APP. a] CALCULATION OF RADIATION 215 



which may be written, with a as the radius, m the mass, 

 and u as the acceleration, of the revolving electron 



man 2 



where v is the velocity of light. 



The fundamental expression for the amount of energy 

 emitted per second as waves in the ether, by a moving 

 charge e, was given by Larmor in Phil. Mag., December, 

 1897, page 512, so far as I know for the first time; 

 also in JZiher and Matter, page 227, namely 



This agrees with the above calculation, since it = u 2 /b = bco 2 ; 

 u being acceleration. Now ju.e 2 may be taken as 10 ~ 40 

 gramme-centimetre, according to most recent measure- 

 ments; and in a circular orbit of radius r the acceler- 

 ation is 



therefore the radiating power of a single electron, so 

 moving, is 



9 ..,,2 9 y TO-* 



w Ai= "9xio"> x 1Q46= 2 x 10 ~ 5 ergs per second - 



But the total available energy possessed by the revolving 

 electron of linear dimensions a is only 



namely its kinetic energy (for of course it cannot radiate 

 away or dissipate its electrostatic energy), and this 

 amounts to 



1 0~ 40 



-r, (2-7T x 5 x 10 U x 10- 8 ) 2 = 3 x 10- 13 ergs, 



3xlO- 13 



