 
 that obtained from the first group. A further confir- 
 mation was obtained by executing the calculation 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 307 
 
 founded on the motions of the third and last group 
 into which he had divided his five hundred stars.— 
 The final result settled, probably forever, the grand 
 fact that the sun, with its entire cometary and plane- 
 tary system, is sweeping through space towards a 
 point whose place must fall somewhere within the 
 circumference of a circle whose diameter is about 
 equal to four times that of the moon. 
 
 The reality of the solar motion once determined, 
 astronomers have not been wanting to verify and ex- 
 tend this wonderful examination. Argelander's re- 
 sults have been confirmed by the investigations of M. 
 Otho Struve, the son of the distinguished director of 
 the Imperial Observatory of Pulkova ; and if, on any 
 fair night, you direct your eye to the constellation 
 Hercules, and select from its stars the two marked 
 on the globe with the Greek letters h and ^, on 
 the line joining these stars, and at a distance from * 
 equal to one-quarter of the distance which divides 
 the stars will be found the point tow T ards which the 
 sun was directing his course in the year 1840. 
 
 Having obtained the direction of the solar motion, 
 we proceed to investigate its actual velocity. How 
 swiftly does the sun, with its retinue of worlds, sweep 
 onward through space ? It will not be possible to 
 present here even an outline of the reasoning of 
 Struve in the resolution of this intricate question. — 
 Two points are involved. The determination of 
 the annual angular motion of the sun, as it would be 
 seen by a spectator situated at a distance equal to 
 that of the stars of the first magnitude. This being 
 determined, the angular motion can readily be con- 
 verted into linear velocity, in case the mean distance 
 
308 STRUCTURE OF THE UNIVERSE. 
 
 of the stars of the first magnitude can be satisfacto- 
 rily obtained. After an elaborate investigation, 
 guarded by every care, and open, as it would appear, 
 to no well founded objections, M. Otho Struve has 
 finally resolved the first of these wonderful questions. 
 It is curious to see how nearly the results agree, which 
 were obtained from data entirely different, and in no 
 way dependent on each other. 
 
 By an examination based on observed right ascen- 
 sions of the stars, he finds that the space passed over 
 by the sun in its progressive movement through the 
 heavens, seen from the mean distance of stars of the 
 first magnitude, is three hundred and twenty-one- 
 thousandths of a second of arc. The result obtained 
 from observed declinations gave for the same quantity 
 three hundred and fifty-seven-thousandths of one 
 second of arc. Here is a difference amounting to 
 only thirty-six-thousandths of a second, a quantity 
 exceedingly small, when we consider the extraordi- 
 nary difficulty of the investigation. 
 
 Let us now convert these numbers into intelligible 
 quantities. In case the sun be supposed to be revolv- 
 ing about some mighty centre, at a distance equal to 
 the mean distance of stars of the first magnitude, the 
 period necessary to accomplish its stupendous revolu- 
 tion will be 3,811,000 years ! 
 
 Vast as this period appears, we shall see hereafter 
 that we have no right to suppose that the centre about 
 which the solar system is revolving, can be located at 
 a distance nearly so small as the mean distance of 
 the larger stars. But what is the actual velocity ? — 
 How many miles does this mighty assemblage of fly- 
 ing worlds accomplish in its unknown journe}' in 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 309 
 
 every year? This is the last question, and even this 
 has not escaped the successful examinations of the 
 human mind. The discovery of the parallax of one 
 or two fixed stars has already been referred to. — 
 Within a few months, an elaborate w r ork, by Struve, 
 on the Sidereal Heavens, has reached us, containing 
 some remarkable investigations on the mean distances 
 of the stars of the various magnitudes. 
 
 Struve, by a most ingenious and powerful train of 
 investigation, obtains a series representing the relative 
 mean distances of the stars of all magnitudes, up to 
 the most minute visible in Herschel's twenty feet re- 
 flector. From the sun, as a centre, he sweeps succes- 
 sive concentric spheres, between whose surfaces he 
 conceives the stars of the several magnitudes to be 
 included. The radius of the first sphere reaches to 
 the nearest stars of the first magnitude ; that of the 
 second sphere extends to the farthest stars of the same 
 magnitude, and the mean of these two radii will be 
 the mean distance of the stars of the first magnitude. 
 The same is true with reference to the concentric 
 spheres embracing within their surfaces the stars of 
 the various orders of brightness. 
 
 Having, from his data, computed a table exhibiting 
 the relative distances of the stars of the different mag- 
 nitudes, an examination of these figures revealed 
 the singular fact that they constituted a regular ge- 
 ometrical progression ; and having assumed the dis- 
 tance of the stars of the sixth magnitude as the unit, 
 the distance of the stars of the fourth magnitude will 
 be one-half; that of those of the second magnitude 
 will be one-quarter, and so of the even numbers ex- 
 pressing magnitude ; while the distance of the stars of 
 
310 STRUCTURE OF THE UNIVERSE. 
 
 the fifth magnitude is obtained by dividing unity by 
 the square root of the number 2, and from this the dis- 
 tances of the odd magnitudes come by dividing con- 
 stantly by 2. In mathematical language, the distances 
 of the stars of the various magnitudes form a geom- 
 etrical progression whose ratio is equal to unity di- 
 vided by the square root of 2. 
 
 Having thus obtained the relative mean distances 
 of the stars, in case we can find the absolute mean 
 distance of those of any one class, that will reveal to 
 us the absolute mean distances of the stars of every 
 class. For the approximate accomplishment of this 
 last great object, we are again indebted to the as- 
 tronomers of Russia. As early as 1808, M. Struve, 
 then of Dorpat, attempted the determination of the 
 parallax of a large number of stars, and obtained re- 
 sults so small that, in the state of astronomical sci- 
 ence as it then existed, no confidence could be placed 
 in them. The final value of the numerical co-effi- 
 cient of the aberration of light had not been then ab- 
 solutely determined. Subsequent investigations by 
 Struve and Peters have fixed this quantity, and the 
 actual determination of the parallax of eight stars 
 recently, has shown that confidence may now be 
 placed in the results obtained by Struve nearly 25 
 years ago. 
 
