CONTEMPORARY ADVANCES IN PHYSICS 585 



transversely, between a pair of electrodes facing one another like the 

 plates of a condenser; and that we can measure, in the circuit con- 

 taining this oscillating voltage and these condenser-plates, the compo- 

 nents of current in phase and in quadrature with the field — then by 

 equations (7) and (8), we can determine N and g. Or if we can 

 measure either component by itself, and N in some independent way, 

 we can determine g and test the equations by comparing its value 

 with one derived from our knowledge of the flow of ions through 

 gases in a steady field. I will describe how this is done, after giving 

 equations for a more special and a more general case. 



If the coefficient g is very large compared to mn — we shall later 

 see that this is the same as saying : if an ion makes very many collisions 

 with molecules during a single cycle of the applied field — the compo- 

 nent of convection-current in quadrature with fieldstrength almost 

 vanishes. The ions describe simple-harmonic vibrations about fixed 

 centres (there is no possibility of a steady drift of the centre of vibra- 

 tion), the velocity being in phase with the field; the amplitude of 

 vibration is easily shown to be given by this expression : 



Amplitude = eEojlirvg = (jlEq/Itv. (9) 



I take this opportunity of mentioning that the quantity e/g, the 

 quotient by E of the drift-speed attained by the ion under a steady 

 field of strength E, is called the "mobility" of the ion at the pressure 

 in question, and is denoted by /x. 



If the equation of motion of the ion includes in addition to the two 

 terms in the left-hand member of equation (5) a third termfx (I have 

 written it out with this additional term farther along in the article, 

 as equation 26), the expressions for the current-components in phase 

 and in quadrature with field strength involve the coefficient /. The 

 formulae for a and e become the following: 



Ne'g - - 1 - 47riVefm-(/M^)] ^ ^^^^ 



[_if/n) — mn'J' + g^ Lif/^) ~ fnnj^ + g^ 



The term in question and its coefficient/ would naturally be introduced 

 if we were dealing with bound electrons, but it seems odd to postulate 

 such a term in speaking of freely-moving electrons or ions ; nevertheless 

 there is reason to do so, as I will later mention.^ 



When a gas containing free electrons is traversed by electromagnetic 

 waves, there is at every point an oscillating electric field having the 

 frequency of the waves, and the electrons vibrate according to the 



^ There is also an allowance for polarization which should be made if extreme 

 accuracy is desired. See Appleton & Chapman, I.e. infra. 



