822 Mr. Gr. H. Livens on Rotational 



or inserting the values of a and /3 we deduce that 



\ n Q 2 — n 2 )\ ntf — rr) 



2co 



n 2 



\ n 2 — irj 



We now assume that 2'— ir — ? taken per unit volume for 



nrf — inr 



any definite set of electrons is proportional to the partial 

 density of the substance with whose molecules they are 

 associated. Thus, if active substances are present in a 

 mixture at partial densities p u p 2 , . . . . with inactive sub- 

 stances at partial densities cr 1? <r 3 , . . . . we shall have 



2« , , n r 1 p 1 + r 2 p 2 + . . . +Si<7-i + g 2 o- 2 + . . . 



_ _ {r lPl + r 2 p 2 +. . .) ^__ a(ripi + r2p2+ u m m +5l0 . 1 + . . j]i. 



wherein r/, r 2 ', . . . ; r 1? r 2 , . . . ; 5 1? s 2 , . . . are all physical 

 constants of the respective substances to which they refer, 

 depending on the nature of these substances and the fre- 

 quency of the light used. Regarding the magnitude of the 

 undashed letters, we know that if fju is the index of refraction 

 for the solution, then 



/<• 



-1 



a(^-l)+l = 2 ^ 1 + 2si<ri - 



We thus see that the rotative power of the mixture depends 

 to a large extent on the presence of the inactive substances, 

 and is not merely proportional to the partial density of the 

 active substances, as the elementary form of Drude's theory 

 would lead one to expect. An examination of this formula 

 in a less general case will throw more light on the exact 

 nature of this dependence of the rotativity on the constitution 

 of the mixture. 



3. Application to a special case : a simple solution. 



We shall now discuss the above formula in as far as it 

 applies to the experimental case, viz. that where a simple 

 active substance is dissolved in an inactive liquid. The 

 results for these cases are usually exhibited as a function of 

 the concentration c of the solution, i. e. the number of grams 

 of active substance per cubic centimetre of solution. If d 



