358 C. Davison — Ejfect of Glacial Period — 



the particular time to be sensible. The excess of temperature at the 

 depth N above that at the surface is represented by D Q, which 

 is obviously less than N P, so that the temperature gradient is 

 diminished at all points to w^hich the heating has become perceptible. 



With a further lapse of time the heating effects will have 

 penetrated to a greater depth, and the temperature-curve will 

 have assumed the form B R E. Here, the excess of temperature 

 at the depth N above that of the surface has increased (D R 

 being greater than DQ); consequently the temperature gradient 

 has also increased, and, continuing to do so, will in time attain 

 a value not differing very greatly from that which it had juat 

 before either the close or the commencement of the Glacial period,. 



before proceeding further it should be remarked that the inaccuracy 

 of the assumption of a sudden change of surface temperature must 

 of course affect all the numerical results hereafter obtained. But, 

 as we do not know the law according to which the rise of tempera- 

 ture took place after the disappearance of the ice-sheet, it seems to 

 me allowable to make the assumption, especially as the provision of 

 exact numerical results is not the purpose of this paper. Moreover, 

 if the change were gradual but continually in one direction, the 

 temperature-curve would be of the form BSF, and this would 

 result in a still further decrease of the gradient, so that the change 

 of gradient would in reality exceed that found on the assumption 

 of a sudden rise of surface temperature. 



The last element required, and that about which the greatest 

 uncertainty exists, is the time that has elapsed since the close of the 

 Glacial period. On account of the small amount of denudation 

 accomplished, the tendency of opinion has recently been to reduce 

 the estimates of the length of this interval. Prof. Prestwich even 

 puts it at only eight or ten thousand years. The maximum figure 

 is probably that given by CroU of about eighty thousand years. 



Under the circumstances, it seems best to calculate the change 

 of temperature gradient for a series of different intervals. In 

 order to give definiteness to the results, I have taken the present 

 gradient at one degree in 50 feet, and, in Table I, have expressed 

 the value the gradient must have had at the close of the Glacial 

 period on the assumptions stated above, for different estimates 

 of post-Glacial time from 5000 to 40,000 years, and for different 

 changes of the mean annual temperature from 16° to 22°.' 



Thus, if the rise of mean temperature since the Glacial period be 

 19°, and if the interval since its close be only 9,400 years, the 



1 The calculations are performed as follows : — If b be the rise of mean annual 

 temperatxire at the surface in degrees, k the conductivity of rock expressed 

 in terms of its own capacity for heat, t the number of years since the change of 

 temperature took place, then the change of gradient is 5 -f '\J-KKt (Eev. 0. Fisher, 

 Phil. Mag., vol. xxxiv, 1892, p. 339). This value, it should be remarked, is 

 independent of the previous gradient. Taking Lord Kelvin's value for /c, namely 400, 

 the above formula becomes -0282154 V^- If * = 20 and C = 10000, b^'\/t=\;, 

 and the change of gradient is •00564 degree per foot. But the gradient now is 

 taken to be "02 degree per foot, so that, at the end of the Glacial period, it must 

 have been -02564 degree per foot, or one degree in 39 feet. 



