138 On JM^achlnes in General. 



consumed by a force P, in a time infinitely short, 1» the 

 produce of this force estimated in the ratio of its velocity, 

 by the path described in this infinitely short time by the 

 point to wliich it is applied. 



I shall call the momentvm of activity, consumed by 

 this force, in a given time, the stun of the mamenta of ac- 

 tivity consumed by it at each instant, in such a manner 

 that sP cosine zudt is the momentum of activity, con- 

 sumed by it in an indeterminate time : for instance, if 

 P be a weight, the momentum of activity consumed in 

 an indeterminate lime t will be P s u d t coi\ne. z ; let us 

 suppose, therefore, that after the time f, the weight P has 

 descended from the quantity H, we shall clearly have 

 d H = 21 d t cos'int: z ; therefore the momentum of activity 

 consumed during d t will be Pi ofH = PH. 



XXXIII. When we are speaking of a system of forces 

 applied to a machine in movement, I shall call momentum 

 of activity, consumed by all the forces of the system, 

 the sum of the momenta of activity consumed at the 

 game time by each of the forces which compose it : thus, 

 the momentum of activity consumed by the soliciting 

 forces, will be the sum of the momenta of activity con- 

 sumed at the same time by each of them : and the mo- 

 Ujentum of activity consumed by the resisting forces 

 will be the sum of the momenta of activity consumed 

 by each of these forces : and as each resisting force makes 

 an obtuse angle with the direction of its velocity, the co- 

 sine of this angle is negative; the momentum of activity 

 consumed by the resisting forces is therefore also a neea- 

 tive quantity ; and therefore the moinentuTn of activity con- 

 sumed by all the forces of the system, is the same thing 

 as the difference between the momentum of activity consum- 

 ed by the soliciting forces, and the momentum of activity 

 consumed at the same time by the resisting forces consider- 

 ed as a positive quantity. 



A force estimated in a sense directly opposite to that of 

 its velocity, and multiplied by the path described in an in- 

 finitely short time by the point where it is applied, will be 

 called the momcjitum of activity produced by this force in 



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