a Gas in an Electrical Field. 

 For the free positive atoms 



For the free negative atoms 



For the molecules 



531 



d# A ^^ 



X»=+A2<?a 



B*x 



-2eah^ cos 3 



O* COS $ COS 3 



~ h d<r * 



Thus the equation of hydrostatic equilibrium is identically 

 satisfied. 



J jet p be the electrical density, then 



da* 



4ttp, 



/o = «wi 



*Wc 



aj, 



where I is the intensity of electrification due to tbe molecules. 

 It is sufficient to retain only squares of ea in calculating I, 

 and there is little difficulty in showing that 



where N is the number of molecules in unit volume at a part 

 the fie] 

 Hence 



By 



of the field where ^~ is zero. 



,2 

 In general the equation is 



|*? = 47r^(N 2 6^_N 1 e- / ^)_i| 7r N AaV|^ 2 . 



o 0'£ 



We see that the effect of the molecules is simply to increase 

 the specific inductive capacity, so that 



K = 1 +i^"N /iaV. 

 o 



I do not propose to discuss this value of K here. Suffice 

 it to say that with the usual estimates of N /i and a it gives 

 very nearly Professor J. J. Thomson's value of e calculated 



