On Thermionic s. 827 



and 



V o<v oz J oy 



x= — 



Vl + « : 



-o 2 (l + V 1 + 2Z l 



<? a{x—as o y 



w 



4a 2 Vl + a 2 (a?-ir ') 2 



.. # — # 



jy— V 





2 

 WrT 



(l + a /l + 2Z ±£&=5l) ) Vi + 2Z^^° \ 



\ V m iv " J V m w,f 



The positive sign in front of the square root has been taken 

 so that this value of ^ corresponds to the ions reaching the 

 plane B from the side making an acute angle with A. 



If ,r / = t i' the solution will correspond to a narrow strip 

 of hot metal lying in the plane A along the line of inter- 

 section of the two planes. In this case 



X 



m\ V mi Wq 6 / 



ia VI + a\x- xM/i + 2Z e - a i±=£o) 

 u V in Wq 



for the current to the inner surface of B. For the current 

 to the outer surface 



m\ V m ay J 



4a </T+*(a-*d\/l + 2Z L < m ~fd 



y V m iv Q - 



If we make a(x — ,r ) = ~ — c approach zero this becomes 

 ZV 



^ 4?n 2 itv 



The plane B then coincides with the plane A and we get the 

 appropriate expression for calculating the number of ions 

 returned to the emitting plane itself. This value agrees with 

 that obtained previously. 



§ 8. A Cylindrical Problem. 



We shall conclude this paper with the discussion of a 

 problem, which has presented itself in work in the laboratory, 



