01 



LAPLACE, PIERRE-SIMON. 



LAPLACE, PIERRE-SIMON. 



80S 





primd facie appearance of ingratitude and pusillanimity, the evideno 

 of which, if cot answered, should be perpetuated. 



" A Napoteon-le-Grand. Sire, La bienveillance avec laquelle V.M 

 a daigne' accueillir I'hommage de mou traite" de Me'canique Ce'leste 

 m'a inspir^ le de'sir de lui de"dier cet ouvrage sur le calcul dea Proba 

 billies. Ce calcul de'licat s' extend aux questions les plus importantea 

 de la vie, qui ne sent en effet pour la plupart que des problmes de 

 probabilite. II doit eur ce rapport interesser V.M., dont le genie sai 

 si bien appre'cier et si dignement encourager tout ce qui peut con 

 tribuer au progres des lumieres et de la prosperity publique. J'ose 

 la supplier d'agreer ce nouvel hommage dictd par la plus vive recon 

 naifsance, et par les sentimens profonds de 1'admiration et de respecl 

 avcc legquels je suis. Sire, de V. M. le tres humble et tres obdissant 

 serviteur et fidele sujet, Laplace." 



As if to make such a suppression as striking as possible, Laplace 

 had said, ten years before, in the dedication of the third volume 01 

 the ' Me'canique Ce'leste,' to the First Consul, "Puisse cot ouvrage, 

 consacre a la plus sublime des sciences uaturelles, etre un monument 

 durable de la reconnaissance que votre accueil et les bienfaits du 

 gouvernement inspirent ii.ceux qui les cultivent. De toutes les verites 

 gu'il renferme, 1'expression de ce sentiment sera toujours pour moi la 

 plus pre'cieuse." Laplace did not live to publish the second edition oi 

 the ' Mecanique Celeste.' 



After the final Restoration Laplace's only public employments were 

 of a scientific character, and he died on the 5th of May 1827. His 

 last words were, " Ce que nous connaissons cat peu de chose ; ce que 

 nous ignorons est immense." 



' The Author of the Mecanique Ce'leste," to use a common synonyme 

 for Laplace, must be an object of the admiration of posterity as long 

 as any record of the 18th century exists. With the exception of some 

 experiments made in conjunction with Lavoisier, to determine the 

 quantity of heat in different bodies, we do not find that Laplace was 

 employed in actual experiment. But for many years he was the head, 

 though not the band of European astronomy; and most of the 

 labours of observation were made in directions pointed out by him, 

 or for the furtherance of his discoveries in the consequences of the 

 law of gravitation. Before however we begin to speak of them, 

 there is an important caution, for the want of which a reader of the 

 ' JI(5cai,ique Cdlente' might even overrate Laplace, great as he is. 



The French school of writers on mathematical subjects has for a 

 long time been wedded to the reprehensible habit of omitting all 

 notice of their predecessors, and Laplace is the most striking instance 

 of this practice, which he carried to the utmost extent. In that part 

 of the ' Me'canique Ce'leste ' in which he revels in the results of 

 Lagrange, there is no mention of the name of the latter. The reader 

 who has studied the works of preceding writers will find him, in 

 the ' Theorie dea Probabilites,' anticipated by De Moivre, James 

 Bernoulli, &c., on certain points. But there is not a hint that any 

 one had previously given those results from which perhaps his 

 sagacity led him to hid own more general method. The reader of the 

 ' Mecanique Celeste ' will find that, for anything he can see to the 

 contrary, Euler, Clairaut, D'Alembert, and above all Lagrange, need 

 never have existed. The reader of the ' SystSme du Monde ' finds 

 Laplace referring to himself in almost every page, while now and then, 

 perhaps not twenty times in all, bis predecessors in theory are 

 mentioned with a scanty reference to what they have done ; while the 

 names of observers, between whom and himself there could be no 

 rivalry, occur in many places. To such an absurd pitch is this sup- 

 pression carried, that even Taylor's name is not mentioned in con- 

 nection with his celebrated theorem ; but Laplace gravely informs hia 

 readers, " Nous donnerons quelques thcoremes gdndraux qui nous 

 seront utiles dans la suite," those general theorems being known all 

 over Europe by the names of Maclaurin, Taylor, and Lagrange. And 

 even in his ' Theory of Probabilities,' Lagrange's theorem is only " la 

 formule (p) du nume'ro 21 du second livre " de la Me'canique Ce'leste. 

 It is true that at the end of the 'Me'canique Celeste' he gives 

 historical accounts, in a condensed form, of the discoveries of others ; 

 but these accounts never in any one instance answer the question 

 Which pages of the preceding part of the work contain the original 

 matter of Laplace, and in which is he only following the track of his 

 predecessor ! 



The consequence is, that a student who has followed the writings 

 of Laplace with that admiration which they must command, is 

 staggered when he comes afterwards to find that iu almost every 

 part of the work there are important steps which do not belong to 

 Laplace at all. He is then apt to imagine that when he reads more 

 extensively he shall find himself obliged to restore more and more to 

 the right owner, until nothing is left which can make a reputation 

 ucu aa is that of Laplace with the world at large. Such an impression 

 would be wholly incorrect; but it would be no more than the just 

 reward of the practice of suppression. Nevertheless the researches 

 on the figure of the planets in the ' Me'canique Ce'leste,' and the 

 general method of the ' Tbdorie des Probability ' for the approxima- 

 tion to the values of definite integrals, are alone sufficient, when all 

 needful restoration has been made, to enable us to say, that Laplace 

 was one of the greatest of mathematicians. 



The first two volumes of the ' Me'canique Ce'leste ' appeared in the 

 year VII. of the Republic (which lasted from the 22nd of September 

 Bloc. BIT. VOL. ill. 



