﻿F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  527 
  

  

  it 
  is 
  not 
  actually 
  necessary 
  to 
  compute 
  the 
  percentage, 
  as 
  this 
  

   can 
  be 
  done 
  graphically 
  on 
  Plate 
  VI, 
  which 
  is 
  intended 
  prima- 
  

   rily 
  for 
  the 
  solution 
  of 
  equation 
  5, 
  but 
  which 
  serves 
  equally 
  

   well 
  for 
  this 
  purpose. 
  

  

  Examples. 
  — 
  Solve 
  equation 
  3 
  for 
  a 
  section 
  of 
  the 
  mineral 
  

   aragonite, 
  the 
  normal 
  of 
  the 
  section 
  to 
  include 
  the 
  angles, 
  

   &' 
  = 
  37° 
  and 
  § 
  = 
  57°, 
  with 
  the 
  two 
  optic 
  axes. 
  The 
  prin- 
  

   cipal 
  refractive 
  indices 
  of 
  aragonite 
  are, 
  a 
  — 
  1*530, 
  /3 
  = 
  1-682, 
  

   and 
  7 
  = 
  1-686. 
  

  

  From 
  Plate 
  V 
  we 
  find, 
  by 
  passing 
  along 
  the 
  abscissa 
  axis 
  

   to 
  # 
  = 
  57° 
  and 
  then 
  up 
  along 
  the 
  vertical 
  ordinate 
  to 
  the 
  diag- 
  

   onal 
  line, 
  #' 
  = 
  37°, 
  that 
  

  

  y' 
  2 
  

  

  = 
  0-505 
  

  

  

  1 
  1 
  

  

  

  

  y 
  

  

  

  

  equation 
  4). 
  

  

  

  

  y' 
  - 
  a' 
  

   y 
  - 
  a 
  

  

  = 
  0-505. 
  

  

  

  we 
  find 
  that 
  

  

  -V 
  = 
  0-427186 
  and 
  

  

  1 
  

  

  0-351791 
  ; 
  hence 
  -A 
  V~ 
  = 
  0-075395. 
  By 
  using 
  this 
  last" 
  

  

  ay 
  

  

  value 
  and 
  passing 
  along 
  the 
  abscissa 
  axis 
  on 
  Plate 
  YI 
  to 
  0*075395 
  

   X 
  1000 
  = 
  75-4 
  and 
  up 
  the 
  ordinate 
  to 
  the 
  diagonal 
  line 
  0*505 
  X 
  

  

  100 
  = 
  50-5, 
  we 
  find 
  that 
  — 
  - 
  % 
  ^ 
  == 
  0-0381. 
  Equation 
  4 
  

  

  above 
  can 
  be 
  solved 
  in 
  similar 
  manner, 
  y 
  — 
  a 
  — 
  0-156 
  and 
  

  

  7 
  ' 
  _ 
  a 
  r 
  

   = 
  0*505. 
  This 
  equation 
  can, 
  however, 
  be 
  put 
  in 
  

  

  a 
  better 
  form 
  for 
  graphical 
  solution 
  by 
  Plate 
  YI 
  by 
  first 
  multi- 
  

   plying 
  both 
  numerator 
  and 
  denominator 
  by 
  a 
  whole 
  number, 
  

  

  as 
  500 
  ; 
  then 
  -^ 
  fe£- 
  5 
  °° 
  (y 
  '~ 
  a>) 
  = 
  0-505. 
  Therefore 
  

  

  500 
  0*156 
  78 
  

  

  500(7' 
  - 
  a 
  r 
  ) 
  = 
  39-4 
  or 
  7' 
  - 
  a' 
  = 
  0;079. 
  

  

  Equation 
  4, 
  which 
  is 
  ordinarily 
  used 
  for 
  computing 
  the 
  bire- 
  

   fringence, 
  furnishes 
  values 
  which 
  are 
  only 
  approximately 
  cor- 
  

   rect. 
  In 
  case 
  more 
  accurate 
  values 
  are 
  desired, 
  they 
  can 
  be 
  

   derived 
  from 
  the 
  standard 
  equations, 
  

  

  