﻿361 
  Mr. 
  a. 
  H. 
  Li 
  

  

  vens 
  on 
  

  

  then 
  p 
  = 
  k 
  — 
  mn 
  2 
  is 
  real. 
  Consequently 
  we 
  obtain, 
  if 
  we 
  

  

  2 
  * 
  

  

  use 
  « 
  - 
  = 
  - 
  

  

  i)i 
  

  

  i* 
  + 
  =i+ 
  

  

  m{» 
  ' 
  

  

  1-2 
  

  

  ae" 
  

  

  (n^ 
  — 
  ri 
  2 
  ) 
  + 
  q 
  

  

  Now 
  since 
  q 
  is 
  always 
  a 
  comparatively 
  small 
  quantity, 
  we 
  

   can 
  approximate 
  to 
  these 
  values 
  by 
  expanding 
  in 
  powers 
  

   of 
  q. 
  We 
  then 
  obtain 
  

  

  qn 
  m*ln 
  2 
  -n 
  2 
  y 
  

  

  co 
  -- 
  - 
  — 
  v 
  

  

  v 
  

  

  ■Hi 
  

  

  (l- 
  S 
  ^ 
  V 
  

  

  2 
  

  

  K 
  2 
  -n 
  2 
  ) 
  2 
  

  

  *" 
  (1-2 
  y^T 
  

  

  and 
  this 
  is 
  the 
  formula 
  which 
  expresses 
  the 
  dependence 
  of 
  

   the 
  rotation 
  on 
  the 
  density 
  of 
  the 
  active 
  electrons. 
  It 
  is 
  

   more 
  complicated 
  than 
  that 
  obtained 
  from 
  the 
  elementary 
  

   theory, 
  to 
  which, 
  however, 
  it 
  reduces 
  if 
  we 
  put 
  a 
  = 
  0. 
  This 
  

   formula 
  can 
  be 
  discussed 
  in 
  a 
  manner 
  exactly 
  analogous 
  to 
  

   that 
  in 
  which 
  we 
  discussed 
  in 
  a 
  previous 
  paper 
  the 
  cor- 
  

   responding 
  formula 
  for 
  the 
  intrinsic 
  optical 
  activity, 
  to 
  which 
  

   it 
  is 
  to 
  a 
  certain 
  extent 
  similar. 
  Bearing 
  in 
  mind 
  the 
  results 
  

   of 
  our 
  former 
  discussion 
  a 
  few 
  deductions 
  are 
  obvious. 
  

  

  In 
  the 
  case 
  of 
  solutions 
  it 
  would 
  appear 
  that 
  a 
  strict 
  

   superposition 
  of 
  the 
  rotations 
  of 
  solvent 
  and 
  solute 
  can 
  never 
  

   take 
  place. 
  If 
  we 
  calculated 
  the 
  specific 
  rotation 
  of 
  the 
  dis- 
  

   solved 
  substance 
  from 
  the 
  elementary 
  formula, 
  it 
  would 
  vary 
  

   with 
  the 
  concentration 
  of 
  the 
  solution, 
  the 
  most 
  common 
  

   case 
  being 
  a 
  decrease 
  with 
  increasing 
  dilution. 
  Moreover, 
  

   the 
  specific 
  rotation 
  calculated 
  in 
  this 
  way 
  might 
  also 
  depend 
  

   on 
  the 
  solvent. 
  All 
  of 
  these 
  deductions 
  have 
  been 
  verified 
  

   by 
  experiment. 
  

  

  An 
  interesting 
  application 
  of 
  the 
  present 
  theory 
  is 
  to 
  the 
  

   case 
  of 
  solutions 
  of 
  aniline 
  dyes 
  in 
  alcohol, 
  where 
  there 
  

   appeared 
  to 
  be 
  some 
  discrepancy 
  in 
  the 
  results 
  obtained. 
  

   In 
  his 
  ' 
  Optics 
  ' 
  (ch. 
  xviii. 
  p. 
  502) 
  Wood 
  says, 
  " 
  the 
  behaviour 
  

   of 
  alcoholic 
  solutions 
  of 
  the 
  aniline 
  dyes 
  in 
  a 
  magnetic 
  field 
  

   has 
  been 
  studied 
  by 
  Schmauss, 
  who 
  claimed 
  that 
  the 
  effect 
  

   of 
  the 
  dye 
  was 
  to 
  increase 
  the 
  rotation 
  of 
  the 
  alcohol 
  on 
  the- 
  

  

  