DAVIS. — CERTAIN THERMAL PROPERTIES OF STEAM. 



291 



a = 



Aff 



t c — L 



from which 



and 



^1A^ 



lim 



AH 



p+Ap — AH^O / _ / ' 

 I'd I'd 



a 



lim 

 AH± 





Now, except for terms of higher order than A^T and Ap y 



' dpJ~ 



< 



*«+/* + 



ft 



ft 



- o] Aft 



ft, - #,) = ft, - O [i + (^) A ^] • 



Substituting this above gives 



Cp+Ap 6 P lim 



pi — A/f=0 



to 



1 + 



and the limit sign is no longer necessary. Dropping it, dividing by 

 Ap, and then letting Ap approach zero, gives 



cAzpJh Uy/ 



Integrating this at constant H gives as the final equation 41 



C P = C Po c po 



-/"&).* 



41 The differential form of this equation can also be proved analytically as 

 follows : For any three related quantities p, t, and H, one has the identity 



\dt)H\dH) p \dp)t 

 But 



(i)* =Mand (¥), = c * 



:h can be 



i second 

 (dCjA (dCA (dp\ (dCA /M\ 

 \dph \ dp )t \dp) H + V dt )p Xdpjn 



and therefore 



1 /ATJ\ 



(1) 



But for any function such as Cp which can be expressed in terms of any two 

 of the variables p, t, and H, one has a second identity 



