368 ANNUAL REPOKT SMITHSONIAN INSTITUTION, 1908. 



the surface, which no longer indicate the sustaining radio-thermal 

 actions within. 



It is easy to see the nature of the difficulties 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 falling temperature, 

 which the decay of the uranium involves. If we take A (the fraction 

 of uranium transforming each year) as approximately lO"^*' 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 hj^pothesis 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 allov/ance 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 question 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 subtractive correction upon our estimates of the limiting 

 amounts of radium which might be present in the earth. 



But, finally, is there in all these difficulties 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 con- 

 trolled mainly by decay of the uranium? I do not think there are 

 any good grounds for rejecting this view. Observe, it is the condition 

 toward which every planetary body and every solar bod}^ 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 unless the radio- 

 active materials are so subordinate 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 reasonable to 

 assign a subordinate influence to radio-thermal actions ; and it apj)ears 

 not imj)robable 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 



