through Gases between Parallel Plates. 673 



Now at the positive plate 



. R 2 6/X 2 <fy 4tt = 



87T d.£ c/l? li 2 ?/ 



while at the negative 



K 2 dX 2 _ r/?/ 47r „ 



e - ^ -y- = or -f — tt— = 0. 



But equations (4) give 



dy 



dy_d*_ 4ir(l-2e) _VH_1^2e)_ 



<fo ~ rfy ~ (l-e)(R 2 -R 1 )3/ €(l-e)(R s -B 1 ) * 



dco 



TJ 



For e = p * this gives 



•"1 "f" -"2 



Thus at the positive plate o) = 0. 

 At the negative plate 



- 4,r di + ir, ) \ + ^ a (i + i) tanh • = °' 



or x /« , 



•^ — v tann &> = 1. 



47T ^ 



Thus if P l5 Q l5 R l5 Si, &>i are the values of the respective 

 functions at the cathode, 



(Pi + Ar 1 Q ] )tanh©, = l (17) 



Suppose I is the distance between the plates, we have 



z = t4 {Rl+ * lSl} < 18 ) 



From (17) and (18) we may eliminate k L and obtain 



This is a transcendental equation giving the value of co 

 or cosh w at the cathode. 



