158 PHYSICS OF THE ELECTRON 



strength is applied, the value V of the velocity of the particles and 

 the ratio ^ of the charge carried by the particle to its apparent mass 

 m can be determined. From the direction of the deviation, the sign 

 of the electric charge carried by the particle can be deduced. 



Examined in this way, the /? rays have been shown to consist of 

 negatively charged particles projected with a velocity approaching 

 that of light. The experiments of Becquerel and Kaufmann have 

 shown that the /? rays are identical with the cathode rays produced 

 in a vacuum tube. This relationship has been established by show- 

 ing that the value of is the same for the two kinds of rays. In 

 both cases the value of ^ has been found to be about 10 7 electro- 

 magnetic units, while the corresponding value of ^ for hydrogen 

 atoms set free in the electrolysis of water is 10 4 . If the charge on the 

 /? particles or electrons as they may be termed is the same as 

 that carried by the hydrogen atom, this result shows that the appar- 

 ent mass of the electrons at slow speeds is about ^ of that of the 

 hydrogen atom. The /? particles from the radio-elements are expelled 

 with a much greater speed than the cathode ray particles in a vacuum 

 tube. The velocity of the /? particles from radium is not the same 

 for all particles, but varies between about 10 10 and 3X 10 10 cms. per 

 second. The swifter particles move with a velocity of at least 95 per 

 cent of that of light. The emission by radium of electrons with high 

 but different velocities has been utilized by Kaufmann to determine 

 the variation of ^ with speed. He found that the value of ^ 

 decreased with increase of velocity, showing that the apparent mass 

 increased with the speed. By comparison of the experimental results 

 with the mathematical theory of a moving charge, he deduced that the 

 mass of the electrons was in all probability electromagnetic in origin, 

 i. e., the apparent mass could be explained purely in terms of elec- 

 tricity in motion without the necessity of a material nucleus on which 

 the charge was distributed. J. J. Thomson, Heaviside, and others, 

 have shown that a moving charged sphere increases in apparent 

 mass with the speed, and that, for speeds small compared with the 

 velocity of light, the increase of mass m = | ^ where e is the charge 

 carried by the body and a the radius of the conducting sphere over 

 which the electricity is distributed. Kaufmann deduced that the 

 value of ^ = 1.86X10 7 for electrons of slow velocity. If the mass 

 of the electrons is electrical in origin, it is seen that a = 10~ 13 cms., 

 since the value of e = 3.4XlO~ 10 electrostatic units. The results of 

 various methods of determination agree in fixing the diameter of 

 an atom as about 10~ 8 cms. The apparent diameter of an electron 

 is thus minute compared with that of the atom itself. 



The highest velocity of the radium electrons measured by Kauf- 



