186 HISTORY OF PHYSICAL ASTRONOMY. 



of new facts, too minute or too complex for obser- 

 vation 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 doctrine. 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 astronomers did not give the place of 

 the moon with satisfactory accuracy ; so that there 

 was room, among these hitherto untractable irregu- 

 larities, 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 23 , that " all the lunar motions and their irre- 

 gularities 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 astro- 

 nomical calculations, is usually referred to the 

 prosthapha3resis of the moon, and confounded with 



it." (G). 



M B. iii. Prop. 22. 



