196 G. F. BECKER ISOSTASY AND RADIOACTIVITY 



Eutherford's estimate for the amoimt of radium in rocks is somewhat too 

 low. Holmes finds for the radium in acid rocks no less than 2.8 X 10~^-, 

 but the selection of the best average value is complicated by the fact that 

 the radium content of acid or persilicic rocks is a maximum. For medio- 

 .silicic, subsilicic, and ultra-subsilicic rocks respectively Holmes gets 2.45, 

 U.85, and 0.51 all multiplied by 10~^-. It is almost certain that radio- 

 activity is confined to a superficial shell of the earth only a few miles in 

 thickness/^ and in such a shell persilicic and mediosilicie rocks prepon- 

 derate, so that with his data 2.5 X 10~^- would be nearer the truth than 

 2 X 10-12. 



I shall adopt the lower value for a reason which at first sight seems 

 strange. On the hypothesis that all of the heat emitted by the earth is 

 due to radioactivity, the higher the surface value of radioactivity the 

 smaller will be the earth's internal temperature. '^^ 



Suppose the highly artificial case of a globe of uniform ordinary tem- 

 perature, say 10°, provided suddenly with a uniform layer of radioactive 

 material just sufficient to supply the amount of heat now escaping. Then 

 assuming (as indicated by the half value period of uranium) that the 

 supply of heat is substantially imdiminished for a couple of thousand 

 million years, it is easy to compute the distribution of temperature for 

 any epoch. Rutherford's'^ estimate, given above, of the heat developed 

 by radioactivity in surface rocks, when expressed in c. g. s. units, is equiv- 

 alent to 6 X 10"^^ calories per cubic centimeter per second. I shall call 

 this constant q. The conductivity,'^ h, Eutherford puts at .004, while 

 for the observed gradient at the surface he adopts 1° C. for each 32 

 meters, or .00031° C. per centimeter. If this gradient is denoted by 

 {dv/dx)o and if s is the thickness of the layer of uniform radioactive 

 matter which will maintain the gradient 



\dx) o 



k 



Substituting the numerical data cited in c. g. s. units gives 



s = 20.7 X 10^ em. = 20.7 kilom. 



'8 That aU of the heat emitted by the earth might be due to a relative thin layer of 

 surface rock seems to have been suggested independeutly by C. Liebenow, Phys. Zeitsch., 

 vol. 5, 1904, p. 625, and by Rutherford, Radio-activity, I'd ed., 1905, p. 644. 



'''' See the value of Vm below. , 



■'^ Radioactive substances and their radiations, 1913, p. 650. 



™ Mr. H. H. Poole concludes from experiments on granite and basalt "that for tem- 

 peratures up to 500° or 000" C. the conductivity of the earth's crust may be taken at 

 about 0.004 without risk of serious error unless the conductivity is sensibly affected by 

 the large pressures involved." Phil. Mag., vol. 27, 1914, p. 58. 



