356 



Sir W. Eamsay and Mr. F. Soddy. 



[Apr. 14, 



experiment. More stringent precautions had been taken to free the 

 capillary tube from gas in the second experiment than in the first, and 

 yet bubbles appeared below the surface of the mercury. It may be 

 that owing to the quality of the glass of which the first tube was made, 

 the helium found means to enter into its substance more easily than 

 into that of the second. But at any rate, the volume produced is of 

 the same order, as the following considerations will show. 



On the view that the emanation results from a definite fraction of 

 the radium disintegrating per second, this fraction can be calculated 

 from the volume of the emanation, and the time of accumulation. The 

 emanation accumulates until the rate of production is balanced by the 

 rate of disappearance, and then the quantity remains constant. Let 

 Q be the equilibrium quantity, and Q« the quantity present after 

 time t, 



where t is expressed in seconds, and A is a constant representing the 

 proportion of the emanation changing per second, and equals 1/463,000.* 

 The radium bromide employed weighed about 60 milligrammes. 

 Assuming that the compound contained about half its weight of the 

 element (radium, 225 ; bromine + 2H 2 0, 196), the quantity of radium 

 may be taken as about 0*03 gramme. In the first experiment, the 

 time of accumulation t was 8 days = 691,200 seconds; Q t therefore 

 equals 0*775 Q lQ0 . The volume taken (0*027 cub. mm.) in the first 

 experiment was that at the end of the first day, and a correction must 

 be applied to allow for the amount that had changed in this interval. 

 The quantity remaining after the lapse of 1 day is 0*83 of the 

 initial quantity. The volume, 0*027 cub. mm., is therefore 



0*83 x 0*775 Q 1oo = 0*643 Q^. 



The average life of the particle in a system in which a constant 

 fraction A of the number of particles changes per second can be shown 

 to be 1/X. The equilibrium quantity, Q^, is the quantity produced 

 in the period of average life of the atom of the emanation, or 

 Q x == Q /X = 463,000 Q , where Q is the quantity produced per 

 second. And 0*643 Q lQ0 = 297,830 Q . The volume of Q is thus 

 0*027/297,830 - 0*9 x 10~ 7 cub. mm. This is in the case of 0*03 

 gramme of radium; 1 gramme of radium, therefore, produces 

 3 x 10~ 6 cub. mm. of emanation per second. 



Since the emanation resembles the gases of the argon family in 

 chemical inertness, its molecule is probably monatomic, and its atomic 

 weight must be twice its density in terms of hydrogen as unity. The 

 density is not accurately known ; but diffusion experiments indicate a 

 value of about 80. The atomic weight being therefore in the neigh- 



* Rutherford and Soddy, ' Phil. Mag./ 1903, 6, vol. 5, pp. 445 and 576. 



