RESEARCHES OF NEWTON'S SUCCESSORS. 311 



Notwithstanding the incomparable sagacity of its author 

 the Principia contained merely a rough outline of the 

 planetary perturbations. If this sublime sketch did not 

 become a complete portrait we must not attribute the 

 circumstance to any want of ardour or perseverance ; 

 the efforts of the great philosopher were always super- 

 human, the questions which he did not solve were inca- 

 pable of solution in his time. When the mathematicians 

 of the continent entered upon the same career, when 

 they wished to establish the Newtonian system upon an 

 incontrovertible basis, and to improve the tables of as- 

 tronomy, they actually found in their way difficulties 

 which the genius of Newton had failed to surmount. 



Five geometers, Clairaut, Euler, D'Alembert, La- 

 grange, and Laplace, shared between them the world of 

 which Newton had disclosed the existence. They ex- 

 plored it in all directions, penetrated into regions which 

 had been supposed inaccessible, pointed out there a mul- 

 titude of phenomena which observation had not yet de- 

 tected ; finally, and it is this which constitutes their 

 imperishable glory, they reduced under the domain of a 

 single principle, a single law, every thing that was most 

 refined and mysterious in the celestial movements. Ge- 

 ometry 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 magnifi- 

 cent labours of Euler, we shall, on the contrary, present 

 the reader with a rapid analysis of the discoveries of his 

 four rivals, our countrymen.* 



* It may perhaps be asked why we place Lagrange among the 

 French geometers'? This is our reply : It appears to us that the indi- 

 vidual who was named Lagrange Tournier, two of the most character- 



