nn 



hit. u.] DISSERTATION SECOND. 51 



treated of this controversy, and remarked, that it had been 

 dropt rather than concluded. In this I confess I differ from 

 the learned author. The controversy seemed fairly ended, 

 the arguments exhausted, and the conclusion established, that 

 the propositions maintained by both sides were true, and 

 were not opposed to one another. Though the mathemati- 

 cal sciences cannot boast of never having had any debates, 

 they can say that those that have arisen have always been 

 brought to a satisfactory termination. 



The observations with which I am to conclude the pre- 

 sent sketch, are not precisely the same with those of the 

 French philosopher, though they rest nearly on the same 

 foundation. 



As the effects of moving bodies, or the changes they pro- 

 duce, may vary considerably with accidental circumstances, 

 we must, in order to measure their force, have recourse to 

 effects which are uniform, and not under the influence of 

 variable causes. First, we may measure the force of one 

 moving body by its effect upon another moving body ; and 

 here there is no room for dispute, nor any doubt that the 

 forces of such bodies are as the quantities of matter multipli- 

 ed into the simple power of the velocities, because the for- 

 ces of bodies in which these products are equal, are well 

 known, if opposed, to destroy one another. Thus one ef- 

 fect of moving bodies affords a measureof their force, which 

 does not vary as the square ; but as the simple pozocr of the 

 velocity. 



There is also another condition of moving bodies which 

 may be expected to afford a simple and general measure of 

 their force. When a moving body is opposed by pressure, 

 by a vis mortua, or a resistance like that of gravity, the 

 quantity of such resistance required to extinguish the motion, 

 and reduce the body to rest, must serve to measure the force 

 of that body. It is a force which, by repeated impulses, ha« 



8 



