102 BELL SYSTEM TECHNICAL JOURNAL 



voltage gradually till suddenly a visible discharge appears; the last 

 previous reading of the voltage is then recorded. Some physicists have 

 reported that the advent of the self-sustaining glow is difficult to 

 observe, or capricious and unreproducible; others mention nothing of 

 the sort. 



There are now two independent variables, frequency and pressure, 

 instead of the former only; this makes it harder to view the data. So 

 long as the frequency is held constant, the curv^e of breakdown- 

 potential versus pressure usually has the familiar form, characteristic 

 of steady as well as alternating voltages: it is concave upward, with a 

 single minimum, perhaps deep and striking, perhaps so flat as scarcely 

 to be visible. There is consequently for each frequency an optimum 

 pressure, Psm say, for the onset of the glow; at pressures either lower 

 or higher than Psm, the critical potential is above its minimum value 

 Vam- In general terms, the reason is this: at high pressures, ionization 

 is restricted by the fact that in their numerous collisions, the electrons 

 lose energy so often that they seldom amass enough to ionize the 

 molecules — at low pressures, it is restricted by the fact that there are 

 few collisions — at the intermediate pressure Psm, the best compromise 

 prevails between the two disadvantages. There can be little doubt 

 that if one were to vary the distance between the electrodes in lieu 

 of the pressure, the effect would be the same, according to Paschen's 

 law that breakdown-potentials depend on the product of pressure and 

 distance. ^^ 



When one compares the breakdown-potential versus pressure or 

 Vs-vs-p curves for various frequencies, the results are often far from 

 simple, and different observations are sometimes hard to reconcile; 

 even when one considers only undamped sinusoidal wavetrains, as 

 I shall do. 



Thus Hulburt, working with oxygen and hydrogen at pressures of 

 1 to 5 mm., in tubes with internal electrodes 5 to 30 mm. apart, experi- 

 mented with steady voltages, with 50-cycle A.C., and with the high 

 frequencies 0.86-10^ and 5.3-10^; and he detected no variation of the 

 voltage for the onset of the glow over all this range. Likewise Rohde, 

 working with a number of gases (oxygen, hydrogen, nitrogen, argon, 

 neon, helium, mercury) in tubes with electrodes (usually internal) 

 19 or 38 mm. apart, applied frequencies ranging from 10^ to 1.5-10^. 

 Up to about 10'^ the breakdown-voltage scarcely changes; thence- 



1' "Electrical Phenomena in Gases," pp. 304-308. Paschen's law in this form is 

 valid only for broad plane-parallel electrodes; to make it hold for curved electrodes, 

 their radii of curvature should be varied in the direct ratio of the distance or the 

 inverse ratio of the pressure. 



