DIFFUSION IN SILICATE MELTS Qua 
absolute temperature, 1.e., o of the scale is o° absolute and 1 of the 
scale is 1000° absolute. After one year the temperatures at the 
margin and at the center are 490° and 760° respectively. Then 
i : Ohi: 
the effective concentration at the center should be eS times that 
at the margin and diffusion should take place until the effective 
concentration is uniform, or until the real concentration at the 
center is times that at the margin. The problem is to find 
how long a time it would require for this diffusion to take place. 
Infinite time would, of course, be required to allow the process to 
go to completion, but we may find the time needed to give any 
assigned approach to this condition. 
As a first step we may calculate the time necessary for the 
acquirement, from any arbitrary initial condition, of a concen- 
tration gradient represented by the curve showing the thermal 
gradient at the end of one year. ‘This may be done by assuming a 
condition analogous to our experiments, viz., that all the material 
was first concentrated in a meter layer and by diffusion had acquired 
the gradient referred to. With the aid of equation (I) we find 
this to be very nearly true when V é¢ in the limits of the integral 
has the value 500. If we take & as having a value close to the 
highest found in any of the experimental determinations, viz., 0.25, 
then t=10° days. But this is not the time we wish to know; 
it is that required to go on from this condition to practical uni- 
formity. Again we find from the equation that practical uni- 
formity (1:0.996) is obtained from the arbitrary initial condition 
when V kf=1000 or when f,=4X10° days. From this we get the 
desired time ¢,—#=3X10° days, or nearly 10,000 years. This 
shows that it would need about 10,000 years to obtain nearly the 
full theoretical Soret effect required by the curve of temperature 
distribution after one year in a mass of the dimensions chosen. 
In the meantime, as shown by the curves of Figure 6, the whole 
mass would have cooled to the temperature of the surrounding 
rocks. Even if we imagine it to be still above its crystallization 
temperature at the end of four years, it will be noted that most of 
the temperature gradient has been destroyed at that time so that 
