and the Earth's Thermal History. 



Ill 



earth, and the other, 6', due to radio-active disintegration. 

 Ingersoll & Zobel's equation 60 (p. 89) we find — 



0" = mx + S 



VvJ 



27tyi -02 



d P 



From 



(13) 



The evaluation of the "probability integral" attached to S can be 

 obtained for different values of x/2h V t ( = - 00263#) from a table 

 on p. 166 of In°ersoll & Zobel's book. The equation for the other 

 component 6' has already been given in Part I, p. 69, as equation (9) : 



6' = Ald l l\_\-e- ax '] (9) 



From 13 and 9 the total temperature 6 = 9'-\-0", at any depth x, can 

 be calculated. The results for various depths are computed in Table V. 

 It should be noticed that A/a 2 k, the maximum possible temperature 

 due to radio-activity, is 800° C. 



Table IV. 



These results are highly satisfactory. In Part I, p. 70, assuming 

 all the earth's heat to be due to radio-activity, it was shown that at 

 a depth of 50 km. (31 miles) the most probable average temperature 

 would be about 1100° C. JSTow, assuming that, in spite of radio- 

 activity, the earth's crust has cooled down from an initial molten 

 state, we find the temperature at a depth of 50 km. to be 1088° C. 

 Moreover, in this case, the temperature continues to rise as the depth 

 increases, so that, for example, at 100 kilometres the temperature is 

 1 575° C. If all the earth's heat is due to radio-activity the maximum 

 possible temperature is not likely to be more than 1200°C. It there- 

 fore appears that the assumption of a cooling earth leads to results 

 more in keeping with the thermal necessities of igneous activity than 

 does the assumption that the earth is in thermal equilibrium, its heat 

 being maintained wholly by radio-thermal energy. It cannot be 

 argued from this that the earth's crust has been molten, but it may be 

 safely concluded that if other geological evidence points to, or requires, 

 an initial molten crust, then there is nothing in the distribution of 

 the radio-active elements to forbid belief in such a hypothesis. 



