24 president's address — section a. 



evidence that the earth was once hotter than now, the only con- 

 tradiction to a " heating-up " earth. 



Assuming as before that the antiquity of the earth to be at 

 least oOO million years (/) then in that period a supply of heat of 

 3 X 10~^^ cal. gm.~^ sec.~^ [h) would have raised the interior of the 

 earth above its initial temperature. This temperature change is 

 given by 



se=ht 

 0=3 X 10-13 X 3 X 108 X 3.2 X 107.2= 14,000°C. 



where s is the specific heat of the internal material. Though loss, 

 by conduction to the surface and latent heat effects are here 

 neglected, the calculation is sufficient to show that a uniforin 

 distribution of the radio-active elements would give rise to internal 

 temperatures too high to be reconciled with the observed tempera- 

 ture gradients^. We may safely conclude that there is very much 

 less uranium, radium, and thorium in the inner portion of the 

 earth than there is in the crust, and a maximum limit may be 

 assigned to the content of radio-active elements. It would appear 

 a minimum limit may also be set. 



According to Lord Kelvin, as we have seen above, a period 

 of cooling of more than 40 million years could not have elapsed 

 between the solidification of the terrestrial crust and the establish- 

 ment of the present temperature gradient. If, however, the 

 antiquity of the earth is over 40 million years, then the tempera- 

 ture gradient has been maintained by some additional source of heat 

 than that assumed by Kelvin and the radio-activity of the rocks 

 is amply sufficient for the purpose if it extends to quite moderate 

 depths. The present temperature gradient would be maintained 

 for a very long time if the stream of heat from the interior came from 

 the radio-activity of the rocks. 



There would need to be QxlO^^/.OQ^lO^^ gms. of terrestrial 

 radium to supply the heat lost by conduction, and a layer of the 

 earth's crust 14 km. deep, if of density 3, has a mass of 2.1 x lO^^ 

 and it would give out 2.1 x 10^^x3 x 10-^3=6 x 10^2 cal./sec, 

 assuming the content of radium and thorium, and therefore the heat 

 emission, was that of the surface rocks. There is very probably at 

 least this amount of terrestrial radio-active elements, otherwise 

 it is not apparent why the temperature gradient of the crust has 

 its present value, assuming the antiquity of the earth to exceed 

 300 million years. If it greatly exceeds that period then the present 

 temperature gradient can depend but little on the secular cooling 

 of the earth from a molten state. 



Professor Strutt^ has determined the minimum age of thorianite 

 by evaluating the ratio 



the quantity of helium in the mineral at prese nt 



the rate at which the helium is produced 



1. This will be seen at once to follow from a calculation eivtn bv Strutt, Proc. Kov. 

 Soc, p. 482, 1906. 



2. Proc. Rny. Soc, 84, :!79, 1910. 



