﻿100 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  q 
  - 
  p 
  = 
  c 
  2 
  — 
  2p, 
  therefore 
  by 
  (21.) 
  

  

  dp 
  2p 
  c 
  2 
  

   a 
  linear 
  equation, 
  which 
  gives 
  

  

  d 
  r 
  r 
  r 
  

  

  1 
  c, 
  

  

  The 
  coefficients 
  c 
  2 
  and 
  c 
  3 
  must 
  be 
  found 
  from 
  the 
  conditions 
  of 
  the 
  surface 
  of 
  

   the 
  solid. 
  If 
  the 
  pressure 
  on 
  the 
  exterior 
  cylindric 
  surface 
  whose 
  radius 
  is 
  a 
  x 
  be 
  

   denoted 
  by 
  h 
  t 
  , 
  and 
  that 
  on 
  the 
  interior 
  surface 
  whose 
  radius 
  is 
  a 
  2 
  by 
  h 
  2 
  , 
  

  

  then 
  p 
  = 
  h 
  x 
  when 
  r 
  = 
  a 
  x 
  

   and 
  p 
  = 
  h 
  2 
  when 
  r 
  = 
  a 
  2 
  

  

  and 
  the 
  general 
  value 
  of 
  p 
  is 
  

  

  a 
  2 
  h 
  } 
  -a 
  2 
  h 
  2 
  a 
  2 
  a 
  2 
  h 
  x 
  ~h 
  2 
  

  

  a 
  2 
  — 
  a 
  2 
  2 
  r 
  2 
  a*—a£ 
  ^ 
  *' 
  

  

  dp 
  a 
  2 
  a 
  2 
  h.—h 
  2 
  . 
  , 
  01 
  . 
  

  

  a? 
  h 
  x 
  -a 
  2 
  h 
  a 
  2 
  a* 
  \-h 
  2 
  

  

  9 
  — 
  — 
  in 
  — 
  ^"2 
  1 
  12 
  — 
  ~2 
  — 
  ^~2 
  • 
  • 
  • 
  \ 
  16 
  -) 
  

  

  r- 
  «i 
  ~ 
  a 
  2 
  

  

  I 
  = 
  &w(p-?) 
  = 
  6w^f^ 
  -4 
  |— 
  \ 
  . 
  . 
  . 
  (24.) 
  

   v 
  ' 
  r 
  2 
  a 
  2 
  — 
  a 
  2 
  2 
  v 
  

  

  This 
  last 
  equation 
  gives 
  the 
  optical 
  effect 
  of 
  the 
  pressure 
  at 
  any 
  point. 
  The 
  

   law 
  of 
  the 
  magnitude 
  of 
  this 
  quantity 
  is 
  the 
  inverse 
  square 
  of 
  the 
  radius, 
  as 
  in 
  

   Case 
  I. 
  ; 
  but 
  the 
  direction 
  of 
  the 
  principal 
  axes 
  is 
  different, 
  as 
  in 
  this 
  case 
  they 
  

   are 
  parallel 
  and 
  perpendicular 
  to 
  the 
  radius. 
  The 
  dark 
  bands 
  seen 
  by 
  polarized 
  

   light 
  will 
  therefore 
  be 
  parallel 
  and 
  perpendicular 
  to 
  the 
  plane 
  of 
  polarization, 
  in- 
  

   stead 
  of 
  being 
  inclined 
  at 
  an 
  angle 
  of 
  45°, 
  as 
  in 
  Case 
  I. 
  

  

  By 
  substituting 
  in 
  Equations 
  (18.) 
  and 
  (20.), 
  the 
  values 
  of 
  p 
  and 
  q 
  given 
  in 
  

   (22.) 
  and 
  (23.), 
  we 
  find 
  that 
  when 
  r=a 
  v 
  

  

  8i 
  

  

  (25.) 
  

  

  x 
  \9 
  \x) 
  V 
  a 
  i 
  — 
  « 
  2 
  / 
  3m 
  \ 
  a^—a 
  2 
  l 
  J 
  

  

  = 
  ° 
  GV 
  3^) 
  +2 
  {K 
  <- 
  h 
  ^ 
  2) 
  7?h? 
  (977-3^) 
  

  

  wu 
  $ 
  r 
  1 
  I 
  n 
  a 
  2 
  h.-a. 
  2 
  h 
  \ 
  , 
  1 
  (a 
  2 
  A, 
  +3 
  a 
  2 
  2 
  7^-4 
  a 
  2 
  h 
  2 
  \\ 
  

   When 
  r=a,,— 
  = 
  7 
  r— 
  ( 
  o 
  + 
  2-J 
  — 
  \ 
  V~ 
  -) 
  +o 
  — 
  ( 
  — 
  — 
  „ 
  2 
  „ 
  2 
  • 
  — 
  °)\ 
  

  

  (1 
  1\ 
  .. 
  1 
  /2« 
  x 
  0! 
  2 
  + 
  3a 
  2 
  3 
  \ 
  _«2 
  / 
  2 
  M 
  

  

  (26.) 
  

  

  From 
  these 
  equations 
  it 
  appears 
  that 
  the 
  longitudinal 
  compression 
  of 
  cylin- 
  

   dric 
  tubes 
  is 
  proportional 
  to 
  the 
  longitudinal 
  pressure 
  referred 
  to 
  unit 
  of 
  surface 
  

   when 
  the 
  lateral 
  pressures 
  are 
  constant, 
  so 
  that 
  for 
  a 
  given 
  pressure 
  the 
  com- 
  

   pression 
  is 
  inversely 
  as 
  the 
  sectional 
  area 
  of 
  the 
  tube. 
  

  

  These 
  equations 
  may 
  be 
  simplified 
  in 
  the 
  following 
  cases 
  : 
  — 
  

  

  