MOTIVE POWER OF HEAT. 79 



tion stated on page 68 a second theory, which will 

 serve as a corollary to that just demonstrated. 



Let us suppose that the gas enclosed in the 

 cylindrical space abed (Fig. 2) be transported into 

 the space a'b'c'd' (Fig. 3) of equal height, but of 

 different base and wider. This gas would increase 

 in volume, would diminish in density and in elastic 

 force, in the inverse ratio of the two volumes abed, 

 a'b'c'd'. As to the total pressure exerted in each 

 piston cd, c'd', it would be the same from all quar- 

 ters, for the surface of these pistons is in direct 

 ratio to the volumes. 



Let us suppose that we perform on the gas in- 

 closed in a'b'c'd' the operations described on page 

 70, and which were taken as having been performed 

 upon the gas inclosed in abed', that is, let us sup- 

 pose that we have given to the piston c'd' motions 

 equal to those of the piston cd, that we have made 

 it occupy successively the positions c'd' correspond- 

 ing to cd, and e'f corresponding to ef, and that at 

 the same time we have subjected the gas by means 

 of the two bodies A and B to the same variations 

 of temperature as when it was inclosed in abed 

 The total effort exercised on the piston would be 

 found to be, in the two cases, always the same at 

 the corresponding instants. This results solely from 



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