 By combining all the results, M. Peters finds no less 
 than thirty-five stars whose parallaxes have now 
 been determined, either absolute or relative, with a 
 degree of accuracy which warrants their employment 
 in investigating the problem of the mean parallax 
 of stars of the second magnitude. Excluding from 
 this number the stars 61 Cygni, and No. 1830 of the 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 311 
 
 Grombridge catalogue, on account of their great 
 proper motion, there remained thirty-three stars to 
 be employed in the investigation. 
 
 From a full and intricate examination of all the 
 data, by a process of reasoning which I will not attempt 
 to explain at this time, M. Peters finds the mean par- 
 allax of stars of the second magnitude to be equal to 
 116 thousandths of one second of arc, with a probable 
 error less than a tenth part of this quantity. Return- 
 ing now, with this absolute result, to the table of 
 the relative distances of the fixed stars of different 
 magnitudes, it is easy to fix their absolute distances, 
 as far as confidence can be placed in this first 
 approximation. We find the stars of the first magni- 
 tude to be located between the surface of two spheres, 
 whose radii are respectively nine hundred and eighty- 
 six thousand times the radius of the earth's orbit, and 
 one million two hundred and forty-six thousand 
 times the same unit. We will express the distance 
 in terms of the velocity of light, as no numbers can 
 convey any intelligible idea. Stars of the first mag- 
 nitude send us their light in about seventeen years ; 
 those of the second magnitude in about thirty years ; 
 — stars of the third magnitude send their light in 
 about forty-five years ; those of the fourth magnitude 
 in sixty-five years ; those of the fifth in ninety years; 
 those of the sixth magnitude, the most remote visible 
 to the naked eye, send us their light after a journey 
 through space of one hundred and thirty years ! while 
 the distance of the lowest order of telescopic stars 
 visible in Herschel's twenty feet reflector is such, that 
 their light does not reach the eye for 3,541 years after 
 it jstarts on its tremendous journey ! 
 
312 STRUCTURE OF THE UNIVERSE. 
 
 Let it be remembered that these results are not 
 conjectures. Though they are first approximations 
 to the truth, they are reliable to within the tenth part 
 of their value, and are thus far certain ; they raise, in 
 the most astonishing manner, our views of the im- 
 mensity of the universe, and of the powers of human 
 genius which have fathomed these vast and over- 
 whelming profundities. 
 
 Let us now return to the examination of the abso- 
 lute amount of progressive motion of our sun and 
 system through space. As already stated, M. Otho 
 Struve determined its yearly angular motion, as seen 
 from the more distant of the stars of the first magni- 
 tude. To convert this angular motion into miles, a 
 knowledge must be obtained of the absolute mean 
 distance of the stars of the first magnitude. This has 
 been accomplished by M. Peters, and combining the 
 researches of Argelander, Struve, and Peters, we are 
 now able to pronounce the following wonderful re- 
 sults. — The sun, attended by all its planets, satellites, and 
 comets, is sweeping through space towards the star marked 
 7t in the constellation Hercules, with a velocity which causes 
 it to pass over a distance equal to thirty-three millions three 
 hundred and fifty thousand miles in every year ! 
 
 And now do you demand how much reliance is to 
 be placed on this bewildering announcement ? I an- 
 swer, that as to the reality of the solar motion, there 
 is but one chance out of four hundred thousand that 
 astronomers have been deceived. We cannot resist 
 the evidence, and startling as the truth appears, we 
 are obliged to yield our assent, reluctant though it 
 may be, to the logical reasoning by which this mag- 
 nificent result has been demonstrated. 
 
MOTIONS AND REVOLUTIONS OF THE FiXED STARS. 313 
 
 But whither is our system tending ? If moving on- 
 ward with such tremendous velocity, is there not danger 
 that ere long it may reach the region of the fixed stars, 
 and by sweeping near to other suns and systems, de- 
 range the order of the planetary worlds ? Let us exam- 
 ine this question for one moment, on the hypothesis that 
 the sun alone is moving among all the stars of hea- 
 ven, and that it will hold on in its present direction 
 until it shall reach the star in Hercules, towards 
 which it is now urging its flight. This star is of the 
 third magnitude, and according to our statement al- 
 ready made, the mean distance of its class is such, 
 that its light does not reach us in a period less than 
 forty-six years. Executing the calculation, we find 
 that in case the solar system should continue to pro- 
 gress towards that star, it cannot pass the enormous 
 interval, even at 33,550,000 miles per annum, in less 
 than 1,800,000 years! 
 
 If the eye of any superior intelligence can behold 
 this amazing scene, how stupendous must be the spec- 
 tacle presented ! In the centre the sun, blazing with 
 splendor, pursues its majestic career; — around it roll 
 the planets, and about it cluster ten thousand fiery 
 comets. Worlds bright and beautiful hover near the 
 sun , — worlds fiery and chaotic seek this great centre 
 with impetuous velocity, and then dash away into 
 the farthest range of their grand revolution. But the 
 monarch moves on, and his magnificent cortege, per- 
 forming his high behests, follow whithersoever he 
 leads through space ! 
 
 Here we reach the boundary which divides the 
 known from the unknown. Steadily we have pur- 
 sued the human mind, as it has moved on in its grand 
 2B 
 
314 STRUCTURE OF THE UNIVERSE. 
 
 researches of the universe of God. Time, and space, 
 and number, and distance, have all been set at defi- 
 ance. No limits have been sufficiently great to cir- 
 cumscribe its movement. For more than six thousand 
 years, onward ! has truly been the word. And here I 
 might very well pause, and rest content in the exhibi- 
 tion of the absolute and actual triumphs of human 
 genius ; but as the rays of the rising sun penetrate 
 the darkness of night, and scattering the gloom, dimly 
 reveal the scenes of earth which are soon to be flooded 
 with splendor, so the light of human knowledge breaks 
 over the boundaries which divide the known from the 
 unknown, and faintly reveals what yet lies far beyond 
 in the dark profound. 
 
 Guided by this light, we shall ask your attention to 
 one of the most sublime speculations to which the 
 mind of man has ever risen. I refer to the supposed 
 discovery of the great centre about w T hich it is pre- 
 sumed the myriads of stars composing our mighty 
 Milky Way are all revolving. 
 
