the Radiation from Electron Orbits. 643 



rate of absorption per unit volume is, as Sir J. J. Thomson * 

 has shown 



J4ttc x V 2 Ex^, 

 where c\ is the conductivity for waves of frequency equal to 

 that of light of wave-length \. For this to be equal to the 

 emission, say \F^dX per unit volume, we must have : — 



F x = 4w x V 2 E x (1) 



Since E\ is the same for all kinds of matter, it follows that 

 the ratio of c^ to Fa must be the same — the conductivity stands 

 in a constant ratio to the emission in the interior of a solid, 

 in spite of the fact that c x varies greatly from one substance 

 to another. It seems legitimate to draw the inference (at 

 any rate as a working hypothesis) that the mechanism of 

 emission must be the same as that of absorption. 



For long waves, the mechanism of absorption is almost 

 certainly to be found in the motion of free electrons, and the 

 supposition that this is also the mechanism of emission is 

 known to lead to results which are in agreement with 

 experiment. 



For short waves, there is less certainty as to the mechanism 

 of absorption. It seems probable that other agencies, such 

 for instance as various types of resonance, contribute some- 

 thing to the absorption of light of short wave-length, and it 

 may be that at the wave-lengths with which we aro primarily 

 concerned this contribution may greatly preponderate over 

 the original contribution from the motion of free electrons. 

 If so, we should have to look for the origin of emission as 

 well as of absorption in a motion subject to resonance, such 

 for instance as the motion of electrons in small closed orbits. 



It follows that we have to analyse the radiation from both 

 closed and open types of orbits, although naturally only those 

 closed orbits need be considered in which the motion is stable 

 for all possible displacements. 



General law /xr~ n . 



2. Consider first the motion of an electron in a single orbit 



described under a law of force fir~ n . The equations of 



motion are : 



d 2 r 



W2 -r6> = ^-\ (2) 



r^ = E, (3) 



where H, the moment of momentum, is a constant of the 



* Phil. Mag. [6] xiv. p. 223 (1907). 



2 U2 



