CONTEMPORARY ADVANCES IN PHYSICS 583 



a very improbable event; it is difficult to conceive of any mechanism 

 plausible or unplausible which would endow all the ions in a gas 

 with such an initial speed. We can scarcely make use of any but the 

 most general formulae; among which I choose those for the drift- 

 speed 71 and the maximum kinetic energy Km of the ions; 



1 eEo 



u = -z 1- vo, 



2icv m 



(4) 



A„ = - m 



1 bEq 



irv m 



If we knew the distribution-in-speed of the ions at the instant / — 0, 

 and they were in a vacuum (i.e., never collided with atoms), we 

 could predict their future motions. But they are not in a vacuum, 

 and we do not know their distribution-in-speed at / = 0. What use, 

 then, can be made of the equations? 



Little or nothing, I am afraid, of such definiteness as to permit of 

 exact and verifiable predictions about high-frequency discharges! 

 After all, it is of the essence of a discharge that the phenomena occur 

 in a gas where molecules and ions make collisions With each other; 

 inferences drawn from the assumption that ions never collide with 

 molecules are not likely to be close to truth. Nevertheless we may 

 make some deductions of general value. 



Thus: the expressions for the amplitude of the vibration of the ion, 

 the constant speed of the point about which it vibrates, and the 

 maximum kinetic energy acquired by the ion, all of them decrease 

 vv^hen m is increased. All of them either are inversely proportional 

 to m, or else involve a term inversely proportional to m. Therefore 

 all of them are much smaller for positive ions than for free electrons. 

 If a gas contains ions of both these kinds, the free electrons have by 

 far the most energy, oscillate the farthest and drift the fastest. On 

 this account we may often pretend that all the ions in the gas are 

 stationary, excepting only the free electrons; and I shall often make 

 this pretence. 



Again: the fact that the center of oscillation of each ion drifts 

 (except in a special case, presumably very rare) suggests that even 

 in a vacuum it is impossible to confine the ions to any restricted part 

 of the region between the electrodes. 



Finally: the value given in (4) for the maximum kinetic energy of 

 the ions, with the particular choice of zero for the value of Vq, may 

 be taken as an indication of the order of magnitude of the energy 

 which an ion might acquire in a gas not so dense but that occasionally 

 it might run without a collision for a time as long as the duration of 



