Theory of the Striated Discharge. 987 



The variations in the intensity will not be periodic unless 

 k' 2 is greater than I 2 . Now from (11) I is a linear function 

 of p and i ; hence I 2 will be a quadratic function of these 

 quantities, while k 2 is at most a linear function of the same 

 quantities. Thus, above certain critical values for the 

 density and the current, I 2 will be greater than k 2 and 

 the solution of (10) will no longer represent a harmonic 

 variation in f but one which diminishes exponentially 

 with x ; the head of the positive column will not be striated ; 

 the energy of the electrons and the intensity of the electric 

 force will fall exponentially with x from the values they 

 possess at the head of the positive column to the values 

 Ej and X x corresponding to a uniform column. 



The expressions we have obtained involve quantities which 

 have not yet been determined with accuracy. They involve, 

 for example, the rate of recombination of electrons and 

 positive ions ; and though the rate of recombination of 

 negative and positive ions has been determined for many 

 gases, there are, as far as I know, no determinations of the 

 rate of recombination of electrons and ions. The tests we 

 are able to apply are qualitative rather than quantitative. 

 Thus from equation (9) we see that, while E x depends to 

 some extent on p and z, we may, as a very rough approxi- 

 mation in equation (13), put E 1 = E . This would make k 2 

 vary as p ; so when I is small, the distance between the 

 maxima — which is inversely proportional to k — would vary 

 as p~i. Goldstein found that the distance between the 

 striations varied as p~ m , and Wehner -(Ann. der Phi/s. xxxii. 

 p. 49) has shown that for hydrogen ??i = '53; so that in this 

 gas the distance between the striations varies very nearly 

 inversely as the square root of the density. 



Though we have not yet the data which would enable us 

 to calculate the absolute value of the distance between the 

 striations, we can, I think, show that the expression we have 

 deduced is not incompatible with known results. Thus in 

 low-pressure tubes i is often of the order of a milliampere 

 in the striated discharge ; in electrostatic measure a milli- 

 ampere is 3 x 10 6 . The energy Ex will be a little greater 

 than that corresponding to the beginning of ionization,, lot it 

 correspond to 15 volts, so that in electrostatic measure 



e 

 E x = ojr; the value of w corresponding to this value of E x is 



2*1 x 10 8 . Substituting the values in equation (11), we rind 



,_27t(3 E 1 -E ) 



~ 7 Ei-Eo ' 



3 T 2 