 M. Maedler, the author of the recent investigations 
 with reference to the Central Sun, has long been 
 known to the astronomical world as the successor of 
 M. Struve in the direction of the observatory at Dor- 
 pat. His computations of the orbitual movements of 
 the double stars have given to him a deservedly high 
 celebrity, and the great theory which he has propoun- 
 ded is only given to the world after a long and patient 
 examination, extending through seven years. 
 
 The extension of the law of gravitation to the fixed 
 stars, now absolutely demonstrated in the revolutions 
 of the binary systems, settles forever the fact, that in 
 the grand association of stars composing our cluster, 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 315 
 
 or, as we shall hereafter call it, our astral system, there 
 must be a centre of gravity, as certainly as there is one 
 to the solar system. In the organization of the solar 
 system we find a central body of vast size, surrounded 
 by small and subordinate satellites. Again, among 
 the planets, we find their magnitude very great, when 
 compared with the moons which circulate around 
 them. Extending this analogy, early astronomers 
 conceived that this principle of a great central pre- 
 ponderating globe would, in all probability, obtain in 
 all the higher orders of physical organization. 
 
 This idea, apparently so well founded, was entirely 
 destroyed by the discovery of the binary stars. Here 
 we find the next higher organization above our solar 
 system, but instead of finding in the bodies thus 
 united a vast preponderance in magnitude of one 
 over the other, there are many examples in which the 
 two suns thus united by gravitation are, in all re- 
 spects, equal. In many others the difference is only 
 slight, yet in all these higher systems there must exist 
 a common centre of gravity. 
 
 With the mind cleared, by these views, from all 
 prejudice in favor of the necessary existence of some 
 stupendous central globe, as far exceeding in magni- 
 tude the myriads of fixed stars by which it is sur- 
 rounded as does the sun all the satellites of its sys- 
 tem, we are prepared to inquire into the actual exis- 
 tence or nonexistence of such a body. 
 
 Admitting its invisibility, either in consequence of 
 its distance or nonluminous character, there are yet 
 remaining the means, not only of detecting its exist- 
 ence, but of discovering its position in space. In case 
 such a body exists, the stars located nearest to it will 
 
316 STRUCTURE OF THE UNIVERSE. 
 
 be most completely subjected to its influence, and 
 will show their proximity by the swiftness of their 
 motion. Since it is possible to penetrate space in 
 every direction, in case the stars of any particular re- 
 gion were endowed with a more rapid motion than 
 all others, these would not fail to be discovered. But 
 no such rapid motions have ever been detected, and 
 hence it is now fair to conclude that such motions do 
 not exist, and consequently no vast central globe can 
 ever be found, because there is no evidence that such 
 a body has any locality in space. 
 
 The question resolves itself, then, into a research 
 for the common centre of gravity of all the stars com- 
 posing our astral system, and the data for such an 
 examination must be found in the direction of the 
 solar motion, and in that of the proper motion of the 
 fixed stars. Difficult as this research undoubtedly 
 is, Maedler's sagacity detected various guides which 
 limited his more minute examinations to a compara- 
 tively small portion of the heavens. Since our great 
 astral system has been shown to take the form of a 
 layer or stratum whose thickness is small compared 
 with its extent, we cannot fail to perceive that the 
 centre of gravity of a mass of stars thus arranged 
 must be found somewhere within the limits of the 
 Milky Way, when seen by an eye located not very 
 distant from the centre. But it is seen that our sun 
 does not occupy the absolute centre of this stratum. 
 In case it did, then would the bright circle of the 
 Milky Way divide the heavens into two equal hemis- 
 pheres. Since there is a manifest difference between 
 the two parts into which the heavens is divided, the 
 smaller portion will be the more distant from us, and 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 317 
 
 in this smaller part we must look for the central 
 point. But, from the soundings of both the Herschels, 
 it is certain that our sun lies nearer the southern half 
 of the Milky Way than the northern. Hence, in our 
 researches for the centre of gravity, we may confine 
 our examinations to the northern half of the smaller 
 of the two parts into which the Milky Way divides 
 the heavens. 
 
 One more approximation may be made. If we 
 knew that our sun, in its presumed revolution about 
 this great centre, described a circle, and if we knew 
 the plane of this circle, and the direction in which the 
 sun was now moving, a line drawn in that plane from 
 the sun, and in a direction perpendicular to its line of 
 motion, would pass directly through the centre about 
 which it is revolving, and would point us directly to 
 it. Now the direction of the sun's motion is alone 
 determined; but since the centre of gravity must be 
 found somewhere in a line perpendicular to the direc- 
 tion, we must give to this perpendicular all possible 
 positions in space, which will cause it to cut from the 
 celestial sphere the circumference of a great circle, 
 within which the centre of gravity must be found. — 
 These limiting considerations brought the distin- 
 guished astronomer to a region of the heavens in and 
 about the constellation Taurus. 
 
 Here the examination took a more definite and 
 more strictly scientific form. The proper motion of 
 the stars in this region could be anticipated and 
 known, at least in character and direction. The 
 great centre would probably be located within the 
 limits of some rich cluster. All the stars composing 
 this cluster as well as those within 20° or 30°, would 
 2b2 
 
318 STRUCTURE OF THE UNIVERSE. 
 
 appear to move in the same direction. Those im- 
 mediately proximate to the central sun or star would 
 appear to move with the same velocity due to that 
 star, and the entire group would sweep, apparently, 
 through space without parting company. 
 
 Having, by such like considerations, narrowed 
 down the limits of research, Maedler commenced his 
 individual examinations. Among other objects sub- 
 jected to rigid scrutiny, was the brilliant star Alde- 
 baran, in the eye of the Bull. This being the bright- 
 est star in this region, and being, moreover, in the 
 midst of a group of smaller stars, seemed, in the out- 
 set, to fulfill some of the conditions required of the 
 central sun. But a more rigid examination proved 
 conclusively that this star could not occupy the centre. 
 Its own proper motion far exceeded that of the sur- 
 rounding stars, and demonstrated its near proximity 
 to our own system, and its mere optical connection 
 with the stars surrounding it. 
 
