THE TERRESTRIAL DISTRIBUTION OF RADIUM 21 



Q = 47rr 2 .k.d#/dr calories per second, 

 where 



4\r 3 , the area of the earth's surface = 51 x io 17 sq. cms. 

 k, the average conductivity of rock = 0*004, 

 and, d#/dr, the average observed temperature gradient 



= i° C. for 32 metres 

 or 0-0003 i°C. per cm. 



Substituting the given data in the above formula, Q is found to 

 be nearly 228 x io 14 calories per hour. 



Thus, if each gram of rock generates 1,105 x io- 12 calories 

 per hour on account of its radioactive contents, it is clear that 

 2 x io 25 grams of rock would suffice to make good the earth's 

 loss. But the total mass of the earth is 600 x io 25 grams. Are 

 we therefore to suppose that the earth gains from radioactive 

 sources 300 times as much heat as it loses by conduction and 

 radiation ? Clearly we are in the face of a serious embarrass- 

 ment. It is impossible to believe that the earth is growing 

 hotter, not only for geological reasons, but also because our 

 planet could never have cooled beyond a state in which the gain 

 of radiothermal energy would just balance the loss of heat by 

 conduction. Equilibrium being once established, the earth 

 would continue to cool at the exceedingly low rate dictated 

 by the atomic decay of the parent elements, uranium and 

 thorium. 



Since the earth is not growing hotter, a remarkable discrep- 

 ancy has to be explained. There are two ways of escaping 

 the difficulty, both of which were originally put forward by 

 Strutt. 1 It is possible that the average radium content of the 

 surface rocks is far above the average for the materials of the 

 earth when taken as a whole. The earth's store of radioactive 

 elements would then be concentrated in, and confined to, a mere 

 superficial shell, and distributed in such away that the observed 

 temperature gradient would be maintained solely by their 

 output of thermal energy. On the other hand, can it be granted 

 that in the deep interior of the earth the radio-elements would 

 continue to disintegrate and generate heat just as they do at 

 the earth's surface ? The parent elements may be present, but, 

 being subjected to high pressure and temperature, it is con- 

 ceivable that their decay may be inhibited. There would then 

 be within the earth an irregularly bounded zone extending to 



1 Proc. Roy. Soc, A., vol. lxxix., p. 476, 1906. 



