146 Prof. E. Butherford on Uranium Radiation and 



be readily made. The results stow that the ions in the two 

 types of conduction are the same. 



In order to compare the velocities an apparatus similar to 

 fig. 10 was used. The ions were blown by a charged wire A, 

 and the conductivity of the gas tested immediately afterwards 

 at an electrode B, which was fixed close to A. The electrode 

 A was cylindrical and fixed centrally in the metal tube L, 

 which was connected to earth. For convenience of calcula- 

 tion it is assumed that the electric field between the cylinders 

 is the same as if the cylinders were infinitely long. 



Let a, b be the radii of the electrode A and the tube L 

 (internal) ; 



Let V be the potential of A (supposed positive). 



The electromotive intensity X (without regard to sign) at 

 a distance r from the centre of the tube is given by 



X= 



i b 

 r lofif - 



Let u l u 2 be the velocities of the positive and negative ions 

 for a potential gradient of 1 volt per cm. If the velocity is 

 proportional to the electric force at any point, the distance dr 

 traversed by the negative ion in the time dt is given by 



dr = X.u%dt, 



log e -rdr 



or dt = — ^f . 



\u 2 



Let r 2 be the distance from the centre from which the 

 negative ion can just reach the electrode in the time t taken 

 for the air to pass along the electrode. 



Then 



£ = -MU^ — ; log. 



2V? 



&e 



a 



If p 2 be the ratio of the number of the negative ions that 

 reach the electrode A to the total number passing by, 



Ta — a 

 then p 2 = ' 



Therefore 



V-a 2 

 p 2 {b*-a*) log 



— - (1) 



2 V 



