86 Prof. J. S. Townsend on the Potentials required 

 When 6 is small this equation reduces to 



»^ 2 log bja 



v-v = 



%k\\ 



which shows that V— Y is proportional to i for small currents. 



Y — Y 2ib 2 



The general equation connecting — ^ — °log bja and , 2 ^ 2 



may be solved by means of a curve having these quantities 



as ordinates, so that when V — V is determined experimentally 



2ib 2 

 for a current i the value of y 2V may be determined, and 



lid -2v.| 



the value of k may therefore be found. 



The theory may be tested by finding the values of k by 

 this method and comparing the results with the values ob- 

 tained by more direct methods, or if the theory is accepted 

 the experiments provide a simple method of rinding the 

 velocities for a large range of pressures of the gas. 



The following are the results of some experiments made 

 to investigate the values of k x and k 2 for positive and negative 

 ions in air at different pressures. The cylinder was 7*49 cm. 

 radius and the co-axial wire *0268 cm. radius. The cylinder 

 was provided with two small side tubes, one at each end, and 

 a stream of dry air that had passed through tubes of phos- 

 phorus pentoxide was drawn through the cylinder. A 

 series of experiments were made before all the moisture was 

 expelled by heating the cylinder, and the results obtained 

 with positive and negative discharges in air at three different 

 pressures are given in Tables I. and II. The pressures p 

 are given in millimetres of mercury, and the potentials V 

 and V and the currents i in electrostatic units. 



Table I. 

 Velocities ^ of positive ions under unit electrostatic force. 



p. 



v . 



Y. 



i. 



321 



* x xio 3 . 



k } p 

 760" 



176 



15-6 



17-3 



1-46 



339 



176 



15-6 



1853 



660 



1-58 



. 365 



84 



9-85 



1095 



306 



3-40 



376 



84 



9-85 



11-73 



642 



365 



404 



30 



5-75 



635 



305 



10-8 



420 



30 



575 



6-72 



560 



120 



470 



1 



