580 Professor J. J. Thomson [March 22, 



have been done by substituting a photographic plate for the wille- 

 mite screen. This, however, was not the method adopted, as, in 

 addition to other inconveniences, it involves opening the tube and 

 re-pumping for each observation, a procedure which would have in- 

 volved a great expenditure of time. The method actually adopted 

 was as follows : The tube was placed in a dark room from which all 

 light was carefully excluded, the tube itself being painted over, so 

 that no light escaped from it. Under these circumstances the phos- 

 phorescence on the screen appeared bright and its boundaries well 

 defined. The observer traced in Indian ink on the outside of the 

 thin flat screen the outline of the phosphorescence. When this had 

 been satisfactorily accompHshed the discharge was stopped, the hght 

 admitted into the room, and the pattern on the screen transferred to 

 tracing-paper ; the deviations were then measured on these tracings. 



Calculation of the Magnetic and Electric Deviation of the Rays. 



If we assume the electric field to be uniform between the plates 

 and zero outside them, then we can easily show that x, the horizontal 

 deflection of a ray whose charge is e, mass m, and velocity v, is given 

 by the equation 



x = lX-^Aa + 2d\ 

 mv'^ 



where X is the force between the plates, I the length of path of the 



rays between the plates, and d the distance of the screen from the 



nearer end of the parallel plates. 



To find the deflection due to the magnetic field, we have, if p is 



the radius of curvature of the path at a point where the magnetic 



force is H. 



m v'^ TT 

 = tiev, 



P 



or 



p mv 

 If y is the vertical displacement of the particle, we have 



- = -^-| approximately, 

 p a z 



where z is measured along the path of the ray. Hence 



d^ = g H; 



d z' m V 



-.^[.fT-"] ™ 



