﻿92 
  

  

  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  8 
  z, 
  and 
  differentiating 
  with 
  respect 
  to 
  x, 
  y, 
  and 
  z, 
  in 
  each 
  equation, 
  we 
  obtain 
  the 
  

   equations— 
  

  

  d 
  8 
  a 
  

   dx 
  

  

  8a 
  „ 
  8 
  8 
  „ 
  £7 
  „ 
  

   a 
  l 
  /3 
  ' 
  7 
  x 
  

  

  d 
  8 
  y 
  8 
  a 
  Q 
  8 
  8 
  , 
  „ 
  £7 
  

   o?y 
  a 
  

  

  e?$ 
  £ 
  £ 
  a 
  

  

  a 
  

  

  dz 
  

  

  P 
  ' 
  ' 
  7 
  

  

  /3 
  3 
  7 
  

  

  rf^z 
  £ 
  a 
  8 
  8,, 
  8 
  7 
  s.^ 
  

  

  — 
  7— 
  = 
  ■ 
  «, 
  «., 
  + 
  ->r 
  «, 
  0„ 
  + 
  '- 
  C.C. 
  2 
  + 
  0., 
  \ 
  

  

  dy 
  a 
  1 
  2 
  j3 
  l 
  2 
  7 
  1 
  2 
  3 
  

  

  d 
  8 
  x 
  8 
  a 
  8 
  8,, 
  8 
  7 
  $■ 
  a 
  

  

  - 
  = 
  —-«, 
  a 
  8 
  + 
  -^ 
  \ 
  J 
  8 
  + 
  — 
  *- 
  c 
  x 
  c 
  s 
  - 
  b 
  6 
  2 
  

  

  (!)• 
  

  

  Equations 
  of 
  

   compression. 
  

  

  d 
  z 
  

  

  d 
  8 
  t/ 
  8 
  a 
  

  

  8 
  8,, 
  8 
  7 
  $ 
  n 
  

  

  — 
  a, 
  2 
  « 
  3 
  + 
  -£- 
  b 
  2 
  b 
  3 
  + 
  —J- 
  c 
  2 
  c 
  s 
  + 
  6 
  6, 
  

  

  d 
  

   d8 
  y 
  8 
  a 
  

  

  d 
  x 
  

   d 
  8 
  z 
  8 
  a 
  

  

  8 
  8 
  , 
  , 
  8 
  y 
  <n 
  a 
  

  

  a. 
  y 
  a. 
  + 
  —p~ 
  b., 
  b. 
  -\ 
  c 
  9 
  c. 
  — 
  o 
  a.. 
  

  

  dx 
  

  

  8 
  8,. 
  8 
  7 
  * 
  /i 
  

  

  «8 
  »1+ 
  "^ 
  6 
  3 
  6 
  l 
  + 
  -~ 
  C 
  S 
  C 
  l 
  + 
  6 
  ^2 
  

  

  P 
  

  

  djz 
  

  

  d 
  8 
  z 
  8 
  a 
  8 
  8,, 
  8 
  7 
  s,/j 
  

  

  (2)- 
  

  

  Equations 
  of 
  the 
  equilibrium 
  of 
  an 
  element 
  of 
  the 
  solid. 
  

   The 
  forces 
  which 
  may 
  act 
  on 
  a 
  particle 
  of 
  the 
  solid 
  are 
  : 
  — 
  

  

  1. 
  Three 
  attractions 
  in 
  the 
  direction 
  of 
  the 
  axes, 
  represented 
  by 
  X, 
  Y, 
  Z. 
  

  

  2. 
  Six 
  pressures 
  on 
  the 
  six 
  faces. 
  

  

  3. 
  Two 
  tangential 
  actions 
  on 
  each 
  face. 
  

  

  Let 
  the 
  six 
  faces 
  of 
  the 
  small 
  parallelopiped 
  be 
  denoted 
  by 
  x 
  x 
  , 
  y 
  v 
  z 
  v 
  x.„ 
  y 
  , 
  

   and 
  z 
  2 
  , 
  then 
  the 
  forces 
  acting 
  on 
  a? 
  x 
  are 
  : 
  — 
  

  

  1. 
  A 
  normal 
  pressure 
  p 
  t 
  acting 
  in 
  the 
  direction 
  of 
  x 
  on 
  the 
  area 
  dy 
  dz. 
  

  

  2. 
  A 
  tangential 
  force 
  q 
  3 
  acting 
  in 
  the 
  direction 
  of 
  y 
  on 
  the 
  same 
  area. 
  

  

  3. 
  A 
  tangential 
  force 
  q 
  2 
  acting 
  in 
  the 
  direction 
  of 
  z 
  on 
  the 
  same 
  area, 
  and 
  so 
  

   on 
  for 
  the 
  other 
  five 
  faces, 
  thus 
  : 
  — 
  

  

  Forces 
  which 
  act 
  in 
  the 
  direction 
  of 
  the 
  axes 
  of 
  

  

  • 
  

  

  X 
  

  

  y 
  

  

  z 
  

  

  On 
  the 
  face 
  x 
  A 
  

  

  —p, 
  dy 
  d 
  z 
  

  

  — 
  q 
  % 
  dydz 
  

  

  — 
  g^ 
  1 
  dy 
  dz 
  

  

  * 
  2 
  

  

  (.Pi 
  + 
  "7T" 
  1 
  d 
  x 
  ) 
  d 
  y 
  dz 
  

  

  Qj 
  X 
  

  

  (%+-j^dx)dydx 
  

  

  (3-2 
  l 
  + 
  /* 
  dx)dydz 
  

  

  Vt 
  

  

  — 
  q.^dzdx 
  

  

  —p 
  2 
  dzd 
  x 
  

  

  — 
  q 
  1 
  dzdx 
  

  

  y 
  2 
  

  

  (?3+ 
  J* 
  dy)dzdx 
  

  

  2 
  + 
  -j?dy)dzdx 
  

  

  (.9 
  1 
  +-jjdy)dzdx 
  

  

  