SYMPOSIUM ON RADIOACTIVITY. 49 



Here, if we call F the strength of the electric field, the particle 

 will be accelerated, along the direction of the electric field, with 



Fe 

 a force F e, that is with an acceleration — . 



m 



The time occupied by the particle in moving across a length 1 

 of the field with a speed z' is, of course, ^. 



Now knowing the acceleration and time, we may at once com- 

 pute the measurable displacement .r of the particle along the direc- 

 tion of the field ; for 



,= 1 f£(iy Eq.(ii). 



2 m V V y 



This is the whole story. The rest is the simplest of algebra ; for 

 we have here two equations each connecting the ratio — and the 



velocity v with measurable quantities. If we eliminate — and 

 V alternately, we obtain 



F 12 



2 Hrx 



and 



m 2 H^ r^ X 



The same set of measurements enables one therefore to deter- 

 mine the speed of these rays and the ratio of the charge to the 

 mass for the particles which constitute them. There is therefore 

 nothing whatever mysterious or recondite in the determination of 

 this stupendous velocity, except in so far as all the invisible pro- 

 cesses of nature are both mysterious and recondite. 

 For the a-particles Rutherford found 

 c' = 0.25x10^° cm./sec. 

 and e/m = 6000. 

 For the ;8-rays from radium, observers have found 

 f = 0.2 to 0.9 speed of light, 

 and e/m = 10,000,000. + = 10" -|-. 

 Before leaving this part of the subject it may be remarked 

 incidentally that all experimental evidence, of which an enormous 

 quantity has been furnished by Sir J. J. Thomson and his school, 

 by Professor R. A. Alillikan and others, goes to show that the 

 charge of the electron, the numerator of this ratio, is constant. 

 But experimental evidence^ equally conclusive shows that the 

 ratio e/m varies with the velocity of the particle. It is difficult 



^Kaufmann Phys. Zeit. 4, 54 0902). 



