S2S 



Prof. 0. W. Richardson : 



in which the surface A is a circular cylinder. Let the 

 radius of: the hot cylinder A be c. This is surrounded by 

 two concentric solid conducting cylinders C and B. The 

 internal and external radii of C are l>i and b respectively, 



Ficr. 2. 



£ dx 



P 



vio 



v^o 



3?=0 



\I = V 



r= o 



the internal radius o£ B being d. All the cylinders are o£ 

 indefinite length, but whereas A and B are continuous, the 

 part of C which lies between two planes perpendicular to 

 the axis of the cylinders is missing, leaving a gap whose 

 width is a. Let the common axis be taken as the axis o£ z, 

 the equations o£ these two planes being £ = and z = a. a is 

 supposed to be small compared with b or d. A and C are 

 maintained at the common potential zero, while B is main- 

 tained at a different potential v. The problem is to determine 

 the thermionic current which reaches the cylinder B. 



If a is sufficiently small the electric intensity will be 

 inappreciable, except in the region bounded by the cylinders 

 whose radii are b and d. When r is less than b we may 

 therefore regard the trajectories as rectilinear ; when r lies 

 between b and d they will be determined by the field o£ 

 force between two charged concentric cylinders together 

 with the initial velocity components. 



Consider a particle starting from any point P on A. Its 

 initial velocity may be resolved into two components, one 

 (i) parallel to the axis of the cylinders, and the other (<p) in 



