﻿284 
  Dr. 
  G. 
  W. 
  Todd 
  on 
  the 
  Velocity 
  of 
  

  

  These 
  figures 
  and 
  the 
  corresponding 
  graphs 
  (fig. 
  3) 
  apply 
  

   to 
  any 
  ter-molecular 
  reaction 
  of 
  the 
  type 
  2A 
  + 
  B->1 
  or 
  more 
  

   resultants, 
  A 
  being 
  in 
  excess. 
  

  

  Quadri-molecular 
  Reaction. 
  

  

  Let 
  the 
  reaction 
  be 
  of 
  the 
  type 
  3 
  A 
  4- 
  B-^l 
  or 
  more 
  resultants, 
  

   and 
  let 
  the 
  initial 
  concentrations 
  be 
  equal. 
  The 
  general 
  

   equation 
  is 
  

  

  ^ 
  V 
  a 
  I 
  \a 
  aj 
  

  

  when 
  — 
  = 
  1 
  

  

  and 
  K 
  = 
  Jca 
  z 
  . 
  

  

  _r* 
  a 
  _if 
  i 
  i 
  

  

  K< 
  =f(T^ 
  

  

  X 
  -1 
  -2 
  -3 
  -4 
  -5 
  -6 
  65 
  -7 
  1-0 
  

  

  Xt 
  -123 
  -32 
  -64 
  121 
  2'33 
  4'87 
  743 
  12-0 
  oo 
  

  

  Now 
  take 
  B 
  in 
  excess, 
  putting 
  -=p>l. 
  The 
  equation 
  

   becomes 
  a 
  

  

  dX 
  

  

  ==-Alog 
  e 
  (l-X) 
  + 
  B^ 
  + 
  §{ 
  ( 
  ^-l} 
  + 
  Dlog^, 
  

  

  where 
  A, 
  B, 
  C, 
  D 
  are 
  constants 
  depending 
  on 
  the 
  value 
  of 
  p. 
  

  

  p=2. 
  ThenA=l. 
  B=-l. 
  0=1. 
  D=-l. 
  

  

  X 
  -2 
  '4 
  -6 
  -7 
  8 
  l'O 
  

  

  Xt 
  -149 
  -501 
  168 
  3-49 
  909 
  oo 
  

  

  p=3. 
  ThenA^. 
  B=-l. 
  C=\. 
  D=-A. 
  

  

  X 
  -3 
  '5 
  -7 
  8 
  -9 
  10 
  

  

  Xt 
  -184 
  »564 
  2-06 
  516 
  22*7 
  oo 
  

  

  P 
  =6. 
  ThenA 
  = 
  ^. 
  B=-^. 
  0= 
  \. 
  D=-± 
  

  

  X 
  0-5 
  7 
  "8 
  -9 
  1*0 
  

  

  Xt 
  -265 
  -925 
  225 
  952 
  oo 
  

  

  These 
  figures 
  give 
  the 
  graphs 
  (fig. 
  4) 
  for 
  a 
  quadri- 
  

   molecular 
  reaction 
  of 
  the 
  type 
  3A-f-B->, 
  the 
  substance 
  B 
  

   being 
  in 
  excess. 
  

  

  