GEOTHERMAL GRADIENT DETERMINATIONS Sil 
from the surrounding trap rock, which composes the great bulk of the mater- 
ial, the weighted average is taken as 0.0075 c.g.s. units. 
With the above value, calculations? have been made of theoretical tem- 
perature-depth curves for some 24 different assumed “thermal histories” of 
this region. The simplest assumption is that the surface temperature has been 
about as at present for 10,000 years and that previous to this the surface 
was covered with ice. In other assumptions the time has been changed and 
in still others several glacial overflows are taken account of. The periods of 
time have been varied between wide limits. The equation for calculating the 
points of these curves is 
x if 3 
——— { F(A)e-* /4h*(t-d) . (t = d)73/2dd 
2h(x)1!2 Jo 
where x is the distance below the surface, at which the temperature @ is to 
be calculated, #? the diffusivity, and F(A) the surface temperature function. 
These curves having been calculated and corrected for the general aver- 
age gradient slope, a careful comparison has been made between them and 
the actual curve as given in Fig. 2. The results are a little disappointing at 
first as the curve is so nearly a straight line anyway and so much depends 
on the justification for certain assumptions which cannot as yet be proved 
satisfactorily, e.g., that the diffusivity of the rock is unchanged for the first 
mile or more in depth. However, certain assumptions fit much better than 
others and point on the whole to a somewhat longer period—say 30,000 
years—since the last glacial overflow for this region, than is usually assumed. 
In addition to the acknowledgements at the beginning of this article, 
special thanks are due to Mr. James McNaughton, President of the Calumet 
and Hecla Company, for placing at the service of this investigation the facili- 
ties of the mines, and particularly to Messrs. H. E. Jefferson, H. S. Donald 
and R. F. Wilson for their care in making the measurements, as well as for 
many valuable suggestions. 
1 I am glad to acknowledge the assistance of the following of my students in making these 
long and arduous calculations: Miss M. C. Wolf and Messrs. R. O. Anderson, R. E. Erickson, 
R. G. Herb, W. L. Hole, R. W. Prucha and M. T. Rodine. 
201 
