CONCLUSIONS FROM CARNOl'S PRINCIPLE. 629 



(form and dimensions) and of its temperature. When the body 

 undergoes any transformation, it absorbs a certain quantity H of 

 energy which depends on the deformation it has experienced, and 

 on the variation of temperature. If only one of the variables x, 

 varies by dx, and the temperature by dT, we may write 



(i) dH = adx + MT. 



The functions a and / have an obvious physical meaning. If 

 we divide them by the mechanical equivalent of heat, the former 

 represents the latent heat relative to the variable x, and the second 

 / the specific heat for a constant mechanical state. 



The work dW done by external forces only depends on the 

 change of form, and we have 



The increase of potential energy is the sum of these two expressions, 

 which gives 



(2) dE = 



For any given closed cycle, the total variation of potential 

 energy is null ; the elementary variation must then be an exact 

 differential of the independent variables, which gives the condition 



(3) 



DT 



This equation may be considered as expressing the principle 

 of the conservation of energy, or the mechanical equivalence of 

 heat. 



646. In order to apply Carnot'si principle, the cycle of trans- 

 formations must be reversible, and the final state of the body 

 must be identical with the initial state. 



The sum of the quotients of the calorific energy absorbed by 

 the corresponding absolute temperature is then null, and we have 



(<*'*,( f*i* : ":Lft\i't 



j T~J VT ;+ T y~' 



