184 Dr. H. A. Wilson on the Electric Tntensiti/ 



It may be thought that the silence o£ the telephone at this 

 stage merely shows that the rate of intermittence is so large 

 that the note emitted by the telephone is of too high pitch to 

 be audible. This may be the case, but it is more probable 

 that when the successive discharges follow each other 

 sufficiently closely they really blend into one continuous 

 current. The high note in the telephone often suddenly 

 disappears when the current is slightly increased, and the 

 discharge at the same time acquires a much sharper outline 

 as though it had suddenly really become continuous. 



I shjill now give an account of a theory of the positive 

 column which leads to an explanation of the variation of X 

 with the current show-n in fig. 2. 



Let ?ii and 712 be the number of positive and negative 

 ions respectively present in one c.c. of the uniform positive 



column. Then, since -7- =0, where x is the distance 



measured along the axis of the discharge, we have 7Zi = ??2- 

 The current density l is given by the formula 



i = ne{vi-\-V2), 



w^here e is the charge carried by one ion and rj and V2 the 

 velocities of the positive and negative ions respectively. 

 Also Vi = ^iX and 1^2 = ^'2X5 where Aj and kc, are functions of 

 the pressure only. 



Let the number of positive or negative ions generated per 

 c.c. per sec. be q : then w^e have 



9 = 1371% 



where yS is the coefficient of recombination, and is a function 

 of the pressure. 



It has been shown by Townsend"^ that ionization is pro- 

 duced by negative ions when moving under the influence of 

 an electric field. If a is the number of negative ions pro- 

 duced by one negative ion in moving one cm., then Tow^nsend 



finds a=pf(-~ ), and he has determined the values of /( — ] 



over a large range of values of — . 



In the positive column another source of ionization besides 

 the negative ions is also present. It was found by E. Wiede- 

 mann f that the positive column emits a kind of easily ab- 

 sorbed radiation which he termed " Entladungstrahlen," and 



* Phil. Mag. February 1901. 

 t Wied. Ami. Ix. p. 269. 



