﻿HO 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  To 
  obtain 
  an 
  expression 
  for 
  the 
  curvature 
  of 
  the 
  plate 
  at 
  the 
  vertex, 
  let 
  a 
  be 
  

   the 
  radius 
  of 
  curvature, 
  then, 
  as 
  an 
  approximation 
  to 
  the 
  equation 
  of 
  the 
  plate, 
  let 
  

  

  X 
  ~ 
  2 
  a 
  

  

  By 
  substituting 
  the 
  value 
  of 
  x 
  in 
  the 
  values 
  of 
  p 
  and 
  <?, 
  and 
  in 
  the 
  equation 
  

   of 
  elasticity, 
  the 
  approximate 
  value 
  of 
  a 
  is 
  found 
  to 
  be 
  

  

  ft 
  *v 
  (rs-iL) 
  - 
  2 
  

  

  a 
  =i 
  T 
  

  

  h 
  - 
  A 
  2 
  

  

  ioO— 
  M-- 
  

  

  \9 
  fx 
  3 
  m) 
  m 
  

  

  a= 
  t 
  -18m 
  p 
  t 
  K 
  + 
  h^ 
  m-3fx 
  

  

  h 
  x 
  — 
  h 
  2 
  10 
  m 
  + 
  51 
  /J. 
  h 
  x 
  — 
  h 
  2 
  10 
  m 
  + 
  51 
  /J. 
  ^ 
  '■ 
  

  

  a 
  

  

  Since 
  the 
  focal 
  distance 
  of 
  the 
  mirror, 
  or 
  ^, 
  depends 
  on 
  the 
  difference 
  of 
  

  

  pressures, 
  a 
  telescope 
  on 
  Mr 
  Nasmyth's 
  principle 
  would 
  act 
  as 
  an 
  aneroid 
  baro- 
  

   meter, 
  the 
  focal 
  distance 
  varying 
  inversely 
  as 
  the 
  pressure 
  of 
  the 
  atmosphere. 
  

  

  Case 
  VII. 
  

  

  To 
  find 
  the 
  conditions 
  of 
  torsion 
  of 
  a 
  cylinder 
  composed 
  of 
  a 
  great 
  number 
  of 
  

   parallel 
  wires 
  bound 
  together 
  without 
  adhering 
  to 
  one 
  another. 
  

  

  Let 
  x 
  be 
  the 
  length 
  of 
  the 
  cylinder, 
  a 
  its 
  radius, 
  r 
  the 
  radius 
  at 
  any 
  point, 
  

   8 
  6 
  the 
  angle 
  of 
  torsion, 
  M 
  the 
  force 
  producing 
  torsion, 
  8 
  x 
  the 
  change 
  of 
  length, 
  

   and 
  P 
  the 
  longitudinal 
  force. 
  Each 
  of 
  the 
  wires 
  becomes 
  a 
  helix 
  whose 
  radius 
  is 
  

   r 
  v 
  its 
  angular 
  rotation 
  8 
  6, 
  and 
  its 
  length 
  along 
  the 
  axis 
  x— 
  8 
  6. 
  

  

  Its 
  length 
  is 
  therefore 
  J( 
  r 
  8 
  6f 
  + 
  * 
  (l- 
  — 
  \ 
  

  

  and 
  the 
  tension 
  is 
  =E 
  (l-J 
  (l-— 
  V 
  + 
  V 
  s 
  (— 
  ) 
  ' 
  ) 
  

  

  This 
  force, 
  resolved 
  parallel 
  to 
  the 
  axis, 
  is 
  

   d 
  dp-i?/ 
  1 
  

  

  re 
  ^ 
  P 
  - 
  E 
  

  

  ^'♦'(v)'" 
  1 
  ) 
  

  

  and 
  since 
  — 
  and 
  r 
  — 
  are 
  small, 
  we 
  may 
  assume 
  

  

  XX 
  J 
  

  

  d6 
  dr 
  \x 
  2 
  \x 
  ) 
  ) 
  

  

  The 
  force, 
  when 
  resolved 
  in 
  the 
  tangential 
  direction, 
  is 
  approximately 
  

   r 
  2 
  dd 
  Tx 
  

  

  '■«-('.£ 
  £-£&)') 
  

  

  86 
  8x 
  r 
  G 
  /86\ 
  3 
  

   M 
  

  

  _, 
  /r 
  4 
  86 
  8x 
  r 
  G 
  /86\ 
  3 
  \ 
  ,„. 
  

  

  ^{jt 
  ~t\t) 
  ) 
  ••• 
  (5o 
  - 
  ) 
  

  

  