﻿116 
  

  

  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

  

  If 
  two 
  cylindric 
  surfaces, 
  whose 
  axes 
  are 
  perpendicular 
  to 
  the 
  plane 
  of 
  an 
  

   indefinite 
  elastic 
  plate, 
  be 
  equally 
  twisted 
  in 
  the 
  same 
  direction, 
  the 
  resultant 
  

   compression 
  in 
  any 
  direction 
  may 
  be 
  found 
  by 
  adding 
  the 
  compression 
  due 
  to 
  each 
  

   resolved 
  in 
  that 
  direction. 
  

  

  The 
  result 
  of 
  this 
  operation 
  may 
  be 
  thus 
  stated 
  geometrically. 
  Let 
  A 
  1 
  and 
  

   A 
  2 
  (fig. 
  1.) 
  be 
  the 
  centres 
  of 
  the 
  twisted 
  cylinders. 
  Join 
  A 
  x 
  A,, 
  and 
  bisect 
  A 
  x 
  A, 
  

   in 
  0. 
  Draw 
  OBC 
  at 
  right 
  angles, 
  and 
  cut 
  off 
  0B 
  t 
  and 
  0B 
  2 
  each 
  equal 
  to 
  0A 
  r 
  

  

  Fig. 
  1. 
  

  

  Then 
  the 
  difference 
  of 
  the 
  retardation 
  of 
  oppositely 
  polarized 
  rays 
  of 
  light 
  

   passing 
  perpendicularly 
  through 
  any 
  point 
  of 
  the 
  plane 
  varies 
  directly 
  as 
  the 
  pro- 
  

   duct 
  of 
  its 
  distances 
  from 
  B 
  L 
  and 
  B 
  2 
  , 
  and 
  inversely 
  as 
  the 
  square 
  of 
  the 
  product 
  

   of 
  its 
  distances 
  from 
  A 
  1 
  and 
  A 
  2 
  . 
  

  

  The 
  isochromatic 
  lines 
  are 
  represented 
  in 
  the 
  figure. 
  

  

  The 
  retardation 
  is 
  infinite 
  at 
  the 
  points 
  A 
  1 
  and 
  A 
  2 
  ; 
  it 
  vanishes 
  at 
  Bj 
  and 
  B 
  

  

  2 
  ■> 
  

  

  