GENERALIZATION OF PRINCIPLES. 85 



action and re-action 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'Hopital; 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 mathematicians, &c." 



We may, from this time, consider as known, 

 but not as fully established, the principle that 

 " When bodies in motion affect each other, the 

 action and re-action are distributed according to 

 the laws of statics ;" although there were still found 

 occasional difficulties in the generalization and ap- 

 plication of the rule. James Bernoulli, in 1703, 

 gave a "general demonstration of the Center 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, when the products of their momenta and 

 the lengths of the levers are equal in opposite 

 directions. For the proof of this proposition, 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 elementary enough. 

 9 Op. ii. 930. in Choq. des Corps, p. 296. " Ib. Prop. xi. 



