u= 



Earth resulting from Secular Cooling, 137 



where 



/8vw Jo c-a/ v >- : w 



where s is the value of y at the depth of the surface of no 

 strain. 



Hence, if 8W be volume of rock crushed in time 8t above 

 the surface of no strain, U = dW/dt, and therefore 



^n/W Jojoc-ay * 



This gives the total volume of the rock-folding since consolida- 

 tion, while equation (8) gives the rate at which rock-folding 

 takes place at time t. 



For a first approximation, we may put 



1 1 



c— ay c 

 and 



f(y)=Ac*a-y/3c 3 -y*c% 

 where 



A=3(v/2^- + 4/3)/8. 



We thus get 



P {~ dy = Acas-i/3c*s*-ic*s\ 



where 



* = ¥[-£+</ (£ 2 +4Aac)], 



and consequently, after reduction. 



w.ic, TvH [ i L,. A ( 1+ ^y + ^(i + ^)' 



If A be the average thickness of this volume of crushed 

 rock spread over the whole globe, then 



Y=W4ttc 2 . 



