986 Sir J. J. Thomson 



on a 



would produce a diminution o£ the electric intensity along 

 the positive column. 



Let us now consider the case when, though the positive 

 column is not quite uniform, the fluctuations in E are small 

 compared with their average value. When this is so we 

 may put in equation (7) E=E! + f, where E x is the value 

 of E along the uniform positive column and £ a quantity 

 whose squares and higher powers may be neglected ; if we 

 do this and assume q = icp(E — E )j Ave get 



iJ +2 ^=-^ ■ ■ ■ ■ ■ do) 



si 



where 2l = ap + \ + ^ . h +ecpE l \ . . .-(11) 



„ eq E x f3i E x 



or, since ecpEk= f B^W = we W^W > 



2l — ap +\+ ^ ^ — , . . . (12) 



r we Li — E v J 



where ^ = {2E 1 /??ij* 



krreHp y _ , Zirehp (3Ei-E ) 

 /l ~^W 2 {6hl ^-—p E^ ' (13) 



27rei 1 (3Ex-E ) 

 u 1 Ei Ei — E 



(14) 



If k is greater than /, the solution of (10) is 



J = Ae-^cos{(P-Z 2 )^ + e}. 



This equation represents a series of periodic variations in f 

 of diminishing amplitude ; it indicates that at the head of 

 the positive column — i. e., the end nearest to the cathode — 

 there will be periodic variations in the intensity of the lumi- 

 nosity, and that the intensity of these variations diminishes 

 as the distance from the head of the positive column 

 increases. Thus there will be a maximum of luminosity 

 at the head of the positive column followed by other 

 maxima at regularly spaced intervals, the intensity of these 

 maxima getting fainter and fainter. These maxima are 

 superposed on a uniform distribution of luminosity, so that 

 there are no absolutely dark spaces. This is just what we 

 observe when the positive column first begins to show 

 striation ; the striations can at first only be seen near the 

 head of the column, and get fainter and fainter as the 

 distance from the head increases. 



