﻿1038 Prof. Townsend and Mr. Bailey on the 



Z/p were on an average less by about 2 per cent, than those- 

 obtained in the previous experiments * with hydrogen. 



5. The velocity of agitation u of the electrons is deduced 

 from measurements of the ratio of the charge received by 

 the central electrode E 2 to the sum of the charges received 

 by the electrodes E 1? E 2 , and E 3 . 



The theory of the method lias already been explained f in* 

 detail, and may be expressed briefly as follows : — When a 

 stream of electrons moves under an electric force, the 

 number per cubic centimetre at any point is a function of 

 the quantity eZ/mu 2 when the steady state corresponding to- 

 the force Z is attained, e being the atomic charge, Z the 

 electric force and mu 2 /2 the energy of agitation of the 

 electrons. If MH 2 /2 be the energy of agitation of a mole- 

 cule of a gas at 15° C, the velocity of agitation u of an 

 electron would be 1*15X10 7 cm. per sec. if its energy of 

 agitation were equal to MXl 2 /2. When moving under an 

 electric force the energy of agitation of the electron is much 

 greater than this quantity, and if mu 2 = kM.fl 2 the quantity 

 eZ/mu 2 becomes eZ/kMfl 2 . This ratio may be written 

 N^Z/^NMH 2 , where N is the number of molecules per cubic 

 centimetre of a gas at 760 mm. pressure and 15° C. ; and 

 since trie quantities Ne and NMI1 2 are known accurately, 

 the number of electrons per cubic centimetre at any point of 

 the stream is a function of Z/k and known constants. 



The ratio R = n 2 / (n A + n 2 + n 3 ) of the charge n 2 received 

 by the central electrode E 2 to the sum of the charges n^ n 2 , n s 

 received by the three electrodes E h E 2 , E 3 may therefore be 

 expressed in terms of the ratio Z/k, and the values of R 

 corresponding to definite values of Z/k may be computet]. 

 The value of R for any value of Z/k may be represented by 

 means of a curve, the form of the curve depending on the 

 sizes of the receiving electrodes and the size and position of 

 the slit. 



It was necessary therefore to calculate the values of R 

 for different values of Z/k when the centre of the stream 

 fell to one side of the centre of the electrode E 2 Avith the 

 slit two and four centimetres from the electrodes E. As it 

 is difficult to construct the apparatus so chat the displace- 

 ment b of the centre of the stream from the centre of E 2 is 

 some exact fraction of a millimetre, the points on four curves 

 were calculated which are given in fig. 3. 



The curves 1 give R for receiving electrodes of the dimen- 

 sions shown in figs. 1 and 2, with the slit two centimetres 



* Phil. Mag. Dec. 1921. 



t J. S. Townsend, Proc. Eoy. Soc. A, lxxxi. p. 464 (1908). 



