134 PROCEEDINGS OF THE AMERICAN ACADEMY. 



probability tj that the oscillator will emit when its energy reaches the 



1 77 



value n h v is given by the formula - - = pi, where p is a constant, 



V 

 and / is the intensity of the electric vibration per unit interval of 

 frequency. That is, the stronger the light, the more likely the oscilla- 

 tor is to go on accumulating energy. The value of p is obtained by 

 setting the mean energy thus found approximately equal, for ex- 

 tremely large values of /, to the value it would have if the oscillator 

 radiated as demanded by the classical theory. This is a new assump- 

 tion, independent of the previous ones, and based on the experimental 

 fact the Rayleigh's law of radiation is true for large values of X T. 



The next step is to identify the distribution of points thus found 

 with that obtained above from entropy considerations, and thus find / 

 in terms of v and T, and from I the energy density per unit frequency 

 interval, 



8tt^ 3 1 



u 



c 3 



kT -. 

 — 1 



Assumptions of the Present Theory. The starting point of the 

 present theory is Parson's magneton, a ring of negative electricity of 

 a diameter perhaps xV that of a hydrogen atom, revolving on its axis 

 with a velocity of the order of that of light. This has been proposed 

 by Parson as a substitute for the classical electron, and has given good 

 results in the explanation of chemical affinities. 



These magnetons are supposed by Parson to be free to move in a 

 sphere of continuously distributed positive electricity, in which, as he 

 shows, they have a strong tendency to group themselves in eights, 

 thus giving the foundation of the periodic table of the elements. A 

 detailed discussion of their groupings and the surprising way in which 

 they explain not only the table, but also the exceptions to its rules, 

 and many other chemical phenomena, will be found in his paper. 



Inquiring into what may be expected of the vibrations of the mag- 

 neton, we find a state of affairs somewhat more complex than in the 

 classical electron theory. For we have not only the attraction of the 

 positive electricity through which it moves, and the electrostatic 

 repulsions of the other magnetons, both tending to make its equili- 

 brium stable, but also the magnetic attractions of the others, tending 

 to make it less stable, and perhaps still other repulsions by them, 

 proportional to some inverse power of the distance higher than the 

 second, and therefore having a strong tendency to promote stability. 

 The combined effect must, of course, be a stable equilibrium. 



