102 HISTORY OF MECHANICS. 



One consequence of the synthetical form adopted 

 by Newton in the Principia, was, that his succes- 

 sors had the problem of the solar system to begin 

 entirely anew. Those who would not do this, made 

 no progress, as was long the case with the English. 

 Clairaut says, that he tried for a long time to 

 make some use of Newton's labours; but that, at 

 last, he resolved to take up the subject in an inde- 

 pendent manner. This, accordingly, he did, using 

 analysis throughout, and following methods not 

 much different from those still employed. We do 

 not now speak of the comparison of this theory 

 with observation, except to remark, that both by 

 the agreements and by the discrepancies of this 

 comparison, Clairaut and other writers were per- 

 petually driven on to carry forwards the calculation 

 to a greater and greater degree of accuracy. 



One of the most important of the cases in 

 which this happened, was that of the movement 

 of the apogee of the moon ; and in this case a mode 

 of approximating to the truth, which had been de- 

 pended on as nearly exact, was, after having caused 

 great perplexity, found by Clairaut and Euler to 

 give only half the truth. This same problem of three 

 bodies was the occasion of a memoir of Clairaut, 

 which gained the prize of the Academy of St. Pe- 

 tersburg in 1751 ; and, finally, of his Theorie de la 

 Lune, published in 1765. D'Alembert laboured at 

 the same time on the same problem ; and the value 

 of their methods, and the merit of the inventors, 



