C 124 ] 



XXI. Essay upon Machines in General. By M. Carnot, 

 Member of the French Institute, &c. <^c. 



{Concluded from vol. xxxi. p. 305.] 



LXIII. .These remarks as to, the momentum of activity, 

 have originated an idea with me of a principle of equilibrium 

 peculiar to the case where the forces exercised in the system 

 are attractions : I think my readers will not be displeased to 

 find it here ; it is in the following terms : 



Several bodies subjected to the laws of mu attraction, ex- 

 ercised in consequence of any function of distances, either by 

 these bodies themselves upon each other, or by different fixed 

 points being applied to any machine; if we make this ma- 

 chine pass from any given position to that of equilibrium, 

 the momentum of activity consumed in this passage by the 

 attractive forces with which these bodies will,be animated, 

 during this movement, will be a maximum. 



That is to say, this momentum will be always greater 

 than it would have been, if, instead of making this system 

 pass to the position of equilibrium, we had constrained it to 

 take a different route, and to pass into any other situation. 



Vox example, if gravity is the subject in question, which 

 we may regard as an attraction exercised towards a point in- 

 finitely removed, the attractive forces will be the weights 

 applied to the machine :the momentum of activity which 

 will be exercised by these forces when we make this ma- 

 chine change its situation, will therefore be equal to the 

 total weight of the system multiplied by the height which 

 the centre of gravity shall have descended or ascended du- 

 ring this change of position (XXXII). Now the situation 

 of equilibrium is that at which the centre of gravity is at the 

 highest or lowest point possible; therefore the height to 

 which the centre of gravity should asceiad, or from which 

 it should descend, in order to pass from any given situation 

 to that of equilibrium, is greater than when it has to pass to 

 any other situation : thus the momentum of activity con- 

 sumed in the passage by the motrix forces, is also greater in. 

 the first case than in any other. 



If 



