VOL LXVIII.] PHILOSOPHICAL TRANSACTIONS. 375 



losophers, there is none which carries a greater degree of plausibility along with 

 it, than a celebrated invention of Mr. Maclaurin. It is extremely simple, easy 

 to be described ; and I do not find that it has ever been answered by any of the 

 advocates for the new doctrine of forces. 



Let A and b, fig. 9, be two equal bodies that are separated from each other 

 by springs interposed between them, in a space efgh, which in the mean time 

 proceeds uniformly in the direction ba (in which line the springs act) with a 

 velocity as i ; and suppose that the springs impress on the equal bodies a and b 

 equal velocities, in opposite directions, that are each as i. Then the absolute 

 velocity of a (which was as i) will now be as 2 ; and according to the new doc- 

 trine its force as 4 ; whereas the absolute velocity and force of b (which was as i) 

 will now be destroyed ; so that the action of the springs adds to a a force as 3, 

 and subducts from the equal body b a force as 1 only ; and yet it seems manifest 

 that the actions of the springs on these equal bodies ought to be equal, and M. 

 Bernoulli expressly owns them to be so.* I shall only just observe, that if 

 M. Bernoulli expressly owns, that springs, interposed between two bodies in a 

 space, which is carried uniformly in the direction in which the springs act, will 

 always generate equal forces in the bodies according to his own definition of that 

 term, he talks more inconsistently than I have observed him to do : on the con- 

 trary, if I could find that he has answered this famous argument (which Dr. 

 Jurin proposed over again in Phil. Trans, vol. 43, with a conditional promise of 

 embracing the Leibnitzian doctrine) by simply saying, that springs he considers 

 as motive forces, or, when the bodies are equal, as accelerating forces ; and that 

 their actions are equal, when in equal times they generate equal velocities, but 

 not necessarily equal forces, in the equal bodies ; I should not make the least 

 scruple to own that I thought his reasoning solid and conclusive, and his dis- 

 tinctions a full answer to every objection of that sort.-|- 



Case 3. — The two preceding cases are curious examples of the force of preju- 

 dice and party-spirit. In the latter particularly it does not appear that J. Ber- 

 noulli knew the preservation of the vires vivae to be an infallible consequence of 

 perfect elasticity in bodies ; or indeed that he had any other reason for taking 

 that principle for granted, but because he was not able to prove it. All the in- 



* Book II. chap. 2. Account of Newton's discoveries. — Orig. 



f No doubt Maclaurin refers to the following passage of Bernoulli, " La force du choc^ ou de 

 Taction des corps les uns sur les autres, depend uniquement de leurs vitesses respectives ; or il est 

 visible que les vitesses respectives des corps ne changent pas avant le choc, soit que le plan ou I'espace 

 qui les contient soit sans mouvement, soit qu'il se meuve uniformement, suivant une direction donnee, 

 les vitesses rebpectives seront done encore les nitmes apres le choc." This quotation puts the matter 

 beyond dispute. It is plain that Bernoulli, though he does make use of the word action, is only 

 speaking of the motion lost or communicated, and the relative velocities of the bodies : there is not 

 the most distant hint at the change in their absolute forces — Orig, 



