126 BELL SYSTEM TECHNICAL JOURNAL 



point onward the electron-stream increases exponentially, so that 

 the current .Ve arriving at the anode is 



.Ve = AV e\p a {d- do) (4) 



In Townsend's experiments the cathode was a zinc plate, the anode a 

 film of silver spread upon a quartz plate; through little windows in 

 the silver film a beam of ultraviolet light entered in from behind, 

 crossed over the interspace and fell normally upon the zinc plate, 

 and drove electrons out of it. The zinc plate was raised and lowered 

 by a screw; the voltage-difTerence between it and the siher film was 

 altered pari passu so that the field strength in the gas remained always 

 the same. The current rose exponentially as the distance between the 

 plates was increased, and thus a was determined. A typical set of 

 data (relating to air at 4 mm. pressure, with a field strength of 700 

 volts/cm.) is plotted logarithmically in Fig. 5, the logarithm of the 

 current as ordinate and the distance from anode to cathode as abscissa. 

 The first few points lie close to a straight line, corresponding to an 

 exponential curve such as equation (4) requires; the value deduced 

 for a is 8.1G. (The distance d„ is about .35 mm. and has been ignored.) 

 Of the divergence of the later points from the straight line I will speak 

 further on. 



Such an experiment shows that there is an a — that the theory is 

 not at any rate in discord with the first obvious physical facts — and 

 it gives the value of a for the existing values of A' and p. Townsend 

 performed many such measurements with different field strangths 

 and different pressures, and so accumulated a large experimental 

 material for determining o as function of the two variables /» and X. 

 To interpret these we will begin by making the tentative and tempo- 

 rary assumjition that whenever a molecule is struck by an electron 

 having energy enough to ionize it, it is ionized — that is, a' = a. 

 Rewriting the equation (3) which expresses a' as function of p and A', 



we '^(•f lh.lt 



a' p = li exp ( - /i I -.p X) =/ (X/p) . (5) 



Therefore, if «' = «, the (|uotient of a by /> is a fiiiictiDii of X and p 

 only in the combination X/p; or, whenever the pressure and the field 

 strength are varied in the same proportion, the number of molecules 

 irinized by an electron in a centimetre of its path varies proportionally 

 with the pressure. I leave it to the reader to invent other wav's of 

 expressing (.")) in words which illumin.ite various aspects of its physical 

 meaning. 



