Critical Velocities for Electrons in Helium. 595 



place at 2o'G volts, because so few of: the electrons can 

 acquire the necessary energy*. It would thus seem that 

 the conditions necessary for the increases of radiation to 

 occur to any large extent at multiples of 204 volts, and the 

 conditions necessary for the indication of ionization at 

 2^'C) volts, are mutually exclusive. 



If the pressure is so adjusted that the distance over which 

 the accelerating voltage is applied is about the same as, or is 

 smaller than, the mean free path of an electron in the gas,, 

 the points at which bends, other than those at 20*4 volts and 

 25*6 volts, occur in the current-potential difference curves 

 will depend upon the length of path traversed by the electrons 

 before their energy is reduced by the retarding field to a 

 value below that at which they can make inelastic collisions. . 

 If this distance is large compared with the mean free path, 

 so that the electrons make several collisions with gas atoms, 

 the current-potential difference curve may be expected to in- 

 dicate an increased production of radiation at (25*6 + 204 = )/ 

 46'0 volts, and an increased production of ionization at 

 (25*6 + 25*6 = ) 51*2 volts. Increases of radiation and ioniza- 

 tion should occur again at 71*6 volts and at 76*8 volts r 

 respectively, and so on. If, however, this distance is about 

 equal to the mean free path or is less than this, the current- 

 potential difference curves would not be expected to show 

 breaks at the velocities just mentioned, but would be ex- 

 pected to do so when collisions between electrons and gas 

 atoms occurred which resulted in the transference, at a 

 single impact, of a larger amount of energy than that corre- 

 sponding to 25*6 volts, such, for instance, as would result in 

 both electrons being removed simultaneously from the helium 

 atom, at which point the curve should indicate an increase 

 of ionization. Such collisions would not be prevented from 

 occurring, even when the path traversed by the electrons 

 after acquiring the energy corresponding to the applied 

 accelerating potential difference, and before they have had 

 their velocity reduced below 20*4 volts, is several times the 

 mean free path (as in the case when bends at 46 0, 51*2, 

 71\6j and 76*8 volts would be expected) ; but it is probable 

 that under these conditions, the effect would be to produce a 

 flattening of the curve, instead of an increase of slope, since 



* Although, under the conditions mentioned, this statement is probably 

 true of the greater proportion of the electrons in the stream, certain 

 experiments which are referred to in Proc. Roy. Soc A. vol. xcvii. p. 1 T 

 seem to show that even when the distance traversed by an electron with 

 a velocity above the critical value is several times the mean free path,, 

 some electrons can traverse this distance without suffering an inelastic 

 collision. 



