NOVEMBEB 20, 1908] 



SCIENCE 



707 



the minute drop of temperature, would 

 probably ascribe to the continued action of 

 the furnace, heat which, although derived 

 from it in the past, should no longer be 

 regarded as indicating the heating value of 

 the combustion. Magnify the boiler to ter- 

 restrial dimensions: the minutest fall in 

 temperature of the entire mass involves 

 immense quantities of heat passing out at 

 the surface, which no longer indicate the 

 sustaining radio-thermal actions within. 



It is easy to see the nature of the difficul- 

 ties in which we thus become involved. In 

 fact, the heat escaping from the earth is 

 not a measure of the radium in the earth, 

 but necessarily includes, and for a great 

 part may possibly be referred to, the fall- 

 ing temperature, which the decay of the 

 uranium involves. If we take A (the frac- 

 tion of uranium transforming each year) 

 as approximately 10-^" and assume for the 

 general mass of the earth a temperature of 

 1,500°, a specific heat of 0.2, and, taking 

 6 X 10^^ as its mass in grams, we have, on 

 multiplying these values together, a loss in 

 calories per annum of 1.8 X 10^°. This by 

 hypothesis escapes at the surface. But the 

 surface loss, as based on earth-gradients of 

 temperature, is but 2.6 X 10^" calories. 

 We are left with 0.8 X 10^° calories as a 

 measure of the radium present. On this 

 allowance our theories, in whatever form, 

 must be shaped. Nor does it appear as if 

 relief from this restriction can be obtained 

 in any other way than by denying to the 

 interior parts of the earth the requisite 

 high thermal conductivity. Taking refuge 

 in this, we are however at once confronted 

 with the possibility of internal stores of 

 radium of which we know nothing, save 

 that they can not, probably, be very great 

 in amount. In short, I believe it will be 

 admitted on full examination of this ques- 

 tion that, while we very probably are 

 isolated thermally from a considerable part 

 of the earth's interior, the decay of the 



uranium must introduce a large subtraet- 

 ive correction upon our estimates of the 

 limiting amounts of radium which might be 

 present in the earth. 



But, finally, is there in all these difficul- 

 ties sufficient to lead us to reject the view 

 that the present loss of earth-heat may be 

 nearly or quite supplied by radium, and 

 the future cooling of the earth controlled 

 mainly by decay of the uranium? I do 

 not think there are any good grounds for 

 rejecting this view. Observe, it is the con- 

 dition towards which every planetary body 

 and every solar body containing stores of 

 uranium must tend; and apparently must 

 attain when the rate of loss of initial stores 

 of heat, diminishing as the body grows 

 colder, finally arrives at equilibrium with 

 the radio-thermal supplies. This final 

 state appears inevitable in every case un- 

 less the radio-active materials are so sub- 

 ordinate that they entirely perish before 

 the original store of heat is exhausted. 



Now, judging from the surface richness 

 in radium of the earth and the present loss 

 of terrestrial heat, it does not seem reason- 

 able to assign a subordinate influence to 

 radio-thermal actions; and it appears not 

 improbable that the earth has attained, or 

 nearly attained, this final stage of cooling. 



How, then, may we suppose the existing 

 thermal state maintained? A uniformly 

 radio-active surface layer possessing a basal 

 temperature in accordance with the re- 

 quirements of geology is, I believe, not 

 realizable on any probable estimate of the 

 allowable radium, or on any concentration 

 of it which my own experiments on igneous 

 rocks would justify. 



But we may take refuge in a less definite 

 statement, and assume a distribution by 

 means of which the existing thermal state 

 of the crust may be maintained. A spe- 

 cially rich surface layer we must recognize, 

 but this need be no more than a very few 

 miles deep ; after which the balance of the 



