384 ANNUAL EEPORT SMITHSONIAN INSTITUTION, 1908. 



from considerable depths. Such outflows as the Deccan may indicate local 

 subcrustal conditions; so also may the eruptions of certain volcanic areas. 

 But those extrusions which have attended mountain building, more especially 

 its closing phases, appear to indicate general conditions, and involve the ex- 

 istence of such radio-active materials at considerable depths. If we assume a 

 thickness for the radio-active part of the crust much less than the 12 kilometers, 

 difBculties are met with on this line of reasoning.^ 



Proceeding now to the derivation of the results given in the table, p. 16. 

 The equation fc(9=Q/i-a?(D— |) (where d is the temperature at the depth x, D 

 being the total depth of the radio-active layer, q the radium per cu. cm. in grams, 

 h the heat output of one gram of radium per second, k the thermal conductivity) 

 is easily derived by considering the conditions of thermal flow in the layer, 

 supposed to lose heat only at the surface.^ 



The aggregate depths of radio-active material in the several cases of sedimen- 

 tary deposit assumed in my address amount to 18, 20, 22, 24, and 26 kilometers. 

 I assume the mean radio-activity to be 3.5, and the average conductivity to be 

 4 X 10-^ From this the basal temperatures are found, as due to radio-thermal 

 actions. These temperatures are to be augmented by the temperatures proper to 

 the several depths, which depend upon the conducted interior heat. To estimate 

 these we require to apportion the observed average surface gradient (taken as 

 82 meters per degree) between radio-active effects in the upper layer and the 

 flow of heat from within. The radio-thermal gradient comes out at about 75 

 meters; the inner gradient is accordingly 56 meters. Hence the total tempera- 

 ture at the base of each radio-active mass is obtained. But the geotherms 

 proper to the several depths, 18, 20, etc., kilometers, under conditions prevailing 

 elsewhere in the crust, are easily found from the value of 6 for the normal layer 

 (82° C), and adding the temperature due to interior heat. From the difference 

 of the temperatures we finally find the rise of the geotherms. 



As conveyed in my address, I have found on several different values of the 

 thickness and radio-active properties of t'^.e surface layer, results in every case 

 showing large values for the rise of the geotherms. The data assumed above 

 are by no means the most favorable. 



« See p. 379, ante, and footnote as bearing on the possible displacement of the 

 geotherms. 



" See Strutt, Proc. Roy. Soc, Vol. LXXVII, p. 482. 



