696 TKANSACTIONS OF SECTION C. 



APPENDIX B. 



Sedimentation and Rise of Geotherms (p. 692) — The depth of the upper radio- 

 active layer is, of course, unknown. We possess, however, the means of arriving 

 at some idea of what it must be. The quantitative thermal conditions impose 

 a mnjor limit to its average thickness, and the indications of injected rocks suggest 

 ft minor limit. 



It will be found that if 2'6 x 10-" calories is the heat output of the whole 

 earth per annum, and if we assign only one-fifth of this amount to cooling due 

 to decay of the uranium, then, on the assumption that the earth is no longer 

 losing any part of its original store of heat, we have about 2 •; 10'-" representing 

 radium heating. From this the allowance of terrestrial radium per square centi- 

 metre inwards is 2'3xl0 ' grams. This would give a major limit. But it is 

 almost certain that some of this radium is located in more deeply seated parts of 

 the earth. If we take 10~^ as contained in the normal radio-active surface layer, 

 and assume (what according to my experiments should not be far from the truth) 

 that the average radio-activity is 8, we arrive at a thickness of 12 kilometres. 



Some such mean value is necessitated by the evidence we derive from the 

 radio-activity of igneous rocks. These rocks must in many cases be derived from 

 considerable depths. Such outflows as the Deccau may indicate local sub-crustal 

 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 existence 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 kilometres, difficulties are met 

 with on this line of reasoning.' 



Proceeding now to the derivation of the results given in the table, p. 692. 



The equation k6 = qhx(l) — _) (where 6 is the temperature at the depth x, 



D being the total depth of the radio-active layer, q the radium per c.c. 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 2G kilometres. 

 I assume the mean radio-activity to be 3'5, and the average conductivity to be 

 4xl0~^, 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 couducted interior heat. To estimate 

 these we require to apportion the ob.served average surface gradient (taken as 

 32 metres 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 metres ; 

 the inner gradient is accordingly 56 metres. Hence the total temperature at the 

 base of each radio-active mass is obtained. But the geotherms proper to the 

 several depths, 18, 20, &c., kilometres, 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 tempera- 

 tures we, finally, find the rise of the geotherms. 



As conveyed in my Address, I have found on several difierent values of the 

 thickness and radio-active properties of the 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 favourable. 



' See p. 093, ante, and foot-note as bearing on the possible displacement of the 

 geotherms. 



? See Strutt, Troc. R.S„ Ixxvii. p, 483, 



