M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 375 



1000° to 2000° higher than that of the boilers, there is an enormous 

 loss of vis viva in the passage of the heat from the furnace into the 

 boiler. It is therefore onlj' from the employment of calo:"ic at high 

 temperatures, and from the discovery of agents proper to realize its 

 motive force, that important improvements may be expected in the art 

 of utilizing the mechanical power of heat. 



NOTE. 



The integral of the general equation 



dQ dj _ dQdT _ ^ 



dv ' dp dp dv 

 is, as we have seen, 



Q = Y{T)-Ci>{p,z-) (1) 



F (T) is an arbitrary function of the temperature T, varying from one 

 body to another ; C is a function of the temperature which is the same 

 for all the substances of nature, and ^ (^p, v) is a particular function of 

 p, and of V satisfying the equation 



dT dcp dT d(l> , /^x 



dv dp dp dv 

 This function f may be determined in the following manner. Let 



=/ 



dp 

 dv 



dv 

 dv 



be substituted in the equation (2), it will be 



dT^ ±$i_dT d^_ dT J_ /^ 

 dv dp dp dv^ dp dvj — — ' 



this equation is satisfied by putting 

 0" satisfying the equation 



d_T d^ _ d_T rf£" _ rfT^ _rf_ •» 'dj}_ J_^ /»^ 



d V dp d p d V ~ d p dv I ^ d T d v j -r— ' 



dv 

 we shall have equally 



r-f^p^^.f^v § i^f^ + r 



dv dv 



AI dp 



