D'ALEMBERT. 427 



have to be developed for the further solution of the 

 problem. 



Now, it is a truly remarkable circumstance that the 

 conclusion at which all these great men separately arrived 

 was afterwards found to be erroneous. They made the 

 revolving motion of the moon's apogee (or the revolution 

 which the most distant part of her orbit makes in a cer- 

 tain time) half as much as the observations shew it to 

 be; and in a revolution of the moon, 1 30' 43% instead 

 of 3 2' 32" the observations giving about nine years for 

 the period, which the revolution really takes, instead of 

 eighteen. Clairaut first stated this apparent failure of 

 the Newtonian theory, and as he had taken pains to 

 make the investigation "avec toute 1'exactitude qu'elle 

 deinandoit," ('Mem/ 1745, p. 336,) he was with great 

 reluctance driven to conclude that the doctrine of gravi- 

 tation 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 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 -y a , (d being the distance,) regard it as proportional 



v' 



partly to -=^ the inverse square, and partly to -^, the 



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 



