and the Earth's Thermal History. 



65 



earth by conduction and radiation is exactly made good by radio- 

 thermal action. Taking the simplest possible distribution of the 

 radio-active elements, let us suppose that the average content of the 

 surface rocks is uniformly maintained down to the maximum possible 

 depth consistent with the limited heat production allowed to it. 

 The depth of such a radio-active layer is easily calculated from 

 the data now available. 



The total amount of heat Q lost by the earth is given by 

 the equation s\ A ■> i 



dejdx 



0) 



in which Awr % , the area of the earth's surface, is taken as 

 51 x 10 17 sq. cm.; h, 1 the average conductivity of rocks, is taken 

 as 0-006 for granite and gneiss, 0-005 for average igneous rock, 

 and 004 for basaltic or gabbroid rock ; and d6/dx, the. average 

 temperature gradient near the surface of the continents, is taken 

 as 0-00032° C. per cm. or 1°C. in 31-25 metres. Since granite is by 

 far the most abundant rock over the continents, the most accurate 

 result is likely to be obtained by using the largest value given for 

 h above. 2 For the sub-oceanic rocks the assumption is made that the 

 heat lost per unit area is equal to the corresponding amount for 

 continental rocks. Substituting the suggested values in equation 1, 

 the total heat loss Q is found to be 9-71 X 10 12 calories per second. 



To determine the average amount of heat generated by the radio- 

 active elements in each cubic centimetre of the crustal rocks, we 

 must combine the average quantities of radium and thorium in the 

 rocks with the respective amounts of heat produced by the two 

 families of radio-active elements which are implied by the presence of 

 radium and thorium. The latter factors are known with considerable 

 accuracy. 3 Radium, implying the series Uranium to Lead (Radium G) 

 in complete radio-active equilibrium, represents a generation of 



1 Thermal Conductivity of Bocks. 



2 If it is thought that this value of k (0-006) Combined with a temperature 

 gradient of 0-00032° C. per cm. gives an unfairly high result, it should be 

 remembered (1) that the tendency in measuring temperature gradients is always 

 to under- rather than over-estimate, and (2) that the heat lost from the earth by 

 igneous activity is not included in the product k . dd/dx. 



3 See Butherford, Radio-active Substances and their Radiations, pp. 583, 

 650, 1913. 



DECADE VI. — VOL. II.— NO. II. 5 



