142 Effect of a Glacial Epoch on Underground Temperature. 



■■■ Kl- 1 )^?-^- 



we must have b 



Vj^-V. 



X 



x _i -I 



*1 



Unless this condition allows us to assume a probable value 

 for b, the investigation would not succeed. For instance, 

 if the present surface-temperature was 50° F. and the tempe- 

 rature beneath the ice was assumed to have been 32° F., we 



must have less than 18. If it is not so, the 



^2 -I 



hypothesis fails. 



This is a criterion easily applied. 



Our object now is to find the upper limit of either of the 

 definite integrals M x or M 2 from the equation 



where the depths x 2 and x x and the temperature c are known. 

 This can be done graphically as follows, and t the time elapsed 

 since the ice melted will be known. 



On the diagram A is the unit ; B is the curve, approxi- 

 mately drawn from Oppolzer's tab. x. vol. ii., of which the 

 abscissae are values of L. For convenience, the scale might 

 be A = 1 decimetre. 



Call the ordinate of the curve M. Then 



M= e-^'dfi. 



Increase the ordinates in the ratios of .r 2 to x 1} and draw a 

 curve Y through the extremities of the increased ordinates. 

 Add a portion =c to the tops of the ordinates of OB, and 

 draw the curve D C through the extremities of the lengthened 

 ordinates. 



Then the problem is reduced to drawing a line NPR 

 parallel to L, such that N R : N P : : x 2 : x\. This may be 

 done by trial with proportional compasses. 



The ordinates M 1 Q 1 = M 1 , and M 2 Q 2 = M 2 will then satisfy 

 the conditions : for 



