﻿98 
  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  dices 
  is 
  nearly 
  the 
  same 
  as 
  that 
  of 
  Canada 
  balsam, 
  while 
  the 
  other 
  is 
  very 
  differ- 
  

   ent, 
  the 
  common 
  surface 
  of 
  the 
  gutta 
  percha 
  and 
  Canada 
  balsam 
  will 
  transmit 
  

   one 
  set 
  of 
  rays 
  much 
  more 
  readily 
  than 
  the 
  other, 
  so 
  that 
  a 
  film 
  of 
  extended 
  gutta 
  

   percha 
  placed 
  between 
  two 
  layers 
  of 
  Canada 
  balsam 
  acts 
  like 
  a 
  plate 
  of 
  nitre 
  

   treated 
  in 
  the 
  same 
  way. 
  That 
  these 
  films 
  are 
  in 
  a 
  state 
  of 
  constraint 
  may 
  be 
  

   proved 
  by 
  heating 
  them 
  slightly, 
  when 
  they 
  recover 
  their 
  original 
  dimensions. 
  

  

  As 
  all 
  these 
  permanently 
  compressed 
  substances 
  have 
  passed 
  their 
  limit 
  of 
  

   perfect 
  elasticity, 
  they 
  do 
  not 
  belong 
  to 
  the 
  class 
  of 
  elastic 
  solids 
  treated 
  of 
  in 
  this 
  

   paper 
  ; 
  and 
  as 
  I 
  cannot 
  explain 
  the 
  method 
  by 
  which 
  an 
  uncrystallised 
  body 
  

   maintains 
  itself 
  in 
  a 
  state 
  of 
  constraint, 
  I 
  go 
  on 
  to 
  the 
  next 
  case 
  of 
  twisting, 
  which 
  

   has 
  more 
  practical 
  importance 
  than 
  any 
  other. 
  This 
  is 
  the 
  case 
  of 
  a 
  cylinder 
  

   fixed 
  at 
  one 
  end, 
  and 
  twisted 
  at 
  the 
  other 
  by 
  a 
  couple 
  whose 
  moment 
  is 
  M. 
  

  

  Case 
  II. 
  

  

  In 
  this 
  case 
  let 
  8 
  6 
  be 
  the 
  angle 
  of 
  torsion 
  at 
  any 
  point, 
  then 
  the 
  resistance 
  to 
  

   torsion 
  in 
  any 
  circular 
  section 
  of 
  the 
  cylinder 
  is 
  equal 
  to 
  the 
  twisting 
  force 
  M. 
  

  

  The 
  resistance 
  at 
  any 
  point 
  in 
  the 
  circular 
  section 
  is 
  given 
  by 
  the 
  second 
  

   Equation 
  of 
  (14.) 
  

  

  m 
  d 
  8 
  6 
  

  

  This 
  force 
  acts 
  at 
  the 
  distance 
  r 
  from 
  the 
  axis 
  ; 
  therefore 
  its 
  resistance 
  to 
  torsion 
  

   will 
  be 
  q. 
  2 
  r, 
  and 
  the 
  resistance 
  in 
  a 
  circular 
  annulus 
  will 
  be 
  

  

  O 
  J 
  r.d 
  8 
  6 
  , 
  

  

  q 
  2 
  r 
  I 
  7T 
  r 
  ar 
  = 
  m 
  r 
  TT 
  r 
  6 
  —^ 
  — 
  dr 
  

  

  Co 
  X 
  

  

  and 
  the 
  whole 
  resistance 
  for 
  the 
  hollow 
  cylinder 
  will 
  be 
  expressed 
  by 
  

  

  „_ 
  mirdoo, 
  , 
  .. 
  ,-,„s 
  

  

  M= 
  ^^T^-0 
  • 
  • 
  < 
  16 
  -> 
  

  

  ™=4M 
  — 
  ^ 
  

  

  720 
  M 
  

   in 
  — 
  

  

  _720 
  M 
  / 
  b 
  \ 
  

  

  ~ 
  n* 
  n 
  Ui 
  4 
  -« 
  2 
  V 
  " 
  ' 
  ( 
  

  

  In 
  this 
  equation, 
  m 
  is 
  the 
  coefficient 
  of 
  linear 
  elasticity; 
  a 
  l 
  and 
  a 
  2 
  are 
  the 
  

   radii 
  of 
  the 
  exterior 
  and 
  interior 
  surfaces 
  of 
  the 
  hollow 
  cylinder 
  in 
  inches 
  ; 
  M 
  is 
  

   the 
  moment 
  of 
  torsion 
  produced 
  by 
  a 
  weight 
  acting 
  on 
  a 
  lever, 
  and 
  is 
  expressed 
  

   by 
  the 
  product 
  of 
  the 
  number 
  of 
  pounds 
  in 
  the 
  weight 
  into 
  the 
  number 
  of 
  inches 
  

   in 
  the 
  lever 
  ; 
  b 
  is 
  the 
  distance 
  of 
  two 
  points 
  on 
  the 
  cylinder 
  whose 
  angular 
  motion 
  

   is 
  measured 
  by 
  means 
  of 
  indices, 
  or 
  more 
  accurately 
  by 
  small 
  mirrors 
  attached 
  to 
  

  

  