306 



Sir J. J. Thomson on a Theory of 



Ksr. 2. 



For slowly moving corpuscles the expression for the mass 



is — instead of ^ -=- , which is the value when the lines 



g) era 6 (fa 



of force are supposed to be uniformly distributed. Since 

 '2ir/(o is a large quantity the value of a founded on the sup- 

 position that the lines of force are concentrated in a cone 

 will be much larger than the value calculated on the basis 

 that the lines of force are uniformly distributed. 



On the effects produced when a moving corpuscle is 

 suddenly stopped. 



Let represent the corpuscle moving forward horizontally, 

 and suppose when it is at A its velocity is reduced by u in a 

 short time t. Let us consider the configu- 

 ration of the tube after a time t measured 

 from the instant when the stoppage began. 

 Before the corpuscle was checked the tube 



was at right angles to its direction of motion, 



... . 



L e. it was vertical. Now any disturbance 



is propagated with a finite velocity c. c being 

 the velocity of light. Hence, if we describe 

 a sphere whose radius is ct and whose centre 

 is at the centre of the corpuscle, the region 

 outside this sphere will be unaffected by the 

 stoppage of the particle, and the tube of force 

 in this region will occupy the position it would 

 have done if the particle had gone on moving 

 uniformly. Again, the fact that the velo- 

 city of the corpuscle has been reduced will 

 have been telegraphed to a distance c(t — r) 

 from the centre of the corpuscle, so that 

 inside a sphere of this radius the tube of 

 force will have the reduced velocity, hence 

 since the tube preserves its continuity it will 



have a configuration similar to that 



repre- 



sented in fig. 2, where the portion inside a 



sphere whose radius OAis c(t — t) is vertical, 



and the portion outside a sphere whose radius OA / is equal 



to ct is also vertical, but separated by a distance u{t — r) or, 



since we take t to be small compared with t, ut approximately 



from the portion inside the smaller sphere. 



The portion of the tube of force connecting the two vertical 

 portions will be constricted, and hence the electric force in 

 this portion will be greater than it would have been at the 

 same distance from the corpuscle if the latter had not been 

 stopped. 



