J. W. G'ihhs — E(iu'dibriHiii of Heterogeneous ISubstances. 193 



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

 lower ))arts of the fluid, aceordiiig as the growth of a crystal at con- 

 stant temperature aud pressure Avill produce expansion or contraction. 

 Again, we may suppose the comjiosition of tlie fluid and its 

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

 vary Avith the pressure, that is, with z. AVe may also suppose the 

 temperature of diflerent crystals or ditterent parts of the same crystal 

 to be dctermhied by the fluid in contact with them. These condi- 

 tions express a state which may perhaps be realized when the fluid is 

 gently stirred. Owing to the ditterences of temperature we cannot 

 regard i\' an<l V\' ^^^ (664) as constant, but we may regai-d their 

 variations as subject to the relation diy' =. t d/,\'. Thei-efore, if we 

 make ;/v' = for the mean temperature of the fluid, (which involves 

 no real loss of generality,) we may treat ey' — t r/y' as constant. We 

 shall then have for the condition that the effect of gravity shall 

 vanish — 



dz 

 which signifies in the present case that 



dj) /7/,m ri" 

 or, by (90), 



i-f-^ )" = ^,. (»'0) 



\dmjTi,p,m ;/, 



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

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

 flxiid will jjroduce neither expansion nor contraction, when the pres- 

 sure 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 difterences of phase in the surround- 

 ing fluid than those which have been considered in the preceding 

 paragraph. This is especially the case when the crystal is growing 

 or dissolving rapidly. When the great mass of the fluid is consider- 

 ably supersaturated, the action of the crystal keeps the part immedi- 

 ately 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.* 



* See 0. Lehmann "Ueber das Wachsthum der Krystalle," Zeiischrift filr Krystai- 

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

 Beibldtter, Bd. ii, S. 1. 



