On Machines in Geneiol. 139 



this infinitely short time : in Such a manner that the mo- 

 mentum of activity comumed, and the momentum of ac- 

 tivity produced, are two equal quantities, but of contrarr 

 signs; and there is a difference between them analogous \n 

 that which we find (XXI) between the momenta of the 

 quantity of movement gained and lost, by a body, in respect 

 of any geometrical movement. 



I shall also give the name of momentum of activity exer- 

 cised by a force, to what 1 have called its momentum of 

 activity consumed, if it be soliciting, and to what I have 

 called its momentum of activity produced, if it be resisting; 

 thus, the momentum of activity exercised by any given force 

 in an infinitely short time is in general the produce of this 

 force, by the path which it describes in this infinitely Short 

 time, and by the cosine of the smallest of the two angles 

 formed by the directions of this force and of its velocity ; 

 whence it clearly follows, that this momentum of activity ex- 

 ercised is always a positive quantity. 



We shall make, with respect to the quantities which we 

 call momenta of activity produced andi momenta of activity 

 exercised, the same remarks with those we have made above, 

 upon the subject of momentu?n of activity consumed by a. 

 force or system of powers in a given time. 



These definitions being adnnited, I shall proceed to the 

 general principle of equilibrium and of movement, in ma- 

 chines properly so called ; and the inquiry into which has 

 been the principal object of this essay. 



Fundamental Theorem, 

 General Principle of Equilibrium and of MoveTnent in Ma- 

 chines. 

 XXXIV. tVhatever is the state of repose or of movement in 

 ivhich any -^iven system of forces applied to a m.achine existSj 

 if we make it all at once assume any given geometrical move- 

 ment, without changing these forces in any respect, the sum 

 9f the products of each of them, by the velocity which the 

 point at which it is applied will have in the fust instant, es- 

 timated in tlie direction (^' this force, will be equal to zero. 



That 



