webster. — planck's radiation formula. 141 



for it to obtain the kinetic energy hv—W indicated by experiments 

 such as those of Richardson and Compton 9 is to have the higher posi- 

 tion in a region of negative electrostatic potential, that is, to have the 

 electron vibrate toward a mass of negative electricity without being 

 thrown to one side of the path by the repulsion. This seems distinctly 

 difficult to accomplish, and I do not know that it has ever been done. 



To account for Planck's law and other experimental results, there- 

 fore, we are driven to the unpredictable and unsatisfactory assumption 

 that when the energy stored in the magneton reaches any integral 

 multiple of h v, the internal mechanism of the ring may start another 

 oscillation, larger than the absorbing one, and that this emitting 

 oscillation will maintain a constant amplitude, deriving its energy in 

 some way from the steady current-, until the excess energy stored in 

 the magneton has been radiated, and its total energy is reduced to a 

 standard amount. The probability 77 of starting to radiate at any 

 particular multiple of h v is the same as in Planck's theory. 



To be sure that this mechanism is not, like Planck's, too big for the 

 atom, we may calculate the amplitude of the emitting oscillation that 

 is required to emit the energy faster than it is absorbed. 



Rewriting equation (3) in the more condensed form 



(4) >»£ + bk + k£ = eE k = cE cos wt 



where b and k are abbreviations for the coefficients in (3), we may 

 evaluate the rate of absorption for the frequencv v = — as 



(5) R„ = eKi 



In using this equation (5) we are implicitly assuming that all the work 

 done by the electric force goes into energy stored by the magneton, 

 and we are therefore neglecting its extremely small re-radiation. 

 Solving (4) for the case of a steady vibration, and substituting in (5), 

 we obtain 



he 2 E 2 a>o 2 b 



R„ 



where co 



' 'm 



J" 



m? (coo 2 "— co 2 ) 2 + & 2 co 2 



We may replace E 2 now by Idv and integrate with respect to v to 

 obtain the rate of storing energy by the magneton. In this integra- 



9 Phil. Mag. 24, 575 (1912). 



