THE earth's radiation 197 



With s given the excess of temperature, v, at any distance x from the 

 surface is*° 



_ gx ( x\ 



k 



so that at the bottom of the radioactive stratum ; that is, for x = s; the 

 maximum temperature is 



""- 2A- ^ k' ' 2g \dx)o ' 2q 



But for the elevation of melting point by pressure, therefore, the maxi- 

 mum temperature developed by radioactivity in the hypothetical earth 

 would about suffice to melt lead. Observe that for a given gradient v„, 

 is inversely proportional to q. 



The hot stratum would somewhat gradually warm up the underlying 

 mass, and it is worth the while to ascertain its effect at Mr. Hayford's 

 level of isostatic compensation, which lies at a depth of 121 kilometers. 

 If u is the distance of this level below the radioactive layer, about 99 

 kilometers, the temperature excess, v, in accordance with Fourier's law, 

 is given by 



V 



TT 



Here < is the diffusivity of the rock or the ratio of the conductivity to the 

 thermal capacity. For the Calton Hill trap this is .00786 in c. g. s. units, 

 or per year and square meter « = 24.8037. If v = vy2, or 161°, so 

 that Hayford's level acquires half the temperature excess of the radio- 

 active shell, then 



= .4769 or i = 434 X 10' years. 



2 }/ Kt 



Thus it appears that heat traverses a layer of rock a hundred kilometers 

 in thickness with extreme slowness. 



It does not seem to me that on such an earth as that just considered 

 there would be any geology. No evident source of energy is available to 

 bring about upheaval, subsidence, or vulcanism, and therefore baseleveling 

 would obliterate the continents. 



On the other hand, as is pointed out above, a superficial shell (»t' a cool- 

 ing earth, extending from the surface down to the level of isostatic com- 



^ Proof of this pquatlon, established Independently by Messrs. R. .T. Strutt and Jobaun 

 Koeulgsberger, may be found In Bull. Geol. Soc. Am., vol. 19, 1908, p. 137. 



