﻿456 
  Dr. 
  J. 
  Morrow 
  07i 
  the 
  Lateral 
  Deflection 
  and 
  

  

  end 
  is 
  given 
  by 
  

  

  ,^■ 
  = 
  •7166 
  /. 
  

  

  For 
  higher 
  harmonics, 
  the 
  zth 
  tone 
  has 
  i 
  — 
  1 
  nodes 
  ; 
  and 
  o£ 
  

   these 
  the 
  first 
  node, 
  that 
  is 
  the 
  one 
  nearest 
  the 
  clamped 
  end, 
  

   is 
  at 
  

  

  A' 
  _ 
  5-0175 
  

  

  the 
  second 
  occurs 
  at 
  

  

  A- 
  _ 
  8-9993 
  

  

  / 
  4^-i 
  ' 
  

   and 
  beyond 
  this 
  the 
  ;th 
  node 
  is 
  given 
  with 
  sufficient 
  accuracy 
  

  

  I 
  4i-l* 
  

  

  Section 
  III. 
  — 
  Unloaded 
  Massive 
  Bar, 
  Longitudinal 
  Tension. 
  

  

  § 
  9. 
  When 
  the 
  bar 
  is 
  subjected 
  to 
  an 
  axial 
  tensile 
  force 
  P 
  

   as 
  shown 
  in 
  figure 
  3, 
  the 
  differential 
  equation, 
  based 
  on 
  the 
  

   ordinary 
  Bernoulli-Eulerian 
  theory^ 
  may 
  be 
  written 
  

  

  %^P'o\'y.{z-.'c)dz 
  + 
  V{y,-y)+li 
  = 
  0. 
  . 
  (8) 
  

  

  »/ 
  X 
  

  

  in 
  which 
  M 
  is 
  the 
  couple 
  required 
  to 
  direct 
  the 
  end 
  and 
  yi 
  is 
  

   the 
  deflexion 
  there. 
  

  

  -Fi-. 
  3. 
  

  

  Differentiating 
  twice 
  with 
  respect 
  to 
  .r, 
  

  

  which 
  is 
  the 
  differential 
  equation 
  common 
  to 
  all 
  unloaded 
  

   bars 
  of 
  constant 
  flexural 
  rigidity. 
  It 
  may 
  be 
  written 
  

  

  dx^^Y^ly,^ 
  ^Idx"-^' 
  . 
  . 
  . 
  . 
  cy; 
  

  

  for 
  the 
  case 
  of 
  stationary 
  simple 
  harmonic 
  vibrations. 
  The 
  

  

  