the Structure of the Electric Field, 305 



axis of the tube is at right angles to the direction in which it 

 is moving. Thus when the field due to a corpuscle is limited 

 to a small cone, the electric field will always set itself at 

 right angles to the direction of motion of the tube, whatever 

 be the value of u, and not merely when w = c, which is the 

 only case where the lines of force become at right angles to 

 the direction of motion when they are uniformly distributed 

 in all directions when the particle is at rest. 



Momentum in the tube. 



Since the electric and magnetic forces are at right angles. 

 the momentum per unit volume is equal to the product of the 

 electric and magnetic forces divided by the square of the 

 velocity of light ; the direction of the momentum is at right 

 angles to both the electric and magnetic force, and hence, if 

 the angle of the cone is small, will be approximately at right 

 angles to the axis, and in the plane containing the axis of the 

 cone and the direction of motion. Since the magnetic force 

 is it sin 6 times the electric force, the moment per unit 



volume is . «. — : taking- into consideration the concen- 



4-7TC 2 ° 



tration of the tubes we find that the momentum in the tube 

 is equal to 



27r u e- . n 



(o c-a / . 9 a , cos" A 



and is at right angles to the axis of the cone. When the 

 motion is steady # = 7r/2 and the momentum is parallel to 

 the direction of motion of the corpuscle aud equal to 



2ir v e 2 

 (o ac 2 q 



Thus the mass of the corpuscle is 



at a<rq 

 when considered as a function of the velocity it varies in- 

 versely as q or /v/ l--^. This is the result given by the 



Principle of Relativity when the lines of force are supposed 

 to be distributed all round the corpuscle. The experiments 

 made by Bucherer on the mass of /3 particles moving with 

 different velocities show that this law agrees well with his 

 observation. 



Phil Mag. S. 6. Vol. 19. No. 110. Feb. 1910. X 



