114 BELL SYSTEM TECHNICAL JOURNAL 



distortion by space-charge, another dubious assumption!). By the 

 equation we derive 0.3 electron-volts for the maximum energy of those 

 electrons for which Vq = — a value barely more than one per cent of 

 the resonance-potential of helium, the least amount which a normal 

 helium atom can absorb as the first stage toward ionization ! If we 

 apply the equation to some of H. Gutton's results, the conclusions 

 are equally startling; thus, putting 2 for E^ and 2-10^ for v (values 

 observed with hydrogen in a tube 20 cm. long), we find 0.9 electron- 

 volts for the maximum energy. 



Were the discrepancies between these values of K^v and the reso- 

 nance-potentials of the gases somewhat smaller — were they, say, of 

 the order of fifty per cent — they could readily be excused. Occasional 

 electrons, for instance, might make collisions with atoms in just such 

 ways and at just such times as to increase their accumulation of 

 energy; thus, an electron which had started from rest (fo = 0) and 

 had been speeded up to its utmost during the first half-cycle of the 

 field and was about to be slowed down again, might have its velocity 

 reversed by an elastic impact just at the end at that first half-cycle, 

 so that the second half-cycle would speed it up still more (Hiede- 

 mann's idea). Or, occasional electrons might acquire a fund of 

 energy in other ways, and have a considerable value of kinetic energy 

 (l/2)m(i'o^ + Vn^) at the instant / = 0; the form of the right-hand 

 member of equation (28) now shows that the high-frequency field 

 would augment their vis viva, not merely by the amount which we 

 have just computed, but by an extra amount proportional to Vq. 

 But a discrepancy of two orders of magnitude seems too large to be 

 explained in such a way; and although it is impossible to make any 

 positive afifirmation, I suspect that there must be a permanent dis- 

 tortion of the field by space-charge, the mean value of the potential 

 in the middle of the gas differing by several volts from its mean value 

 near the electrodes — being presumably more positive, owing to an 

 accumulation of positive ions.^^ 



We ought now to compute the distance D through which a free 



electron moves in the high-frequency field, while its energy is mounting 



from zero (or the minimum value, whatever that may be) to the 



greatest value which it attains. For, if it should turn out that this 



distance is not more than a small fraction of the electronic mean-free- 



"This is the condition in the direct-current "low-voltage arc" ("Electrical 

 Phenomena in Gases," pp. 383-386) where the P.D. between anode and cathode is 

 less than the resonance-potential of the gas, but the P.D. between a certain region 

 of the gas on the one hand and the cathode on the other is at least as great as the 

 resonance-potential. In the low-voltage arc the electrons are expelled from the 

 cathode by heat independently applied, so that there is no need of a cathode-fall. 



