D'ALEMBERT. 415 



that the doctrine of gravitation failed to account for 

 the progression of the apogee or revolution of the lunar 

 orbit; and if so, as Euler justly observed, (Prix., torn, 

 vii., 'Recherches sur Jupiter et Saturne,' p. 4,) we 

 must have been entitled to call in question the opera- 

 tion of the same principle on all the other parts of the 

 planetary system. Clairaut even went so far as to 

 propose, in consequence of the supposed error, a 

 modification of the law of gravitation ; and that we 

 should, instead of considering it as in the proportion of 



-rg, (d being the distance,) regard it as proportional 

 d 



partly to -~-, the inverse square, and partly to --T-, the 

 d d 



inverse fourth power of the distance. But this sugges- 

 tion was far from giving satisfaction even to those who 

 admitted the failure of the theory. A controversy 

 arose between this great geometrician and a very un- 

 worthy antagonist, BufTon, who on vague, metaphysical, 

 and even declamatory grounds, persisted in showing 

 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 es- 

 timation of either his weight or his strength quanti- 

 ties 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 natu- 

 rally 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 



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

 prize memoir, in 1746, on Jupiter and Saturn, but he mentioned it more 

 fully in a letter to Clairaut. ('Mem.' 1745, p. 353, note.) 



