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Mr. J. H. Jeans on the 



At an anode the terminal condition has been seen to be 

 n x = or j~ = — ~rr • ^ is therefore possible for an anode 

 to be at a point such as a or a! in fig. 4, but nowhere else. 



Fig. 4. 



And similarly a cathode can only exist at a point such as 

 /3 or /3'. If then it is possible to satisfy the condition for an 

 anode and the condition for a cathode at two points on the 

 same curve, that curve must be of the fourth class. 



§ 9. The question which now suggests itself is the following : — 

 If we plot out the actual graph for y along any discharge, 

 does the curve so obtained necessarily coincide with a single 

 curve of the infinite series typified in fig. 4 ? 



If this question must be answered in the affirmative, the 

 graph must, as we have seen in the last section, be a curve of 

 the fourth class, terminated by the points a and /?. This is 

 in fact the only solution which satisfies equation (8) at 

 every point, satisfies the assumed boundary conditions at 

 the electrodes, and makes n ly n 2 , and y positive at every point. 

 It is a solution of this type that is arrived at in Thomson's 

 paper. 



The only alternative to this solution would lie in making 

 up a graph discontinuously out of a number of the curves or 

 parts of curves shown in fig. 4. We are therefore led to 

 inquire whether it is ever possible to pass from one curve to 

 another without violating physical conditions of continuity. 



Since the velocity of the ions must be continuous, #, and 



