INDUCTIVE EPOCH OF NEWTON. 413 



is not so, except in special cases. And, again, in the instauce of any 

 effect produced by the force of a body, how are we to know whether 

 the force resides in the whole mass as a unit, or in the separate parti- 

 cles ? We may reason, as Newton does, 21 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. Accordingly, 

 Newton had to solve a new series of problems suggested by this in- 

 quiry ; 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 prop- 

 ositions 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 

 mathematical 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 

 mechauical 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 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, Newton's process could be consid- 

 ered only as a rude approximation. In one (the Precession) he com- 

 mitted an error, and in all, his means of calculation 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 em- 

 ployed upon some of them with very partial success ; and the facts, in 

 all of them, required to be accurately ascertained and measured, a pro- 

 cess which is not completed even now. Nevertheless the form and 

 nature of the conclusions which Newton did obtain, were such as to 

 inspire a strong confidence in the competency of his theory to explain 



81 Princip. B. iii. Prop. 7. 



