GENERALIZATION OF PRINCIPLES. 81 



Such was the problem, an example only of the 

 general problem of indirect action, which mathe- 

 maticians had to solve. That it was by no means 

 easy to see in what manner the law of the commu- 

 nication of motion was to be extended from simpler 

 cases to those where rotatory motion was produced, 

 is shown by this; that Newton, in attempting to 

 solve the mechanical problem of the Precession of 

 the Equinoxes, fell into a serious errour on this 

 very subject. He assumed that, when a part has to 

 communicate rotatory movement to the whole, (as 

 the protuberant portion of the terrestrial spheroid, 

 attracted by the sun and moon, communicates a 

 small movement to the whole mass of the earth,) the 

 quantity of the motion, " motus," will not be altered 

 by being communicated. This principle is true, if, 

 by motion, we understand what is called moment of 

 inertia, a quantity in which both the velocity of 

 each particle and its distance from the axis of rota- 

 tion are taken into account: but Newton, in his 

 calculations of its amount, considered the velocity 

 only; thus making motion, in this case, identical 

 with the momentum which he introduces in treating 

 of the simpler case of the third law of motion, when 

 the action is direct. This errour was retained even 

 in the later editions of the Principia*. 



The question of the center of oscillation had 

 been proposed by Mersenne somewhat earlier 6 , in 

 1646. And though the problem was out of the 



* B. iii. Lemma iii. to Prop, xxxix. e Mont. ii. 423. 

 VOL. II. G 