 Thus did this great astronomer move from point to 
 point, from star to star, subjecting each successively 
 to the severest tests, until, finally, a point was found, 
 a star was discovered, fulfilling, in the most remarka- 
 ble manner, all the requisitions demanded by the na- 
 ture of the problem. All are familiar with the beau- 
 tiful little cluster, called the Pleiades, or seven stars. 
 Clustered around the brilliant star Alcyone, which oc- 
 cupies the optical centre of the group, the telescope 
 shows fourteen conspicuous stars. The proper mo- 
 tions of all these have been determined with great ex- 
 actitude. These are all in the same direction, and are 
 all nearly equal to each other ; and, what is still more 
 important, the mean of their proper motions differs 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 319 
 
 from that of the central star, Alcyone, by only one- 
 thousandth of a second of arc in right ascension, and 
 by two-thousandth's of a second in declination. — 
 Here, then, is a magnificent group of suns, either ac- 
 tually allied together, and sweeping in company 
 through space, or else they compose a cluster so situ- 
 ated as to be affected by the same apparent motion 
 produced by the sun's progressive motion through 
 the celestial regions. 
 
 But an extension of the limits of research around 
 Alcyone exhibits the wonderful truth, that out of one 
 hundred and ten stars within 15° of this centre, there 
 are sixty moving south, or in accordance with the hy- 
 pothesis that Alcyone is the centre, forty-nine exhibit- 
 ing no w r ell defined motion, and only one single in- 
 dividual which appears to move contrary to the com- 
 puted direction ! 
 
 It is impossible, here, to do justice to the profound 
 and elaborate investigations of the learned author of 
 this great speculation. Assuming Alcyone as the 
 grand centre of the millions of stars composing our 
 astral system, and the direction of the sun's motion, 
 as determined by Argelander and Struve, he investi- 
 gates the consequent movements of all the stars in 
 every quarter of the heavens. Just where the swift- 
 est motions should be found, there they actually exist, 
 either demonstrating the truth of the theory, or exhib- 
 iting the most remarkable and incredible coincidences. 
 We shall not pursue the research. After a profound 
 examination, Maedler reaches the conclusion that Al- 
 cyone, the principal star in tlie group of the Pleiades, 
 now occupies the centre of gravity, and is at present the 
 
320 STRUCTURE OF THE UNIVERSE. 
 
 sun about which the universe of stars composing our as- 
 trcH system are all revolving. 
 
 Here, then, we stand on the confines of the un- 
 known. One mighty effort has thus been made to 
 bring beauty and order out of the chaos of motion 
 which has hitherto distinguished the stars of heaven. 
 Once the planets, freed from law, darted through 
 space, or relaxing their speed, actually turned back 
 on their unknown routes. Chaos reigned among these 
 flying globes until the mind, rising by the efforts of 
 its own genius, reached the grand centre of the plan- 
 etary orbs, and lo ! confusion ceased, and harmony 
 and beauty held their sway among these circling 
 worlds. The same daring human genius which, 
 sweeping across the interplanetary spaces, finally 
 reached the controlling centre of our own great sys- 
 tem, has now boldly plunged into the depths of space, 
 has swept across the interstellar spaces, and roam- 
 ing from star to star, from sun to sun, from system to 
 system, looks out upon the universe of stars, and 
 seeks that point from whence these millions of sweep- 
 ing suns shall exhibit that grand and magnificent 
 harmony which doubtless reigns throughout the vast 
 empire of Jehovah. 
 
 We are too apt to turn away from the first efforts 
 to resolve these mighty problems. How were the 
 doctrines of Newton received ? How much regard 
 was paid to HerschePs grand theory of the solar mo- 
 tion ? And yet how triumphantly have these great 
 theories been established. But do you inquire if there 
 be any possibility of proving or disproving the doc- 
 trines of Maedler? The answer is simple. Should 
 the time ever come when the direction of the solar 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 321 
 
 motion shall be sensibly changed, in consequence of 
 its curvilinear character, then will the plane in which 
 this movement lies be revealed, and then the centre 
 about which the revolution is performed must be 
 made known, at least in direction. Should the line 
 reaching towards this grand centre pass through Al- 
 cyone, this added to all the other evidences, will fix 
 forever the question of its central position. We know 
 not when this great question may be settled, but judg- 
 ing from the triumphs which have marked the career 
 of human genius hitherto, we do not dare to doubt 
 of the final result. 
 
 Admitting the truth of Maedler's theory, we are led 
 to some of the most astonishing results. The known 
 parallax of certain fixed stars gives to us an approxi- 
 mate value of the parallax of Alcyone, and reveals to 
 us the distance of the grand centre. Such is the 
 enormous interval separating the sun from the central 
 star about which it performs its mighty revolution, 
 that the light from Alcyone requires a period of 537 
 years to traverse the distance ! And if we are to rely 
 on the angular motion of the sun and system, as al- 
 ready determined, at the end of 18,200,000 years, this 
 great luminary, with all its planets, satellites, and 
 comets, will have completed one revolution around its 
 grand centre ! 
 
 Look out to-night on the brilliant constellations 
 which crowd the heavens. Mark the configurations 
 of these stars. Five thousand years ago the Chal- 
 dean shepherd gazed on the same bright groups. — 
 Two thousand years have rolled away since the 
 Greek philosopher pronounced the eternity of the 
 heavens, and pointed to the ever-during configuration 
 
322 STRUCTURE OF THE UNIVERSE. 
 
 of the stars as proof positive of his assertion. But a 
 time will come when not a constellation now blazing 
 in the bright concave above us shall remain. Slowly, 
 indeed, do these fingers on the dial of heaven mark 
 the progress of time. A thousand years may roll 
 away with scarce a perceptible change ; — even a mil- 
 lion of years may pass without effacing all traces of 
 the groupings which now exist ; but that eye which 
 shall behold the universe of the fixed stars when ten 
 millions of years shall have silently rolled away, will 
 search in vain for the constellations which now beau- 
 tify and adorn our nocturnal heavens. Should God 
 permit, the stars may be there, but no trace of their 
 former relative positions will be found ! 
 
