1&6 lie v. 0. Fisher on the Residual Effect of a Former 



This is analogous to the equation which I proved in the Phil 

 Mag. for Oct. 1892, mutatis mutandis. 



It gives, when x = 0, Y=b, the surface temperature, 

 when t = 0, Y = mx, the glacial temperature, 

 when a 1 = 30, Y=mx, the glacial temperature at 

 great depths, to which the warming of the 

 surface has not reached. 

 Differentiating with regard to x, 



dV b li 



— — = m e - iKt , 



dx ^Tr K t 



This is the temperature gradient at the depth x (not the 

 mean gradient to that depth) . It shows that the temperature 

 gradient is less than it was during the glacial epoch, unless 

 the time elapsed since then has been so long that t may be 

 considered infinite ; in which case the gradient recovers the 

 value m which it had during the glaciation. Also, since the 

 negative term diminishes as x increases, we see that the 

 gradient increases as the depth increases. This also appears 

 from 



d 2 Y x b il 



dx 2 "lict ^/-mct 



being positive, which shows that the temperature-curve is 

 convex towards the axis of depths, and that the convexity 

 diminishes in descending. 



We will now apply the formula to the hypothetical case 

 proposed. Here 



£=40000, 6=20, m=l/51, /c = 400. 



With these values, 



log -^ = 1*3534860, 



\ IT 



and V 4^ =8000. 



If we express the upper limit of the definite integral by L, 

 then the depth x 



= Lx s/'iKt, 



= Lx8000. 



Mow in table x. vol. ii. of Oppolzer * we find the values of 

 the definite integral given for intervals of # 01 of the upper 

 limit L, which will correspond to the depths 80, 160, &c. feet, 



* Bahnbestimmung der Kometen und Planeten, 1880. 



