84 HISTORY; OF MECHANICS. 



detached pendulums ;" and " that the time of the 

 vibration of a compound pendulum is an arithmetic 

 mean between the times of the vibrations of the 

 weights, moving as detached pendulums." Huy- 

 ghens easily showed that these suppositions would 

 make the center of gravity ascend to a greater 

 height than that from which it fell ; and after some 

 time, James Bernoulli stept into the arena, and 

 ranged himself on the side of Huyghens. As the 

 discussion thus proceeded, it began to be seen 

 that the question really was, in what manner the 

 Third Law of Motion was to be extended to cases 

 of indirect action; whether by distributing the 

 action and re-action according to statical principles, 

 or in some other way. "I propose it to the con- 

 sideration of mathematicians," says Bernoulli in 

 1686, "what law of the communication of velocity 

 is observed by bodies in motion, which are sus- 

 tained at one extremity by a fixed fulcrum, and 

 at the other by a body also moving, but more 

 slowly. Is the excess of velocity which must be 

 communicated from the one body to the other to 

 be distributed in the same proportion in which a 

 load supported on the lever would be distributed ?" 

 He adds, that if this question be answered in the 

 affirmative, Huyghens will be found to be in errour; 

 but this is a mistake. The principle, that the action 

 and re-action of bodies thus moving are to be 

 distributed according to the rules of the lever, is 

 true ; but Bernoulli mistook, in estimating this 



