EQUILIBEIUM OF HETEROGENEOUS SUBSTANCES. 323 



To take account of the influence of gravity, we must give to fi^ f 

 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 at the center of gravity of the side. The values of 

 y\t GV> *lv ma y b 6 regarded as constant, so far as the influence of 

 gravity is concerned. Now since by (612) and (617) 



and 



we have 



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 the fluid is regarded as in a state 

 of internal equilibrium. If we suppose the composition and tem- 

 perature 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 differential coefficient is determined in 

 accordance with this supposition. This condition reduces to 



y x " 



which, by equation (92), is equivalent to 



=A- (669) 



The tendency of a crystal to grow will be greater in the upper 

 or lower parts of the fluid, according as the growth of a crystal 

 at constant temperature and pressure will produce expansion or 

 contraction. 



Again, we may suppose the composition of the fluid and its entropy 

 per unit of mass to be uniform. The temperature will then vary with 

 the pressure, that is, with z. We may also suppose the temperature 

 of different crystals or different parts of the same crystal to be deter- 

 mined by the fluid in contact with them. These conditions express a 

 state which may perhaps be realized when the fluid is gently stirred. 

 Owing to the differences of temperature we cannot regard e v ' and rj v ' 



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

 may occur in the differential coefficient. 



