THEOREM IN MECHANICS. 25 



You see, Gentlemen, that there are cases, it cannot 

 be too often repeated, in which we must resign ourselves, 

 whether we will or no, to the loss of force consequent on 

 machines, since, without their help, certain works would 

 become impossible. 



The losses of force which depend on the flexibility of 

 the materials of which machines are composed, on the 

 roughness of cords, and on friction, had been remarked 

 by the most ancient mechanicians ; modern ones have 

 gone farther ; their experiments enable them to appreci- 

 ate these losses and value them in numbers with tolerable 

 exactness. Science had arrived thus far, when Carnot 

 published his Essay. In this work, our member, looking 

 on machines, and even more generally on every system 

 of movable bodies, from an entirely new point of view, 

 indicates a cause unperceived, or at any rate imperfectly 

 analyzed, by his predecessors, and which in certain cases 

 must also give rise to considerable losses ; he shows that 

 we ought, by all means, to avoid abrupt changes of 

 velocity. Carnot does more ; he finds the mathematical 

 expression of the loss of active force which such changes 

 occasion ; he shows that it is equal to the active force 

 by which all the various bodies of the system would be 

 animated, if each of them were endowed with the com- 

 plete velocity which it lost at the instant of the abrupt 

 change being affected. 



Such is, Gentlemen, the enunciation of the principle 

 which, under the name of " Carnot's Theorem," plays so 

 great a part in the calculation of the effect of machines. 



This beautiful and valuable theorem is now well 

 known to all engineers ; it guides them in practice, and 

 secures them from the gross faults committed by their 

 precursors. 



SEC. SER. 2 



