224 SEE— TEMPERATURE, SECULAR COOLING [April 20, 



therefore we may pass over the diagrams which are based on very 

 high initial temperature. In Hke manner we may reject those dia- 

 grams which are based on such long periods as 1000 million years. 

 For the same reasons a period of 100 million years is much too long. 

 It seems certain that the time since the consolidation of the globe is 

 of the order of 10 million years ; and that the surface temperature 

 at the initial epoch did not much exceed 2000° Fahr., and it may 

 never have quite equaled this figure. 



But as the actual temperature rises downward, not only in virtue 

 of the surface cooling, but also in accordance with the initial distri- 

 bution of temperature throughout the globe as a whole, before cooling 

 began, we have to consider the effects of a uniform temperature of 

 say 2000°, and of an independent temperature gradient increasing 

 with the depth. The loss of heat now going on is similar to that 

 depending on the gradient alone — small in amount and very uniform 

 in its rate. Each separate part of this double flow implies rise of 

 temperature downward, and thus we may be sure that the true 

 curve of temperature is steeper than those calculated on the hypothe- 

 sis of uniform temperature. Thus the rate of augmentation of tem- 

 perature downward also becomes greater than that calculated in the 

 diagram. The effect then of the original independent gradient is to 

 considerably raise the Fourier temperatures at any depth, and to 

 maintain also a larger rate of augmentation of temperature than the 

 calculated rate. 

 § 14. Approximation to the Actual Lazv of Temperature near the 



Surface. 



If we take the Fourier gradient established by secular cooling 

 after 10 million years as giving the original rise of temperature 

 within the earth, before cooling began, which in any case can differ 

 but little from the truth, we may calculate the actual distribution of 

 temperature within the earth's crust as follows : 



1. Having computed the rate of augmentation of temperature, 

 and by integration, found the curve of temperature itself for a sur- 

 face temperature of 2000° and a duration of 10 million years, we 

 calculate likewise the same curves for a duration of 20 million years. 



2. The difference between these two sets of curves, one for 

 / = 20 million, the other for ^=10 million years, when carefully 



