(21) 
ON THE ELECTROSTATIC DEFLECTION IN A CATHODE 
EAY TUBE. 
By a. Ogg, F.E.S.S.A., Professor of Physics, South African School of 
Mines and Technology, Johannesburg. 
(1) In the ordinary Thomson cathode ray tube for determining the value 
of for cathode rays we have to allow for the irregularity of the electro- 
static field near the edges of the charged plates. Sir T. T. Thomson,* in 
determining the value of ^/^^ for rays of positive electricity, has given the 
solution for the case when the rays are parallel to the plates as they enter 
between them. It is therefore interesting to find the electrostatic deflection 
given by the complete solution when the rays are projected parallel to the 
plates but at some distance from them. The following note is written with 
the object of drawing attention to the method of the calculation, and of com- 
paring the deflection given by the complete solution with that given on the 
assumption of a uniform field. 
Two check calculations are added to test the accuracy of the method of 
calculation. 
The dimensions of the tube given are those of a tube used at Rhodes 
University College, G-rahamstown. 
(2) Parallel Plate Condenser. 
The complete solution of the semi-infinite parallel plate condenser is 
given by the Schwarzian transformation — 
z = dp - [ogT^/3 + U) . . . . (1), 
where z = x -i- iy. This transforms the infinite plate y — o, and the semi- 
infinite plate y = Ctt into the real axis of [3. The range of [3 is shown 
in the following figure : 
- 13 = 0 f3= oc 
f3 = o 7-^'.= -^ 
(3 = — oc /5 = - 1-2785 /3 = -1 
The further transformation. 
w =zD log 1 f3 (2), 
* 'Phil. Mag./ S. 6, vol. xx. No. 118, Oct., 1910. 
