NOVEMBEB 27, 1908] 



SCIENCE 



739 



the resultant state being obtained fey their 

 summation. 



In dealing with the rise of temperature 

 at the base of a radio-active layer we arrive 

 at an expression which involves the square 

 of the depth. This is a very important 

 feature in the investigation, and leads to 

 the result that, for a given amount of 

 radium, diffuse distribution through a great 

 depth of deposit gives rise to a higher basal 

 temperature than a more concentrated dis- 

 tribution in a shallower layer. 



But this will not give us the whole effect 

 of such a deposit. Another and an impor- 

 tant factor has to be taken into account. 

 We have seen that the immediate surface 

 rocks are of such richness in radium as to 

 preclude the idea that a similar richness 

 can extend many miles inward. 



Now, it is upon this surface layer that 

 the sediments are piled, and as they grow 

 in thickness this original layer is depressed 

 deeper and deeper, yielding under the load 

 until at length it is buried to the full depth 

 of the overlying deposit. This 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 tem- 

 perature 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 re- 

 sults of various depths of deposit supposed 

 to collect under conditions of crustal tem- 

 perature 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 

 canee of the figures. 



Thickness of 



Sedimentary 



Deposit 



KilometerB 



Resulting 



Rise of 



Isogeotherms 



Kilometers 



7.4 



10.2 



13.3 



16.7 



20.4 



explain the signifi- 



Weakening of Earth's 

 Crust as Defined by 

 the Rise of the Geo- 

 therm at 40 Kilo- 

 meters 

 Kilometers 

 40 to 32.6 

 40 to 29.8 

 40 to 26.7 

 40 to 23.3 

 40 to 19.6 



The first column gives the depth of sedi- 

 mentary deposit supposed to be laid down 

 on the normal radio-active upper crust of 

 a certain assumed 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 column 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 

 intended to exhibit the effect of this shift 

 of the geotherms in reducing the strength 

 of the crust. I assume that at a tempera- 

 ture 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 kilometers 

 the geotherm defining the base of the rigid 

 crust shifts upwards by 13 kilometers, so 

 that there is a loss of effective section to 

 the amount of 30 per cent. 



As regards the claims which such figures 

 have upon our consideration, my assmnp- 

 tions as to thickness and radio-activity of 

 the specially rich surface layer are, doubt- 

 less, capable of considerable amendment. 

 It will be found, however, that the assumed 

 factors may be supposed to vary consider- 