 Here I must close. The intellectual power of man, 
 as exhibited in his wonderful achievements among the 
 planetary and stellar worlds, has thus far been our 
 single object. I have neither turned to the right hand 
 nor to the left. Commencing with the first mute gaze 
 bestowed upon the heavens, and w r ith the curiosity 
 awakened in that hour of admiration and wonder, we 
 have attempted to follow rapidly the career of the hu- 
 man mind, through the long lapse of six thousand 
 years. What a change has this period wrought. Go 
 backward in imagination to the plains of Shinar, and 
 stand beside the shepherd astronomer as he vainly 
 attempts to grasp the mysteries of the waxing and 
 waning moon, and then enter the sacred precincts of 
 yonder temple devoted to the science of the stars. — 
 Look over its magnificent machinery ; examine its 
 space-annihilating instruments, and ask the sentinel 
 who now keeps his unbroken vigil, the nature of his 
 investigations. 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 323 
 
 Moon, and planet, and sun, and system, are left be- 
 hind. His researches are now within a sphere to 
 whose confines the eagle glance of the Chaldean 
 never reached. Periods, and distances, and masses, 
 and motions, are all familiar to him, and could the 
 man who gazed and pondered six thousand years ago 
 stand beside the man who now fills his place, and 
 listen to his teachings, he would listen with awe, in- 
 spired by the revelations of an angel of God. But 
 where does the human mind now stand? Great as 
 are its achievements, profoundly as it has penetrated 
 the mysteries of creation, what has been done is but 
 an infinitesimal portion of what remains to be done. 
 
 But the examinations of the past inspire the high- 
 est hopes for the future. The movement is one con- 
 stantly accelerating and expanding. Look at what 
 has been done during the last three hundred years, 
 and answer me to what point will human genius 
 ascend, before the same period shall again roll away? 
 But in our admiration for that genius which has been 
 able to reveal the mysteries of the universe, let us 
 not forget the homage due to Him who created, and 
 by the might of his power sustains all things. At 
 some future time, I hope to be permitted to direct 
 your attention to this branch of the subject. If there 
 be anything which can lead the mind upward to the 
 Omnipotent Ruler of the universe, and give to it an 
 approximate knowledge of His incomprehensible attri- 
 butes, it is to be found in the grandeur and beauty of 
 His works. 
 
 If you would know his glory, examine the intermi- 
 nable range of suns and systems which crowd the 
 Milky Way. — Multiply the hundred millions of stars 
 
324 STRUCTURE OF THE UNIVERSE. 
 
 which belong to our own " island universe " by the 
 thousands of these astral systems that exist in space, 
 within the range of human vision, and then you may 
 form some idea of the infinitude of his kingdom ; for 
 lo ! these are but a part of his ways. Examine the 
 scale on which the universe is built. — Comprehend, 
 if you can, the vast dimensions of our sun.— Stretch 
 outward through his system, from planet to planet, 
 and circumscribe the whole within the immense cir- 
 cumference of Neptune's orbit. This is but a single 
 unit out of the myriads of similar systems. Take 
 the wings of light, and flash with impetuous speed, 
 day and night, and month, and year, till youth shall 
 wear away, and middle age is gone, and the extremest 
 limit of human life has been attained ; — count every 
 pulse, and at each speed on your way a hundred 
 thousand miles ; and when a hundred years have 
 rolled by, look out, and behold ! the thronging millions 
 of blazing suns are still around you, each separated 
 from the other by such a distance that in this journey 
 of a century you have only left half a score behind 
 you. 
 
 Would you gather some idea of the eternity past 
 of God's existence, go to the astronomer, and bid him 
 lead you with him in one of his walks through space; 
 and as he sweeps outward from object to object, from 
 universe to universe, remember that the light from 
 those filmy stains on the deep pure blue of heaven, 
 now falling on your eye, has been traversing space 
 for a million of years. Would you gather some 
 knowledge of the omnipotence of God, weigh the 
 earth on which we dwell, then count the millions of 
 its inhabitants that have come and gone for the last 
 
MOTIONS AND REVOLUTIONS OF THE FIXED STARS. 325 
 
 six thousand years. Unite their strength into one 
 arm, and test its power in an effort to move this 
 earth. It could not stir it a single foot in a thou- 
 sand years ; and yet under the omnipotent hand of 
 God, not a minute passes that it does not fly for more 
 than a, thousand miles. But this is a mere atom ; — 
 the most insignificant point among his innumerable 
 worlds. At his bidding, every planet, and satellite, 
 and comet, and the sun himself, fly onward in their 
 appointed courses. His single arm guides the mil- 
 lions of sweeping suns, and around His throne circles 
 the great constellation of unnumbered universes. 
 
 Would you comprehend the idea of the omniscience 
 of God, remember that the highest pinnacle of knowl- 
 edge reached by the whole human race, by the com- 
 bined efforts of its brightest intellects, has enabled 
 the astronomer to compute approximately the pertur- 
 bations of the planetary worlds. He has predicted 
 roughly the return of half a score of comets. But 
 God has computed the mutual perturbations of mil- 
 lions of suns, and planets, and comets, and worlds, 
 without number, through the ages that are passed, 
 and throughout the. ages which are yet to come, not 
 approximately, but with perfect and absolute pre- 
 cision. The universe is in motion, — system rising 
 above system, cluster above cluster, nebula above 
 nebula, — all majestically sweeping around under the 
 providence of God, who alone knows the end from 
 the beginning, and before whose glory and power 
 all intelligent beings, whether in heaven or on earth, 
 should bow with humility and awe. 
 
 Would you gain some idea of the wisdom of God, 
 look to the admirable adjustments of the magnificent 
 2 C 
 
326 STRUCTURE OF THE UNIVERSE. 
 
 retinue of planets and satellites which sweep around 
 the sun. Every globe has been weighed and poised, 
 every orbit has been measured and bent to its beauti- 
 ful form. All is changing, but the laws fixed by the 
 wisdom of God, though they permit the rocking to and 
 fro of the system, never introduce disorder, or lead to 
 destruction. All is perfect and harmonious, and the 
 music of the spheres that burn and roll around our 
 sun, is echoed by that of ten millions of moving 
 worlds, that sing and shine around the bright suns 
 that reign above. 
 
 If overwhelmed with the grandeur and majesty of 
 the universe of God, we are led to exclaim with the 
 Hebrew poet king, — "When I consider thy heavens, 
 the work of thy fingers, the moon and the stars which 
 thou hast ordained, what is man, that thou art mind- 
 ful of him ? and the son of man, that thou visitests 
 him?" If fearful that the eye of God may overlook 
 us in the immensity of his kingdom, we have only to 
 call to mind that other passage, "Yet thou hast 
 made him but a little lower than the angels, and hast 
 crowned him with glory and honor. Thou madest 
 him to have dominion over all the works of thy hand ; 
 thou hast put all things under his feet." Such are 
 the teachings of the word, and such are the lessons 
 of the works of God. 
 
