-Js 



results of the Contraction of a Solid Globe. 19 



The vertical contraction of the crust above this level is 

 inconsiderable. It may be thus found : — 



which, being taken from w = to x — mt, the depth of the 

 level of no strain, 



V4^3 2 



eb 9« 4 

 = 6a4^ = « A = 3feet - 

 We may therefore say that the 



Radial contraction of the globe = 6*3 miles. 



It will be noticed that, in the above calculations, no 

 reference has been made to the numerical value of the con- 

 ductivity, nor to the time elapsed since the surface first 

 assumed its present temperature. All that has been assumed 

 is that the present temperature-gradient, expressed by bja, 

 is 1/51, which is about the mean result of innumerable 

 observations ; and that the temperature of solidification was 

 7000° F. These have been sufficient for our purpose. How- 

 ever, the temperature-gradient being known, and the tem- 

 perature of solidification assumed, there follows a relation 

 between the time and conductivity ; and this appears to have 

 been the original object of Sir William Thomson's investi- 

 gation. If we make use of the value for the conductivity 

 which he has deduced from certain observations on rocks 

 in situ (viz. 400), the results just obtained will correspond to 

 98 millions of years. But a lower temperature, say 4000° F., 

 seems more probable ; in which case the time would be about 

 33 millions of years. In that case all our estimates will have 

 to be reduced. These depend upon the constant a ; and 



a= a2Y = 5i 2 V 

 b yV yV 



aaV. 

 If, then, we reduce the temperature from 7000° to 4000°, 

 //="($)* X A feet =2 feet. 



The excess of the temperature of the level of no strain over 



02 



