216 RADIATION OF ELECTRON [APR a 



its velocity being 3 x 10 7 centimetres per second, or one- 

 thousandth that of light. So if the electron were isolated 

 from any supply of energy, and if it could maintain the 

 pace, it would at this rate radiate away all its kinetic 

 energy in 10 ~ 8 of a second, that is to say in three or 

 four million revolutions. This may seem a rapid rate of 

 cooling, but it is not surprising for an isolated and 

 luminous atom : it is a Hertzian vibrator or emitter of 

 simple type. The number of revolutions which an 

 electron must make in one second, in order to emit 

 sodium light, is about 8000 times the number of seconds 

 which have passed since the Christian era. 



We may express the ratio of the radiating power of a 

 single electron to its total kinetic energy, by the fraction 



2<z/'iA 2 2a /0 , a ^ n -n- 

 I - ) = (27m) 2 = S7r 2 n ^- = 70 million per second. 

 v \u/ v A 



In any large assemblage of atoms the radiation is not 

 free and unrestrained, nor is it unmaintained, like this ; 

 but it must always be considerable at anything like 

 luminous frequency, and it is proportional to the fourth 

 power of the frequency. At a frequency which emits a 

 wave ten times as long as a luminous wave, the radiating 

 power of a revolving electron is only one ten-thousandth 

 of that above calculated, but even so it is very significant ; 

 so there must be compensation of some kind or a substance 

 could not permanently exist. The criterion that a mole- 

 cule shall not be destroyed by radiation-losses is given in 

 the concluding sentence of Larmor's paper above quoted : 

 Phil. Mag., Dec., 1897. 



The subject of radiation from a symmetrical group of 

 electrons was pursued above in Chapter XIX. 



The radiating power of an electron suddenly stopped by 

 a collision is of course much greater than the above, and is 

 estimated in Chapter IX. To get copious Rontgen rays 



