218 Prof. F. Soddy and Miss A. F. R. Hitchins on the 



of radium in time t, and X 2 and X 3 are the radioactive con- 

 stants of ionium and radium respectively. The ratio of the 

 mass of radium in equilibrium with 1 gram of uranium is 

 taken throughout this paper to be 3*4xl0" 7 . This factor 

 agrees best with the experiments before referred to, and is 

 somewhat higher than the Rutherford and Bolt wood value, 

 recalculated to the International Standard, viz. 3*23 x 10 -7 * 

 and in better agreement with the value of Heimann and 

 Marckwald, viz. 3*33 x 10~ 7 f. 



Hence R =3'4 x 10~ 7 x 238/226 x P, 



where P is the number of uranium atoms experimented upon. 

 If M is the mass of radium formed from a mass U of uranium, 



M/U-R/Px 226/238, 

 and 



R/P:=iX 2 V 2 x 3-4 xlO- 7 x 238/226. 



Hence M/U = i\ 2 X 3 * 2 x 3*4 x 10 " 7 . 



If l/\ 3 is 2375 years t, 



±A 2 =(7-16xlO- n )W/M. 



For Preparation IV., taking the mean of the first two and 

 last two measurements given in the Table (p. 215), when t was 

 0-26 M was 41, and when t was 5'85 M was 116*5 ( X 10~ 12 g.). 

 Hence 



1/X 2 = 7-16 x 10" n X 3000 X (5-85 2 -0-26 2 )/75-5 x 10" 12 



= 97,000 years. 



In previous calculations the factor 6 instead of 7'16, 

 deduced above, has been used in these calculations. The 

 old factor would make the period 81,000 years if used above. 

 With this may be compared the previously published 70,000 

 years, deduced three years ago from this experiment as the 

 minimum period of ionium. The curve drawn through the 

 observations on Preparation IV. in fig. 1 is the theoretical 

 curve deduced from the above equation, taking 1/A, 2 as 

 100,000 years in the above equation. It agrees fairly well 

 with the experimental observations. 



Of the other preparations only Preparation III. can yet 

 give any information. In this the initial quantity of radium 

 was excessively minute and the greater relative accuracy 

 of the measurements, in consequence, and the greater age in 

 part compensate for the smallness of the quantity of uranium, 



* Sir E. Rutherford, Phil. Mag. [6] xxviii. p. 323 (1914). 



t Heimann and Marckwald, Physikal. Zeitsch. xiv. p. 303 (1913). 



\ Sir E. Rutherford, loc. cit. p. 323. 



