LAPLACE. 133 



the spheroidal figure of the earth, and of the discovery of the variation 

 of gravity upon the surface of our phmet. These were two great results ; 

 our country, however, had a right to demand more : wheu France is not 

 in the first rank she has lost her place.* 



This rank, which was lost for a moment, was brilliantly regained, an 

 achievement for which we are indebted to four geometers. When 

 Newton, giving to his discoveries a generality which the laws of Kepler 

 did not imply, imagined that the different planets were not only at- 

 tracted by the sun, but that they also attract each other, he introduced 

 into the heavens a cause of universal disturbance. Astronomers could 

 then see at the first glance that in no part of the universe, whether near 

 or distant, would the Keplerian laws suflice for the exact representation 

 of the phenomena ; that the simple, regular movements with which the 

 imaginations of the ancients were pleased to endue the he.avenly bodies 

 would experience numerous, considerable, perpetually changing pertur- 

 bations. 



To discover several of these perturbations, to assign their nature, and 

 in a few rare cases their nnmeiical values, such was the object which 

 Newton proposed to himself in writing the Priucipia Mathematica Pbi- 

 losophia^. Naturalis. 



Notwithstanding the incomparable sagacity of its author, the Priu- 

 cipia 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 ardor or perseverance ; the 

 efforts of the great philosopher were always superhuman ; the questions 

 which he did not solve were incapable 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 incon- 

 trovertible basis, and to improve the tables of astronomy, they actually 

 found in their way difficulties which the genius of Newton had failed to 

 surmount. 



Five geometers, Clairaut, Euler, D'Alembert, Lagrange, and Laplace^ 

 shared between them the world of which Newton had disclosed the 

 existence. They explored it in all directions, penetrated into regions 

 which had been supposed inaccessible, pointed out there a multitude of 



* The spheroidal figure of the earth was established by the comparison of an arc of the 

 meridian that had been measured, in France, with a similar arc measured in Lapland, from 

 which it appeared that the length of a degrcd of the meridian increases from the equator 

 toward the poles, conformably to what ought to result upon the supposiUlon of the earth 

 having the figure of an oblate spheroid. The length of the Lapland arc was determined 

 by means of au expedition which the French government had dispatched to the nortli of 

 Europe for that purpose. A similar expedition had been dispatched from France about the 

 same time to Peru, in South America, for the purpose of measuring an arc of the meridian 

 under the equator, but the results had not been ascertained at the time to which the author 

 alludes in the text. The variation of gravity at the surface of the earth was established by 

 Richer's experiments with the pendulum at Cayenne, in South America, (lG73-'74,) from 

 which it appeared that the pendulum oscillates more slowly, and consequently the force of 

 gravity is less intense, under the equator than in the latitude of Paris. — Translatok. 



