Glacial Epoch upon Underground Temperature. 139 



varies, it would not be possible to submit the effect of glacia- 

 tion to calculation ; but it is probable that the chief result 

 would still be to reduce the gradient without materially 

 altering the irregular character of the temperature-curve due 

 to the varying conductivity. 



It is easily seen that the mean gradient to the depth x 

 will be 



m 



x V7rJ (1 



-If in an observed case we find the gradient dY/das very 

 slowly increasing, we might hope to obtain a date for the 

 glacial epoch, provided we could feel any certainty about the 

 gradient m beneath the ice ; but the following instance will 

 show the difficulty of this. Ai Wheeling the mean gradient to 

 the depth of 4500 feet was 1 71*8. We may then apply the 

 above equation to find t, in which we must assume m and b. 

 There is good reason for assuming b = 20; but there is a wider 

 choice for m. If we assume m=l/51, it leads us to 



J 4500 

 ViKt €-» 2 dfi= 0-0540952, 

 o 



which would make the integral greater than unity. But it 

 cannot exceed \Ztt/2. Hence the assumptions for b and m, or 

 for one of them, are inadmissible. But it' we assume m — 1/60, 

 a probable gradient, we obtain for the definite integral the 

 value 0-54614 ; 



and referring to the table for the corresponding value of the 

 upper limit, we find 0*61. 



,. *5E=0-61, 



s/±Kt 



whence £ = 34013 years; 



which is a probable result. But it is untrustworthy, de- 

 pending as it does on the arbitrary assumption of ?n = l/60. 



On the supposition that the land during the glacial epoch 

 was covered with ice, there seems good reason to assume, as 

 we have done, that the surface of the ground beneath the ice 

 was at about 32°. During November 1892 Dr. v. Drygalski 

 penetrated a hundred paces beneath the great Karayak ice- 

 stream ; and when the temperature outside varied from 14° to 

 — 6° F., he found within the temperature at the melting-point, 

 and the ice- walls wet. 



