﻿based on Free Electrons. 108!) 



of the motion. Thus we have a succession of stages in each 

 of which occurs a pulse of radiation, with no appreciable 

 radiation between the pulses. How the interval of time 

 between the pulses may be related to the period found in 

 Part I. is not known. 



If it were permissible to apply the formula, radiation 

 xX~\ to the comparison of the above radiation for different 

 values of >?, we should get \ cc (pa) n x n~ 2 ; but the manner 

 in which pa may change with n is not known. 



Now, in Bohr's theory there is what appears to be an 

 arbitrary assumption of unitary stages under circumstances 

 in which no step or stopping place occurs. The conditions 

 suggest rather an invariable orbit if radiation is ignored, or 

 a smooth spiral if it is taken into account. If results yielded 

 by Bohr's theory are held to be in agreement with experi- 

 mental know led o-e, there still remains an absence of 

 mechanism to explain its operation. If the above description 

 of the .whole motion in the two-ring scheme is correct in 

 outline, a succession of stages is realized without abandoning 

 the conception of electromagnetic radiation. 



§ 22. The above account of stability is, for the two-ring 

 system, based on oscillations of the special configuration. 

 When the wider view of the whole motion is taken, the 

 position in respect to tangential instability is certainly eased, 

 but the extent of the relief is uncertain. As positive and 

 negative elements still remain in close conjunction, the 

 position is not .worsened in respect to axial and radial 

 stability. But it is natural to expect either an interruption 

 or a finite modification of the oscillations at regular 

 intervals. 



A brief account will now be given of the actual periods 

 obtained in examining the question of stability. When the 

 atomic numbers are not small the periods for axial and radial 

 oscillation tend to agreement. The periods (quite numerous) 

 of type P 3 are comprised within a range represented approxi- 

 mately by a factor '873, and the shortest period has the 

 asymptotic value 27r/lQ'72nco. The range is certainly very 

 near to that of the extreme columns of the K series. An 

 identification of this formula with the figures of the K(/y) 

 series, or 27r/1446>/w with those of the « series, involves a 

 determination of a, the radius defining the scale of the 

 configuration. It makes the number na n 3 gradually diminish 

 with increase of n ; or if A n is atomic weight, it gives 

 to A,M n 3 a fairly constant value 1*32 x 10~ 25 with some rise 

 for lower values of n. For example, the use of the K(a) 



