﻿114 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  tion 
  of 
  the 
  oppositely 
  polarized 
  rays 
  of 
  light 
  is 
  proportional 
  to 
  the 
  square 
  of 
  the 
  

   radius 
  r, 
  or 
  

  

  dr 
  

  

  dp 
  c 
  

  

  1 
  ,.2 
  

  

  Since 
  if 
  a 
  be 
  the 
  radius 
  of 
  the 
  cylinder, 
  p=o 
  when 
  r=a, 
  

  

  p 
  = 
  °^(r 
  2 
  -a 
  2 
  ) 
  

  

  Hence 
  ?=|(3 
  r*-a*) 
  

  

  By 
  substituting 
  these 
  values 
  of 
  p 
  and 
  q 
  in 
  equations 
  (19) 
  and 
  (20), 
  and 
  making 
  

  

  d 
  8r 
  ddr 
  T 
  fl 
  , 
  

  

  r=- 
  T 
  — 
  , 
  1 
  hnd, 
  

  

  dr 
  r 
  dr 
  1 
  

  

  c 
  being 
  the 
  temperature 
  of 
  the 
  axis 
  of 
  the 
  cjdinder, 
  and 
  c 
  3 
  the 
  coefficient 
  of 
  linear 
  

   expansion 
  for 
  glass. 
  

  

  Case 
  XL 
  

   Heat 
  is 
  passing 
  uniformly 
  through 
  the 
  sides 
  of 
  a 
  spherical 
  vessel, 
  such 
  as 
  the 
  

   ball 
  of 
  a 
  thermometer, 
  it 
  is 
  required 
  to 
  determine 
  the 
  mechanical 
  state 
  of 
  the 
  

   sphere. 
  As 
  the 
  methods 
  are 
  nearly 
  the 
  same 
  as 
  in 
  Case 
  IX., 
  it 
  will 
  be 
  sufficient 
  

   to 
  give 
  the 
  results, 
  using 
  the 
  same 
  notation. 
  

  

  dv 
  c. 
  

  

  r~ 
  -rr- 
  =C, 
  .'. 
  V=C„ 
  

  

  dv 
  r 
  

  

  6, 
  — 
  6 
  9 
  0, 
  a. 
  — 
  6., 
  a., 
  

  

  c, 
  = 
  a. 
  a, 
  — 
  * 
  * 
  c„ 
  = 
  — 
  u 
  i 
  — 
  J 
  

  

  1 
  L 
  * 
  a 
  x 
  — 
  a 
  2 
  £ 
  a 
  x 
  — 
  a 
  2 
  

  

  1 
  / 
  2 
  l\-i 
  I 
  

  

  4 
  r 
  3 
  \9 
  fx 
  3 
  m) 
  x 
  J 
  r 
  5 
  

  

  When 
  ^=A 
  2 
  =0 
  the 
  expression 
  for 
  p 
  becomes 
  

  

  From 
  this 
  value 
  of 
  p 
  the 
  other 
  quantities 
  may 
  be 
  found, 
  as 
  in 
  Case 
  IX., 
  from 
  

   the 
  equations 
  of 
  Case 
  IV. 
  

  

  Case 
  XII. 
  

  

  When 
  a 
  long 
  beam 
  is 
  bent 
  into 
  the 
  form 
  of 
  a 
  closed 
  circular 
  ring 
  (as 
  in 
  

   Case 
  V.), 
  all 
  the 
  pressures 
  act 
  either 
  parallel 
  or 
  perpendicular 
  to 
  the 
  direction 
  of 
  

   the 
  length 
  of 
  the 
  beam, 
  so 
  that 
  if 
  the 
  beam 
  were 
  divided 
  into 
  planks, 
  there 
  would 
  

   be 
  no 
  tendency 
  of 
  the 
  planks 
  to 
  slide 
  on 
  one 
  another. 
  

  

  But 
  when 
  the 
  beam 
  does 
  not 
  form 
  a 
  closed 
  circle, 
  the 
  planks 
  into 
  which 
  it 
  

   may 
  be 
  supposed 
  to 
  be 
  divided 
  will 
  have 
  a 
  tendency 
  to 
  slide 
  on 
  one 
  another, 
  and 
  

  

  