1798, to the 21at of September 1799), and may have beeu the induce- 

 ment of the First Consul to make Laplace a member of the govern- 

 ment. The third volume appeared ill 1802, the fourth in 1S05, and 

 the fifth in 1825. A posthumous Supplement has appeared. The 

 headings of the chapters throughout will be a more useful appendage 

 to an article in a work of reference than any account which we could 

 find room for, especially with regard to a philosopher whose dis- 

 coveries are, like those of Newton, dwelt on in every popular work. 

 Iu vol. i. are found 



BOOK I. On the General Lau-i of Equilibrium and Motion. Chap. 1, 

 On the Equilibrium and Composition of Forces which act on a Mate- 

 rial Point ; chap. 2, On the Motion of a Material Point ; chap. 3, On 

 the Equilibrium of a System of Bodies; chap. 4, On the Equilibrium 

 of Fluids; chap. 5, General Principles of the Motion of a System of 

 Bodies; chap. 6, On the Laws of Motion of a System of Bodies, for 

 all Relations between the Force and Velocity which are mathematically 

 possible; chap. 7, On the Motion of a Solid Body of any Figure; 

 chap. 8. On the Motion of Fluid*. 



BOOK II. On the Law of Universal Gravitation, and on the Motion 

 of the Centra of Gravity of the Heavenly .Bodies. Chap. 1, Ou the 

 Law of Universal Gravitation, collected from Phenomena; chap. 2, 

 On the Differential Equations of the Motion of a System of Bodies 

 acting on each other by their mutual Attraction; chap. 3, First 

 Approximation to the Celestial Motions, or Theory of tho Elliptic 

 Motion; chap. 4, Determination of the Elements of the Elliptic 

 Motion ; chap. 5, General Methods for determining the Motions of the 

 Heavenly Bodies by successive Approximation; chap. 6, Second 

 Approximation to the Celestial Motions, or Theory of their Perturba- 

 tions ; chap. 7, On the Secular Inequalities of the Celestial Motions ; 

 chap. 8, Second method of Approximation, to the Celestial Motions 

 (by the Variation of Elements). 



In vol. ii. are contained 



BOOK III. On the Figure of the Celestial Bodie3.*-Cha.y. 1, On the 

 Attraction of Homogeneous Spheroids, terminated by surfaces of the 

 second order ; chap. 2, Development of the Attraction of all Spheroids 

 in Series ; chap. 3, On the Figure of Equilibrium of a Homogeneous 

 Fluid Mass which has a Rotatory Motion ; chap. 4, On the Figure of 

 a Spheroid which differs little from a Sphere, and is covered by a, 

 stratum of fluid in equilibrio ; chap. 5, Comparison of the preceding 

 theory with observation; chap. 6, On the Figure of Saturn's Ring; 

 chap. 7, On the Figure of the Atmospheres of the Heaveuly Bodies. 



BOOK IV. On the Oscillations of the Sea and the Atmosphere. 

 Chap. 1, Theory of the Ebb and Flow of the Sea ; chap. 2, On the 

 Stability of the Equilibrium of the Sea ; chap. 3, On the method of 

 taking into account, in the Theory of the Tides, the various circum- 

 stances peculiar to each port ; chap. 4, Comparison of the preceding 

 theory with observation. 



BOOK V. On the Motion of the Celestial Bodies about their Centres 

 of Gravity. Chap. 1, On the Motion of the Earth about its Centre 

 of Gravity ; chap. 2, On the Motion of the Moon about its Centre of 

 3ravity ; chap. 3, On the Motion of the Rings of Saturn about their 

 Centres of Gravity. 



In vol. iii. are contained 



BOOK VI. Particular Theories of the Planets. Chap. 1, Formulas 

 'or the Planetary Inequalities depending on the squares and higher 

 lowers of the Excentricities and Inclinations of the Orbits ; chap. 2, 

 :nequalities depending on the Square of the Disturbing Force; 

 ihap. 3, Perturbations due to the Kllipticity of the Sun; chap. 4, 

 Perturbations of the Motion of the Planets, arising from the action, 

 >f their Sutellites ; chap. 5, Considerations on the Elliptic part of the 



Theory of the Motion of the Earth'; chap, "ll, Theory of Mars; 

 chap. 12, Theory of Jupiter; chap. 13, Theory of Saturn; chap. 14, 

 .'heory of Uranus; chap. 15, On some equations of condition which 

 xist between the Planetary Inequalities, and which serve to verify 

 hem ; chap. 16, On the Masses of the Planets and the Moon ; chap. 17, 

 On the Formation of Astronomical Tables, and on the Invariable 

 Plane of the Planetary System; chap. 18, On the Action of the Stars 

 upon the Planetary System. 



BOOK VII. Theory of the Moon. General considerations not arranged 

 as a chapter. Chap. 1, Integration of the Differential Equations of tho 

 Lunar Motion; chap. 2, On the Lunar Inequalities due to the Non- 

 sphericity of the Earth and Moon ; chap. 3, On the Lunar Inequalities 

 due to the Action of the Planets ; chap. 4, Comparison of the preceding 

 theory with observation ; chap. 5, On an Inequality of long period which, 

 appears to exist in the Lunar Motion ; chap. 6, On the Secular Varia- 

 tions in the Motion of the Moon and the Earth, which may be produced 

 by the resistance of an Ethereal Fluid. 



In vol. iv. are contained 



BOOK VIII. Theory of the Satellites of Jupiter, Saturn, and Uranus. 

 Chap. 1, Equations of Motion of the Satellites of Jupiter, taking into 

 consideration their Mutual Attractions, that of the Sun, and that of 

 the Oblate Spheroid of Jupiter; chap. 2, On the Inequalities of the 



