Dispersion in Relation to the Electron Theory. 455 



constant of absorption. The present paper deals with the 

 application of magnetic rotary dispersion to the elucidation 

 of the same problem. 



If N denotes the number of resonators present in the 

 unit of volume, p the number per molecule, m the mass and 

 e the charge of each ; d the density and M the molecular 

 weight of the substance; and h the absolute mass of the 

 hydrogen atom : then 



^W-H-Tf (1) 



The ratio of e\ to h, if we confine our attention to electrons, 

 is equivalent to the electrolytic constant — 96530 coulombs 

 or 9653 x 3 x 10 10 electrostatic units per gram. 



When Ni£] can be obtained from optical data, (1) gives at 

 once the value of p lm 



(A) Number of Electrons deduced from Natural Disper- 

 sion. — In the case of ordinary dispersion we may write 



According to Drude's theory, X x is the wave-length 

 corresponding to the free-period of the vibrator and 



N lgl y 



This expression for a-i holds good also in the theory of 

 Lorentz and Planck, but \ x is less than the wave-length \ f 

 corresponding to the free period, the two being connected 

 by the equation 



V = ^; where ,4 *W 



In either case, therefore, if X x is the wave-length of the 

 dispersional period, determined from the course of the 

 dispersion-curve, 



**-=§?/£ ^ 



When the constants a lf a 2 . . ., X l5 X 2 . . ., have been 

 completely determined, equations (1) and (2) can be applied 

 to evaluate p % , p 2i &c. This, however, is not in general 

 practicable, as the value of the dispersional period is as a 

 rule only an effective mean. This is particularly the case 

 when \j, \ 2 » & c -> li e i" the Schumann region. 



In the visible and ultraviolet the effect of infra-red bands 

 is very small, and can be represented by a term — c\ 2 . 



