oM Mr. G. W. Walker on the Distribution of 



If the group velocities are small compared with v the velocity 

 of light the potential is given by 



Now t*, and ?/ 2 may be small compared with — =,i. e. small 



V hm 



compared with the velocity of sound, and still give large 

 currents. 



If this is so we have approximately 



XT , f, hm B, 2 . ) 



- -^£a€-*«J. 



2 NAn s 



Thus, taking K as 1 



which is an equation of the same form as before. 

 The solution is thus 



, ehy + a 1 



cosh — ^r — = — 7 — — 



2 sn (\# + £,/:) 



where 





^2 + o xT 



N 1 + 



A_JV' 



2m N 9 



.-wV^h^^b*; 



b 



-x/^-^bh&JO+kA). 



The particular form of solution adopted depends on the 

 values of the arbitrary constants introduced. When there is 

 no potential and no current we have N^N^. Again, if we 

 assert the condition that the total number of atoms, viz. 

 (N 2 + Nx + 2N ) x (vol.) is constant, we may regard N 2 , N 2 , and 

 N as known. 



Since the current is made up of two streams we cannot 



