200 G. F. BECKER ISOSTASY AND RADIOACTIVITY 



a uniform shelP® is 106°. To be sure, the limit of s/s^^ chosen is an 

 arbitrar}^ one, but it will answer the purpose in view. Were three-fourths 

 of the heat emitted due to radioactivity, the age would be over 6,200 X 

 10^ years. Even so, initial heat would play an important part in the 

 earth's heat emission. Thus it appears that thermal equilibrium can not 

 have been attained by the earth as yet, and that however important 

 radioactivity may be, the earth must be considered as a cooling globe. 

 While these results are dependent on the choice of constants, those 

 selected can not be very erroneous, and it seems impossible to avoid the 

 conclusion that, even if the earth is 1,300,000,000 years old, something 

 like a third of the surface gradient, and therefore also approximately one- 

 third of the earth's emission, is due to initial heat, while the contribution 

 of radioactivity to the earth's internal temperature is hardly great enough 

 to account for hot springs. 



That depth at which the excess of temperature curve most nearly 

 approaches the diabase melting-point curve I have called the eutectic 

 level, because a smaller heat increment will bring about fusion at this 

 level than at any other. For any age equal to or greater than 68 X 10^ 

 years the eutectic level lies 70 miles or more below the radioactive layer, 

 and the temperature gradient at this level will be independent of q. It 

 can readily be proved^' that if .r^ is the distance of the eutectic level 

 from the surface the conditions stated above are satisfied by 



- '- 1 



V TT K t ■ • = £ •* * ' 



.01 /• r 



r being the earth's radius and b the melting point of diabase at the sur- 

 face, or 1,170°, according to Barus. The values of x^ for each of the 

 ages is given in the table. For f = 68 X 10^, a\ = 121 kilometers, and 

 for t = 1,314 X 10^, .Ti = 300 kilometers. 



^ If the radioactivity were to diminish linearly with depth, the total amount remain- 

 ing the same as in the uniform shell, activity would vanish at a depth, say. o- = 2s, and 

 at this depth the temperature would be four-thirds of that computed for the bottom of 

 the uniform shell. Thus redistribution in this sense would increase the value 106' to 

 141°. Bull. Geol. Soc. Am., vol. 19, 1908. p. 144. On the other hand if, following 

 Holmes, I had taken the Ra- content of surface rock at 2.5 X 10 ~'^, the temperature 

 of 106° would sink to 91°. 



« Smithsonian Misc. Coll., vol. 56, 1910, No. 6, p. 24. 