DESCRIPTION OF THE TELESCOPIC VIEWS. 
 
 PLATE I. 
 
 Halley's Comet, as figured by Sir John Herschel, at the Cape of Good 
 Hope. Oct 29, 1835. 
 
 The rapid changes in this extraordinary object, at its last appearance, 
 have attracted great attention among astronomers. Sir John Herschel 
 describes its appearance, at the date of the drawing, as follows : 
 
 " Its nucleus small, bright and highly condensed, was shielded, or capped^ 
 on the side next the sun, by a vivid, but narrow crescent of nebulous light, the 
 front of which presented an outline nearly circular, having an amplitude of 
 somewhat more than 90° from horn to horn. Within this was situated 
 the nucleus, at a distance behind the vertex, such that the horns of the 
 crescent extended a good way behind the nucleus, on either side. * * * 
 The nucleus was decidedly not planetary, and as decidedly exhibited no phase. 
 As the evening advanced, the exterior strata of the crescent — the coma and 
 the tail which were before obliterated by the twilight — became visible, and 
 the whole finally put on the appearance represented in Plate I." 
 
 From this time to the month of January, 1 836, many changes are noted. 
 During part of the time a necessary absence from the observatory, suspended 
 observations. They were resumed, and continued up to the final disappear- 
 ance of the comet. 
 
 PLATE II. 
 
 Halky's Comet, as figured by Sir John Herschel, at the Cape of Good 
 Hope. Jan. 28, 1836. 
 
 Sir JoHtf Herschel uses the following language: 
 
 " Most astonishing The coma is all but gone, but there are long irregu- 
 
 (327} 
 
328 DESCRIPTION OF THE TELESCOPIC VIEWS. 
 
 lar nebulous tails in various directions. The nucleus is now no longer a dim 
 misty speck, but a sharp brilliant point. I cannot, however, « raise a disc ' 
 on it, at least a well defined one ; but the light comes on so suddenly, it is like 
 a planetary nebula, a little hazy at the edges, 2 or 2^ seconds in diameter. 
 * * * Being now high, and the telescope acting to admiration, I see a 
 sharp, all but planetary, disc, diameter fully 1 J seconds, quite distinct from 
 the haze about it. Power 320 shows it well. It is like one of Jupiter's 
 satellites in a thick fog of hazy light. Nothing can be more delicate and 
 regular than the curve of the head, and the symmetry of the whole upper 
 part of the figure." * * * The observations of this night conclude with the 
 following memorandum : — "So ended a most remarkable night. I can 
 hardly doubt that the comet has fairly evaporated in perihelia, by the heat, 
 and resolved into transparent vapor, and is now in process of rapid conden- 
 sation and reprecipitation on the nucleus." 
 
 The drawings of Herschel are numerous, and exhibit the progressive 
 changes in the dimensions of the comet. Two only have been selected as 
 specimens. 
 
 PLATE III. 
 
 Halleifs Comet, as figured by Struve, Director of the Imperial Obser 
 vatory, Polkova, Russia. Oct. 12, 1835. 
 
 The comet was observed and drawn with great care, by Prof. Struve. 
 He has published a large work, containing all his observations and drawings, 
 from which the plate in this volume is copied, and the following notices are 
 translated. " On the setting of the moon the clouds dispersed, and the comet 
 appeared for a short time in great beauty. Soon the heavens were again 
 covered with light clouds, through which all the parts of the comet were 
 concealed, except the nucleus and flame, which remained distinctly visible. 
 The appearance of the flame was wonderful. It resembled a ray of fire 
 shot out from the nucleus, as from some engine of artillery, and driven on 
 one side by the wind. Nearly in the opposite direction a second emanation, 
 or flame, more faint than the first, was visible. The clouds prevented 
 farther observation on that evening." 
 
DESCRIPTION OF THE TELESCOPIC VIEWS. 329 
 
 The beautiful symmetry exhibited in this drawing, must attract every 
 eye. Nothing can be more delicate than the forms and bounding curves of 
 these singular appendages to the comet. The nucleus is sharp and well 
 defined, and from it emanate these strange gaseous out-shoots. The rapid 
 changes noted by Herschel, are equally represented in the drawings 
 of Struve. 
 
 PLATE IV. 
 
 The Great Comet of 1744. 
 
 This object is one of the most remarkable among the comets. It is not 
 uncommon for two tails to present themselves, but a display of six luminous 
 trains, of vast extent, has, so far as I know 7 , never been witnessed, except in 
 this case. The spaces between the tails are represented, by the writers of the 
 day, as having been as dark as the heavens, while each tail was bordered by 
 a luminous edging of great beauty. The enclosed space was faintly illumina- 
 ted. The tail was no where bright enough to produce the slightest effect on 
 the appearance of the fixed stars, as seen through it. Their light was not, 
 in the smallest degree, dimmed. 
 
 After the head of the comet had sunk below the horizon, these brilliant 
 trains of light, radiating from a common point, were long visible, presenting 
 a most wonderful appearance. I am not aware that the period of this body 
 has ever been determined. 
 
 PLATE V. 
 
 A Globular Cluster of Stars in the Constellation of Hercules. A. R. 
 15 h. 36 m. N. Dec. 36° 46'. 
 
 This object, one of the most beautiful in the heavens, was discovered by 
 Halley, as far back as 1714. It was regarded by its discoverer as a nebula, 
 and was not known to contain any stars. This is remarkable, as a very 
 moderate power suffices to exhibit its stellar characteristics, while the great 
 instruments of modern times exhibit within its limits a countless multitude 
 2 c2 
 
330 DESCRIPTION OF THE TELESCOPIC VIEWS. 
 
 jL of stars, condensing towards the center into a glow of great brilliancy and 
 " beauty. This is doubtless one of the " Island Universes *' found in space, 
 and of an extent not inferior to that of the Milky Way. The heavens, as 
 seen from a sun of this astral system, near its center must present a most 
 gorgeous appearance. In all directions may be seen innumerable stars 
 of all magnitudes, forming a spectacle such as would be presented by our 
 heavens, in case the Milky Way were expanded to cover the entire celestial 
 sphere. I have examined this object with the great Refractor of the Cincin- 
 nati Observatory, on many occasions, and the engraving is made from one 
 of my drawings. No one can behold this magnificent object, for the first 
 time, without exclamations of wonder and astonishment. The whole extent 
 is embraced at once in the field of the large telescope, with a power of 250. 
 
