'222 PHILOSOPHICAL TRANSACTIONS. [aNNO 1746. 



it was very elegant, and ought not to be longer withheld from the public ; yet in 

 August he knew not what L. meant by the word action, on which that whole 

 demonstration depends, " You ought," says he, " to define what you mean by 

 action ; otherwise nothing can ever be demonstrated." This was a just admo- 

 nition, but to no purpose ; for in L.'s answer to this, there is not a tittle of that 

 definition, so highly necessary. 



But L. himself, in his letter of June, expresses himself thus : " My demon- 

 stration a priori, for our estimation of forces, depends on a certain supposition ; 

 viz. that an action performs any thing uniformly, in a single time, is double of 

 an action performing the same thing uniformly, in a double time. This suppo- 

 sition ought to have been granted by Catalan and the rest, with whom I have 

 disputed." But what if they will not grant it > why then the demonstration, 

 which depends on this supposition, falls to the ground, at least till that suppo- 

 sition is demonstrated. " But," says L., " I have not yet found out a way of 

 demonstrating this proposition a priori, by the way of congruency ; nay not even 

 this, that an action performing the same thing, in a shorter time, is greater; 

 which ought to have been the beginning." Therefore, since that so much 

 boasted demonstration a priori needed another demonstration, which L. had not 

 yet discovered, nor ever after did discover, nor any mortal ever will discover, it 

 is no wonder that this seed, though committed to a most fruitful soil, did not 

 grow up to a large plant. For Bernoulli took a final leave of this clear light of 

 truth, when he saw it dwindle away to a mere snuflT. 



But a gentleman of much higher courage, the learned Chr. Wolf, having at- 

 tempted to treat the theory of forces in a geometrical manner, communicated it, 

 in the Comment. Acad. Petrop. under the title of Principia Dynamica. " When 

 he had communicated" part of this, " in 17 10 to Count Herberstein, Leibnitz, 

 and others, Leibnitz, in a letter 1 7 1 1 , said that it agreed with his, which he 

 had communicated to Bernoulli, Herman, and others, confirming it in these 

 words : I lay down this calculus of pure forces or actions. Let s be the space, t 

 the time, v the velocity, c the corpus or body, e the effect, p the power, a the 

 action. Then in equable motion, tv will be as s, and e as cs, and tp as a : and 

 these may be assumed without demonstration. Add, what is to be demonstrated, 

 ev as a. Hence many other theorems may be demonstrated ; for instance, p as 

 cy*. For tp is as ev ; but e is as cs, and s as, tv; therefore tp is as c/i;', or p as 

 cv*. And in these is contained part of my Dynamics, abstracted from sensible 

 things, though afterwards verified by experiments." " I doubt not, therefore," 

 says Wolf, " but I have here proposed Dynamical principles, which are conform- < 

 able to the sentiments of Leibnitz." 



This indeed is manifest enough, as W.'s theorems exactly agree with the alge- 

 braic notations of L. But whether these principles be as conformable to <truth as 



