Relative Activities of Radio-Products of Thorium. 347 



The precipitate contained the Ms 2 , Rt, B, and C, together 

 with traces of barium carbonate (due to the carbon dioxide 

 o£ the air) and Ms x associated with the barium salt. This 

 precipitate was dissolved in dilute hydrochloric acid, and the 

 aluminium reprecipitated by means of ammonia. Several 

 repetitions of this treatment removed all the barium and 

 mesothorium-one. After three days, practically all the 

 Ms 2 had decayed, and then the ThX which had formed, and 

 the B and C which were present, were removed from the 

 aluminium by a series of precipitations of the aluminium by 

 ammonia, and by precipitating mercuric chloride with hydro- 

 gen sulphide in the faintly acid solution of aluminium 

 chloride. Six to eight repetitions of each of these treat- 

 ments were found to remove more than 99*5 per cent, of the 

 ThX, B, and C which were present. After the last precipi- 

 tation of the aluminium hydroxide which corresponds to 

 time zero, the precipitate was dissolved in dilute hydrochloric 

 acid, a few milligrams of barium chloride added, and 

 barium sulphate precipitated in the boiling solution by the 

 addition of sulphuric acid. After being washed by decan- 

 tation several times, finally with alcohol, a few milligrams 

 of the barium sulphate was painted on a flat metal disk so 

 as to give a fairly uniform thin film. The activity of this 

 film was measured at intervals in the electroscope, and was 

 found to vary linearly during the first four hours, so that 

 by extrapolation to time zero the initial activity could be 

 calculated. Calling the initial activity of radiothorium free 

 from its products « , and the observed activity after an 

 interval of t days, a : then 



^=/i+/0, • (8) 



where f\ is the fraction of the original number of radio- 

 thorium atoms left after the interval t days, f 2 the fraction 

 at the time t t which the number of atoms of thorium X then 

 present forms of the equilibrium number corresponding to 

 the original number of Rt atoms, and y the activity of 

 equilibrium amounts of the active products of Rt (including 

 ThX, Em, A, B, 0, and D) based on the activity of Rt as 

 unity. If we take for Rt the period 737 days, and for ThX 

 plus its products the period 3*64 days, then X for Rt is 

 9-405 X 10" 4 and \ x for ThX is 1'904 x 10" 1 (day" 1 ) : 



fi = e- Xt , (9) 



f2=^~(e' xt + e-^) (10) 



