VOL. XXXII.] PHILOSOPHICAL TRANSACTIONS. ()33 



out any regard to what others had said on that subject, brings new arguments, 

 which Dr. Clarke has fully answered, in his 5th letter to him. Messieurs John 

 Bernoulli, Wolfius, Herman and others, have followed and defended Leib- 

 nitz's opinion, and in the same manner, so that what is an answer to him, is 

 so to them. 



Poleni, professor at Padua, has acted after the same manner in the experi- 

 mental way, making some experiments to defend Leibnitz's opinion, without 

 having shown those to be false which are made use of to prove the contrary ; 

 (Ptolenus de Castellis, p. 56, 57, &c.) and now lately, an ingenious professor 

 abroad, who was of the opinion commonly received, and in his writings had 

 demonstrated it in the usual way, (Gravesande Introductio, Vol. I. N^ 132,) 

 confirming it with the common experiments made in that case, happening to 

 make some experiments like those of Poleni, has drawn conclusions from them, 

 to show the force of moving bodies to be proportionable to the square of their 

 velocity ; and being wholly come over to that opinion, endeavours to deduce 

 it from physical principles. 



As there can hardly be said any thing new, or better than has been said, to 

 show the force to be proportionable to the mass multiplied into the velocity; 1 

 only repeat here the substance of what others have said, and make some old 

 experiments over again ; but then I consider some circumstances that perhaps 

 have been overlooked, and at last, by a new experiment, endeavour to show 

 what has led into an error some of those who defend the new opinion. 



If a man with a certain force can move a weight of 50lb. through a space of 

 4 feet, in a determinate time; it is certain he must employ twice that force to 

 move lOOlb. through the same space in the same time. But if he uses only the 

 same force, he will move the lOOlb. weight only 2 feet in the same time. For 

 as the lOOlb. weight contains two 50lb. weights, if each of them has 2 degrees 

 of velocity given to it, it will exactly require the vSame force that would give one 

 of them 4 degrees of velocity; hence it appears, that the force is proportion- 

 able to the mass multiplied into the velocity. 



Exper. 1. Let the balance ab, fig. Q, pi. l6, whose fulcrum, or centre of 

 motion, is at c, be so divided, that the brachium ac be but the 4th part of 

 the brachium cb; then lOOlb. at a, will keep in eqailibrio a weight of 25lb. at 

 B, where it will have a velocity 4 times greater than that of the weight at a. 

 For, not only when the balance is horizontal, there will be an equilibrium, 

 but when the balance is put in motion, it will return to an equilibrium in a 

 horizontal position ; the equal and contrary forces, applied at each, destroying 

 each other. Whereas, if the forces were as the mass multiplied into the 

 square of the velocity, the 25lb. weight should have been suspended at d, only 



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