PROFESSOR W. THOMSON ON THE SECULAR COOLING OF THE EARTH. 163 



16. If, now, we suppose the time to be 100 million years from the commence- 

 ment of the variation, the equation becomes 



dv V 



160000000000 



6^,2; "354000 



The diagram, therefore, shows the variation of temperature which would now 

 exist in the earth, if, its whole mass being- first solid and at one temperature 100 

 million years ago, the temperature of its surface had been everywhere suddenly 

 lowered by V degrees, and kept permanently at this lower temperature : the 

 scales used being as follows : — 



(1) For depth below the surface, — scale along OX, 10 quarter inches, or a, 

 represents 400,000 feet. 



(2) For rate of increase of temperature per foot of depth, — scale of ordinates 



parallel to OY, 10 half inches, or h, represents g^^ of V per foot. If, for 



example, F= 7000°, this scale will be such that 10 half inches, or h, represents ~ 

 of a degree per foot. 



(3) For excess of temperature, — scale of ordinates parallel to OY, 10 half inches, 



or 5, represents . , , or 7900°, if V = 7000°. 



Thus the rate of increase of temperature from the surface downwards would 

 be sensibly ^ of a degree per foot for the first 100,000 feet or so. Below that 

 depth the rate of increase per foot would begin to diminish sensibly. At 400,000 

 feet it would have diminished to about j^ of a degree per foot. At 800,000 feet 

 it would have diminished to less than — of its initial value, — that is to say, to 

 less than ^ of a degree per foot ; and so on, rapidly diminishing, as shown in 



the curve. Such is, on the whole, the most probable representation of the earth's 

 present temperature, at depths of from 100 feet, where the annual variations cease 

 to be sensible, to 100 miles ; below which the whole mass, or all except a nucleus 

 cool from the beginning, is (whether liquid or solid) probably at, or very nearly 

 at, the proper melting temperature for the pressure at each depth. 



17. The theory indicated above throws light on the question so often 

 discussed — ^Can terrestrial heat have influenced climate through long geological 

 periods ? and allows us to answer it very decidedly in the negative. There would 

 be an increment of temperature at the rate of 2° Fahr. per foot downwards near 

 the surface, 10,000 years after the beginning of the cooling, in the case we have 

 supposed. The radiation from earth and atmosphere into space (of which we 

 have yet no satisfactory absolute measurement) would almost certainly be so 

 rapid in the earth's actual circumstances, as not to allow a rate of increase of 

 2° Fahr. per foot underground to augment sensibly the temperature of the sur- 



