452 RICE ART. K 



Therefore 



Lr-t ^^ > (61) 



giving us six equations connecting the heat required to maintain 

 the temperature constant when the stresses are altered with the 

 variations of strain which accompany changes of temperature 

 when the stresses are maintained constant. In addition we 

 derive from (58) the equation 



dC{U X) ^ d^r^it, X) 



and by (60) 



dXr dtdXr 



d^riit, X) b%{t, X) 



dtdX, ~ df^ 

 Hence we obtain the six relations 



A relation analogous to (51) can also be derived, which connects 

 the difference of the two specific heats with the temperature 

 coefficients of the strain-functions and the stress-constituents. 

 Thus let an infinitesimal change take place at constant stress; 

 the change of entropy can be expressed in two ways. For by 

 (52) it is equal to 



]{c(u)dt + J;uu)'-^ 



and by (58) it is also equal to 



7 at, X) dt. 



V 



Equating these two expressions we obtain the result 

 C{t,X)=c{t,f)^^Ut,f)^-^^' 



