134 NEWTON S PKINCIPIA. 



at the poles. If, on the other hand, there is more matter 

 at the poles, or matter of a less dense kind at the equator, 

 the nodes will advance instead of receding. So that by 

 knowing the motion of the nodes, we can estimate the 

 constitution of the globe; and a perfectly spherical and 

 homogeneous globe will move equally and with a single 

 motion only round its axis. No other will. 



The Sixty-sixth Proposition, or rather its twenty-two 

 corollaries, constitute perhaps the most extraordinary por 

 tion of the Principia. We have seen that Sir Isaac 

 Newton here deduces most of the leading disturbances in 

 the motions of three bodies, for example, the moon, 

 earth, and sun, from the propositions which had been 

 before demonstrated. We perceive in succession the mo 

 tion of longitude and latitude ; the various annual equa 

 tions, motion of the apsides (in which, however, by omitting 

 the consideration of the tangential force, he calculated 

 the amount at one half its true value), the evection*, the 

 alteration, and inclination ; the motion of the nodes. Even 

 the doctrine of the tides, and the precession of the equinoxes, 

 are all handled clearly, though concisely, in this pro 

 position. The greater part of the Third Book is occupied 

 with the application of these corollaries to the actual case 

 of the moon, earth, and sun; and it is not any exaggeration 

 to affirm that the great investigations which have been 

 undertaken since the time of Sir Isaac Newton, and of 

 which we have just been surveying the principal results, 

 are an application of the improved calculus to continue the 

 inquiries which he thus here began. 



The propositions respecting the masses of the attracting 

 bodies which we considered before the corollaries to the 



* Laplace has erroneously stated that Newton overlooked the Evection ; 

 but it forms, though not by name, the subject of the ninth corollary to this 

 Sixty- sixth Proposition. 



