﻿EXPLANATION 
  OF 
  PLATES 
  II 
  TO 
  IX. 
  

  

  Plate 
  II. 
  Graphical 
  solution 
  of 
  the 
  refractive 
  index 
  equation 
  sin 
  i=n 
  . 
  

   sin 
  r. 
  The 
  ordinates 
  represent 
  the 
  angles 
  i, 
  the 
  abscissas, 
  the 
  refractive 
  

   indices, 
  n, 
  and 
  the 
  diagonal 
  lines 
  the 
  angles 
  r. 
  Figure 
  a 
  is 
  a 
  graphical 
  solu- 
  

   tion 
  of 
  the 
  equation 
  sin 
  35° 
  = 
  1 
  "7(30 
  . 
  sin 
  19°. 
  

  

  Plate 
  III. 
  Graphical 
  solution 
  of 
  the 
  refractive 
  index 
  equation 
  sin 
  2 
  i*=n 
  2 
  

   sin 
  2 
  r. 
  The 
  ordinates 
  represent 
  the 
  angles 
  i, 
  the 
  abscissas, 
  the 
  refractive 
  

   indices, 
  n, 
  and 
  the 
  diagonal 
  lines 
  the 
  angles, 
  r. 
  Figure 
  a 
  is 
  a 
  graphical 
  solu- 
  

   tion 
  of 
  the 
  equation 
  sin 
  56°= 
  1710 
  . 
  sin 
  29 
  c 
  . 
  

  

  Plate 
  IV. 
  Graphical 
  solution 
  of 
  the 
  refractive 
  index 
  equation 
  sin 
  i=n 
  . 
  

   sin 
  r. 
  The 
  abscissae 
  represent 
  the 
  angles, 
  i, 
  the 
  ordinates, 
  the 
  angles 
  r, 
  

   and 
  the 
  diagonal 
  lines, 
  the 
  refractive 
  indices 
  n. 
  Figure 
  a 
  is 
  a 
  graphical 
  

   solution 
  of 
  the 
  equation 
  sin 
  53° 
  = 
  1*700 
  . 
  sin 
  28°. 
  

  

  Plate 
  V. 
  Graphical 
  solution 
  of 
  the 
  birefringence 
  equation 
  

   1 
  J_ 
  

  

  o'» 
  /» 
  

  

  = 
  K 
  = 
  sin 
  # 
  . 
  sin 
  ■&' 
  

  

  1 
  1 
  

  

  a 
  2 
  y 
  2 
  

  

  y' 
  — 
  a 
  

   or 
  the 
  approximate 
  equation 
  — 
  = 
  K= 
  sin 
  ■& 
  . 
  sin 
  ■&'. 
  The 
  abscissas 
  

  

  represent 
  the 
  angles 
  ■&, 
  the 
  ordinates 
  the 
  values 
  of 
  K, 
  and 
  the 
  diagonal 
  lines 
  

   the 
  angles 
  ■&'. 
  Figure 
  a 
  is 
  the 
  graphical 
  solution 
  of 
  the 
  equation 
  0*500 
  == 
  

   sin 
  43° 
  . 
  sin 
  47°. 
  

  

  Plate 
  VI. 
  Graphical 
  solution 
  of 
  the 
  optic 
  axial 
  angle 
  equation 
  

  

  (3* 
  f 
  _ 
  q 
  

   tan 
  Va 
  = 
  — 
  • 
  also 
  of 
  thf> 
  antirnximatfi 
  formula, 
  tan 
  2 
  Va 
  rz: 
  — 
  _• 
  

  

  p 
  

  

  Y* 
  

  

  1 
  

  

  a- 
  

  

  1 
  

  

  also 
  of 
  the 
  approximate 
  formula 
  tan 
  2 
  Va 
  

  

  In 
  this 
  plate 
  the 
  abscissas 
  represent 
  — 
  ~ 
  -zf 
  , 
  the 
  ordinates 
  — 
  — 
  

  

  and 
  the 
  diagonal 
  lines 
  the 
  angles 
  Va. 
  Figure 
  a 
  is 
  a 
  graphical 
  solution 
  of 
  

   the 
  equation 
  tan 
  2 
  40° 
  = 
  -r-xrr- 
  • 
  

  

  Plate 
  VII. 
  Graphical 
  solution 
  of 
  the 
  optic 
  axial 
  angle 
  equation 
  

  

  /~ 
  V 
  

  

  I 
  1 
  

   • 
  

  

  r 
  

  

  tan 
  Va 
  — 
  / 
  ; 
  also 
  of 
  the 
  approximate 
  equation 
  

  

  1 
  1 
  

  

  a- 
  /3 
  

  

  tan 
  Va—y 
  -^ 
  In 
  this 
  plate 
  the 
  values 
  of 
  y 
  — 
  % 
  ™- 
  are 
  plot- 
  

   ted 
  along 
  the 
  abscissas, 
  those 
  of 
  j/ 
  -^ 
  -^ 
  along 
  the 
  ordinates, 
  while 
  

  

  the 
  diagonal 
  lines 
  represent 
  the 
  angles 
  Va 
  . 
  Figure 
  a 
  is 
  a 
  graphical 
  solution 
  

  

  / 
  0*025 
  

   of 
  the 
  equation 
  tan 
  38° 
  = 
  y 
  • 
  

  

  Plate 
  VIII. 
  Graphical 
  solution 
  of 
  the 
  transformation 
  equation 
  cot 
  A 
  — 
  

   sin 
  B 
  . 
  cot 
  C. 
  On 
  the 
  plate 
  the 
  angles 
  B 
  have 
  been 
  plotted 
  as 
  abscissas, 
  the 
  

   angles 
  C 
  as 
  ordinates, 
  and 
  the 
  angles 
  A 
  as 
  diagonal 
  lines. 
  In 
  case 
  the 
  angle 
  

   C> 
  45°, 
  the 
  construction 
  indicated 
  in 
  figure 
  b 
  should 
  be 
  followed, 
  Figure 
  a 
  

   is 
  a 
  graphical 
  solution 
  of 
  the 
  equation 
  cot 
  40°= 
  sin 
  32° 
  . 
  cot 
  24°. 
  Figure 
  b 
  is 
  

   a 
  graphical 
  solution 
  of 
  the 
  equation 
  cot 
  65° 
  = 
  sin 
  46° 
  . 
  cot 
  57°. 
  

  

  Plate 
  IX. 
  Graphical 
  solution 
  of 
  the 
  equation 
  sin 
  A 
  — 
  sin 
  B 
  . 
  sin 
  C, 
  the 
  

   angles 
  A 
  being 
  the 
  ordinates, 
  the 
  angles 
  B 
  the 
  abscissas, 
  and 
  the 
  angles 
  C 
  

   the 
  diagonal 
  lines. 
  Figure 
  a 
  is 
  a 
  graphical 
  solution 
  of 
  the 
  equation 
  

   sin 
  24° 
  rr 
  sin 
  32°. 
  sin 
  50°. 
  

  

  