﻿42 
  

  

  PROFESSOR 
  KELLAND 
  ON 
  A 
  PROCESS 
  

  

  H+p 
  

  

  l 
  + 
  g 
  

  

  Hence 
  (* 
  Jdz) 
  log«=— 
  j 
  ,j^—- 
  *" 
  - 
  r+j 
  

  

  h»i 
  

  

  r 
  m 
  — 
  m 
  / 
  

  

  — 
  X 
  r 
  

  

  7= 
  I 
  log«- 
  (l 
  + 
  iT7 
  + 
  TT2-, 
  + 
  &C 
  - 
  + 
  i 
  + 
  («Ll;r) 
  } 
  

  

  - 
  + 
  m 
  v 
  

  

  1 
  r 
  

  

  9. 
  T^wd 
  dte 
  differential 
  equation, 
  on 
  the 
  solution 
  of 
  which 
  depends 
  the 
  value 
  

   0fd^e 
  ax 
  . 
  

  

  Since 
  e 
  a 
  ^=l 
  + 
  ax 
  + 
  ^-^ 
  + 
  kc. 
  

  

  -\+r(X 
  j 
  — 
  2 
  + 
  r 
  fx 
  

  

  dTe 
  =(-r) 
  x 
  

  

  p 
  —rft. 
  

  

  ax 
  

  

  1 
  + 
  1.2 
  / 
  2 
  

  

  This 
  equation 
  can 
  be 
  made 
  to 
  depend 
  on 
  the 
  solution 
  of 
  a 
  differential 
  equa- 
  

   tion, 
  when 
  r 
  is 
  a 
  whole 
  number 
  ; 
  for, 
  in 
  that 
  case, 
  the 
  terms 
  wiU 
  recur 
  after 
  the 
  

   rth. 
  To 
  reduce 
  the 
  equation, 
  we 
  observe 
  that 
  

  

  r 
  

  

  7+T 
  

  

  + 
  1 
  — 
  r 
  fX 
  

  

  ' 
  — 
  = 
  — 
  , 
  and 
  so 
  on. 
  

  

  V"„ 
  ax 
  —( 
  r 
  N 
  ;'*r 
  _r 
  '* 
  

  

  Hence 
  dV 
  ? 
  =(-ry* 
  

  

  -4-1 
  r 
  + 
  1 
  

  

  — 
  1 
  + 
  rfJL 
  

  

  _jl_ 
  ( 
  ax+ 
  ."!_ 
  il* 
  +&c 
  ) 
  

  

  / 
  1 
  V 
  r 
  + 
  l-r/Lt 
  ir+l 
  / 
  

  

  / 
  

  

  + 
  

  

  -2 
  + 
  ru 
  

   j 
  r 
  (##_ 
  r+2 
  a 
  r+ 
  ~x 
  r+ 
  " 
  

  

  _r 
  / 
  a 
  2 
  x~ 
  

  

  T~2 
  VIT2 
  

  

  + 
  &c. 
  

  

  r 
  + 
  2 
  — 
  r 
  jJ. 
  j 
  r 
  + 
  2 
  

  

  J 
  + 
  &c, 
  &c, 
  

  

  (A) 
  

  

  Let 
  

  

  J/ 
  =x 
  l 
  -'> 
  + 
  

  

  /r 
  + 
  1 
  r 
  + 
  1 
  — 
  r/i 
  

  

  frjr+l-rp 
  

  

  (r 
  + 
  1) 
  (2 
  r+1) 
  +&c> 
  . 
  

  

  | 
  2r+1 
  (r+l-r/i)(2r 
  + 
  l-r/z) 
  

  

  -/-a 
  _ 
  /-a; 
  aV 
  +1 
  (r 
  + 
  l) 
  

  

  1 
  H 
  

  

  ; 
  then 
  

  

  rf 
  r_1 
  /.r„«/y\ 
  _«'(£ 
  + 
  «V 
  + 
  -(r 
  + 
  l) 
  _ 
  &c 
  \ 
  

  

  Again, 
  if 
  y= 
  I 
  ^ 
  a 
  r 
  2 
  -^ 
  '- 
  

  

  j 
  — 
  (r 
  + 
  2) 
  + 
  rfl 
  

  

  l-2+rjx 
  

  

  r__ 
  gg^H 
  _J1_. 
  + 
  &c 
  . 
  

  

  2 
  /r 
  + 
  2 
  /_r 
  + 
  2 
  

  

  r 
  r 
  

  

  