356 HISTORY OF MECHANICS. 



that the principles expounded in this work will afford some light, 

 either to this mode of philosophizing, or to some mode which is more 

 true." 



Before we pursue this subject further, we must trace the remainder 

 of the history of the Third Law. 



Sect. 2. — Generalization of the Third Law of Motion. — Centre of 

 Oscillation. — Huyghens. 



The Third Law of Motion, whether expressed according to New- 

 ton's formula (by the equality of Action and Reaction), or in any 

 other of the ways employed about the same time, easily gave the solu- 

 tion of mechanical problems in all cases of direct action ; that is, when 

 each body acted directly on others. But there still remained the prob- 

 lems in which the action is indirect ; — when bodies, in motion, act on 

 each other by the intervention of levers, or in any other way. If a 

 rigid rod, passing through two weights, be made to swing about its 

 upper point, so as to form a pendulum, each weight will act and react 

 on the other by means of the rod, considered as a lever turning about 

 the point of suspension. What, in this case, will be the effect of this 

 action and reaction ? In what time will the pendulum oscillate by the 

 force of gravity ? Where is the point at which a single weight must 

 be placed to oscillate in the same time ? in other words, where is the 

 Centre of Oscillation? 



Such was the problem — an example only of the general problem of 

 indirect action — which mathematicians had to solve. That it was by 

 no means easy to see in what manner the law of the communication 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 error 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 under- 

 stand what is called moment of inertia, a quantity in which both the 

 velocity of each particle and its distance from the axis of rotation are 

 taken into account : but Newton, in his calculations of its amount, con- 

 sidered the velocity only ; thus making motion, in this case, identical 

 with the momentum which he introduces in treating of the simpler case 



