Relative Activities of Radio-Products of Thorium. 343 



I£ F 2 represents, at the end of the same interval, the 

 fraction which the number or! atoms of C then present forms 

 of the equilibrium number n' based on the original number 

 n of the ThX atoms, 



F 2 =-, =10" 2 ^/00 =0-8620/^) ... (4) 



n Ax 



Let the alpha-ray activity of equilibrium amount of G 

 be x times the activity of ThX plus Em and A. If a is 

 the initial activity of the film, and a is the activity after the 

 interval £, then 



a 



a 



= F 1 +F 2 tf, (5) 







or 



(=•-'■) 



_^o / (6) 



When the interval t is ten hours, e~ x ^ becomes so small 

 that its omission would cause an error in R of only 0*02 

 per cent., so for longer intervals this term may be neglected. 

 Similarly, after two hundred hours the term containing 



■e~~ 2 becomes entirely negligible, and then, 



F 2 = 0'8620x 1-336 ^-V = i.i52F 1 . . . (7) 



This shows that, even after a long time, the relative amount 

 of present is not that which we call the equilibrium 

 amount, which is the relative amount that would be present 

 in an old thorium preparation, but a quantity 1*152 times as 

 great. 



In the preparation of radioactively pure ThX for these 

 measurements, the ThX was separated from the pure Rt, 

 which had produced it, by precipitating the Rt with alu- 

 minium hydroxide by means of pure ammonia. The filtrate 

 contained the ThX. In order to remove any trace of Rt 

 that might remain in this ThX solution, we acidified it with 

 hydrochloric acid and added a few milligrams of thorium 

 chloride which had just been reprecipitated three times by 

 ammonia. The added thorium was then separated, thus 

 insuring the absolutely complete removal of Rt. The ThX 

 solution was concentrated to 20 c.c. and faintly acidified, a 

 few drops of mercuric chloride solution were added and the 

 mercury precipitated in the cold solution by means of 



