STRAINED ELASTIC SOLIDS 453 



and using (56) we reach, finally, 



Some further relations can be obtained from the differential 

 equations for the entropy and various energy functions. Thus 

 from (52) we see that 



l.{t,j) = t 



dfr 



dvitj) 



dfs 



Hence 



dlrjtj) ^ dhjtj) 

 dfs ~ dfr 



(64) 



and there are fifteen such "reciprocal relations" between the 

 latent heats and the strains. 



Similarly from (54) we obtain fifteen reciprocal relations 

 between the stresses and strains, viz., 



By using equations (58) and (59) we can obtain two sets of 

 reciprocal relations, one between the latent heats and stresses, 

 one between the strains and stresses, viz, 



dLrjt, X) ^ dLsjt, X) ,QQ^ 



dXs dXr 



and 



dfr(t, X) _ dfs(t, X) 



dX, dXr 



(67) 



From the thermodynamic equations we can also give a more 

 general signification to the elastic constants of a solid, which were 



