INDUCTIVE EPOCH OF NEWTON. 170 



edition", that it follows from the theory of gravity, 

 that the aphelia of Mercury, Venus, the Earth, and 

 Mars, slightly progress. 



In one celebrated instance, indeed, the deviation 

 of the theory of the Principia from observation 

 was wider, and more difficult to explain ; and as this 

 deviation for a time resisted the analysis of Euler 

 and Clairaut, as it had resisted the synthesis of 

 Newton, it at one period staggered the faith of 

 mathematicians in the exactness of the law of the 

 inverse square of the distance. I speak of the 

 Motion of the Moon's Apogee, a problem which has 

 already been referred to; and in which Newton's 

 method, and all the methods which could be devised 

 for some time afterwards, gave only half the ob- 

 served motion ; a circumstance which arose, as was 

 discovered by Clairaut in 1750, from the insuffi- 

 ciency of the method of approximation. Newton 

 does not attempt to conceal this discrepancy. After 

 calculating what the motion of apse would be, upon 

 the assumption of a disturbing force of the same 

 amount as that which the sun exerts on the moon, 

 he simply says 19 , "the apse of the moon moves 

 about twice as fast." 



The difficulty of doing what Newton did in this 

 branch of the subject, and the powers it must have 



18 Scholium to Prop. 14. B. iii 



19 B. i. Prop. 44, second edit. There is reason to believe, 

 however, that Newton had, in his unpublished calculations, 

 rectified this discrepancy. 



N2 



