﻿94 
  

  

  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  The 
  quantity 
  /j. 
  is 
  the 
  coefficient 
  of 
  cubical 
  elasticity, 
  and 
  m 
  that 
  of 
  linear 
  

  

  elasticity. 
  

  

  By 
  solving 
  these 
  equations, 
  the 
  values 
  of 
  the 
  pressures 
  F 
  v 
  P 
  2 
  , 
  P 
  3 
  , 
  and 
  the 
  

  

  8a 
  8(3 
  Sy 
  , 
  „ 
  , 
  

  

  compressions 
  — 
  , 
  -£-, 
  — 
  - 
  may 
  be 
  found. 
  

  

  „ 
  , 
  1 
  ./8a 
  8(3 
  8y\ 
  8a\ 
  

  

  1 
  vr 
  3 
  J 
  \ 
  a 
  (3 
  y 
  ) 
  a 
  

  

  3 
  r 
  3 
  y 
  U 
  /5 
  y 
  ) 
  y 
  

  

  T^rrsy^+P'+P^^ 
  ' 
  • 
  (7) 
  

  

  £ 
  7 
  

  

  From 
  these 
  values 
  of 
  the 
  pressures 
  in 
  the 
  axes 
  a, 
  (3, 
  y, 
  may 
  be 
  obtained 
  the 
  

   equations 
  for 
  the 
  axes 
  x, 
  y, 
  z, 
  by 
  resolution 
  of 
  pressures 
  and 
  compressions.* 
  

  

  = 
  (^ 
  — 
  o—) 
  Pi 
  +Po 
  + 
  P 
  3 
  ) 
  + 
  — 
  P 
  3 
  

  

  For 
  

   and 
  

  

  p 
  = 
  a 
  2 
  P, 
  + 
  6 
  2 
  P 
  2 
  + 
  c 
  2 
  P 
  3 
  

   ^ 
  = 
  aaPj 
  + 
  6 
  b 
  P 
  2 
  + 
  ccP 
  3 
  

  

  1 
  s 
  (d8 
  x 
  d8y 
  d 
  8 
  z\ 
  

  

  ^^-^ 
  m) 
  Kdx- 
  + 
  'df 
  + 
  -d7) 
  + 
  

  

  p 
  

  

  = 
  (M~3 
  ?W 
  )( 
  : 
  

  

  d 
  8 
  x 
  d8y 
  d 
  8 
  z 
  

  

  dx 
  

  

  + 
  

  

  ) 
  

  

  + 
  m 
  

  

  dy 
  dz 
  } 
  dy 
  

  

  , 
  1 
  . 
  id 
  8 
  x 
  d8 
  \i 
  d 
  8 
  z\ 
  d 
  8 
  z 
  

  

  P 
  ^^-3 
  m 
  A-dV 
  + 
  -df 
  + 
  -dx-) 
  +m 
  ^Vf 
  

  

  _ 
  m 
  (d 
  8\) 
  d 
  8 
  z\ 
  

   qi 
  -~2\~~dz~ 
  + 
  ~dy~) 
  

  

  id 
  8 
  z 
  d8 
  x\ 
  

   V 
  dx 
  dz 
  ) 
  

  

  (8.) 
  

  

  SV 
  

  

  m 
  

  

  'd 
  8 
  z 
  d 
  8 
  x^ 
  

   dx 
  d, 
  

  

  _m 
  fd 
  8 
  x 
  d8 
  y\ 
  

   qi 
  ~~2\dy~ 
  + 
  ~dx~) 
  

  

  (9.) 
  

  

  d8 
  

  

  1 
  8x 
  ( 
  1 
  1 
  \ 
  1 
  

  

  d: 
  

   d8y 
  ( 
  1 
  1 
  \ 
  1 
  

  

  d 
  8 
  z 
  

   d 
  z 
  \j 
  jJL 
  

  

  (10.) 
  

  

  * 
  See 
  the 
  Memoir 
  of 
  Lame 
  and 
  Clapeyron, 
  and 
  note 
  A. 
  

  

  