80 HISTORY OF MECHANICS. 



searches in vain. And I hope 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 Lam of Mo- 

 tion. Center of Oscillation. Huyghens. 



THE Third Law of Motion, whether expressed ac- 

 cording to Newton's formula, by the equality of 

 Action and Reaction, or in any other of the ways 

 employed about the same time, easily gave the so- 

 lution of mechanical problems in all cases of direct 

 action; that is, when each body acted directly on 

 others. But there still remained the problems 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 Center of Oscillation f 



