PREFACE. THE main object of the work here submitted to the reader is to exhibit a view of the labours of successive enquirers in establishing a knowledge of the mechanical principles which regulate the movements of the celestial bodies, and in explaining the various phenomena relative to their physical constitution which observation with the telescope has disclosed. It may, perhaps, be desirable to trace out briefly the plan I have pursued in attempting to execute this undertaking. The first part of the work, extending to the close of the thirteenth chapter, is devoted to the history of the Theory of Gravitation. In the first and third chapters I have endeavoured to give some account of the immortal discoveries by which Newton established this theory in its utmost generality. The researches of the learned Prof. Rigaud have recently disclosed some interesting details respecting the original publication of the Principia, of which I have not failed to avail myself in the execution of this portion of the work. The future history of Celestial Mechanics naturally admits of a division into two distinct periods. The first comprehends the researches of geometers from the time of Newton to the commencement of the nineteenth century. Towards the close of this period the analytical methods devised for the developement of the Theory of Gravitation had attained a high state of perfection, and the various phenomena which had seemed irreconcilable with its principles, were all satisfactorily accounted for. The second period embraces the further developement of the theory down to the present time. The third and following chapters to the ninth inclusive, are devoted to the first of the above-mentioned periods. The third chapter contains an account of the early researches of Euler, Clairaut, and D'Alembert on the Problem of Three Bodies, and of the application of their respective solutions to the lunar theory. The difficulty which for some time attended the computation of the movement of the lunar apogee, was at length effectually removed by Clairaut, and the triumph of the Newtonian principles was practically exhibited in the construction of lunar tables by Mayer, which possessed sufficient accuracy to be employed with confidence in the solution of the great Problem of the Longitude. It is a curious fact that, in the original edition of the Principia, Newton gave the results of an investigation of the movement of the lunar apogee, which seemed to imply that he had treated the subject by a method of a sufficiently comprehensive character. These results were suppressed by him in the second edition, doubtless in consequence of their not exhibiting so complete an accordance with observation as was manifest in his other researches on the lunar theory *. That Newton really was in possession of a method adequate to a complete investigation of the subject, is rendered still further probable by the recent researches of Mr. Adams, who, by the aid of geometrical considerations, analogous to those expounded with so much elegance in the Principia, has obtained results relative to the movement of the lunar apogee, which present a complete accordance with observation. The fourth chapter is devoted to the early researches of geometers on the perturbations of the planets and the stability of the planetary system. While occupied with the former of these subjects, the illustrious Euler devised a method of investigation which must be regarded as one of the most remarkable in the annals of science. It consisted in regarding the perturbations of a planet as arising from an incessant change in the elements of its elliptic motion. This fertile idea was destined to acquire an immense developement from the labours of succeeding geometers. The sublime results which the analytical researches of Lagrange and Laplace have disclosed, relative to the stability of the planetary system, while they have served to invest astronomical science with additional features of interest, are entitled to be classed among the noblest triumphs which the human mind has achieved in the investigation of the laws of the physical universe. The labours of these great geometers, which were of a kindred nature throughout their whole career, are on this occasion more especially interlaced. As some misapprehension appears to have not unfrequently arisen from this circumstance, I have endeavoured, by a careful reference to the volumes of the Academy of Sciences and other original sources, to exhibit the results independently arrived at by each. geometer in the course of his researches on the subject. The fifth chapter contains an account of the physical explanation of the great inequality in the mean longitudes of Jupiter and Saturn, and of the secular inequality in the mean motion of the Moon, as well as an allusion to several points of minor importance in the Theory of Gravitation. The irregularities in the mean longitudes of Jupiter and Saturn long continued to form an inexplicable enigma to geometers. In vain did Euler employ all the resources of his fertile genius in endeavouring to account for their existence by the principles of the Theory of Gravitation. Equally fruitless was the result of Lagrange's application of his commanding powers of analytical research to the subject. It was reserved for Laplace to detect the true origin of these anomalous phenomena in the mutual action of the two planets. Perhaps a still more remarkable result, due to the same geometer, was the explanation of the secular inequality in the mean motion of the Moon. The records of certain eclipses of the Moon observed at Babylon about seven hundred years before the Christian era, when compared with observations of similar phenomena by the Arabian astronomers about the tenth * See Appendix IV. |