436 REPORT—1904. 
4. The Reaction of the Radiation on a Moving Electron. 
By Professor M. ABRAHAM. 
The moving electron gives rise to an electromagnetic field which exerts a force 
on the electron. For velocities small compared with the velocity of light, the 
expression for this force is 
(1) ReaK/ + RU +o . 
where the first term 
(2) Ki/= — Ho § 
is equal to the vector of acceleration multiplied by the electromaguetic mass, the 
existence of which was first suggested by J. J. Thomson in 1881. 
The second term 
(3) R,""= 
first given by H. A. Lorentz, is a dissipative force, coming from the reaction of 
the radiation. 
Indeed, if you consider a motion of the electron, in which the vector velocity 
g is constant up to the time ¢,, and after the time ¢,, but which has an acceleration 
during the interval ¢,<¢<¢,, the work done during this interval by the force 
K7”” is 
[ae 3K =b | “dt 3. 
1 1 
As g=0 for ¢,, ¢,, integration by parts gives 
no 2 
(4) | ae g R= —b | ae Pe pore 
where W,, is the energy, calculated by J. Larmor and others, which the waves 
formed during the interval ¢,<¢<#, carry with them, Therefore §;’’ may be 
called the dissipative force exerted by the radiation on a slowly moving 
electron. 
The electrons emitted by radio-active bodies are moving with very high 
velocities. The experiments of W. Kaufmann show that the 8-rays of radium are 
negative electrons with velocities greater than two-thirds of the velocity of light, 
and, if F. Laschen is right, the so-called y-rays contain electrons moving with 
nearly the velocity of light, and maybe the velocity of light itself is attained, 
The theory therefore must be extended to the general case of rapid motion, where 
/ —B is smaller than, but not small compared with 1. 
c 
As to the first term §;’, I have previously given the general value 
pes Cs 
() R’= OP, 
where © is the vector of the electromagnetic momentum which the electron 
carries with it. From this formula I get the general expression for the electro- 
magnetic mass. The ‘longitudinal mass,’ corresponding to acceleration in the 
direction of motion, is 
—dG 
(6) oe G=(®), 
while the ‘transverse mass’ which comes into play in the case of deviation of 
B-rays is 
(7) $1 
For slow motion, in which the momentum is a linear function of the velocity, 
the two masses are equal, but in general they are different. 
