﻿102 
  

  

  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  r 
  ~ 
  ** 
  \9 
  ul 
  + 
  3 
  m) 
  

  

  "When 
  the 
  longitudinal 
  pressure 
  o 
  vanishes, 
  

  

  ^-2k 
  U 
  U 
  

  

  x 
  ~ 
  " 
  l 
  \9jJi 
  3 
  m) 
  

  

  When 
  the 
  cylinder 
  is 
  pressed 
  on 
  the 
  plane 
  sides 
  only, 
  

  

  ?£ 
  - 
  fJL 
  2 
  \ 
  

  

  ar 
  \9 
  /z 
  3 
  ?«/ 
  

  

  r 
  ~~ 
  ~~ 
  ° 
  \9f* 
  3 
  m) 
  

   4. 
  When 
  the 
  solid 
  is 
  infinite, 
  or 
  when 
  o, 
  is 
  infinite, 
  

  

  P= 
  h 
  2 
  + 
  IT 
  «i 
  2 
  (A- 
  7 
  '*) 
  

  

  ? 
  =/i 
  2 
  -^-«l 
  2 
  (*i-^ 
  2 
  ) 
  

  

  1= 
  «(? 
  - 
  />) 
  = 
  — 
  p- 
  of 
  (A!-A 
  2 
  ) 
  

  

  \ 
  

  

  F 
  = 
  97r 
  (0 
  + 
  2 
  ^ 
  ) 
  + 
  ^ 
  (w 
  ~ 
  /i2) 
  

  

  3»« 
  

  

  = 
  (97I 
  + 
  3^) 
  +2 
  * 
  2 
  (97J-3^) 
  

  

  — 
  =5^-(o 
  + 
  2 
  A,) 
  + 
  _L(4A 
  2 
  -3A 
  2 
  -o) 
  

  

  >• 
  9 
  fj. 
  v 
  J 
  3 
  we 
  v 
  * 
  * 
  / 
  

  

  = 
  \9j~3Vi) 
  + 
  2 
  * 
  2 
  (97I 
  + 
  3^) 
  ~w 
  

  

  5. 
  When 
  £r=0 
  in 
  a 
  solid 
  cylinder, 
  

  

  d 
  x 
  2>o 
  

  

  x 
  

  

  8 
  x 
  

  

  6. 
  When 
  

  

  = 
  

  

  2?n 
  + 
  3/j. 
  

  

  8r 
  Zh 
  

  

  r 
  

  

  (29.) 
  

  

  (30.) 
  

  

  x 
  r 
  m 
  + 
  6 
  jJ. 
  

  

  Since 
  the 
  expression 
  for 
  the 
  effect 
  of 
  a 
  longitudinal 
  strain 
  is 
  

  

  — 
  -- 
  ( 
  — 
  —\ 
  

  

  x 
  ' 
  \ 
  9 
  ju 
  + 
  3 
  ?»/ 
  

  

  9«u 
  ,, 
  8 
  x 
  1 
  

  

  = 
  £ 
  -, 
  then 
  — 
  = 
  -^ 
  . 
  

  

  if 
  we 
  make 
  

  

  E 
  

  

  (31.) 
  

  

  m 
  + 
  6/JL' 
  "*""■ 
  a: 
  E 
  

  

  The 
  quantity 
  E 
  may 
  be 
  deduced 
  from 
  experiment 
  on 
  the 
  extension 
  of 
  wires 
  

   or 
  rods 
  of 
  the 
  substance, 
  and 
  // 
  is 
  given 
  in 
  terms 
  of 
  m 
  and 
  E 
  by 
  the 
  equation, 
  

  

  Em 
  

  

  and 
  

  

  ^~ 
  9w-6E 
  

   P6 
  

  

  E 
  = 
  

  

  8 
  

  

  (32.) 
  

  

  (33.) 
  

  

  