'T. W. Glbhft — l^iulUbrhmt, of Heterogeneous Siibstances. 359 



dt _Vv-v _ vy~ V 



where Q denotes the heat wliich 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 



dt 

 subject to hydrostatic pressiire. But the value of -j 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 i] (and therefore 

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



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



dp 



whether we consider the pressure when \aried as still normal and 



(X^QC WtJC iJ/1/ 



equal on all sides, or consider the quantities -=-,, -^„ -j-, as constant, 



ct'tju ^y ^y 



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 ex- 

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

 coefficients all vanish, when the pressui-es on all sides are normal and 



, , , T^. . , ,,. . dt dx dx dy 



equal, but the differential coefficient -j-, when ^— „ -^-„ -f-. are con- 



dp dx dy dy 



stant, or when the pressures on all sides are normal and equal, van- 

 ishes only when the density of the fluid is equal to that of the solid. 



The case is nearly the same when the fluid is not identical in sub- 

 stance with the solid, if we suppose the composition of the fluid to 

 remain unchanged. We have necessarily with respect to the fluid 



d,c, = (^^)2 '^' + f"'^- v^ ^^^'* (^^«) 



\ dp ft, m 



where the index (f) is used to indicate that the expression to wliich 

 it is aftixed relates to the fluid. But by equation (92) 



(pf =-(p.r , .a,Kl i;^)" =(*r . (4„0) 



\ dt /^, m \d)n^/t,2), m \ dp It, m \dm^lt,i), m 



Substituting these values in the preceding equation, transposing 

 terms, and multiplying by m, we obtain 



* A sufiBxed m stands here, as elsewhere in this paper, for all the symbols m,, m.^. 

 etc., except such as may occur in the differential coefiBcient. 

 Trans. Conn. Acad., Vol. III. 46 May, 1877. 



