C14 Prof. J. S. Townsend on the Genesis of Ions 



It may be seen from this result thnt the sparking potential 

 v'\_^=a'^'\ depends only on the quantity of gas a'x/> between 

 the electrodes. 



Substituting in the aboye expression the general equations 

 found for a and ^ in terms of the force and pressure, the 

 followino' yalue of o! is obtained : 



P 

 or 



■og/(|)-lo.<|) 



Wf)-^(|)) 



which shows that ?'^ is a function of the product o!p. 



This property of the sparking potential for a gas between 

 parallel plates has been well established experimentally. 

 The researches made recently by W. R. Carr (Phil Trans, 

 yol. cci. 1903) over a large range of pressures and potentials 

 confirm this result, which was obtained previously by De La 

 Rue and MuUer (Phil. Trans. \o\. clxxi. 1879) and others 

 oyer smaller ranges of pressures and potentials. 



Since the functions ,/" and (^ have not yet been determined 

 in simple algebraical forms, the relation between v' and a'p 

 as found from theoretical considerations may be shown by 

 means of a curA'e. 



Thus in Table 11. for air at one millimetre pressure when 

 X=:350, a = 5*25, and y8 = '0141, the sparking distance in 

 centimetres is given by the formula 



log 5-25 ^log -QUI 

 «- -^3 =113, 



so that i/ = 350x 1-13 = 395, and pa' = l-l?>. 



The values of v' and pa' deduced in a similar manner from 

 the other experiments with air are marked on the accom- 

 panying diagram (fig. 4) by the small crosses. The values 

 of v' and p x a' calculated from the values of a and /5 for 

 hydrogen are represented in the diagram fig. 5 (p. 617). The 

 curves passing through these points correspond very accu- 

 rately wnth the curves found experimentally. Some values 

 of sparking potentials were determined experimentally with 

 the same apparatus which was used to determine the quan- 

 tities q. When making the experiments it was found neces- 

 SMry to have a large resistance (50,000 ohms) in the battery 

 circuity in order that the current should not rise too high 



