VOL. XLIII.] PHILOSOPHICAL TRANSACTIONS. 129 



cessary to show how far the two parties agree, and in what point their disagree- 

 ment consists. 



Both sides agree, that the measure of this force depends partly on the mass or 

 weight of the body, and partly on the velocity with which it moves ; so that, on 

 any increase, either ,of the weight or of the velocity, the moving force will be- 

 come greater. They also agree, that if the velocity continue the same, but the 

 mass, or weight of the body, be increased in any proportion, the moving force 

 is increased in the same proportion : so that, in this case, the measure of the 

 moving force is the same with that of the weight : or, when 2 bodies move with 

 the same velocity, if the weight of the second be double, triple, quadruple, of 

 that of the first, the moving force of the second will also be double, triple, qua- 

 druple, of that of the first. 



But when two bodies are equal, and the velocities with which they move are 

 different, the two parties no longer agree about the measure of the moving force. 

 One side maintains, that when the velocity of the second body is double, triple, 

 quadruple, of that of the first, the measure of the moving force of the second is 

 also double, triple, quadruple, of that of the moving force, being the same with 

 that of the velocity. The other side pretends, that in the same case the moving 

 force of the 2d body is 4 times, Q times, 1 6 times, as great as that of the first ; 

 the measure of the moving force being the same with that of the square of the 

 velocity. 



In consequence of the agreement in the first of these two cases, and the dis- 

 agreement in the second, the one side pretends, that the measure of the moving 

 force is, in all cases, the product of the weight into the velocity ; and the other, 

 that it is the product of the weight into the square of the velocity. 



This controversy was first started by the famous Mr. Leibnitz, and has been 

 carried on by him and his followers for near 6o years ; during which time a great 

 number of pieces have been published on both sides of the question, and a great 

 number of experiments have been made, or proposed to be made, in order to 

 decide it. But though both parties agree in the event of the experiments, whe- 

 ther actually made, or only proposed ; yet, as the writers on each side have found 

 a way of deducing from those experiments a conclusion suitable to their own opi- 

 nion, the disagreement still continues as wide as ever, to the great scandal of 

 the learned world. 



Now, if we examine carefully into the reason of this, and would see by what 

 means it happens, that two opposite conclusions are so often drawn from the 

 same experiment, we shall find it not so much owing to false reasoning on either 

 side, as to another cause ; namely, to their disagreement in the principles on 

 which the reasoning is founded. For whereas whatever is laid down on either 

 side as a principle, ought to be something all the world agrees in, at least what 



VOL. IX. S 



