PRESIDENTIAL ADDRESS, 085 



ttat the central interior is rising in temperature, is difficult to dispose of, altbougli 

 we can adduce the evidence of certain surface-phenomena to show that the rise 

 in temperatnre during geological time must be small or its effects in some manner 

 Icept nnder control. In a word, whether we assnme that the whole heat-loss of 

 the earth is now being made good by radio-active heating or not, Ave find, on 

 any probable value of the conductivity, a central core almost protected from loss 

 by the immense mass of heated material interposed between it and the surfac, 

 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 energy is given up, is not everlasting. The decf / of the parent substance is 

 continually reducing the amount of heat which eacli 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. And this limitation seems as destructive 

 of definite geothermal theories as the first. To understand its significance 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 eartli 

 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 case of a boiler maintained at a particular 

 temperature by a furnace 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 tlie 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 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 X (the fraction of uranium transforming each year) as approximately 

 10 '" and assume for the general mass of the earth a temperature of 1500°, 

 a specific heat of 02, 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. IJut the surface loss, as based on 

 oarth-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 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 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, 



' Professor H. A. Wilson has made a suggestive estimate of the thermal efifects of 

 vadium enclosed in the central parts of the earth {Nature, February 20 1908). 



