324 Radio-active Products present in the Atmosphere. 



number obtained, however, is only the virtual ratio, the 

 actual number being somewhat larger, since, as Blanc has 

 shown, the active deposit present, especially at some distance 

 from the ground, is not produced in situ but is carried away 

 from the surface and remains suspended in the air for a 

 considerable time before it is removed. 



We can, however, form some idea of the amount of thorium 

 present in the earth's crust from the foregoing results. 



Since radium is a disintegration product of uranium the 

 number of atoms of the radium emanation breaking up per 

 second is equal to the number of atoms of uranium breaking 

 up per second, the two being in equilibrium. 



Similarly, the numbers of atoms of thorium and the 

 corresponding emanation breaking up per second are equal. 



Now, we have seen that there is per c.c. of the atmosphere 

 near the earth's surface, 3700 times as much radium emanation 

 as thorium emanation. On account of its longer life the 

 radium emanation extends upwards into the atmosphere to a 

 much greater extent than does that of thorium ; and thus 

 there is present in the whole of the atmosphere 3700 K 

 times as much radium as thorium emanation, where K can 

 be deduced from the coefficients of diffusion and the periods 

 of the two emanations. 



For the same reason, however, it can penetrate into the 

 atmosphere from a depth in the ground equal to K times 

 that from which the thorium emanation can emerge, and so 

 comes from a volume K times as great. 



The ratio then of the amounts of the emanations of radium 

 and thorium which are in equilibrium with the uranium and 



thorium per c.c. of the earth's crust is - — r? — =3700. • 



We see from this that, taking the radioactive constants of 



the thorium and radium emanations as t^t and 



87 463,000 



respectively, there must be per c.c. of the earth's crust 1*42 

 times as many thorium as radium atoms breaking up per 

 second. 



Now, Bragg * has shown that the uranium atoms break 

 down five times as quickly as the thorium atoms, which 

 points to there being about 7 times as much thorium as 

 uranium present per c.c. of the earth's crust. Uranium and 

 thorium then exist in the earth in amounts of the same order 

 of magnitude; and in calculations bearing on the heat of the 



* Bragg, Phil. Mag. June 1906. 



