Page:Scientific Papers of Josiah Willard Gibbs.djvu/360

in (664) as constant, but we may regard their variations as subject to the relation $d\epsilon _{V}'=td\eta _{V}'$. Therefore, if we make $\eta _{V}'=0$ for the mean temperature of the fluid (which involves no real loss of generality), we may treat $\epsilon _{V}'-\eta _{V}'$ as constant. We shall then have for the condition that the effect of gravity shall vanish

${\frac {d(\gamma _{1}'\mu _{1}''-p'')}{dz}}=0,$

which signifies in the present case that

$\left({\frac {d\mu _{1}}{dp}}\right)_{\eta ,m}''={\frac {1}{\gamma _{1}'}},$

or, by (90),

$\left({\frac {dv}{dm_{1}}}\right)_{\eta ,p,m}''={\frac {1}{\gamma _{1}'}}\cdot$

(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 paragraph. 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 considerably below saturation.^[1]

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 $\textstyle \sum \displaystyle (\sigma s)$ 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 continuous 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)

1. See O. Lehmann, "Ueber das Wachsthum der Krystalle," Zeitschrift fur Krystallographie und Mineralogie, Bd. i, S. 453; or the review of the paper in Wiedemann's Beiblätter, Bd. ii, S. 1.