CONTEMPORARY ADVANCES IN PHYSICS 



115 



path in gases under the conditions of the actual experiments, then the 

 foregoing theory would be vitiated at the start; electrons would 

 seldom or never acquire the maximum amount of energy for which 

 we have derived the general formula and which we have computed 

 in certain special cases. 



The distance D is described during a half-cycle of the high-frequency 

 field, but the phase at which that half-cycle must be supposed to 

 begin depends on Vq, which makes the problem intricate. If we put 

 vq = 0, the electron starts from rest at / = and attains its maximum 

 speed at t = l/(2i/), after traversing the distance given by the first of 

 the following formulae. If we put for Vo the particular value which 

 corresponds to an electron describing oscillations about a fixed centre, 

 the doubled amplitude of these oscillations is what we want; it is 

 given by the second formula: 



D = -P- 



^ ^ = 2M-w(^ 



2ir m v^ 



D 



1 c F 

 ^r-2--2= 8.95-1013 



{vo = 0) 



{vo = — eEjlirvm), 



{ZZ) 



Ev standing as before for the amplitude of the fieldstrength in volts 

 per centimeter. 



The most which we can infer from these formulae is, that when we find 

 recorded a value of E^ (amplitude of the fieldstrength in the self- 

 sustaining high-frequency glow) we should evaluate the product 

 lO^^E^/p^, and compare it with the electronic mean-free-path in the 

 gas in question at the pressure in question ; if it is much smaller than 

 the electronic mean-free-path the foregoing theory is worth whatever 

 can be got out of it; if it is much larger than the electronic mean-free- 

 path the theory is worthless. For the two special cases (from Rohde 

 and Gutton) for which I have just computed the values of Kmv, those 

 of the product lO^^E^/v'^ come out as 0.06 cm. and 0.50 cm. respectively. 

 The pressure of the gases (helium and hydrogen respectively) amounted 

 in the two experiments to 0.400 and 0.001 mm. Hg respectively. 

 Now the measurements of electronic mean-free-path for electrons of 

 these speeds are imprecise and uncertain, and the concept itself is 

 vague. The values which it is probably best to take are those derived 

 by Townsend and his school from measurements of the diffusion of 

 free electrons in gases.^^ That for hydrogen at .001 mm. Hg is so 

 high (of the order of 40 cm.) that the theory is justified by an ample 

 margin; that for helium at 0.4 mm. Hg (of the order of 0.1 mm.) is 



" "Electrical Phenomena in Gases," pp. 248-252. 



