Positive Ray Spectrograph. 711 



electric spectrum by means of the parallel plates Pi,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 SA- A group 

 of these rays is now selected by means of the stop or dia- 

 phragm 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 </> be ,the angles (taken algebraically) through 

 which the selected beam of rays is bent by passing through 

 fields of strength X and H, then 



0v 2 = lX~ (1), and <^ = LH- (2), 

 m rn 



where I, 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 

 selected by the diaphragm Ov 2 and <£r are constant for all 

 rays of given e/m, therefore 



so that 



*1+ 



e 



2Bv 



V 



= 0; 



and 





V 







S<9 

 



_28cf> 



> 





o, 



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



In order to illustrate in the simplest possible way how this 

 relation may be used to obtain focussing, let us suppose the 

 angles (exaggerated in the diagram) small and the magnetic 

 field acting as if concentrated at the centre of the pole- 

 pieces. If the length ZO = 6, the group selected will be 

 spread out to a breadth ISO at 0, and at a further distance r 

 the breadth will be 



b86 + r(80 + 8<t>) or 80p + r(l+^)]. . . (3) 



Now as the electric and magnetic deflexions are in opposite 

 directions, is a negative angle. Say 6=—0'. Then if 

 <j)>20', the quantity (3) will vanish at a value of r given by 



r(<f>^26')=:b.2d\ 



which equation appears correct within practical limits for 

 large circular pole-pieces. 



