Page:Reflections on the Motive Power of Heat.djvu/101

Rh 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 abcd (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 abcd, a'b'c'd'. As to the total pressure exerted in each piston cd, c'd', it would be the same from all quarters, for the surface of these pistons is in direct ratio to the volumes.

Let us suppose that we perform on the gas inclosed in a'b'c'd' the operations described on page 70, and which were taken as having been performed upon the gas inclosed in abcd; that is, let us suppose 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' corresponding 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 abcd 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