154 THOMSON ON CARNOT'8 



and second, on account of the temperature being 

 lower. Thus, at the end of a complete cycle of 

 operations, mechanical effect has been obtained ; 

 and the thermal agency from which it is drawn is 

 the taking of a certain quantity of heat from A, 

 and letting it down, through the medium of the 

 engine, to the body B at a lower temperature. 



25. To estimate the actual amount of effect thus 

 obtained, it will be convenient to consider the altera- 

 tions of volume of the mass of air in the several 

 operations as extremely small. We may afterwards 

 pass by the integral calculus, or, practically, by 

 summation to determine the mechanical effect 

 whatever be the amplitudes of the different motions 

 of the piston. 



26. Let dq be the quantity of heat absorbed 

 during the first operation, which is evolved again 

 during the third; and let dv be the corresponding 

 augmentation of volume which takes place while 

 the temperature remains constant, as it does during 

 the first operation.* The diminution of volume 



* Thus, -^ will be the partial differential coefficient, 



with respect to , of that function of wand t which expresses 

 the quantity of heat that must be added to a mass of air 

 when in a " standard " state (such as at the temperature zero, 

 and under the atmospheric pressure), to bring it to the 

 temperature t and the volume v. That there is such a 



