VOL. XLIV.] PHILOSOPHICAL TRANSACTIONS. 217 



QSOlb. weight. As one was mounting a horse, the poor creature's back broke 

 under him, and he died on the spot. 



Dynamical Principles, or Metaphysical Mechanical Principles. By James Jurin, 

 M.D., F.R.S. Presented March 13, J 746. N° 479, P- 103. From- the 

 Latin. 



When the celebrated Leibnitz published* his new doctrine, by which he de- 

 termines that the force of a body in motion is to be measured by the square of 

 the velocity, it raised a great controversy in the mathematical world. The same 

 author, in April 1695, published his Specimen Dynamicum, in confirmation of 

 this doctrine; where, among other things, he says, " I arrived at the same true 

 estimation of forces by different ways : one a priori, by a very simple consideration 

 of space, time, and action ; another a posteriori, by estimating the force by the 

 effect which it produces in exhausting itself." 



It seems he intended the publication of his a priori, which he promised to ex- 

 plain in another place, in May following; for towards the end of his Specimen 

 Dynamicum he adds, " And now, having dispelled error, we shall produce the 

 true and really admirable laws of nature, more distinctly, in the 2d part of this 

 essay, to be published in the month of May." Yet this 2d part never appeared 

 in public. However, to clear this great man from the imputation of not having 

 performed his promise, it has been lately given in the Commercium Literarum 

 between himself and another celebrated mathematician, John Bernoulli. 



This author it seems, on seeing the Specimen Dynamicum, wrote to Leibnitz, 

 in June following, applauding some things; but at the same time being so far 

 from approving his estimation of forces, that he even endeavoured to demonstrate, 

 that the forces of moved bodies are not as the squares of their velocities, but 

 simply as the velocities only. But at length, after several letters had passed be- 

 tween them, Bernoulli came over to Leibnitz's opinion, who, being willing to 

 reward the docility of so eminent a disciple, communicates to him his argument 

 a priori, which he had hitherto kept to himself, and at the same time assigns the 

 reason why he did not divulge it sooner. " I would not, says he, honour with 

 this clear light of truth, those who did not receive as they ought those arguments 

 drawn from the affections of heavy or other sensible bodies ; and therefore I would 

 not make them public; but reserved them to be communicated to such as had 

 shown themselves proper judges." 



Bernoulli therefore, having shown himself to be a proper judge, and having 

 received as he ought those arguments a posteriori, that is, having come over 

 entirely to the opinion of Leibnitz, was thought worthy of the honour to be ad- 



• Act. Erud. Lips. 1686. 

 VOL. IX. Ff 



