Dispersion in Relation to the Electron Theory. 459 



of radiation, that of course no appreciable variation of electro- 

 magnetic mass is to be expected from this cause ; but the 

 mutual action of: neighbouring electrons mav increase their 

 effective mass, and it is preferable, for the sake of generality, 

 to retain separate values for e/m. If we write rje/m for the 

 effective ratio, where e/m is the normal value deduced from 

 the Zeeman effect in gases (5*325 x 10 17 e.s.u.), and retain 

 onlv this normal value within the constants a l5 a 2 . . ., & 1? k 2 . . ., 

 the equations for refraction and magnetic rotation may be 

 written 



\ 2 \ 2 

 -l = a + 7) 1 a l ^ 2 _ x2 +7 ]2 a 2 x2 _ x y (6) 



*- ^ { ^d + &%£?)' +%*a + a Uj^f } • co 



The factor f, as mentioned in Part I., represents the 

 effect of the impressed field on the intramolecular fields. 

 It may also be taken to include the influence of the impressed 

 field on electronic coupling, such as would give rise to 

 abnormal Zeeman resolution. 



It has been shown that the mean value of the dispersional 

 period deduced from magnetic rotation may be smaller than 

 that obtained from natural dispersion. When f=0 we may 

 conclude that this result indicates that rj is smaller for longer 

 periods than for short ones ; for if \ 1? \ 2 • • • are in order 

 of diminishing magnitude, rj 2 will have greater weight in 

 comparison with rjf than r\ 2 has in comparison with rji. 

 The effective value of e/m is always less than the normal 

 value, and rj is therefore always le^s than unity. 



In proceeding to obtain an expression for p we may omit 

 £, bearing in mind that the result will need modification if 

 this factor is operative. 



We have 



e" 



nd 



2C 2 m 



= N ^uy ^ 



Taking \ 1? \ 2 . . . in order of diminishing magnitude, we 

 may write 



\2-\ 2 X3 '^ 3=r/g V_ x 2 W &e. 



