STRAINED ELASTIC SOLIDS 479 



faces of the solid which is compatible with the given state of 

 strain an, an, . . . 033. Thus p is a function of an, an, ... 033 

 and the temperature; dp/dt is therefore the rate of variation of 

 this pressure with temperature at constant strain, i.e., with the 

 solid constrained to keep its size and shape (in the state of 

 strain) unchanged. This is the analogue of the usual equation 

 for the variation of the melting point with pressure. The 

 melting point is t at pressure p and strain an, an, . • . ass- At 

 pressure p -\- dp and the same strain an, a,n, . ■ . clss the melting 

 point is ^ + dt, the latent heat per unit volume is Q, and so 

 Q/t(vp — v) is equal to the limit of dp/dt. It is necessary to real- 

 ize the conditions under which Q is the latent heat of fusion. 

 From [393] the energy of the solid with the proper pressure p' 

 on a pair of faces is given by 



€ = trj — p'v -{- m'm. 



That of the same mass of the fluid in equihbrium with the faces 

 is given by 



Hence 



€f = tr\F — p'vf + ni'm. 



€f — e = t{r]F — ri) = Q. 



As Gibbs points out, if we imagine the cube surrounded entirely 

 by the fluid so that the conditions are those of the case usually 

 considered, the quantities e and rj have different values from those 

 considered above (see equations [396]), and Q is also different 

 in value. 



The more general case considered on page 200 when the fluid is 

 not identical in substance with the solid can be followed up as 

 is done by Gibbs, and we arrive at [411] in the form 



{ 



djii (t, p, nir) \ 



m — v> dp 



dp ) 



( dfll {t, P, nir) dm (t, p, Mr) 



+ m< ~ — :; dm2 + 1 dnia + etc. 



( dm2 drriz 



= {Xx' + An p) dan + {Xy + An p) dan ■ • • 



+ {Zz' + ^33 p) dass. 



