324 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



in (664) as constant, but we may regard their variations as subject to 

 the relation de v ' = t dq v '. Therefore, if we make q? = for the mean 

 temperature of the fluid (which involves no real loss of generality), 

 we may treat e v ' fo/ v ' as constant. We shall then have for the con- 

 dition that the effect of gravity shall vanish 



dz 

 which signifies in the present case that 



=1 



m y/' 

 or, by (90), 



=- (670) 



Since the entropy of the crystal is zero, this equation expresses 

 that the dissolving of a small crystal in a considerable quantity of 

 the fluid will produce neither expansion nor contraction, when the 

 pressure is maintained constant and no heat is supplied or taken 

 away. 



The manner in which crystals actually grow or dissolve is often 

 principally determined by other differences of phase in the surrounding 

 fluid than those which have been considered in the preceding para- 

 graph. This is especially the case when the crystal is growing or 

 dissolving rapidly. When the great mass of the fluid is considerably 

 supersaturated, the action of the crystal keeps the part immediately 

 contiguous to it nearer the state of exact saturation. The farthest 

 projecting parts of the crystal will therefore be most exposed to the 

 action of the supersaturated fluid, and will grow most rapidly. The 

 same parts of a crystal will dissolve most rapidly in a fluid con- 

 siderably below saturation.* 



But even when the fluid is supersaturated only so much as is 

 necessary in order that the crystal shall grow at all, it is not to be 

 expected that the form in which Z(crs) has a minimum value (or 

 such a modification of that form as may be due to gravity or to the 

 influence of the body supporting the crystal) will always be the 

 ultimate result. For we cannot imagine a body of the internal 

 structure and external form of a crystal to grow or dissolve by an 

 entirely continuous process, or by a process in the same sense con- 

 tinuous as condensation or evaporation between a liquid and gas, or 

 the corresponding processes between an amorphous solid and a fluid. 

 The process is rather to be regarded as periodic, and the formula (664) 



*SeeO. Lehmann, "Ueber das Wachsthum der Krystalle," Zeitschrift fur Krystal- 

 lographie und Mineralogie, Bd. i, S. 453 ; or the review of the paper in Wiedemann's 

 BeiMdtter, Bd. ii, S. 1. 



