INDUCTIVE EPOCH OF NEWTON. 185 



observation ; for instance, the difference of gravity 

 in different latitudes, and the Nutation of the earth's 

 axis. It is true, that in most of these cases, New- 

 ton's process could be considered only as a rude 

 approximation. In one (the Precession) he com- 

 mitted an errour, and in all, his means of calcula- 

 tion were insufficient. Indeed these are much more 

 difficult investigations than the Problem of Three 

 Bodies, in which three points act on each other by 

 explicit laws. Up to this day, the resources of 

 modern analysis have been employed upon some of 

 them with very partial success ; and the facts, in all 

 of them, required to be accurately ascertained and 

 measured, a process which is not completed even 

 now. Nevertheless the form and nature of the con- 

 clusions which Newton did obtain, were such as to 

 inspire a strong confidence in the competency of his 

 theory to explain all such phenomena as have been 

 spoken of. We shall afterwards have to speak of 

 the labours, undertaken in order to examine the 

 phenomena more exactly, to which the theory gave 

 occasion. 



Thus, then, the theory of the universal mutual 

 gravitation of all the particles of matter, according 

 to the law of the inverse square of the distances, 

 was conceived, its consequences calculated, and its 

 results shown to agree with phenomena. It was 

 found that this theory took up all the facts of 

 astronomy as far as they had hitherto been ascer- 

 tained ; while it pointed out an interminable vista 



