460 



NA TURE 



[Sei'tember 10, igo8 



originated in the discovery that internal atomic changes 

 may prove a source of heat — can only be answered (if it 

 can be answered at all) by the facts of geological science. 



I will not stop to discuss the evidence for and against 

 a highly heated interior of the earth. I assume this 

 heated interior as the obvious and natural interpretation of 

 a large class of geological phenomena, and pass on to 

 consider certain limitations to our knowledge which have 

 to be recognised before we are in a position to enter on 

 the somewhat treacherous ground of hypotheses. 



In the first place, we appear debarred from assuming 

 that the surface and central interior of the earth are in 

 thermal connection, for it seems certain that, since the 

 remote period when (probable) convective effects became 

 arrested by reason of increasing viscosity, the thermal 

 relations of the surface and interior have become dependent 

 solely on conductivity. From this it follows if the state 

 of matter in the interior is such as Lord Kelvin assumed 

 — that is, that the conductivity and specific heat may be 

 inferred from the qualities of the surface materials — we 

 have remained in thermal isolation from the great bulk 

 of the interior for hundreds of millions of years, and 

 perhaps even for more than a thousand millions of years. 

 Assuming a diffusivity similar to that of surface rocks, 

 and starting with a temperature of 7000° F. , Kelvin found 

 that after 1000 million years of cooling there would be no 

 sensible change at a depth from the surface greater than 

 568 miles. In short, even if this great period — far beyond 

 our estimates of geological time — has elapsed since the 

 consistentior status^ the cooling surface has as yet borrowed 

 heat from only half the bulk of the earth. 



It is possible, on the other hand, that the conductivity 

 increases inwards, as Prof. Perry has contended ; and if 

 the central parts are more largely metallic, this increase 

 may be considerable. But we find ourselves here in the 

 regions of the unknown. 



With this limitation to our knowledge, the province of 

 geothermal speculation is a somewhat disheartening one. 

 Thus if with Rutherford, who first gave us a quantitative 

 estimate of the kind, we say that such and such a quantity 

 of radium per gram of the earth's mass would serve to 

 account for the 2.6x10'° calorics which, according to the 

 surface gradients, the earth is losing per annum, we can- 

 not be taken as advancing a theory of radio-active heating, 

 but only a significant quantitative estimate. For, in fact, 

 the heat emitted by radium in the interior may never 

 have reached the surface since the convective conditions 

 came to an end. 



.\nd here, depending upon the physical, limitations to 

 our knowledge of the earth's interior, a possibility has to 

 •be faced. That uranium is entirely absent from the interior 

 is, as I have said, in the highest degree unlikely. If it 

 is present, then the central parts of the earth are rising 

 . in temperature. This view, that the central interior is 

 rising in temperature, is difficult to dispose of, although 

 we can adduce the evidence of certain surface-phenomena 

 to show that the rise in temperature during geological 

 time must be small or its effects in some manner kept 

 under control. In a word, whether we assume that the 

 whole heat-loss of the earth is now being made good 

 by radio-active heating or not, we find, on any probable 

 value of the conductivity, a central core almost protected 

 from loss by the immense mass of heated material inter- 

 posed between it and the surface, and within this core 

 ' very probably a continuous source of heat. It is hard to 

 set aside any of the premisses of this argument.' 



We naturally ask, Whither does the conclusion lead us? 

 We can take comfort in a possible innocuous outcome. 

 The uranium itself, however slowly its energv is given 

 up, is not everlasting. The decay of the parent substance 

 is continually reducing the amount of heat which each 

 year may be added to the earth's central materials. And 

 the result may be that the accumulated heat will ultimately 

 pass out at the surface by conductivity, during remote 

 future times, and no physical disturbance result. 



The second limitation to our hypotheses arises from this 

 transformation and gradual disappearance of the uranium. 

 -\nd this limitation seems as destructive of definite geo- 



1 Prof. H. A. Wilson has made a suff^estive estimate of the tliermal 

 effects of radium enclosed in the central pans of the earth (Natcre, 

 February so, 1908). 



NO. 2028, VOL. 78] 



thermal theories as the first. To understand its signifi- 

 cance requires a little consideration. The fraction of 

 uranium decaying each year is vanishingly small, about 

 the ten thousand-millionth part ; but if the temperature of 

 the earth is maintained by uranium, and consequently its 

 decay involves the fall in temperature of the whole earth, 

 the quantity of heat escaping at the surface attendant on 

 the minute decrement would be enormous. An analogy may 

 help to make this clear. Consider the familiar case of a 

 boiler maintained at a particular temperature by a furnace I 

 within. Let the combustion diminish and the furnace * 

 temperature fall a little. The whole mass of the boiler 

 and its contents follow the downward movement of 

 temperature, heat of capacity escaping at the surface. An 

 observer, only noting the outflow of radiated heat and 

 unable to observe 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 terrestrial 

 dimensions : the minutest fall in temperature of the entire 

 mass involves inmicnse 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 difficulties in which 

 we thus become involved. In fact, the heat escaping from 

 the earth is not a ineasure 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 \ (the fraction of 

 uranium transforming each year) as approximately 10-'" 

 and assume for the general mass of the earth a tempera- 

 ture of 1500°, a specific heat of 02, and, taking Oxio"' 

 as its mass in grams, we have, on multiplying these values 

 together, a loss in calories per annum of 1-8x10"°. This 

 by hypothesis escapes at the surface. But the surface 

 loss, as based on earth-gradients of temperature, is but 

 2-bXio-° calories. We are left with o-8xio-° 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 cannot, 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 consider- 

 able 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 inay 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 condition 

 towards which every planetary body and every solar bodv 

 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 entirelv 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 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 possess- 

 ing a basal temperature in accordance with the require- 

 ments of geology is, I believe, not realisable on anv prob- 

 able estimate of the allowable radium, or on any concen- 

 tration of it which my own experiments on igneous rocks 

 would justif}'. 



But we may take refuge in a less definite statement, 



