824 



Prof. 0. W. Richardson : 



positive roots we shall get the points where the trajectories 

 cut the surface B for the first time. The positive roots will 

 thus give us the number of ions striking the plane B from 

 the side nearest to A. We shall for the present confine our 

 attention to this case. 



The equation to the plane B is 



z-a = = ^. 

 We therefore have 



by d# 



B* " by U ' *z " ±5 * 



. (12) 



a.c ay z—z„ V v m wtf J 



3* ■(*-*)»"• 



1 +Z li=*+ 



v' 



1 + 2Z 



£ Z—Zc 



in ivq 



s/ 



1 + 2Z 



e z—z 

 in ic 2 



b<j>±_ i y-yo 



l + Z^^ + A /i + 2Z-' ' 



?n Wq 



in w r 



v 



171 Wq 



(13) 



Hence the value of % (see p. 817) is 



M_a^ = i V / 1+ ^ 1+2Z ±*=2>V 



* d# oy (^--o) 2 \ v m V / 



Hence, for example, the current to a rectangle in the plane B 

 bounded by the lines £c=a! 2 , x = x 1 , y=y 2 , and y=yi will be 



^^2 kmW0 ^^^^(l + ^l + ^^ 



47r(a-z y 



_km w0 ( Z -r )2 + (y-y )2 / / 2Z e (q-7^ Y 



where the integral with respect to dS is extended over the 

 heated part of the plane A. Changing the variables to 



2 v a — z \ V m iv 2 J 



v = lVk 



<m 



a — z \ 



1 + 





m 