 PLATE VI. 
 
 Lord Rosse's Crab Nebula. 
 This object had long been known as a faint, ill defined, nebula of an 
 elliptical figure, with nothing to distinguish it from many other similar 
 luminous clouds. When examined by Lord Rosse's three feet reflector, its 
 aspect was entirely changed. The central part was seen to be composed of 
 a vast multitude of stars, while branching filaments of hazy light extended 
 from the center, in all directions. There can be little doubt of the actual 
 character of this singular object. It is probably an immense cluster of suns, 
 of a figure which seems to bid defiance to all our ideas of regularity or order. 
 As it still rests on a bed of misty light, indicating still more distant portions 
 of it, a higher power may hereafter work a complete change in the character 
 of its outline. It is among the most distant objects visible in the telescope, 
 and exhibits a specimen of the singular variety of form, occasionally shown 
 among these vast congeries of stars. 
 
 PLATE VII. 
 
 The Great Nebula in Orion. R.A.5L 27 m. Decl. S. 5° 30'. 
 Discovered by Huygens in 1656. It is one of the largest among the 
 
DESCRIPTION OF THE TELESCOPIC VIEWS. 331 
 
 nebula, and certainly one of the most magnificent. It was examined by the Jft 
 elder Herschel, with the entire range of his telescopic power, without ex- 
 hibiting any appearance of being composed of stars. Within the outline of 
 the nebula there are a great many large and brilliant stars, but these are 
 undoubtedly between the eye and the nebula, and in no way connected with 
 it. Among these stars there is one marked on the maps as 6 Orionis, which 
 has long been known to consist of four component stars. Prof. Struve, of 
 Dorpat, detected a fifth, and a sixth has recently been added to this remark* 
 able set. Here we have an example of six suns, probably, in physical union, 
 and revolving about their common center of gravity. Near these six stars, 
 and between the short point of light and the long projecting branch, there 
 appears to be an absolute vacuity, intensely black. Whether this be an 
 effect of contrast with the brilliancy of the nebula, or occasioned by some 
 peculiar constitution of this region, it is impossible to determine. In exhibit- 
 ing this object to persons who had never seen any thing of the kind, I have 
 frequently heard them remark, that a part of the nebula was hid by a black 
 cloud. 
 
 Sir W. Herschel being unable to resolve this nebula, with his most power- 
 ful telescopes, placed it among those which he regarded as probably composed 
 of the nebulous fluid, or chaotic matter. The subsequent investigations of 
 Sir John Herschel confirmed the views of his father, and it has only been on 
 the application of the six feet reflector of Lord Rosse, that the true character 
 of this object has been ascertained. The space penetrating power of the 
 monster telescope has carried the observer near enough to discern the in- 
 dividual stars of which it is composed. Its resolution has also been accom- 
 plished by the magnificent "Refractor of the Cambridge (U. S.) Observatory, 
 
 The distance and magnitude of this object, as thus determined, absolutely 
 overwhelm the mind. In case light be not absorbed in its journey through 
 the celestial spaces, the light of the nebula in Orion cannot reach the eye in 
 less than sixty thousand years, with a velocity of twelve millions of miles in 
 every minute of time ! and yet this object may be seen from this stupendous 
 distance even by the naked eye ! What then must be its dimensions 1 
 Here indeed, we behold a universe of itself too vast for the imagination to 
 grasp, and yet so remote as to appear a faint spot upon the sky. 
 
332 DESCRIPTION OF THE TELESCOPIC VIEWS. 
 
 The resolution of this nebula has been the signal for the renunciation 
 of Herschers nebular theory, by some of its former supporters, with what 
 reason I know not. Herschel only gained the first idea of his great theory, 
 after resolving nearly all the previously known nebula, and now it is to be 
 surrendered because a solitary one has been unexpectedly resolved into stars. 
 The theory can hardly yield on such easy terms. 
 
 PLATE VIII. 
 Nebula in the Shield of SobiesM. E. A. 18 h. 11 m. Decl. S. 16° 16'. 
 This is an irresolvable nebula, figured by Sir John Herschel, during his 
 residence at the Cape of Good Hope. Its favorable position, as seen in 
 southern latitudes, enabled Herschel to trace the outline of the nebula much 
 farther than any preceding observer had done. The singular figure of this 
 object, seems to suggest some power of attraction operating on the particles 
 of matter, or the stars of which it is composed. In one place we see a bright 
 condensed mass of light, nearly round, while it is encircled by a perfectly 
 dark vacuity, on the outside of which nebulous light is again seen. The 
 smaller curve, at the opposite extremity, was discovered by Herschel while 
 at the Cape, and has not been seen at any northern observatory, so far as I 
 know. The stars scattered through this nebula are not, probably, connected 
 with it, but accidental in their position. It is impossible to assert, with cer- 
 tainty, the absolute nebulosity of any object. It may be that higher powers 
 will resolve even this one into stars, but thus far there has been lio evidence 
 gained of its resolvable character. 
 
 PLATE IX. 
 
 Nebulous Stars, and Stars connected with Nebulae, 
 Stars are sometimes found in the heavens surrounded by a hazy light of 
 great extent, in the center of which the star is placed. It was an object of 
 
DESCRIPTION OF THE TELESCOPIC VIEWS. 333 
 
 this kind, which first suggested to Sir W. Herschel his great theory of the 
 formation of suns out of a nebulous fluid. He thought it impossible to 
 account for the central location of stars, surrounded by nebulous matter, in 
 any way except by supposing this to be a sort of atmosphere attracted to, 
 and sustained in its spherical form, by the power of the central body. I have 
 examined specimens of these objects, and always with increasing wonder. 
 Their magnitude must be enormous, as the stars are certainly not nearer 
 than other stars, and yet the circular halo around them is of a diameter 
 easily measured, and proves them to have a circumference, perhaps, greater 
 than that of the entire orbit of Neptune. 
 
