GENERALIZATION OF PRINCIPLES. 359 



generalization and application of the rule. James Bernoulli, in 1703, 

 gave " a General Demonstration of the Centre of Oscillation, drawn 

 from the nature of the Lever." In this demonstration 9 he takes as a 

 fundamental principle, that bodies in motion, connected by levers, 

 balance, \vhen the products of their momenta and the lengths of the 

 levers are equal in opposite directions. For the proof of this proposi- 

 tion, he refers to Marriotte, who had asserted it of weights acting by 

 percussion, 10 and in order to prove it, had balanced the effect of a 

 weight on a lever by the effect of a jet of water, and had confirmed it 

 by other experiments. 11 Moreover, says Bernoulli, there is no one who 

 denies it. Still, this kind of proof was hardly satisfactory or elemen- 

 tary enough. John Bernoulli took up the subject after the death ot 

 his brother James, which happened in 1705. The former published 

 in 17 14 his Meditatio de NaturcL Centri Oscillationis. In this memoir, 

 he assumes, as his brother had done, that the effects of forces on a 

 lever in motion are distributed according to the common rules of the 

 lever. 12 The principal generalization which he introduced was, that 

 he considered gravity as a force soliciting to motion, which might have 

 different intensities in .different bodies. At the same time, Brook 

 Taylor in England solved the problem, upon the same principles as 

 Bernoulli ; and the question of priority on this subject was one point 

 in the angry intercourse which, about this time, became common be- 

 tween the English mathematicians and those of the Continent. Her- 

 mann also, in his Phoronomia, published in 1716, gave a proof which, 

 as he informs us, he had devised before he saw John Bernoulli's. This 

 proof is founded on the statical equivalence of the "solicitations oj 

 gravity" and the "vicarious solicitations'' 1 which conespond to the 

 actual motion of each part ; or, as it has been expressed by more 

 modern writers, the equilibrium of the impressed and effective forces. 



It was shown by John Bernoulli and Hermann, and was indeed 

 easily proved, that the proposition assumed by Huyghens as the foun- 

 dation of his solution, was, in fact, a consequence of the elementary 

 principles which belong to this branch of mechanics. But this as- 

 sumption of Huyghens was an example of a more general proposition, 

 which by some mathematicians at this time had been put forward as 

 in original and elementary law ; and as a principle which ought to 

 supersede the usual measure of the forces of bodies in motion ; this 

 principle they called " the Conservation of Vis Viva? The attempt to 



9 Op. ii. 930. la Choq. des Gr-os, p. 296. 



11 Ib. Prop. xi. 12 p. 172. 



