﻿4-t 
  PROFESSOR 
  KELLAND 
  ON 
  A 
  PROCESS 
  

  

  l> 
  2r 
  (r 
  + 
  2s)(2r+2s)x 
  2s+3r 
  

  

  + 
  &c 
  

  

  / 
  2s 
  + 
  3r-l 
  (r 
  + 
  2s-rfx)(2r 
  + 
  2s-rfx)(3r 
  + 
  2s-rfxj 
  T 
  ,4e 
  * 
  J 
  

  

  d 
  r* 
  d 
  r 
  - 
  1 
  x 
  r^dy 
  __ 
  f 
  (2s-rfi)(2s-r-rfjL) 
  gg— 
  -l-»> 
  

   dx 
  dx 
  r 
  - 
  x 
  dx 
  { 
  2s(2s-r) 
  ftg-r-l 
  

  

  /2* 
  + 
  r-l 
  /2* 
  + 
  3r-l 
  (r 
  + 
  2*-r/x)(2r 
  + 
  2*-r/u) 
  + 
  J 
  

  

  d 
  r 
  * 
  rp 
  d 
  r/i 
  d 
  r 
  1 
  r/M 
  , 
  dy 
  f 
  (2 
  g-r 
  p) 
  (2 
  s-r-r 
  fi) 
  8 
  «-2r 
  

  

  dx 
  r 
  ~ 
  l 
  dx 
  % 
  dx 
  r-l 
  d.r" 
  °{ 
  2s(2s-r)i2s-2r 
  X 
  

  

  + 
  JLJ< 
  + 
  b 
  ' 
  2r 
  (r 
  + 
  2s)(2r 
  + 
  2s) 
  2s 
  + 
  2r 
  , 
  

  

  + 
  12s 
  i2r 
  + 
  2s 
  (r 
  + 
  2s~rfx)(2r 
  + 
  2s-riJL)- 
  c 
  + 
  <". 
  j 
  

  

  c 
  (2 
  s-r 
  p)(2s-r 
  — 
  r 
  p) 
  o 
  s 
  _ 
  2r 
  r 
  

  

  2 
  s 
  (2 
  s 
  — 
  r) 
  ,2 
  s—2r 
  * 
  

  

  If 
  '^'•ST^ 
  

  

  2 
  s 
  

   Tf 
  s 
  _, 
  g(2*-r 
  A 
  i)(2 
  J 
  -r-r//) 
  8i 
  . 
  2r 
  yt 
  /"T 
  + 
  ^ 
  + 
  2 
  

  

  It 
  « 
  _ 
  r, 
  o 
  2g 
  (2g-r) 
  /2*-2r 
  * 
  ~ 
  (_0 
  "TIT^ 
  

  

  / 
  h2 
  

  

  / 
  r 
  

  

  -C-tff-o, 
  

  

  Therefore, 
  generally, 
  if 
  y=cC 
  cos 
  a 
  *= 
  we 
  have 
  

  

  rfjB 
  r-l 
  dx 
  dx 
  T 
  ' 
  x 
  dx 
  K 
  > 
  " 
  

  

  or, 
  if 
  x 
  rih 
  y—z, 
  the 
  equation 
  may 
  be 
  written 
  

  

  Hi 
  

  

  (£i."h'-"')''-i-*r+-<n 
  

  

  a 
  form 
  which 
  exhibits 
  its 
  relation 
  with 
  the 
  differential 
  equation 
  resulting 
  from 
  e 
  a 
  *. 
  

   11. 
  There 
  exist 
  numerous 
  relations 
  between 
  the 
  differential 
  coefficients 
  of 
  a 
  

   function 
  ; 
  such 
  as 
  the 
  following 
  : 
  — 
  

  

  ft 
  1 
  d 
  \n 
  „ 
  / 
  r 
  ^ 
  

  

  Smce 
  * 
  \7^dx) 
  " 
  = 
  (-*•) 
  ~r=5 
  

  

  /-—+/* 
  

  

  n 
  

  

  let 
  ^(^) 
  = 
  i_^ 
  ;the 
  n 
  

  

  /"T 
  

  

  