132 G. F. BECKER RELATIONS OF RADIOACTIVITY TO COSMOGONY 



of the distance to the center, and Wiechert =* one-fifth. The cooling of 

 the earth must depend almost wholly on the properties of this rock, and 

 the film of detrital matter on the surface bears no greater proportion to 

 the mass of the earth than might the coating of oxide on a hot cannon 

 ball. Hence it seems to me that the value of diffusivity to be chosen is 

 that of trap, and that the significant gradients are those to be found in 

 massive rocks, not among strata. Furthermore, many causes tend to 

 increase the gradient. Such are thermal springs, volcanic heat, dissipa- 

 tion of mechanical energy, chemical decomposition, and radioactivity, 

 M-hile only exceptionally high diffusivity in a massive rock of a given 

 type or the neighborhood of large bodies of cold water tends to lower the 

 gradient. What is requisite for the problem of a cooling earth is not an 

 average gradient, but the average of unexceptionable gradients in massive 

 rocks. 



Suggestions of this character have been made by various writers, but 

 the subject has been discussed in detail only, so far as I know, by Mr 

 Johann Koenigsberger."^ He has classified observations on temperature 

 gradient and points out that those taken in nearly level regions in [rela- 

 tively speaking] chemically unaltered rocks which are not recent eruptives 

 are the most characteristic for the earth as a whole. He gives 26 such 

 values, ranging from 1° centigrade in 27.8 meters to 1° centigrade in 

 37.9 meters. Five of the 26 are lower than 1° in 37 meters and average 

 1° in 37.7 meters or, in round numbers, 1° centigrade in 38 meters. 

 This is equivalent to 1° Fahrenheit in 69.3 feet. Since a minimum 

 gradient, rather than an average one, is demanded by the problem, I 

 shall suppose this to be the normal value; and if the gradient due to 

 cooling alone is 1° centigrade to 42.2 meters, as I find it for the 60- 

 million-year earth, the gradient due to radioactivity and other analogous 

 causes would be 



1° 1^ _ 1° 



38" 42™.2 385"' ' 



or almost exactly a tenth of the normal value. 



No doubt this is only a rough approximation. If the earth were only 

 55 million years old, the other data remaining the same, the remainder 

 attributable to radioactivity would be only 1° in 588 meters, while for a 

 65-million-year earth it would be 1° in 294 meters. 



'^GOttlngen Nachrichten, 1897, p. 221. 



■^^Congrfes ggologique Internationale, tenth session, Mexico. Compte Rendu, 1907, 

 p. 1127. In this very important paper Mr Koenigsberger shows that the temperatures 

 in tunnels can he calculated by Fourier's law when the local topography is duly taken 

 into account. 



'^'1 



