536 



Mr. Gr. W. Walker on the Distribution of 



In order to test this further, let us consider how the dis- 

 tance between these maxima planes varies as the constant 

 B varies. 



Suppose 



N, = N 2 , 



so that the current 



and B : = — B 2 , 



2* 



m 



Our first integral takes the form 



m- 1 



y-Nj <> 1 + — ^ y \ icosheh X -- , r > n — 



h 1 imN^ J * / u /* J V\ V 



The least value which cosh My can have is 1 . 

 Suppose F the value of ^- where % = 0. 



QX 



1 + 



so that 



-B AF 2 



/ / 4 B^\ XT " _ _ T / h B x 2 \ - ' 



2 + 



B 



4 — 



AF 2 



When F = the appropriate solution is 



cosh— j* = coth Xx + # 



where / /t B, 2 \ 



V = b7r/^-^Ji( 1 + 7T- -rr-5 ) 

 V 2»iJN 1 V 



Here the distance (/ is infinite. 



As F 2 increases from to r— l *l 1 + — ^ U 



the proper form is 



cos h^= — 



C0 ^ n 2 sn(\* + ft*) 



where 



4 — 



AF 2 



x2=8 ^ Nl ( 1+ _^) 



8 ^( 1 lllS =1 - 



7*F S 



32^(1+ 2 -, v j 



