Rays of Positive Electricity. 567 



If y is the vertical displacement of the patch of phosphor- 

 escent light on the screen produced by the magnetic field, 

 ss the horizontal displacement due to the electrostatic field, 

 we see that 



_ Ill JL^B— 



(//T) mv mv 



mv 



where A and B are constants depending on the position of 

 the screen and the magnitudes of the electric and magnetic 

 forces. These quantities can be calculated by means of the 

 equations just given. 



Since y B 



x A 



y- _r> e 



x A ni 





We see that if the pencil is made up of rays having a con- 

 stant velocity but having all values of e/m up to a maximum 

 value, the spot of light will be spread out by the magnetic 

 and electric fields into a straight line extending a finite dis- 

 tance from the origin. While if it is made up of two sets of 



Fig-. 4. Fia:. 5. 



rays, one having the velocity v x the other the velocity v 2 , the 

 spot will be drawn out into two straight lines as in fig. 4. 



If ejm is constant and the velocities have all values up to a 

 maximum, the spot of light will be spread out into a portion 

 of a parabola, as indicated in fig. 5. 



We shall later on give examples of each of these cases. 



The discharge was produced by means of a large induction- 

 coil, giving a spark of about 50 cm. in air, with a vibrating 

 make and break apparatus. Many tubes were used in the 

 course of the investigation, the dimensions of these varied 

 slightly. The distance of the screen from the hole from which 

 the rays emerged was about 9 cm., the length of the parallel 

 plates about 3 cm., and the distance between them *3 cm. 



