134 LAPLACE. 



phenomena which observation had not yet detectecl — finally- — and it is 

 this which constitutes their imperishable glory — they reduced under 

 the domain of a single principle, a single law, everything that was most 

 refined and mysterious in the celestial movements. Geometry had thus 

 the boldness to dispose of the future. The evolutions of ages are 

 scrupulously ratifying the decisions of science. 



We shall not occupy our attention with the magnificent labors of 

 Euler. We shall, on the contrary, present the reader with a rapid 

 analysis of the discoveries of his four rivals, our countrymen.* If a 

 celestial body — the moon, for example — gravitated solely toward the 

 center of the earth, it would describe a mathematical ellipse. It would 

 strictly obey the laws of Kepler, or, which is the same thing, the 

 principles of mechanics expounded by Newton in the first sections of 

 his immortal work. 



Let us now consider the action of a second force. Let us take into 

 account the attraction which the suu exercises upon the moon. In other 

 words, instead of two bodies, let us suppose three to oi)erate on each 

 other. The Keplerian ellipse will now furnish merely a rough indication 

 of the motion of our satellite. In some parts the attraction of the suu 

 will tend to enlarge the orbit, and will in reality do so. In other parts, 

 the effect will be the reverse of this. In a word, by the introduction of 

 a third attractive body, the greatest comi)lication will succeed to a simple, 

 regular movement upon which the mind reposed with complacency. 



If Newton gave a complete solution of the question of the celestial 

 movements in the case wherein two bodies attract each other, he did 

 not even attempt an analytical investigation of the infinitely more 

 difticult problem of three bodies. The problem of three bodies, (this is 

 the name by which it has become celebrated,) the problem for deter- 

 mining the movement of a body subjected to the attractive influence of 

 two other bodies, was solved for the first time by our countryman 

 Clairaut.t From this solution we may date the important improve- 

 ments of the lunar tables effected iu the last century. 



The most beautiful astronomical discovery of antiquity is that of the 

 precession ofi the equinoxes. Hipparchus, to whom the honor of it is 

 due, gave a complete and precise statement of all the consequences 



* It may, perhaps, be asked why we place Laj^rango among the French geometers. This 

 is our reply: It appears to us that the individual who was named Lagrange Tournier — two 

 of the most characteristic French names which it is possible to imagine — whose maternal grand- 

 father was M. Gros; whose paternal great grandfather was a French ofiicer, a native of Paris, 

 who never wrote except in French, and who was invested iu our country with high honors 

 during a period of nearly thirty years, ought to be regarded as a Frenchman, although born at 

 Turin. — Author. 



t The problem of three bodies was solved independently about the same time by Euler, 

 D'Alembert, and Clairaut. The two last-mentioned geometers communicated their solutions 

 to the Academy of Sciences on the same day — November 15, 1747. Euler had already, in 

 1746, published tables of the moon, founded on his solution of the same problem, the details 

 of which h subsequently' published, in 1753. — Tkanslatou. 



