﻿118 
  

  

  MR 
  JAMES 
  CLERK 
  MAXWELL 
  ON 
  THE 
  

   D 
  D 
  E 
  t> 
  D 
  

  

  curves 
  for 
  every 
  fifteenth 
  degree 
  of 
  inclination. 
  They 
  correspond 
  to 
  the 
  lines 
  of 
  

   equal 
  variation 
  of 
  the 
  needle 
  in 
  a 
  magnetic 
  chart. 
  

  

  From 
  these 
  curves 
  others 
  may 
  be 
  found 
  which 
  shall 
  indicate, 
  by 
  their 
  own 
  

   direction, 
  the 
  direction 
  of 
  the 
  principal 
  axes 
  at 
  any 
  point. 
  These 
  curves 
  of 
  direc- 
  

   tion 
  of 
  compression 
  and 
  dilatation 
  are 
  represented 
  in 
  fig. 
  4 
  ; 
  the 
  curves 
  whose 
  

   direction 
  corresponds 
  to 
  that 
  of 
  compression 
  are 
  concave 
  toward 
  the 
  centre 
  of 
  the 
  

   triangle, 
  and 
  intersect 
  at 
  right 
  angles 
  the 
  curves 
  of 
  dilatation. 
  

  

  Let 
  the 
  isochromatic 
  lines 
  in 
  fig. 
  2 
  be 
  determined 
  by 
  the 
  equation 
  

  

  <Pi 
  (*i2f) 
  =I-=«(y 
  -p)~ 
  

  

  where 
  I 
  is 
  the 
  difference 
  of 
  retardation 
  of 
  the 
  oppositely 
  polarized 
  rays, 
  and 
  q 
  and 
  

   p 
  the 
  pressure 
  in 
  the 
  principal 
  axes 
  at 
  any 
  point, 
  z 
  being 
  the 
  thickness 
  of 
  the 
  

   plate. 
  

  

  Let 
  the 
  lines 
  of 
  equal 
  inclination 
  be 
  determined 
  by 
  the 
  equation 
  

  

  <p 
  2 
  (x 
  x 
  y) 
  =■ 
  tan 
  6 
  

  

  6 
  being 
  the 
  angle 
  of 
  inclination 
  of 
  the 
  principal 
  axes 
  ; 
  then 
  the 
  differential 
  equa- 
  

   tion 
  of 
  the 
  curves 
  of 
  direction 
  of 
  compression 
  and 
  dilatation 
  (fig. 
  4) 
  is 
  

  

  By 
  considering 
  any 
  particle 
  of 
  the 
  plate 
  as 
  a 
  portion 
  of 
  a 
  cylinder 
  whose 
  axis 
  

   passes 
  through 
  the 
  centre 
  of 
  curvature 
  of 
  the 
  curve 
  of 
  compression, 
  we 
  find 
  

  

  q 
  - 
  P 
  =r% 
  . 
  . 
  (21.) 
  

  

  Let 
  R 
  denote 
  the 
  radius 
  of 
  curvature 
  of 
  the 
  curve 
  of 
  compression 
  at 
  any 
  

   point, 
  and 
  let 
  S 
  denote 
  the 
  length 
  of 
  the 
  curve 
  of 
  dilatation 
  at 
  the 
  same 
  point, 
  

  

  g-p 
  = 
  H 
  

  

  dp 
  

   ds 
  

  

  