11-i HISTORY OF PHYSICAL ASTRONOMY. 



till such phenomena as have been spoken of. "We shall afterwards 

 have to speak of the labors, undertaken in order to examine the phe- 

 nomena 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 re- 

 sults 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 

 ascertained ; while it pointed out an interminable vista of new facts, 

 too minute or too complex for observation alone to disentangle, but 

 capable of being detected when theory had pointed out their laws, 

 and of being used as criteria or confirmations of the truth of the doc- 

 trine. For the same reasoning which explained the erection, variation, 

 and annual equation of the moon, showed that there must be many 

 other inequalities besides these ; since these resulted from approximate 

 methods of calculation, in which small quantities were neglected. And 

 it was known that, in fact, the inequalities hitherto detected by astrono- 

 mers did not give the place of the moon with satisfactory accuracy ; so 

 that there was room, among these hitherto untractable irregularities, 

 for the additional results of the theory. To work out this comparison 

 was the employment of the succeeding century ; but Newton began it. 

 Thus, at the end of the proposition in which he asserts, 22 that "all the 

 lunar motions and their irregularities follow from the principles- here 

 stated," he makes the observation which we have just made ; and 

 gives, as examples, the different motions of the apogee and nodes, the 

 difference of the change of the eccentricity, and the difference of the 

 moon's variation, according to the different distances of the sun. "But 

 this inequality," he says, "in astronomical calculations, is usually re- 

 ferred to the prosthaphseresis of< the moon, and confounded with it." 



Reflections on the Discovery. Such, then, is the great Newtonian 

 Induction of Universal Gravitation, and such its history. It is indis- 

 putably and incomparably the greatest scientific discovery ever made, 

 whether we look at the advance which it involved, the extent of the 

 truth disclosed, or the fundamental and satisfactory nature of this truth. 

 As to the first point, we may observe that any one of the five steps into 

 which we have separated -the doctrine, would, of itself, have been con- 

 sidered as an important advance ; would have conferred distinctio* 

 on the persons who made it, and the time to which it belonged. All 



E. iii. Prop. 22. 



