184 HISTORY OF PHYSICAL ASTRONOMY. 



does 22 , that the rule which proves gravity to belong 

 universally to the planets, proves it also to belong 

 to their parts; but the mind will not be satisfied 

 with this extension of the rule, except we can find 

 decisive instances, and calculate the effects of both 

 suppositions, under the appropriate conditions. Ac- 

 cordingly, Newton had to solve a new series of pro- 

 blems suggested by this inquiry; and this he did. 



These solutions are no less remarkable for the 

 mathematical power which they exhibit, than the 

 other parts of the Principia. The propositions in 

 which it is shown that the law of the inverse square 

 for the particles gives the same law for spherical 

 masses, have that kind of beauty which might well 

 have justified their being published for their mathe- 

 matical elegance alone, even if they had not applied 

 to any real case. Great ingenuity is also employed 

 in other instances, as in the case of spheroids of 

 small eccentricity. And when the amount of the 

 mechanical action of masses of various forms has 

 thus been assigned, the sagacity shown in tracing 

 the results of such action in the solar system is 

 truly admirable ; not only the general nature of the 

 effect being pointed out, but its quantity calculated. 

 I speak in particular of the reasonings concerning 

 the Figure of the Earth, the Tides, the Precession 

 of the Equinoxes, the Regression of the Nodes of a 

 ring such as Saturn's ; and of some effects which, at 

 that time, had not been ascertained even as facts of 

 22 Princip. B. iii. Prop. 7- 



