358 HISTuKY OF MECHANICS. 



Clear as Huyghen's principle appeared to himself, it \Vas, after some 

 time, attacked by the Abbe Catelan, a zealous Cartesian. Catelau 

 also put forth principles which he conceived were evident, and deduced 

 from them conclusions contradictory to those of Huygheus. His prin- 

 ciples, now that we know them to be false, appear to us very gratu- 

 itous. They are these ; " that in a compound pendulum, the sum of 

 the velocities of the component weights is equal to the sum of the 

 velocities which they would have acquired if they had been detached 

 pendulums ;" and " that the time of the vibration of a compound pen- 

 dulum is an arithmetic mean between the times of the vibrations of 

 the weights, moving as detached pendulums." Huyghens easily 

 showed that these suppositions would make the centre 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 Huygheus. As the discussion thus proceeded, it began 

 to be seen that the question really was, in what manner the Third 

 Law of Motion Avas to be extended to cases of indirect action ; whether 

 by distributing the action and reaction according to statical principles, 

 or in some other way. " I propose it to the consideration of mathe- 

 maticians," says Bernoulli in 1686, "what law of the communication 

 of velocity is observed by bodies in motion, which are sustained 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 communi- 

 cated from the one body to the other to be distributed in the same 

 proportion in which a load supported on the lever would be distrib- 

 uted ?" He adds, that if this question be answered in the affirmative, 

 Huyghens will be found to be in error ; but this is a mistake. The 

 principle, that the action and reaction of bodies thus moving are to 

 be distributed according to the rules of the lever, is true ; but Ber- 

 noulli mistook, in estimating this action and reaction by the velocity 

 acquired at any moment ; instead of taking, as he should have done, 

 the increment of velocity which gravity tended to impress in the next 

 instant. This was shown by the Marquis de 1'IIopital ; who adds, 

 * with justice, "I conceive that I have thus fully answered the call of 

 Bernoulli, when he says, I propose it to the consideration of mathema- 

 ticians, &c." 



We may, from this time, consider as known, but not as fully estab- 

 lished, the principle that " When bodies in motion affect each other, 

 the action and reaction are distributed according to the laws of Sta- 

 tics ;" although there were still found occasional difficulties in the 



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