Origin of the Radiation from Hot Bodies. 221 . 



per second in consequence of the collisions is equal to 



2N<? 2 



where N is the number of collisions per second : taking the 

 value of </>! given by equation (7) this equals 



37rY u e .aq, 



where u is the velocity of the cathode rays. Expressing it 

 in terms of the wave-length instead of the frequency, E\, the 

 energy between wave-lengths X and X-\-dX is 



3,—^e .dX. 



This is a maximum when X = 2irYa. 



When the cathode rays are moving with a velocity of 

 10 8 cm./sec. or over, a will be less than 2*1 x 10~ 16 , and the 



4t7Ft 



term e~ a a will be very nearly equal to unity all through the 

 visible spectrum, and the energy in the visible part of the 

 spectrum, say between 



X = 7xl0" 5 cm. and X = 3'5 x 1(T 5 cm., 



will be 



4 jST A* 



21xl(T 5 " 



Now if each corpuscle only makes one collision, Ne = i, 

 the current carried by the cathode rays, and since £ = 10 -20 , 

 the energy in the visible part of the spectrum is 



2pl0- 15 .^; 



or if the velocity of the cathode rays is 10 8 , the energy 

 radiated will be 



19 X i ergs. 



Now by the use of Wehnelt tubes with lime cathodes we 

 can get a stream of cathode particles carrying a current of a 

 milliampere. Hence putting z = 10 -4 , the energy in the visible 

 part of the spectrum would in this case be 



1-9 x 10~ 3 erg. 

 Radiation carrying as much energy as this ought to be 



