580 

 Then 



Mr. H. Jeffreys on the Compression 



Z(l-ErfZ) + 



This gives l = '066, whence 



X=2'49xl0 6 cm 



(l-*-' a )=-063. 



(13) 



Thus the thickness of the radioactive layer on this 

 hypothesis of a uniform distribution of active matter is 

 25 kilometres. 



It may be remarked here that for any value of t such that 



l( = X/2ht?) is small, u can be expanded in powers of /. Put 



then 



xj2h$ = q (14) 



Then o? 972 



Erf (q + 1) = Erf q + ~ *-* 2 - ^qe'* 



V 7T V IT 



to the second order in I. 



Also e-te +l V=e-* 2 (l - 2ql + 2qH 2 -l 2 ) 



to the same order. 



Now substitute in u and work to the second order in I. 

 Then it is found that Y reduces to the form 



Y = m#+(S 



(■-tS) 



AV\ _x_ 

 2k) 2h</t 



+ 



AX 2 



2k 



(15) 



where 

 and 



//, = if x>X, 



pu=A(X-x) 2 /2kiix<X. 



III. T7i£ effect of other distributions of radioactive matter. 



So far the liberation of heat by radioactive matter has 

 been assumed to be given by the special law that the distri- 

 bution is uniform down to a particular depth, and zero 

 below that depth. This restriction will now be removed. 



Consider a distribution compounded of an infinite number 

 of such distributions ; the amount of heat liberated per unit 

 volume per unit time by those extending to depths between 

 X and X-\-dX is <j)'(X)dX for depths less than X and zero for 

 depths greater than X. If <//(A,) is supposed specified for all 

 values of X from to infinity, then the total rate of evolution 

 of heat at depth A, is 



i 



0'(X)dX = 0(co)-£(A,). 



Hence if we want to find the effect of a supply of heat 

 according to the law £(co )— <j>(\), we must write <j)'(X)dX 



