﻿Optical 
  Rotativity 
  of 
  Solutions. 
  537 
  

  

  approaches 
  a 
  definite 
  constant 
  value 
  as 
  the 
  dilation 
  is 
  in- 
  

   creased, 
  and 
  (ii.) 
  the 
  different 
  constant 
  values 
  are 
  the 
  same 
  

   for 
  any 
  one 
  alkaloid. 
  These 
  facts 
  have 
  been 
  confirmed 
  in 
  

   numerous 
  cases 
  since 
  Had 
  rich's 
  original 
  experiments, 
  but, 
  of 
  

   course, 
  substances 
  have 
  been 
  found 
  for 
  which 
  the 
  rule 
  is 
  not 
  

   true. 
  It 
  may, 
  however, 
  be 
  said 
  in 
  favour 
  of 
  the 
  original 
  idea 
  

   that 
  these 
  abnormal 
  substances 
  are 
  either 
  such 
  as 
  cannot 
  be 
  

   obtained 
  in 
  very 
  dilute 
  solution, 
  or 
  else 
  their 
  nature 
  is 
  such 
  

   that 
  other 
  very 
  obvious 
  actions 
  tend 
  to 
  hinder 
  the 
  occurrence 
  

   of 
  the 
  ordinary 
  regularity. 
  

  

  On 
  closer 
  investigation 
  we 
  find, 
  however, 
  that 
  Hadricb's 
  

   theory 
  does 
  not 
  appear 
  to 
  give 
  the 
  true 
  cause 
  or! 
  the 
  variations, 
  

   because 
  the 
  same 
  phenomena 
  have 
  been 
  noticed 
  in 
  solutions 
  

   where 
  the 
  degree 
  of 
  dissociation 
  is 
  certainly 
  very 
  small. 
  For 
  

   example, 
  Walden 
  found 
  with 
  a-bromoeamphorsulphonic 
  acid 
  

   and 
  some 
  of 
  its 
  salts 
  that 
  the 
  molecular 
  rotations 
  of 
  the 
  

   solutions 
  of 
  the 
  free 
  acid 
  and 
  the 
  different 
  salts 
  all 
  ap- 
  

   proximate 
  to 
  the 
  same 
  value 
  as 
  the 
  dilution 
  was 
  increased, 
  

   although 
  the 
  degree 
  of 
  the 
  dissociation 
  is 
  very 
  different 
  in 
  the 
  

   different 
  cases. 
  

  

  Before 
  proceeding 
  further 
  we 
  might 
  for 
  a 
  moment 
  turn 
  

   to 
  our 
  theoretical 
  formula 
  to 
  see 
  how 
  the 
  specific 
  rotation 
  of 
  

   dilute 
  solutions 
  should 
  behave. 
  We 
  found 
  that 
  the 
  specific 
  

   rotation 
  of 
  the 
  solution 
  containing 
  active 
  substance 
  at 
  a 
  

   partial 
  density 
  p 
  in 
  a 
  solvent 
  at 
  a 
  partial 
  density 
  cr 
  was 
  of 
  tho 
  

   form 
  

  

  L 
  J 
  (1 
  — 
  aXp-apa) 
  2 
  ' 
  

  

  We 
  now 
  make 
  the 
  probably 
  correct 
  assumption 
  that 
  the 
  

   rotative 
  power 
  of 
  an 
  active 
  atomic 
  group 
  is 
  not 
  altered 
  when 
  

   it 
  enters 
  a 
  chemical 
  molecule 
  as 
  a 
  constituent 
  part 
  of 
  the 
  

   combining 
  acid 
  or 
  base. 
  This 
  assumption 
  is, 
  of 
  course, 
  not 
  

   new, 
  and 
  receives 
  some 
  support 
  from 
  other 
  than 
  the 
  present 
  

   phenomena. 
  We 
  can 
  then 
  write 
  

  

  where 
  pi 
  refers 
  to 
  the 
  partial 
  density 
  of 
  the 
  active 
  group, 
  

   and 
  po 
  to 
  the 
  density 
  of 
  the 
  combined 
  inactive 
  base 
  or 
  acid. 
  

   Thus 
  " 
  

  

  L 
  * 
  (l 
  — 
  a\ 
  l 
  pi~a\ 
  2 
  p2~ 
  a 
  / 
  jL<J 
  ') 
  2 
  ' 
  

   From 
  this 
  formula 
  we 
  see 
  at 
  once 
  that 
  as 
  the 
  dilution 
  of 
  

  

  