Dispersion in Relation to the Electron Theory. 471 

 Hence 



Converting from rational to ordinary symmetrical units 

 and taking v in periods per second, we must write 



H _ 



for H, e^/^ir for e, and 2ttv for v. 



s/krr 

 Thus 



, _Trf& (n 2 + 2)% / V-l \ 2 



6h ~ 2C 2 ^- n ^W + 2/ " 



The summation here extends to all the electrons in the 

 unit of volume ; but as every type of electron present in 

 one molecule is repeated in every molecule (except those- 

 of class I. which do not produce a measurable effect) we 

 may write 



where N is now the number of molecules in the unit of 

 volume, and the summation extends to the p individual 

 effective electrons in the molecule. The components of the 

 molecular refraction as usually calculated with the same 

 notation are expressed in 



-K-— - -j = ( N l 2 , ., ) -r + . . . to » terms, 

 n 2 + 2 d \ nf + 'IJ d r 



= Pi + P 2 + + P,. 



The expression for the absolute molecular rotation R 

 ( = M.B/d) may therefore be written 



irf ( ^ + 2) 2 d fpa 



But since N = ^/M/t this becomes 



7tv 2 (n 2 + 2) 2 

 ±t ~2CVA n •l^i+12+.... + ^j- ■ (1) 



Hence the quantity in which we must seek the additive 

 relations is not the molecular rotation R simply * , but 



B, 



{n 2 + 2f 

 See Note 4. 



