th 



llieory of the Striated Discharge. 989 



I! E x is the value of E in the uniform positive column, 



en 



hence 

 If 



" ewmj^ = f (El ~ Eo) ' 



4 VEE" 1 (E 1 -E o ) = (E-E ) 2 . 

 E x — E =/E , 



E-E =^E , 



4/V(l+/)(l + </)=/; 

 or, when /and g are small, 



Thus, when /is small, <? is considerably larger than /, so that 

 the maximum value of E exceeds E by an amount con- 

 siderably larger than the excess of E x over E . 



The graph representing the relation between E and x is 

 represented in fig. 1. 



Fig. 1. 

 D 



Starting from a point A where E is small, the curve 

 between A and B — the point where E = E — is represented 

 by equation (15). After passing B, the curve is repre- 

 sented by equation (16). There is a point of inflexion 

 at C where E = Ej ; the ordinates reach a maximum at D. 

 The curves before and after passing D are symmetrical 

 with respect to the vertical through D ; the ordinates reach 

 a minimum at E and the next stage of the curve is a 

 repetition of that from A to E. The graph represents a 

 periodic curve ; the portions above the horizontal line through 

 B correspond to places where the gas is ionized : at other 

 places the energy of the electrons is too small for them to 

 produce ionization. The distance between two place* where 

 the energy of the electrons is a maximum ='2(.v Y) — .r A ). 

 = 2(x B ^x A -\-x- D — .v B ), where .r A , a? B , ,v D are the values of 

 x at A, B, D. The value of # B — # A is easily found from 



