

of the Earth's Crust in Cooling. 579 



In the case here considered, f{x) is only specified from 

 x — to # = co , but we have the condition that u is always 

 when x = 0. This is satisfied automatically if! we specify 

 f(x) for negative values of a?, so that /(a?) = — /( — #). Thus 

 w can be determined. 



We find then 



2h 



-J { (.-x)«+a»}lW^-i{(.+X)»+»W}l!rf^g: 



-AiV-^ + X)?-^^ 2 '" 2 '], • (9) 



and V is at once obtained on substitution in (4) and (5). 

 It can easily be verified that it satisfies all the conditions. 



If we differentiate V and then put # = 0, we find for the 

 temperature gradient at the surface the value 



+V(;)(i-"^)]- ( 10 ) 



In this substitute the values given by Holmes *, namely 



mt = 0°-00005 C. per cm., St = 1200° C, 

 /|^\ =Q°-00038 C. per cm., 



/ = 5'05 x 10 16 sees. = 1-6 x 10 9 years, 

 A = 63*9x 10~ 14 calorie per cm. cube per sec, 

 /; = 0-005 C.G.S. units, fc=0'084. . . (11) 



Put \/2hti = l (12) 



* Geol. Mag. March 1915, p. 108. 



t This value of m agrees well with that given by J. Johnston, Journ. 

 Geol. xxiii. p. 73b' (1915). 



X This melting-point is approximately that of basalt, representing 

 material just under the acid shell and intermediate in composition 

 between the acid rocks and the deep-seated peridotites. 



2 R2 





u = mx + S Erf -^ $ 



