MODELS OF POSITIVE ION 321 



corpuscle will for the same element be related 

 to each other according to a definite law, and 

 the period by which the gyrostat is affected will 

 depend upon the relationship of corpuscles with 

 the atom, so that the various periods of the 

 gyrostats in different atoms will follow a corre- 

 sponding law. 



Balmer's Law 



We have endeavoured to arrive at a general law 

 connecting the frequencies of these various vibra- 

 tions communicated to the aether by the atoms of 

 an element. 



Thus if no be the fundamental frequency of an 

 electron and n its period when it radiates under 

 the influence of the corpuscle, then supposing we 

 regard a Faraday tube extending between the 

 corpuscle and the atom as a bundle of vortex 

 filaments, as Thomson has shown, the effective 

 inertia of the tube would involve a term propor- 

 tional to the square of the polarisation. Now the 

 ratio of the change in the moment of momentum 

 of the radiating system to that in its original state 

 is equal to the ratio of the difference between the 

 original inertia and the inertia of the Faraday tube 

 to the original inertia, so that 



^^5 = -r when * = inertia of Faraday tube, 



Wo H 



if, — total inertia of field. 



Y 