 Specimens are found, in which there is but a mere condensation of light 
 in the center ; others in which this central light is brighter, and so up to a 
 perfect star, with the surrounding haze. 
 
 In some instances the star is found with a stream of light issuing from it, 
 resembling the tail of a comet. These are, certainly, objects of very difficult 
 explanation, in case we abandon the idea of nebulous matter. 
 
 PLATE X. 
 
 The Great Southern Cluster. 47 Toncani of Bode's Catalogue. 
 
 This remarkable object was resolved by Sir John Herschel, while in the 
 south. Its position renders it invisible in the northern latitudes. There 
 seems to be a curious change in the law of condensation, presenting three 
 successive stages, Herschel regards it as a globular cluster of vast extent. 
 There is said to be a marked difference in the color of the central portions 
 and the exterior stars. The interior is of a rose color, while the exterior is a 
 pure white. The stars of the southern heavens are said to present a greater 
 variety of vivid colors than those of the north. Yet in the north there are 
 some beautiful specimens of double stars, in which vivid colors are beautifully 
 contrasted. Orange and blue are of frequent occurrence ; red and green are 
 sometimes found. In the double star Antares, the principal component is 
 orange, while the small companion is decidedly blue. 
 
 The condition of planets revolving around a sun whose light is orange 
 
334 DESCRIPTION OF THE TELESCOPIC VIEWS. 
 
 or red, associated with another sun, whose light is blue or green, may be 
 more easily conceived than described. The exquisite mingling of hues, pro- 
 duced by this double illumination, must exceed any thing within the limits 
 of the changes of light due to our own planet. 
 
 PLATE XI. 
 
 HerscheVs Section of the Milky Way. 
 
 This figure represents the form of the figure, cut from the Milky Way by 
 a plane passing through the sun, and perpendicular to the two streams, in 
 which this stratum of stars is divided. The branch extending from the 
 bright spot in the center to a, is the section of the upper stream, while that 
 extending to e is cut from the lower stream. The bright points representing 
 stars, it is manifest, that on the hypothesis of equal distribution, the greatest 
 number of stars ever counted in the field of view of the same telescope, 
 would be when directed along the line to e. 
 
 The bright central spot represents the sun's position in the stratum, 
 and its circumference limits the range of penetration of the naked eye ; so 
 that all the stars exterior to this small, bright spot, are only to be seen by the 
 aid of the telescope ; and yet the eye, according to Struve, reaches stars so 
 remote that their light would stream on for one hundred and thirty-seven 
 years, if they were now struck from the heavens ! What an idea does this 
 figure present of the vastness of our " island universe ! " 
 
 PLATE XII. 
 
 The Ring Nebula, in the Constellation Lyra. A. R. 18h. 47m. Dec. 
 32° 50'. 
 
 The remarkable size and form of this remote object, have combined to 
 render it one of the most curious and interesting in the heavens. It is beau 
 tifiilly shown by the Refractor of the Cincinnati Observatory, and appears as 
 
DESCRIPTION OF THE TELESCOPIC VIEWS. 335 
 
 a ring of misty light hung in the heavens, with a diameter as large as that 
 of the moon, when seen with the naked eye. In instruments of inferior 
 power, the interior of this ring appears quite dark ; but I have always seen 
 this space filled with more or less light, according to the purity of the atmo- 
 sphere at the time of examination. 
 
 It is supposed to be a vast congeries of stars, united into one grand system. 
 This object is so remote, as to be utterly invisible to the naked eye, and its 
 light cannot reach us in less than twenty or thirty thousand years ! 
 
 It has shown symptoms (as Herschel remarks) of resolvability ; but has 
 not been fully resolved. There is one other ring nebula known in the 
 northern heavens, and, I believe, but one. Herschel has found several in 
 the south. 
 
 PLATE XIII. 
 Great Southern Nebula, No. 30 Doradus. A. K. 5h. 40m. Dec. 69° 11'. 
 Herschel describes this as one of the most singular and extraordinary 
 objects in the heavens. " It derives no small addition to its intrinsic interest 
 from its situation, which is among the thickest of the nebula? and clustering 
 groups of the greater Nebecula, of whose total area it occupies about one 
 five hundredth part. It contains a large number of stars probably not con- 
 nected with the nebula.'" 
 
 PLATE XIV. 
 
 A large Elliptical Nebula in the Constellation Andromeda. 
 
 PLATE XV. 
 
 A large Nebula in Sagittarius ; figured by Sir John Herschel. A. R. 
 17h. 53m. Dec. S. 24° 21'. 
 
 I have frequently examined this beautiful object. It exceeds in magni- 
 tude all the nebulae visible in our latitude, except that in Orion. It is fol- 
 lowed by a brilliant, coarse cluster of stars. 
 
336 DESCRIPTION OF THE TELESCOPIC VIEWS. 
 
 PLATE XVI. 
 
 Lord Rosse's Whirlpool or Spiral Nebula. A. R. 13h. 23m. Decl. 
 48° 02'. 
 
 This is certainly one of the most wonderful objects in the heavens. I 
 have frequently examined it with the Cincinnati Refractor. The principal 
 outlines are well shown, but the filling up is only accomplished by the 
 monster refractor of the Irish nobleman. The two great central clusters are 
 seen with my large instrument, and were originally drawn by Herschel as 
 distinct objects. The curious spiral form is exhibited with great beauty, and 
 seems to indicate the action of some powerful and controlling law, in this 
 remote body or cluster of universes ; for such indeed it seems to be. 
 
 PLATE XVII. 
 
 The Dumb-hell Nebula, as figured by LordRosse. A. R. 19h. 52m, Dec. 
 22° 17'. 
 
 This object was discovered by Messier as early as 1764. It occupies one 
 of the richest portions of the heavens, and is surrounded by thousands of 
 stars. In ordinary telescopes it may be seen in the shape of a double-headed 
 shot, or dumb-bell; hence its name. With more power its outlines are 
 changed, until, with Lord Rosse's great telescope, it is seen under the figure 
 shown in the plate. I have seen the object very nearly under the form in 
 the drawing, but cannot say that I have ever fairly resolved it into stars. 
 The Cambridge refractor, in the hands of Mr. Bond, is said to have accom- 
 plished its resolution. I see many stars on the nebula, but presume them 
 to be accidental, or located between the observer and the nebula. 
 

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