36 PRESIDENTIAL ADDRESS SECTION A. 



Lord Kelvin showed many years ago. that if we can regard 

 the earth as cooHng in the manner of a small ball of uniform 

 conductivity and uniform initial temperature, and if we know 

 that initial temperature and the surface gradient, we can specify 

 the temperature at any depth, and can also tell the duration of 

 cooling. The diagram ( Fig. i ) illustrates Kelvin's result, and one 

 striking point about it is the slight extent to^ which the tempera- 

 ture of the innermost parts elf the earth would be affected by con- 

 duction even after the lapse of many millions of years. Thus if 

 the earth had been initially at 4,000° C. throughout, and its 

 surface had at once been reduced to our ordinary temperature, 

 its fall of temperature after 1,000,000 years, at a depth of 7.6 

 miles, would have been about 630 Centigrade degrees, at 15.2 

 miles only 17 degrees, and at 22.8 miles barely one-tenth of a 

 degree; while after the lapse of 100.000,000 years these falls of 

 temperature would have penetrated only ten times as far, that 

 is, the fall at the comparatively small depth of 228 miles would 

 have been less than one-tenth of a degree, while the remaining 

 3,700 miles of the radius would have been still more minutely 

 affected by the surface cooling. 



Kelvin used his calculations to determine the so-called age 

 of the earth, that is, the limits of time Vv-ithin which the conditions 

 oi the earth's surface were likely to have been such as to make 

 life possible thereon. Several things go to invalidate the sound- 

 ness of his ?ireument. but two facts are made clear by his reason- 

 ing which will always have an important bearing on our subject. 

 The first is that owing to the enormous distances and to the poor 

 conducting powers of rocks, the various layers of the earth are 

 much isolated from each other as far as the distribution of heat 

 is concerned. The second is that a wave of cooling progresses 

 slowly from the .surface inwards, so that while at first the free 

 surface itself cools most quickly, thereafter the layers that cool 

 most cjuickly are to be found always deeper and deeper as time 

 goes on. This is independent of any maintenance of temperature 

 that may arise from the presence of radium, but is slightly af- 

 fected by the heating that is generated by shrinkage. The dia- 

 gram (Fig. i) shows the curves of Kelvin's imaginary earth 

 after periods of cooling of 25,000.000 aufl 50,000.000 years re- 

 spectively, and it will be seen by the third curve, which repre- 

 sents the fall of temperature in the intervals, that a layer 30 

 miles deep had cooled most during the second 25,000,000 years. 

 It is ea.sy to calculate what layer is cooling most rapidly after 

 any given lapse of time on Kelvin's data. For instance, if apart 

 from radio-active action a fairly uniform temperature had pre- 

 vailed in the surface layers 100,000,000 years ago, the layer that 

 would now be cooling most rapidly would be only 54 miles deep, 

 and this is not unlikely to be something like the actual fact. 

 Further, if the initial temperature had been 3.700° C, as Kelvin 

 assumed, the rate of cooling of this layer would at present be 

 one Centigrade degree in loo.oco years. The shrinkage pro- 

 duced in this layer by its more rapid cooling would have tended 



