﻿(58.) 
  

  

  112 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  ajh^a^ 
  _ 
  £k 
  /EX 
  

  

  When 
  a 
  2 
  =0, 
  as 
  in 
  the 
  case 
  of 
  a 
  solid 
  cylinder, 
  c 
  1= 
  o, 
  and 
  

  

  2 
  7T 
  2 
  * 
  /„ 
  E\ 
  

  

  *= 
  h 
  i 
  + 
  £l* 
  { 
  2 
  ^ 
  + 
  + 
  ^( 
  3 
  ^ 
  2 
  -« 
  1 
  2 
  )} 
  • 
  • 
  • 
  • 
  (59.) 
  

  

  When 
  7^ 
  = 
  0, 
  and 
  r— 
  a^ 
  

  

  7r 
  2 
  /fe« 
  2 
  /E 
  \ 
  

  

  ?= 
  ^?-U- 
  2 
  ) 
  • 
  • 
  • 
  • 
  w 
  

  

  When 
  q 
  exceeds 
  the 
  tenacity 
  of 
  the 
  substance 
  in 
  pounds 
  per 
  square 
  inch, 
  the 
  

   cylinder 
  will 
  give 
  way 
  ; 
  and 
  by 
  making 
  q 
  equal 
  to 
  the 
  number 
  of 
  pounds 
  which 
  a 
  

   square 
  inch 
  of 
  the 
  substance 
  will 
  support, 
  the 
  velocity 
  may 
  be 
  found 
  at 
  which 
  the 
  

   bursting 
  of 
  the 
  cylinder 
  will 
  take 
  place. 
  

  

  Since 
  1=6 
  w 
  (g—p) 
  = 
  — 
  — 
  f 
  — 
  —2\br 
  2 
  , 
  a 
  transparent 
  revolving 
  cylinder, 
  when 
  

  

  polarized 
  light 
  is 
  transmitted 
  parallel 
  to 
  the 
  axis, 
  will 
  exhibit 
  rings 
  whose 
  diame- 
  

   ters 
  are 
  as 
  the 
  square 
  roots 
  of 
  an 
  arithmetical 
  progression, 
  and 
  brushes 
  parallel 
  

   and 
  perpendicular 
  to 
  the 
  plane 
  of 
  polarization. 
  

  

  CASE 
  IX. 
  

  

  A 
  hollow 
  cylinder 
  or 
  tube 
  is 
  surrounded 
  by 
  a 
  medium 
  of 
  a 
  constant 
  temper- 
  

   ature 
  while 
  a 
  liquid 
  of 
  a 
  different 
  temperature 
  is 
  made 
  to 
  flow 
  through 
  it. 
  The 
  

   exterior 
  and 
  interior 
  surfaces 
  are 
  thus 
  kept 
  each 
  at 
  a 
  constant 
  temperature 
  till 
  

   the 
  transference 
  of 
  heat 
  through 
  the 
  cylinder 
  becomes 
  uniform. 
  

  

  Let 
  v 
  be 
  the 
  temperature 
  at 
  any 
  point, 
  then 
  when 
  this 
  quantity 
  has 
  reached 
  

   its 
  limit, 
  

  

  r 
  d 
  v 
  _ 
  

   ~dV~° 
  l 
  

  

  x 
  = 
  c 
  l 
  \ogr 
  + 
  c 
  2 
  .... 
  (61.) 
  

  

  Let 
  the 
  temperatures 
  at 
  the 
  surfaces 
  be 
  6 
  X 
  and 
  6 
  2 
  , 
  and 
  the 
  radii 
  of 
  the 
  sur- 
  

   faces 
  a 
  y 
  and 
  a 
  2 
  , 
  then 
  

  

  1 
  log 
  a 
  x 
  — 
  log 
  «, 
  2 
  log^ 
  — 
  log 
  a 
  2 
  

  

  Let 
  the 
  coefficient 
  of 
  linear 
  dilatation 
  of 
  the 
  substance 
  be 
  c 
  s 
  , 
  then 
  the 
  pro- 
  

   portional 
  dilatation 
  at 
  any 
  point 
  will 
  be 
  expressed 
  by 
  c 
  $ 
  v, 
  and 
  the 
  equations 
  of 
  

   elasticity 
  (18.), 
  (19.), 
  (20.), 
  become 
  

  

  d 
  8 
  x 
  

  

  - 
  (n 
  Q 
  ) 
  (°+P 
  + 
  9)+ 
  ~ 
  

  

  d 
  x 
  \9 
  fx 
  Zm) 
  K 
  r 
  * 
  ' 
  m 
  

  

  ■c„ 
  v 
  

  

  