244 Mr. G. ^y. Walker on the 



behveen the two pairs of plates, and displaced from the 

 symmetrical position. 



This problem is soluble by the Schwarzian method, so that 

 I think it would be superfluous to giye the details of the 

 solution. I shall therefore indicate the transformations, and 

 giye the final solution : — 



X •*- —a -\-a -^ X 



A < -Jci > 



--plane 

 —IS <;3><3> +1 



V 



— c o -{-d 



<y> 



w-plane 



-I -c o b +1 



The plane of the needle is a plane of symmetry, and we 

 may transform the given problem in the ;:-p]ane into the 

 problem indicated in the u-plane, the points of correspondence 

 being marked as I haye shown. 



The transformation is 



2S r ic 1 T zr f 1 .TT ) 



77 la^ — 1 2 ®zr — 1 2 i 



Let 2a be the breadth of the air-gap, 

 2/3 „ ^ „ „ needle, 



7 ;, displacement from the zero position, 

 23 ,, distance between the upper and lower pair 

 of plates. 



Then we haye the following equations to determine a. hy 

 and c : — 



a 1, a + 1 TT a 



oJ^-i^'°--^l = 2-l .... (9) 



1, 1 + ?' I IT ,8 + 7 ,,„. 



2 ^\ — c a- — \ 2 ^ ^ 



We may note that these give a real value for a greater 

 than unity, and real values for h and c less than unity when 

 7 is < ^. When 7 is zero, the values of h and c are equal. 



