STABILITY OF THE SOLAR SYSTEM. 323 



duction, the reader will have no difficulty in admitting 

 that the word elegance may be appropriately applied to 

 mathematical researches. 



In this analysis we have merely glanced at the astro- 

 nomical discoveries of Clairaut, D'Alembert, and La- 

 grange. We shall be somewhat less concise in noticing 

 the labours of Laplace. 



After having enumerated the various forces which must 

 result from the mutual action of the planets and satellites 

 of our system, even the great Newton did not venture to 

 investigate the general nature of the effects produced by 

 them. In the midst of the labyrinth formed by increases 

 and diminutions of velocity, variations in the forms of the 

 orbits, changes of distances and inclinations, which these 

 forces must evidently produce, the most learned geometer 

 would fail to discover a trustworthy guide. This extreme 

 complication gave birth to a discouraging reflection. 

 Forces so numerous, so variable in position, so different 

 in intensity, seemed to be incapable of maintaining a con- 

 dition of equilibrium except by a sort of miracle. New- 

 ton even went so far as to suppose that the planetary 

 system did not contain within itself the elements of indef- 

 inite stability ; he was of opinion that a powerful hand 

 must intervene from time to time, to repair the derange- 

 ments occasioned by the mutual action of the various 

 bodies. Euler, although farther advanced than Newton 

 in a knowledge of the planetary pertubations, refused 

 also to admit that the solar system was constituted so as 

 to endure for ever. 



Never did a greater philosophical question offer itself 

 to the inquiries of mankind. Laplace attacked it with 

 boldness, perseverance, and success. The profound and 

 long-continued researches of the illustrious geometer 



