100 BELL SYSTEM TECHNICAL JOURNAL 



to the electrodes potential-differences of successively higher and 

 higher frequencies, with a certain constant peak value just inferior to 

 the sparking-potential aforesaid. Electrons and positive ions will 

 both oscillate in the field. For their oscillations, two sets of equations 

 were written down in Part I : one for the extreme case of vacuum, the 

 other for the opposite extreme case in which the collisions of the 

 electrons with atoms are very numerous in a single cycle of the voltage. 

 It is the latter extreme which fits more closely the present case of air 

 at atmospheric pressure. I repeat from Part I the equation (there 

 numbered 9) for the amplitude A of vibration of an ion of which the 

 mobility is represented by n : 



A = nejlirv. (27) 



The value is much greater for the electrons (because of their greater 

 mobility) than for the positive ions.^^ At low frequencies this matters 

 little, for both amplitudes are much greater than the gap-width and 

 nearly all particles of both kinds are swept to the electrodes. As the 

 frequency is raised, however, we eventually reach a point at which 

 the amplitude of oscillation of the positive ions is depressed below the 

 amount of the gap-width; many will then remain in the gas during 

 cycle after cycle of the voltage while the electrons, as previously, will 

 mostly be cleared out during the cycle in which they are formed. 

 The effect of the positive ions in distorting the field by their space- 

 charge will then be enhanced; the "rough inference" aforesaid is that 

 on this account (or on some other) the breakdown -voltage will then 

 be appreciably diminished. 



To test the inference, one should measure the breakdown-voltage 

 and compute the corresponding fieldstrength, at or near the "critical 

 frequency" where the diminution begins; and into equation (27) one 

 should insert the value ixE for the drift-speed of the positive ions at 

 the said fieldstrength, and for the amplitude A one should put the gap- 

 width ; and compare the resulting value of v with the observed critical 

 frequency. One is then baffled by the lack of measurements of drift- 

 speed at such high fieldstrengths (the imminence of breakdown makes 

 the customary methods of measurement difficult if not impossible). 

 For this and other reasons, no more than an order-of-magnitude 

 agreement is to be expected; and such a one is attained. Thus in 



^^ This statement remains valid, despite the fact that (27) is probably not applica- 

 ble to free electrons. It is based on the assumption that drift-speed is proportional to 

 fieldstrength, i.e. that the mean kinetic energy of random motion of the electrons is 

 independent of the field; this is certainly not true for electrons in a steady field, 

 probably not in a high-frequency field. For positive ions it is true for low field- 

 strengths, but should depart somewhat from exactness as the field is raised toward 

 the value prevailing just before breakdown. 



