THE earth's radiation 199 



tions are unaffected by any hypothesis as to the origin of the lieat; f(n- 

 even if all the heat had been due to atomic disintegration, the rocks could 

 not solidify until the temperature sank to their melting points at the 

 prevailing pressure. 



Let Y be the initial surface temperature (1,300°) and let c be the 

 initial gradient, 300/63,710 degrees per meter.** Then the- present 

 superficial gradient is 



(^'-•)=^L. + .+f 



Vrfx/o V TT K t 1^ 



k Udv\ V 1 ) 



_k I fdv\ _ 

 q I \r/,r/o 



q \ \(l.e)o V K K V t ) 



so that if / is assumed s can be found, or vice versa. Rutherford gives 

 g at 19 gram calories per annum, and the conductivity A- T shall take as 

 that of the Calton Hill trap, .00415 in c. g. s. units, or per meter per 

 year, 13.096 X 10*^. For the present surface gradient my preference is 

 1° C. in 38 meters. Rutherford's l''/32" is a fair average of observed 

 values, but there are reasons*^ for selecting as normal the gradients in 

 undecomposed massive rocks in relatively level country rather than a 

 mere average of observations. Many influences tend to raise the gradient 

 abnormall}', while none, excepting the neighborhood of large bodies of 

 cold water and the escape of gas, are known to lower it. 



With ^ =co and c = o the data I have chosen would give a maximum 

 value of the uniform radioactive shell, say, .5,,, = 18.14 kilometers, and 

 all of the emission would be due to radioactivity. For any other case — 

 that is, if only a part of the heat lost by the earth is of radioactive 

 origin — the thickness of the radioactive layer would be in kilometers 



s = 14.893 - 101509/ i/T 



111 a little table below will be found values of .« for / i-anging fnun 

 68 X 10^ years to 1,314 X 10*^ years. This latter portentous age is 

 chosen because it would seemingly satisfy even the requirements of the 

 uranium-lead ratios and because it gives s/s_,^ = 2/3, meaning that just 

 2/3 of the heat emitted is of radioactive origin. Tf this age is regarded 

 as a superior limit, then at least one-lliird of (lie surface gradient is due 

 to initial heat, and the maximum tempcraluic due to the radioactivity of 



"•In oHuT worfls, (lip initial tPtTipr-raliirc oxcoss is (aknn as ."'.on" af a dopdi ri|iial lo 

 1 per cpnt of the partli's radius, or (!:?,710 mptpis. 

 w Smithsonian Misc. Coll., vol, 56, 1010, No. 6, p. 26. 



