EFFECT OF LAST ICE AGE 71o 



depth — and inversely proportional to the square root of the time, and 

 also to the square root of the diffusivity (a^) = 203 in foot-year units. 



One important thing must be noted. If the temperature has risen or 

 fluctuated in any way since the time when the original increase is sup- 

 posed; but always kejDt above the assumed initial sudden change, the tem- 

 perature will always be above the temperatures which we thus compute. 



Xow we find that the rate of increase or temperature at (figure 2) the 

 bottom of the mines is almost precisely the same as the rate of increase 

 which we get by connecting, for instance, Van Orstrand's observation 

 (probably the most accurate we have) with a surface temperature of 32 

 degrees. The gradient from Van Orstrand's temperature of 86.4 degrees 

 at 4,900 feet to 32 degrees is 1 degree in 90 feet. Strictly, the depth 

 should be taken from the topographic mean depth, giving more weight 

 to the material immediately overhead ; but that would probably not mean 

 a difference in depth of over 100 feet, and the ventilation error is prob- 

 ably as important, but more uncertain. 



According to Chamberlin, the gradient of 1 degree in 103 feet from 

 the surface increased to 1 degree in 93.4 feet from 3,324 to 4,837 feet, 

 which will make the bottom gradient just about 1 degree in 90 feet. 

 Figure 2 shows this line and observations of all sorts compiled, and one 

 may tell by inspection how far the statement is true. 



AYe then have this problem : To adjust the curve given by the black 

 area of figure 2 to the excesses of temperature above the line showing the 

 bottom gradient in figure 1 and see how large we can make the scale of 

 abscissas. 



After a good deal of study to describe a method which will obtain time 

 estimates with reasonable rapidity and with an accuracy as great as the 

 data at present warrant, I suggest the following: Plot the observations 

 with the temperatures as one set of ordinates and the depths as the other, 

 as they are in figures 2 and 3. Draw a line from a point representing 

 the temperature at the bottom, whose slope shall represent the rate of 

 .change of temperature there per unit of depth. In figure 2 its slope is 

 1 degree in 90 feet. Such a line should pass near or close to the actual 

 temperatures below 3,500 feet. Then plot to the same scale of feet the 

 amounts by which the observed temperatures at the various depths ex- 

 ceed thpse given by the line just drawn, for the same depth. This has 

 been done in figure 1. It is clear that up to a depth of about 3,000 feet 

 the observations do not systematically exceed the temperatures given by 

 the line drawn. It is also clear that this line hits the surface at a tem- 

 perature not far from that of freezing. 



XLVII — Bull. Geol. Soc. Am., Vol. 34, 1922 



