VOL. XXXIV.] PHILOSOPHICAL TRANSACTIONS. 1 67 



ties of matter multiplied by the squares of the velocities; so that in equal 

 masses the moving forces will not be as the velocities themselves, but as 

 their squares. 



The latest experiments, brought to prove the truth of the new opinion, are 

 made on soft or yielding substances. Now these have been already observed 

 to be a little complicated, and unfit for this purpose. The proper use of ex- 

 periments of this kind being rather to discover, and settle the laws, which 

 such kind of substances observe in the resistance they make to bodies moving 

 in them, than the forces themselves, with which the bodies move; which 

 ought to be determined before hand by some simple experiment, fit to deter- 

 mine that matter. 



A variety of experiments have been made, and reasoning used in England 

 and France, to prove the truth of the common opinion; but they do not 

 entirely satisfy all the gentlemen on the other side of the question. The pre- 

 sent professor of mathematics and philosophy at Utrecht (Muschenbroeck), 

 tells us in the preface to his Epitome Elementorum Physico-Mathematicorum, 

 published this year, anno 1726, " In computing the forces of moving bodies, I 

 have embraced the opinion of M. Leibnitz, Huygens, Poleni, and Gravesande, 

 and have rejected the old opinion, which I formerly maintained and taught; 

 and that notwithstanding the arguments of very learned men, both in France 

 and Britain, who maintain it. And when the experiments, described by Poleni 

 and Gravesande, are examined, they so plainly prove the forces of striking 

 bodies to be in a ratio compounded of the square of the velocities, and of the 

 simple ratio of the masses; that we must submit to them, unless we would 

 contradict the plainest evidence." 



Mr. Fames examines the truth of the new opinion in the case here proposed, 

 viz. as to the forces of striking bodies ; and endeavours to show, from their 

 own principles, that it cannot be true in all the cases of non-elastic bodies. 



It is allowed, that the common rules of finding the velocities of non-elastic 

 bodies after the stroke are true: for thus the ingenious Mr. Gravesande says in 

 paragraph 251, of his Supplementum Physicum : " From this principle, i. e. of 

 multiplying the mass by the velocity, philosophers have deduced these very 

 rules, N° 234 and 237, which I have several ways deduced from my principles : 

 but it was surprising that in this case one error destroyed another, and a double 

 error led me to discover the truth: they followed a false principle in computing 

 the forces, and supposed what is not at all consonant with truth, viz. that 

 bodies lose nothing of their force by the intropression on the parts, and over- 

 coming their cohesion." 



