DIFFUSION IN SILICATE MELTS 313 
when crystallization of an early-formed mineral A takes place 
‘only near the border, the rest of the mass being still above the 
temperature of crystallization. The greater concentration of the 
substance A in the interior of the mass where none has yet pre- 
cipitated should constitute a driving force tending to cause that 
material to diffuse toward the margin. This case may be stated 
fairly simply as a definite diffusion problem. When the tem- 
perature of a thin layer at the margin has fallen to such a value 
that a certain fraction of the amount of substance A in that thin 
layer has precipitated, then the magma in this layer is saturated 
with A. If this condition is maintained for an infinite period of 
time, the whole body of magma will eventually acquire the same 
concentration in A as this marginal saturated solution’ and all of 
substance A in excess of this concentration will be precipitated 
at the margin. If we assume the contact surface plane as in a 
tabular mass, this is essentially the same problem as the heat- 
conduction problem involved in the cooling of a sheet of metal one 
face of which is kept at constant temperature. A solution of the 
problem is given by the equation: 
which gives the concentration c in terms of the original concentra- 
tion ¢, at any point at distance x from the margin after the time 
it, the concentration of the marginal saturated solution being 
taken =o. 
Values of c for various values of x and ¢ have been calculated 
for a diffusivity 0.25 in cm. per day, approximately the highest 
experimental value, and are plotted as concentration curves 
in Figure 7. The figure shows that after two-thirds of a year 
the precipitating effect has been felt for a distance of 0.33 m. from 
the margin, all the rest of the magma being entirely unaffected. 
After sixty-four years the precipitating effect has been felt for a 
t Neglecting the Soret effect. 
