160 NEWTON S PRINCIPIA. 



lysis, would have failed to do anything here), but the 

 great discoverer actually completed the most difficult in 

 vestigation of this new region, and reached to its most 

 inaccessible heights, with a clearness so absolute, and a 

 certainty so unerring, that all the subsequent researches 

 of his followers, and all their vast improvements on his 

 calculus, have not enabled them to correct by the fraction 

 of a cipher his first results. The Ninetieth and Ninety- 

 first Propositions of the First Book, containing the most 

 refined principles of his method, are applied by him in 

 the Nineteenth of the Third Book to the problem of the 

 Earth s figure; his determination of the ellipticity, sup 

 posing the mass homogeneous, is obtained from that appli 

 cation. A century of study, of improvement, of dis 

 covery has passed away ; and we find Laplace, master of 

 all the new resources of the calculus, and occupying the 

 heights to which the labours of Euler, Clairaut, D Alem- 

 bert, and Lagrange have enabled us to ascend, adopting 

 the Newtonian fraction of ^y, as the accurate solution 

 of this speculative problem. New admeasurements have 

 been undertaken upon a vast scale, patronized by the muni 

 ficence of rival governments ; new experiments have been 

 performed with improved apparatus of exquisite delicacy ; 

 new observations have been accumulated, with glasses 

 far exceeding any powers possessed by the resources of 

 optics in the days of him to whom the science of optics, 

 as well as dynamics, owes its origin ; the theory and the 

 fact have thus been compared and reconciled together in 

 more perfect harmony ; but that theory has remained un 

 improved, and the great principle of gravitation, with its 

 most sublime results, now stands in the attitude, and of 

 the dimensions, and with the symmetry, which both the 

 law and its application received at once from the mighty 

 hand of its immortal author. 



