218 Prof. J. J. Thomson on the Electrical 



where E 2 is the energy carried by waves with frequency 

 between q and q -f dq, mu 2 is the kinetic energy of the corpuscle, 

 and V the velocity of light. If we suppose that the kinetic 

 energy of the corpuscle is the same as that of a molecule of 

 a gas at the temperature of the hot body, 



mu 2 = 2a6, 



where a is a constant equal to 1*4 x 10~ 16 on the C.G.S. system 

 of units, and 6 the absolute temperature. Hence 



™ 2-8xlQ- 1G nzj 

 g" 3tt 2 V 3 q q; 



and this has been shown by Lorentz to be in good agreement 

 with experiments made on the very long wave radiation from 

 hot bodies. 



Lorentz's investigation is limited to frequencies so small 

 that a corpuscle describes very many free paths during the 

 time taken by light of this frequency to make a complete 

 vibration. The preceding expression represents a radiation 

 increasing indefinitely as the frequency increases ; whereas 

 the radiation from hot bodies attains a maximum at a 

 frequency depending upon the temperature, and then 

 diminishes as the frequency increases. The following in- 

 vestigation is an attempt to find an expression for the 

 radiation which does not involve the assumption that the 

 frequency is small. 



If a particle carrying a charge e is moving with an 



acceleration /, waves are emitted by it and the rate at which 



2 e 2 f 2 

 energy is radiated is ^- —==*■ where V is the velocity of 



light ; and if / is an harmonic function of the time having 

 a frequency g, the radiation will be light having this 

 frequency. 



If by Fourier's theorem we express /in the form 



/=^r<K?) ?*•<*?, w 



Jo 



where <f>(g) is some function of q, then, since the rate of 



2e 2 f 2 

 radiation is -q~\7~) the radiant energy emitted by the moving 



particle through the whole of its career is 



2 e 1 C +0 ° 



3 V 



