68 Arthur Holmes — Radio-activity 



the oceans lie in heavy basaltic depressions with a lower conductivity 

 than the lighter granitic elevations of the continents, it follows that 

 the gradients to be expected would be steeper for the former case 

 than the latter, if the average loss of heat be everywhere approximately 

 equal. Moreover, such a steepening can be explained at least partially 

 as a result of the earth's superficial features. Near the surface the 

 isogeotherms are approximately parallel to the surface; at greater 

 depths they tend to become more and more nearly spherical and 

 independent of superficial irregularities. Under the continents 

 successive isogeotherms will therefore be more widely apart than their 

 continuations under the oceans. That such a difference may actually 

 exist is suggested by the fact that volcanoes are much more abundant 

 well within the oceans than they are in the continental masses. 



It would appear, then, that the two assumptions to which we are 

 led are not without foundation, and for the present purpose they may 

 be admitted without further discussion. It now becomes important 

 to notice that if the continents are essentially granitic, with basic rock 

 below, and the sub-oceanic rocks predominantly basic with little 

 granitic covering and in some places even none, then the radio-active 

 elements must be more abundant on and below the continents than 

 below the oceans. Exactly how much so depends on the thickness 

 of the granite covering in each case. If, to give an example, we 

 assume that in the continents one-third of the total quantity of 

 radio-elements in any vertical section is confined to the upper zone of 

 granite and that the remaining two-thirds are distributed in basic 

 rocks below, then it would appear that under the oceans a similar 

 vertical section would provide only two-thirds of the total quantity 

 of radio-elements found in a continental section. This would be 

 a necessary consequence of any igneous mechanism by which granite 

 was originally concentrated in the continental areas. In such a case 

 the depth of the radio-active layer under the ocean would be about 

 47 km. instead of 7o, and (from equation 3) the maximum 

 temperature would then be reduced to 750° C. Thus the same 

 difficulty arises as before, and we are led to the final conclusion that 

 even on the extreme view here taken of the sub-oceanic rocks, their 

 radio-activity must decrease with depth in order to provide sufficiently 

 high temperatures. Here, however, the necessity for decrease is less 

 severe, for a consideration of equation 4 shows that a temperature of 

 750° C. corresponds to a gradient just below the floor of the ocean, 

 which is the same as assumed for the continents. If the actual 

 gradient is steeper than this so as to bring up the heat output to the 

 continental standard, then the additional gradient must be due to 

 some source of heat more effective under the oceans than under the 

 continents (e.g. igneous activity from below, compression, etc.), which 

 in turn would provide higher temperatures in depth. 



5. The Law of Decrease. 



Case 1. — In the present state of our knowledge, it is, of course, 

 impossible to state with mathematical precision the rate at which 

 radio-activity decreases in depth. The continental case suggested 

 above, in which one-third of the radio-activity is confined to a granite 



