﻿and 
  Deflection 
  of 
  Braced 
  Girders, 
  47 
  

  

  and 
  for 
  the 
  panels 
  m 
  + 
  1 
  to 
  N, 
  

  

  m 
  

  

  Poo- 
  +P<b 
  = 
  — 
  ( 
  - 
  lj»-«r 
  5 
  . 
  

  

  Accordingly 
  if 
  p 
  m+ 
  1, 
  

  

  and 
  if 
  p 
  > 
  m, 
  

  

  S»r,= 
  ( 
  - 
  l)' 
  +1 
  /v' 
  + 
  ( 
  - 
  l) 
  N 
  +" 
  +1 
  »» 
  { 
  ^ 
  - 
  [2] 
  } 
  (\t* 
  +^) 
  

  

  = 
  (_l)P+i 
  /)oV 
  ' 
  + 
  (_l)s-p 
  m 
  ||_(_iyJ(x^ 
  +/ 
  ^). 
  

   On 
  examining 
  these 
  results 
  we 
  find 
  that 
  

  

  is 
  zero, 
  except 
  when 
  /9=o", 
  and 
  that 
  in 
  this 
  case 
  it 
  is 
  equal 
  to 
  

   2 
  (\t 
  2 
  + 
  fis 
  2 
  ) 
  ; 
  'also 
  that 
  

  

  %epr 
  p 
  _i 
  + 
  22«pr 
  p 
  + 
  2epr 
  p+1 
  

  

  is 
  zero 
  except 
  when 
  p 
  = 
  m, 
  and 
  that 
  in 
  this 
  case 
  it 
  is 
  equal 
  to 
  

  

  -(\t 
  2 
  +/is 
  2 
  y. 
  

  

  Accordingly, 
  if 
  we 
  take 
  the 
  p 
  — 
  lth, 
  pth, 
  and 
  p 
  + 
  lth 
  of 
  

   Maxwell's 
  equations 
  and 
  add 
  them 
  together 
  after 
  multiplying 
  

   the 
  pih 
  by 
  2, 
  all 
  the 
  R's 
  will 
  be 
  eliminated 
  except 
  three, 
  the 
  

   resulting 
  equation 
  being 
  

  

  v 
  ( 
  Vi 
  + 
  2K 
  P 
  + 
  B„ 
  + 
  + 
  2 
  ptf» 
  + 
  ^) 
  R 
  p 
  = 
  0, 
  

  

  subject 
  to 
  the 
  following 
  exception, 
  namely, 
  that 
  when 
  p 
  = 
  m 
  

   we 
  must 
  add 
  the 
  term 
  — 
  (\t 
  2 
  + 
  fis 
  2 
  ) 
  W, 
  and 
  that 
  in 
  the 
  last 
  

   equation 
  vH^r 
  must 
  be 
  replaced 
  by 
  v'E^-. 
  

  

  Let 
  V/f=«, 
  and 
  2(\t 
  2 
  -\-jj,s 
  2 
  )/v=l3, 
  then 
  each 
  three 
  succes- 
  

   sive 
  It's 
  of 
  the 
  series 
  R 
  x 
  R 
  2 
  . 
  . 
  . 
  E 
  ?>i 
  satisfy 
  the 
  difference 
  

   equation 
  

  

  E 
  p 
  _ 
  1 
  + 
  (2+yS)R 
  p 
  + 
  R 
  p+1 
  = 
  0. 
  .... 
  (8) 
  

  

  Accordingly, 
  this 
  series 
  of 
  It's 
  are 
  given 
  by 
  the 
  equation 
  

  

  R 
  p 
  = 
  Au 
  m 
  -p 
  + 
  'Bv 
  m 
  -p, 
  (9) 
  

  

  where 
  u 
  and 
  v 
  are 
  the 
  roots 
  of 
  the 
  equation 
  

  

  u 
  2 
  +{2 
  + 
  /3)u 
  + 
  l 
  = 
  0, 
  

  

  