492 J. W. Glhhs — Equilihrinm of Heterogeneous Substances. 

 and, since TFs and Wy vanish together, 



W,-Wy = iW, = iWy, (668) 



— the same relation which we have before seen to subsist with respect 

 to a spherical mass of fluid as well as in other cases, (See pages 421, 

 425, 465.) 



The equilibrium of the crystal is unstable with respect to variations 

 in size when the siirrounding fluid is indefinitely oxteuded, but it 

 may be made stable by limiting the quantity of the fluid. 



To take account of the influence of gravity, we must give to ///' 

 and p" in (665) their average values in the side considered. These 

 coincide (when the fluid is in a state of internal equilibrium) with 

 their values nt the center of gravity of the side. The values of 

 Yij *v'» '/v' iiii^y ^^^ regarded as constant, so far as the influence of 

 gravity is concerned. Now since l)y (612) and (617) 



dp" =. — g y" dz, 

 and 



d^i;' = ~gdz, 

 we have 



diy^'f,^"-p")=g(y"-y^')dz. 



Comparing (664), we see that the upper or the lower faces of the 

 crystal will have the greater tendency to grow, (other things being 

 equal,) according as the crystal is lighter or heavier than the fluid. 

 When the densities of the two masses are equal, the effect of gravity 

 on the form of the crystal may be neglected. 



In the preceding paragraph tlie fluid is regarded as in a state of 

 internal equilibrium. If we sujipose the composition and tempera- 

 ture of the fluid to be uniform, the condition which will make the 

 effect of gravity vanish will be that 



dz 



when the value of the diffln-ential coefticient is determined in accord- 

 ance with this supi)Osition. This condition reduces to 



\ dp /(,m ;// 



which, by equation (92), is equivalent to 



1 



/ dv \" 



\dm.Jt,p,' 



(669) 



* A suffixed m is used to represent all the symbols 7n,, m.^, etc., except such as 

 may occur in the differential coefficient. 



