﻿50 
  PROFESSOR 
  KELLAND 
  ON 
  A 
  PROCESS 
  

  

  equation, 
  which 
  are 
  reduced 
  to 
  ordinary 
  differentiation 
  or 
  integration 
  in 
  other 
  

   cases. 
  The 
  other 
  forms 
  are 
  as 
  follow 
  : 
  

  

  2. 
  By 
  making 
  / 
  (If 
  + 
  l) 
  =5^5/ 
  (-f) 
  

  

  '(-*)~r£ 
  

  

  .D 
  

  

  2 
  

  

  /-f 
  — 
  + 
  1 
  

  

  ■k- 
  +« 
  — 
  1 
  

  

  _ 
  a 
  -(2n-2)j 
  \ 
  * 
  e 
  (2n-2)t 
  

  

  / 
  T 
  

  

  and, 
  consequently, 
  w 
  = 
  (-2)- 
  ( 
  "- 
  1} 
  (~) 
  " 
  * 
  2n 
  - 
  2 
  r; 
  where 
  e 
  is 
  found 
  from 
  the 
  

   equation 
  of 
  the 
  first 
  order 
  _ 
  P+^«-2-p 
  g 
  2^ 
  = 
  (/(_») 
  \ 
  " 
  1 
  0< 
  

  

  This 
  solution 
  is 
  of 
  the 
  ordinary 
  form, 
  whenever 
  n 
  is 
  a 
  positive 
  or 
  negative 
  

   integer. 
  

  

  By 
  making 
  /(~ 
  "? 
  +1) 
  = 
  DT2^2^ 
  / 
  (~t) 
  

  

  / 
  D 
  

   0^ 
  /(-?) 
  

  

  

  

  and 
  

  

  = 
  e 
  -(2n-2-p) 
  I 
  2 
  2 
  e 
  2n-2-p 
  

  

  /"2 
  

  

  where 
  v 
  is 
  found 
  from 
  the 
  solution 
  of 
  the 
  equation 
  of 
  the 
  first 
  order, 
  

  

  D 
  + 
  2n-2 
  26 
  f 
  i 
  D\ 
  -1 
  n 
  

  

  This 
  solution 
  is 
  of 
  the 
  ordinary 
  form 
  when 
  n 
  — 
  ^ 
  is 
  an 
  integer. 
  

   4. 
  By 
  making 
  /(-»+!)- 
  D+2 
  ^_ 
  2 
  / 
  (- 
  g), 
  

  

  or 
  / 
  ( 
  --U 
  ' 
  2 
  2 
  

  

  /--H-+»— 
  j»-l 
  

  

  _(2n_p_2)* 
  / 
  ^ 
  (2n-/>-2)# 
  

  

  = 
  e 
  

  

  2 
  

  

  