152 THOMSON ON CARNOT'S 



the line A A 1 , or the line A^A^ or any line of in- 

 termediate magnitude. 



The expression (2) is rigorously correct for any 



dp 



interval S T, if the mean value of (1 <r)-r- for 



that interval be employed as the coefficient of 

 H(S-T). 



CARNOT'S THEORY OF THE AIR-ENGINE. 



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 condi- 

 tion; the construction being the same as that which 

 was described above for the steam-engine, a body 

 A, permanently retained at the temperature 8, and 

 B at the temperature T\ an impermeable stand K\ 

 and a cylinder and piston, which in this case con- 

 tains 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. 



