428 D'ALEMBERT. 



between this great geometrician and a very unworthy 

 antagonist, Buffon, who, on vague, metaphysical, and even 

 declamatory grounds, persisted in shewing his ignorance 

 of analysis, and his obstinate vanity; nor, though he 

 was by accident, quite right, could any one give him the 

 least credit for his good fortune. Clairaut answered him, 

 and afterwards rejoined to his reply, with a courtesy 

 which betokened entire civility and even respect for the 

 person, with an infinitely low estimation of either his 

 weight or his strength quantities truly evanescent. At 

 length it occurred to him that the process should be 

 repeated, a course which he certainly must have taken at 

 first had he not naturally enough been misled by the 

 singular coincidence of both Euler and D'Alembert* 

 having arrived at the same conclusion with himself. He 

 found that he ought to have repeated his investigation of 

 the differential equation to the radius, after obtaining, by 

 a first investigation, the value of the third term above 

 given in that equation 



T - &c 



d v (as above given.) 



u 3 (w 2 + &c. 



This omission he now supplied, and he found that the 

 result, when applied to the case, made the progression of 

 the moon's apogee twice as quick as the former operation 

 had given it, or nine years, agreeing with the actual obser- 

 vation. He deposited, in July, 1746, with the secretary 



* Euler had stated it incidentally, as regarded the lunar apogee, 

 in his prize memoir, in 1746, on Jupiter and Saturn, but he men- 

 tioned it more fully in a letter to Clairaut. ('Mem.' 1745, p. 353, 

 note.) 



