Glacial Epoch upon Underground Temperature . 135 



We must of course make certain assumptions in order to 

 render the calculations possible. The chief difficulties in 

 these temperature observations arise from the fact that the con- 

 ductivity varies from stratum to stratum in the rocks. We 

 must, however, assume that it is constant, and we may use 

 the value which Lord Kelvin has deduced from observations 

 made at Edinburgh. We shall also assume that the glacial 

 epoch lasted sufficiently long to render the flow of heat steady. 

 In making these assumptions we will examine a hypothetical 

 case, and notice the results which we obtain. 



Let us suppose, then, that during the glacial epoch the tem- 

 perature gradient was 1° Fahr. per 51 feet of descent, which is 

 an average value ; and that beneath the ice the temperature of 

 the surface was the melting-temperature, viz. 32° Fahr. We 

 will then suppose that the present temperature of the surface 

 is 52°, so that it was raised 20° upon the disappearance of the 

 ice ; and that it has continued at that temperature ever since. 

 Professor Spencer has come to the conclusion that the ace 

 of the Falls of Niagara is about 30,000 years ; which gives a 

 probable approximate estimate for the period since glacial 

 conditions passed away. 



We will therefore take it that the time elapsed since the 

 glacial period has been 40,000 years ; and having examined 

 the consequences of these assumptions, we shall be in a 

 position to form a judgment of the kind and degree of the 

 traces which we may expect a former glaciation to have left 

 behind it. 



Let x be the depth in feet. 



t the time in years since the glacial epoch passed away. 

 b the temperature Fahr. by which the surface was 



raised upon the disappearance of the ice. 

 m the temperature gradient before the disappearance of 



the ice. 

 k the conductivity of rock expressed in terms of its 

 own capacity for heat, viz. 400, the units being 

 as above. 

 V the temperature at the depth x at the time t. 

 Then the flow of heat being assumed steady before the dis- 

 appearance of the ice, the temperature at the depth as will at 



that time have been 



mx. 



We shall then have, to express the temperature at the depth 

 x at the time t, the equation 



a 



V = mx f b - ~ f ^ Kt eSdfi. 

 VttJo 



