Weights of Radium and Thorium Emanations. 71 



about 100 square centimetres in area (V, fig. 1) were placed 

 parallel and attached to each other by sealing-wax round 

 their edges at a distance of about two millimetres apart ; a 

 layer of! soft wax over the sealing-wax served to make this 

 joint air-tight. At two opposite corners, glass tubes were 

 attached so that a current of air could be passed through the 

 vessel. By weighing the quantity of mercury required to 

 till the vessel, its volume was found to be 24'6 c. c. 



If t is the average time taken by a particle of gas to pass 

 through the diffusion-vessel, then, if when a current of 

 radium emanation is passed through, its concentrations before 

 entering and after leaving the diffusion-vessel are y l and y 2 

 respectively, 



V2=yie- Xt , (4) 



where X is a measure of the quantity of emanation which has 

 escaped by diffusion in the time t. 



In the case of thorium emanation, however, since the rate 

 of decay is so much more rapid than for radium emanation, 

 the concentration would change in the time taken to pass 

 through the diffusion-vessel, even though none escaped by 

 diffusion. In this case the concentration {z 2 ) just after 

 emerging from the diffusion-vessel is given by the equation 

 s 2=Si *-<k+*)< (5 ) 



where V is a measure of the quantity of thorium emanation 

 which has escaped by diffusion in the time t, z x is the con- 

 centration of the emanation just before entering the vessel, 

 and K is a constant depending on the natural rate of decay. 

 The air-current was so adjusted that t had the same value as 

 in the experiment with radium emanation. 



In order to determine the ratio —p it was necessary to 



A, 



measure y l} y 2 . ~\ and : 2 . It was further necessary to deter- 

 mine the value of Kt ; this was done by replacing the porous 

 ves-el by a non-porous glass one of the same volume, and 

 passing a current of thorium emanation through it. If, as 

 before, Z\ is the concentration of the emanation on entering 

 the glass vessel, and z 2 ' is its concentration on leaving it. 



-2 



/ ,-KV 



--i*- K ' (6) 



From equations (4), (5), and (6) 



log* 1 



x - y* . . . (7) 



log? — log -^ 



-2 "1 



The method of measuring the quantities involved will appear 

 from the foF 



