104 Arthur Holmes — Radio-activity 



additional difficulty of maintaining belief in a molten earth which 

 the new source of energy had introduced. This difficulty, however, 

 which has been very generally realized, is really one of time. If the 

 earth lias cooled down at all, the effect of radio-activity will have 

 been to slow down the rate of secular cooling. What the presence of 

 radio-activity does prove in such a case is that the earth must be very 

 much older than the twenty or forty million years allowed by Kelvin 

 for the process of cooling from a molten state to present conditions. 



8. The Age of the Earth. 



A very simple method will serve to show approximately the effect 

 of radio-activity on the normal rate of cooling, and on the age of the 

 earth to be deduced from it. The temperature gradient dO/dx is 

 inversely proportional to the square root of the time of cooling, t, 

 which is, on this view, the age of the earth (i.e. dO/dx oc 1 /y/t). If 

 five-sixths of the present temperature gradient be due to radio-activity, 

 then only one-sixth can be attributed to cooling. The above formula 

 indicates that if the gradient dojdx is reduced to one-sixth, then the 

 time of cooling, t, must be thirty-six times as great. The effect of radio- 

 activity is thus to raise Kelvin's limits from twenty and forty million 

 years to 720 and 1,440 million years. A more rigid mathematical 

 treatment shows that radio-activity is even more powerful in slowing 

 down the rate of cooling than appears from these figures, and it 

 becomes clear that if ever the earth was molten at the surface it 

 could not, with the existing distribution of the radio-active elements, 

 have cooled down to its present state in less than 1,600 million years. 



It is therefore of interest to know that an independent method of 

 determining geological time — though also based on radio-activity — 

 gives results which for the oldest rocks closely approach this figure. 

 Every uranium-bearing mineral is like a clock ticking out its age in 

 molecules of helium and lead. Helium is generated also during the 

 decay of thorium, but the end-product of thorium is still unrecognized. 

 It cannot be an equivalent of lead, since in thorium minerals this 

 element does not accumulate in geological time. 1 In uranium-bearing 

 minerals, however, lead does accumulate, and the rate of its production 

 is accurately known. 2 In any primary mineral the amount of 

 uranium engaged in the generation of lead, and the amount of lead 

 which has accumulated, factors which can generally be estimated 

 by analysis, suffice to determine the age of the mineral. The geo- 

 logical time scale, as far as at present determined, is given on p. 105. 



The oldest rocks in this table, which appear to be the gneissose 

 granites of Mozambique, are probably not more ancient than the 

 oldest rocks in any of the great Archaean areas. In Fenno-Scandia 

 and North America there are rocks of much greater geological 

 antiquity than those for which ages are here given. There is, 

 naturally, great difficulty in obtaining suitable minerals for analysis. 



1 Holmes & Lawson, Phil. Mag., vol. xxviii, p. 823, 1914. 



~ For a full discussion of this method of estimating the age of minerals, see 

 Proc. Eoy. Soc, A, vol. lxxxv, p. 248, 1911, and The Age of the Earth, 

 ch. x, 1913. 



