JISTRIBUTIOl 



DEPTH 139 



2.85, and the heating effect of radium 0.02778 gram calories per gram 

 per second, 



q = lAx 10-^^ X 2.85 X 0.02778 = 0.1108 X 10-^^ . 3-^ = gs.ekilom. 

 The condition of tangency gives 



Y (5 — .To) = 67.5 X 10-« 



or 



s = 119. kilometers = 74 miles. 



and when -i- = .y or for the under surface of the shell 



QS~ 



V = -^7- = 1887° centigrade. 

 Finally, when x^ 0, the surface gradient is 



f — 7":) = -^ = 0.0003176° centigrade per centimeter, 



or 1° Fahrenheit per 57.4 feet. 



I am thus led to the striking conclusion that with the data now known 

 any surface gradient of temperature due to uniform radioactivity alone, 

 which exceeds 1° Fahrenheit in 57 feet, would result in tidal instability 

 and is impossible. The utmost thickness which can be ascribed to a shell 

 of uniformly radioactive rock is 74 miles and the highest temperature 

 which its under surface can possess is 1887° centigrade. 



The surface gradient, 1° Fahrenheit in 57 feet, or 0.03176° centigrade 



.per meter, or 1° centigrade in 31.5 meters, is well within the range of 



, observed gradients ; but if all the heat of the earth is to be accounted for 



by radioactivity, it appears too low. Mr Strutt, following Prestwich, 



took 1° Fahrenheit in 42.4 feet as the mean, and Mr Eutherford 1° 



Fahrenheit in 50 feet. 



' As appears from the formulas, the surface gradient is simply propor- 

 ■tional to the thickness of the shell or to s. Hence, if only a fraction of 

 the actual gradient is due to radioactivity, the corresponding thickness of 

 the radioactive shell can be found by simple proportion. Thus if the 

 normal average gradient is 1° centigrade in 38 meters and the average 

 gradient due to radioactivity is 1° in 385 meters, the values suggested on 

 a preceding page for a 60-million-year earth, then the radioactive shell 

 would be 9.8 kilometers, or about 6 miles, in thickness. The correspond- 

 ing thickness for ages of 55 and 65 million years are respectively, in 

 round' numbers, 6 kilometers and 13 or 4 miles and 8. 



