VOL. XLIII.] PHILOSOPHICAL TKANSACTIONS. 135 



As we do not thiiik, that any flaw can be found in either of the demonstra- 

 tions above laid down ; and the axioms, on which they are founded, have never 

 yet been disputed, as far as we know; we presume that the Leibnitian opinion 

 about the measure of moving forces, is incontestably overthrown by the first 

 proposition, and the opposite sentiment is as evidently established by the second. 

 But if any reader shall be of a different opinion, we must beg leave to propose 

 to his consideration the following experiment, which we hope may j ustly deserve 

 the name of an experimentum crucis, and, as such, may put a final period to 

 this controversy. 



Exper. — On a horizontal plane at rest, but moveable with the least force, 

 suppose on a boat in a stagnant Avater, let there be placed, between two equal 

 bodies, a bent spring, by the unbending of which the two bodies may be pushed 

 contrary ways. 



In this case it is evident, that the velocities, which the two bodies receive from 

 the spring, will be exactly equal, and their moving forces will also be exactly 

 equal; and that the plane they move on, and also the boat on which it lies, will 

 have no motion given them either way. Let us call the velocity of each body 1, 

 and the moving force also 1 . 



Now let us suppose the spring to be bent afresh to the same degree as before, 

 and to be again placed between the two bodies lying at rest; then let the plane, 

 on which the spring and the bodies lie, be carried uniformly forward, in the 

 direction of the length of the spring, with this same velocitv 1. In this case it 

 is manifest, that each of the bodies will have the velocity 1 , and the moving 

 force 1 , both in the direction of the axis of the spring. During this motion, 

 let the spring again unbend, and push the two bodies contrary ways, as before, 

 the one forward, the other backward: then the spring will give to each of these 

 bodies the velocity 1, as before, when the plane was at rest. 



By this means the hindmost body, or that which is pushed backward, will have 

 its velocity 1, which it had before by the motion of the plane, now entirely de- 

 stroyed, and will be absolutely at rest. But the body, which is pushed forward, 

 will now have the velocity 1, namely 1 from the motion of the plane, and 1 from 

 the action of the spring. 



Thus far every body agrees in what will be the event of this experiment. But 

 the question is, what will be the moving force of the foremost body, or of that 

 which is pushed forward, and which has the velocity 1 ; viz. 1 from the motion 

 of the plane, and 1 from the action of the spring. By the Leibnitian doctrine, 

 its moving force must be 4 : and, if so, it must have received the moving force 

 3 from the action of the spring; for it had only the moving force 1 from the 

 motion of the plane. 



Let us examine, whether this be jx)ssible, or reconcileable to their own doc- 



