﻿440 
  Mr. 
  R. 
  Hargreaves 
  on 
  a 
  

  

  all 
  o£ 
  the 
  required 
  form. 
  By 
  addition, 
  collecting 
  terms 
  

   diagonally, 
  

  

  -de 
  

  

  I 
  . 
  rBL 
  rf 
  BL 
  ,„./-' 
  BL-, 
  

  

  n 
  3 
  7-*BT 
  + 
  - 
  +( 
  - 
  1) 
  5=*^] 
  

  

  J» 
  rBL 
  d 
  BL 
  , 
  iv 
  .- 
  2 
  rf 
  "" 
  3 
  9 
  L 
  1 
  , 
  

  

  Thus 
  with 
  any 
  number 
  of 
  variables, 
  

  

  dL 
  r 
  . 
  d 
  . 
  .. 
  ct)"l 
  

  

  sr 
  = 
  2lQ 
  e+j 
  t 
  (G 
  1 
  e+® 
  i 
  e+...Q 
  n 
  e)], 
  . 
  (7) 
  

  

  where 
  

  

  u 
  » 
  b* 
  dt^e^ 
  ' 
  l 
  b& 
  *a» 
  + 
  -| 
  

   e 
  2 
  =t 
  L 
  -t^. 
  + 
  ..., 
  e„=^ 
  ' 
  (8) 
  " 
  

  

  B* 
  **» 
  $ 
  J 
  

  

  If 
  then 
  we 
  put 
  

  

  Fo=-e 
  , 
  E=-L 
  + 
  2(0^ 
  + 
  e 
  2 
  ^+ 
  ... 
  +0„<9 
  ) 
  ), 
  (9) 
  

   the 
  result 
  (7) 
  is 
  expressed 
  by 
  

  

  !?-**•' 
  • 
  • 
  do) 
  

  

  But 
  if 
  L 
  has 
  the 
  form 
  1 
  where 
  /is 
  a 
  function 
  of 
  ... 
  0, 
  

   then 
  L 
  or 
  

  

  and 
  

  

  _ 
  Mi 
  4. 
  u 
  -/ 
  2)* 
  , 
  y 
  U 
  J 
  a 
  

  

  which 
  has 
  the 
  form 
  of 
  (7) 
  with 
  

  

  e 
  =o, 
  e 
  1= 
  f 
  e 
  s 
  =g,... 
  ®, 
  +1 
  =^. 
  . 
  (ii) 
  

  

  * 
  Or 
  n 
  = 
  T^y 
  , 
  and 
  9,.= 
  Jfi 
  - 
  f 
  8r 
  + 
  1 
  from 
  >-=n-l 
  down 
  to 
  r=0. 
  

  

  