﻿4()2 
  Dr. 
  J. 
  Morrow 
  on 
  the 
  Lateral 
  Deflexion 
  and 
  

   For 
  j^>a 
  the 
  equation 
  is 
  

  

  Elg'=T(t,,-y)-M, 
  

  

  and 
  the 
  solution 
  

  

  M 
  

  

  y' 
  = 
  A2 
  sin 
  n.v 
  + 
  ^2 
  ^^^ 
  '^^^ 
  "^ 
  yi 
  — 
  m 
  

  

  where 
  the 
  dashed 
  symbols 
  refer 
  to 
  values 
  of 
  y 
  in 
  the 
  region 
  h. 
  

   The 
  conditions 
  at 
  .27 
  = 
  and 
  x 
  = 
  l 
  lead 
  respectively 
  to 
  

  

  J/ 
  

  

  M 
  

  

  -yi)[GOsn.v-ij+-^a; 
  i 
  

  

  M/ 
  . 
  , 
  . 
  . 
  \ 
  M 
  > 
  (^^) 
  

  

  '= 
  7p 
  ( 
  sin 
  nl 
  sin 
  naj 
  -\- 
  cos 
  nl 
  cos 
  nccj-\- 
  2/1 
  — 
  

  

  ! 
  

  

  M 
  

   T 
  

  

  The 
  conditions 
  of 
  continuity 
  of 
  y 
  and 
  -^ 
  when 
  a; 
  = 
  a 
  give 
  

   an 
  expression 
  for 
  the 
  couple 
  at 
  the 
  directed 
  end, 
  namely 
  

  

  ^^ 
  •• 
  cos 
  na 
  — 
  1 
  

  

  M 
  = 
  ??iv„ 
  -. 
  7- 
  . 
  

  

  nsm^il 
  

  

  Putting 
  £C 
  = 
  a 
  in 
  the 
  expressions 
  for 
  y 
  and 
  y^ 
  we 
  find 
  

  

  k~^=-Trr<^ 
  smna(2-'Cosna) 
  — 
  cot 
  nl 
  {1 
  — 
  COS 
  nay— 
  na 
  l- 
  . 
  (24) 
  

  

  When 
  a 
  = 
  l, 
  this 
  reduces 
  to 
  the 
  result 
  of 
  § 
  16. 
  

  

  It 
  can 
  be 
  shown, 
  from 
  equations 
  (23), 
  that 
  the 
  amplitude 
  

   is 
  a 
  maximum 
  at 
  the 
  directed 
  end. 
  

  

  Section 
  YI. 
  — 
  Deduction 
  of 
  the 
  Results 
  of 
  some 
  

   Statical 
  P7vblems. 
  

  

  § 
  19. 
  The 
  calculations 
  in 
  Section 
  V. 
  are 
  similar 
  to 
  those 
  

   required 
  for 
  the 
  corresponding 
  statical 
  problems. 
  Thus 
  if 
  a 
  

   clamped-directed 
  bar 
  be 
  subjected 
  to 
  a 
  force 
  W 
  at 
  and 
  per- 
  

   pendicular 
  to 
  the 
  directed 
  end, 
  the 
  centre-line 
  assumes 
  the 
  

   form 
  (see 
  § 
  15) 
  

  

  

  