

Glacial Epoch upon Underground Temperature. 141 



knowing the surface temperature, have three points in the 

 temperature-curve defined, and the problem of finding the 

 time t without assuming the original gradient m might be 

 solved theoretically by the folio .ving graphical method; for 

 the equations cannot be solved in an ordinary manner on 

 account of the definite integrals involved. 

 We have the two equations 



V 1 = mx x + b L ViKt e~^ dfi ; 



vVJo 



V 2 = mx 2 + b-^L f 7 ^ e-^ 2 dfi. 

 vVJo 



Let us call the definite integrals M x and M 2 , and their 

 upper limits L x and L 2 . Then eliminating m we have 



- 2 Mi- M,= ( b f- 2 - 1) - (Y 1 - 2 - Y ) \ 1 



= c, suppose. 

 And t being the same in both equations, we also have 



Lj _ x l 

 L 2 x 2 ' 



We wish now to find either of the limits L x or L 2 , and then, k 

 being known, t will be known, which is the time elapsed since 

 the glacial epoch passed away. 



In the expression 



M= f e-^clfi 



we know from Oppolzer's table x. that -^ increases conti- 

 nuously from 1 to go . 

 Hence 



L 2 i-i\ 

 L 2 M 3 



* * x\ Mj* 

 .*. —Mi— M 2 is positive. 



