CALCULUS OF PARTIAL DIFFEREKCES. 53 



('Mem.' 1745, p. 336), he was with great reluctance driven 

 to conclude 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., 

 ' Eecherches sur Jupiter et Saturne,' p. 4), we must have 

 been entitled to call in question the operation 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 , (d being the distance,) regard it as proportional partly 

 to , the inverse square, and partly to , the inverse 



(Jj (A 



fourth power of the distance. But this suggestion 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 unworthy antagonist, Buffon, 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 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 investiga- 



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

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

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



