228 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1920. 



This is done in the present apparatus as diagrammatically indi- 

 cated in figure 1. The rays after arriving at the cathode face pass 

 through two very narrow parallel slits of special construction S X S 2 , 

 and the resulting thin ribbon is spread out into an electric spectrum 

 by means of the parallel plates P„ P 2 . After emerging from the 

 electric field the rays may be taken, to a first order of approximation, 

 as radiating from a virtual source Z halfway through the field on 

 the line S X S 2 . A group of these rays is now selected by means of the 

 stop or diaphragm D, and allowed to pass between the parallel poles 

 of a magnet. For simplicity the poles are taken as circular, the field 

 between them uniform and of such sign as to bend the rays in the 

 opposite direction to the foregoing electric field. 



If 6 and 4> be the angles 4 (taken algebraically) through which the 

 selected beam of rays is bent by passing through fields of strength 

 X and H, then 



6v* = TX.—(l), and 4>v = LB—{2), 



where 7, L are the lengths of the paths of the rays in the fields. 

 Equation (1) is only true for small angles, but exact enough for 

 practice. It follows that over the small range of 6 selected by the 

 diaphragm v 2 and <f>v are constant for all rays of given e/m, therefore 



dd , 28v n , 8$ , Sv 



— + — = 0, and -r + — =0, 



so that 



50_25tf> 

 d~ <j> 



when the velocity varies in a group of rays of given e/m. 



In order to illustrate in the simplest possible way how this rela- 

 tion may be used to obtain focusing, let us suppose the angles (ex- 

 aggerated in the diagram) small and the magnetic field acting as if 

 concentrated at the center O of the x^ole pieces. If the length ZO=5, 

 the group selected will be spread out to a breadth 7>B0 at O, and at 

 a farther distance r the breadth will be 



UO + r (dd + 84>) or 60 [b + rfl + ^ Y| (3) 



Now as the electric and magnetic deflections are in opposite direc- 

 tions, is a negative angle. Say 0=— 0'. Then if 4> > 20', the quan- 

 tity (3) will vanish at a value of r given by 



r(<£-20')=5.20', 



which equation appears correct within practical limits for large cir- 

 cular pole pieces. 



* In the figure these angles are greatly exaggerated for clearness. 



