CONTEMPORARY ADVANCES IN PHYSICS 79 



a mixture in equilibrium, and the half-period of either, we can de- 

 termine the half-period of the other.'^ 



This method could be applied to estimate the half-period of radium, 

 which is so long that in the years since it was first isolated no sample 

 has yet become perceptibly feebler in emitting its rays, while the half- 

 periods of its descendants are all much shorter, and that of its child is 

 only 3.82 days and is rather accurately known. However, the volume 

 of radon gas in equilibrium with one gramme of radium (about the 

 largest quantity of radium which has ever been gathered together in 

 one place) is at normal temperature and pressure only about .0006 cc, 

 and the measurement of so small a quantity of gas is inevitably so in- 

 exact that this method cannot compete even with the not-very-accurate 

 alternative methods which we shall presently meet. However, its 

 results do not disagree with theirs. 



The most fascinating application of this method is made upon the 

 rocks of the earth, which have presumably been existing so, long that 

 there has been ample time for the longest-lived member of the uranium- 

 radium series to attain equilibrium with all of its descendants. As it 

 happens, the longest-lived member of this series is the first, uranium I. 

 Probably this is no mere accident; if uranium is the descendant of less 

 lasting ancestors, they would all be gone by now. However that may 

 be, it is a fair presumption that at least the older rocks of the earth have 

 been formed and buried long enough for the uranium in them to have 

 attained to equilibrium with its descendants. The ratio of the 

 concentration of uranium to the concentration of any member of its 

 posterity, radium for example, should then be equal to the reciprocal 

 of the ratio of their half-periods. Great numbers of samples of rock 

 from all over the world were analyzed by Rutherford and his pupils, and 

 in the laboratories of France and Germany ; and for a large proportion 

 among them the ratios of the radium content to the uranium content 

 were found to lie close to one another, and to a mean value which 

 Rutherford assigns as 3.40-10"''. Accepting this as the equilibrium- 

 ratio, and 1690 years as the half-period of radium, we obtain for the 

 half-period of uranium the truly colossal figure of 4.4 billions of years! 

 This value is substantiated, as we shall presently see, by an altogether 

 different method. ^^ 



'* In some of the older rocks of the earth, uranium and its descendants have 

 attained mutual equiUbrium, and the value of XN for uranium in such a rock is 

 equal to the rate at which the inert end-product (RaG) of the series is accumulating, 

 so that by measuring the amount of RaG already accumulated and the amount 

 of uranium still remaining one can estimate the age of the rock. Consult O. Hahn, 

 Handbtich der Physik, 22, pp. 289-306. 



1^ This is a fortunate circumstance, as it gives greater confidence in rejecting the 

 data obtained with samples of rock which yield values of the radium-to-uranium 

 ratio differing considerably from 3.4- 10~'. In some cases these deviations may be 



