342 Prof. McCoy and Dr. Viol : Chemical Properties and 



ThX should be entirely free, initially, from all the other 

 radio-bodies. It is also necessary that the preparation should 

 not lose appreciable proportions of the emanation. We used 

 barium sulphate preparations of ThX and found them much 

 less emanating than highly-heated oxides, such, as ferric 

 oxide. Our preparations were so active that exceedingly 

 thin films were used, containing a milligram or less of barium 

 sulphate. Thus, appreciable absorption of the alpha rays in 

 the film itself was avoided. 



The mathematical treatment of the problem has been given 

 by Rutherford *. If R is the number of atoms of C formed 

 in t seconds from n atoms of ThX originally present, then 



H = n(ae-^ t + be- X ^-bce-^ t ) J . . . . (1) 

 where 



'M-Vo .09 r v 1 fk-2 



c — ^lh =1-242 x 10" 3 . 



(Xi— ^3) (^2 — X 3 ) 



"We have taken the decay constants in reciprocal seconds, as 

 follows : — 



ThX, \ 1 = 2-204 X 10- 6 ; B, X a =l"816 x 10" 5 , 

 and 



C, X 3 = 1-899 xlO- 4 , 



the periods corresponding being 3*64 days, 10*60 hours, and 

 60 '8 minutes. The details of our measurements to confirm 

 these constants are given in Section IV. of this paper. 

 Then 



R =. mx 10" 2 (l-336 ^-V_l-460 6'-V + 0-l242^-Vj, (2) 

 or R = rcxlO- 2 /0), 



where f (e) is the expression in parenthesis. If n r represents 

 the equilibrium number of atoms of G corresponding to n 

 atoms of ThX, then 



if F l represents the fraction of the original number of atoms 

 of ThX left after an interval t, then, 



F 1 = ^-V (3) 



* • Radioactivity,' 2nd ed., p. 360. We may neglect ThEm and A in 

 the equation, since after ten minutes the equilibrium proportions of these 

 products will be present with the ThX. 



