Page:Reflections on the Motive Power of Heat.djvu/176

152 the line AA1, or the line A3A2 or any line of intermediate magnitude.

The expression (2) is rigorously correct for any interval S - T, if the mean value of $$(1-\sigma)\tfrac{\tfrac{dp}{dt}}{k}$$ for that interval be employed as the coefficient of H(S - T).

22. In the ideal air-engine imagined by Carnot four operations performed upon a mass of air or gas enclosed in a closed vessel of variable volume constitute a complete cycle, at the end of which the medium is left in its primitive physical condition; the construction being the same as that which was described above for the steam-engine, a body A, permanently retained at the temperature S, and B at the temperature T an impermeable stand K and a cylinder and piston, which in this case contains a mass of air at the temperature S, instead of water in the liquid state, at the beginning and end of a cycle of operations. The four successive operations are conducted in the following manner:

(1) The cylinder is laid on the body A, so that the air in it is kept at the temperature S; and the piston is allowed to rise, performing work.