378 



ANNUAL REPORT SMITHSONIAN INSTITUTION, 1908. 



depth of the overlying deposit. Tliis slow and measured process is 

 attended by remarkable thermal effects. The law of the increase of 

 temperature with the square of the depth comes in, and we have to 

 consider the temperature effect not merely at the base of the deposited 

 layer, but that due to the depression and covering over of the radium- 

 rich materials upon which the sediments were laid down. 



The table which follows embodies an approximate statement of the 

 thermal results of various depths of deposit supposed to collect under 

 conditions of crustal temperature such as prevail in this present 

 epoch of geological history : 



I have deferred to the conclusion of this address an account of the 

 steps followed in obtaining the above results. It is clearly impossible 

 within the limited time allotted to me to make these quite clear. It 

 must suffice here merely to explain the significance of the figures. 



The first column gives the depth of sedimentary deposit supposed to 

 be laid down on the normal radio-active upper crust of a certain as- 

 sumed thickness and radio-activity. From the rise of temperature 

 which occurs at the base of this crust (due to the radio-activity, not 

 only of the crust, but of the sediments) the results of the second col- 

 umn are deduced, the gradient or slope of temperature prevailing 

 beneath being derived from the existing surface gradients corrected 

 for the effects of the radio-thermal layer. The third column is in- 

 tended to exhibit the effect of this shift of the geotherms in reducing 

 the strength of the crust. I assume that at a temperature of 800° 

 the deep-seated materials lose rigidity under long-continued stress. 

 The estimated depth of this geotherm is, on the assumptions, about 

 40 kilometers. The upward shift of this geotherm shows the loss of 

 strength. Thus in the case of a sedimentary accumulation of 10 kilo- 

 meters the geotherm defining the base of the rigid crust shifts up- 

 ward by 13 kilometers, so that there is a loss of effective section to 

 the amount of 30 per cent.*^ 



"■ See Appendix B to this article. 



