1 he Relation between Uranium and Radium. 483 



PI ] = PI 2 , and hence in the spherical triangle IiPl 2 , 



cos Iilg = cos 2 PIx + sin 2 PI L . cos IiPI 2 , 



that is cos D = sin 2 rj + cos 2 r\ . cos D , 



or 1 — cos D = cos 2 rj(l — cos D ), 



• D D o , A , 



sin -— = cos?/ . sin— . ....... (4) 



— L 



(N.B. The two above diagrams are meant merely as 

 rjugh sketches, to explain the lettering.) 



XLVI. The Relation between Uranium and Radium. — j 

 Part VII. By Frederick Soddy, M.A., F.R.S.* 



'pWO sets of measurements on the quantity of radium 

 *- now in the uranium preparations purified in 1905 to 

 1909 have been carried out this year. The results completely 

 confirm those published in conjunction with Miss Hitchins in 

 1915 1- In the two main preparations, III. and IV., con- 

 taining respectively 0*408 and 3 kilograms of uranium 

 (element), the growth of radium has proceeded according 

 to theory, with the period of average life of ionium of 

 100,000 years, if that of radium is tak^n as 2375 years. 

 This determination of the period of ionium now appears 

 to be at least as, if not more accurate than the value 

 for radium. The product of the two periods, 237,500,000 

 years, which alone is involved in these measurements, 

 may be accepted as accurate to within 5 per cent. 



The quantity of radium now present in the largest uranium 

 preparation is already such that no increase in accuracy of 

 measurement is to be anticipated on account of its further 

 growth. The growth, 2. 10~ 10 gram of radium, from 3 kilo- 

 grams of uranium in 10 years, is equal to the quantity in 

 -one milligram of pitchblende containing 60 per cent, of 

 uranium. With the methods employed a quantity much 

 greater could not be measured so accurately. Indeed the 

 measurements for the smaller preparation, III., containing 

 <0'408 kilogram of uranium, in which the initial quantity of 

 radium, relatively to the uranium, was smaller, and in which 

 the quantity of radium measured has been from 0*1 to 0*2 



* Communicated by the Author. 



t F. Soddy and Miss A. F.R. Hitchins, Phil. Mag. xxx.p.209 (1916). 



2 L 2 



