EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 199 



It will also be observed, that if we regard the forces acting upon 

 the sides of the solid parallelepiped as composed of the hydrostatic 

 pressure p together with additional forces, the work done in any infini- 

 tesimal variation of the state of strain of the solid by these additional 

 forces will be represented by the second member of the equation. 



We will first consider the case in which the fluid is identical in 

 substance with the solid. We have then, by equation (97), for a mass 

 of the fluid equal to that of the solid, 



q 9 dtVydp+mdfi l *aO, (405) 



T) F and V F denoting the entropy and volume of the fluid. By sub- 

 traction we obtain 



dy dz\-.dx v ,dx (^ dz dx\^dy /Ai\ a \ 



d + x * d +*+* d " (406) 



( I JT dx dii 

 Now if the quantities -v->, -, ,, -A remain constant, we shall have 



for the relation be^veen the variations of temperature and pressure 

 which is necessary for the preservation of equilibrium 



dp t] F -r} Q 



where Q denotes the heat which would be absorbed if the solid body 

 should pass into the fluid state without change of temperature or 

 pressure. This equation is similar to (131), which applies to bodies 



subject to hydrostatic pressure. But the value of -y- will not gener- 



ally be the same as if the solid were subject on all sides to the uni- 

 form normal pressure p ; for the quantities v and r\ (and therefore 

 Q) will in general have different values. But when the pressures on 



all sides are normal and equal, the value of T- will be the same, 



whether we consider the pressure when varied as still normal and 



doc doc di/ 

 equal on all sides, or consider the quantities -7 -v->, ~A as constant. 



But if we wish to know how the temperature is affected if the pres- 

 sure between the solid and fluid remains constant, but the strain of 

 the solid is varied in any way consistent with this supposition, the 

 differential coefficients of t with respect to the quantities which 

 express the strain are indicated by equation (406). These differential 

 coefficients all vanish, when the pressures on all sides are normal 



and equal, but the differential coefficient -7-, when -j,, -^., J are 



dp dx dy dy 



