THEOREM IN MECHANICS. 95 
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 eyen 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 
