﻿F. 
  K 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  517 
  

  

  vertical 
  line 
  through 
  the 
  abscissa 
  1*535 
  and 
  note 
  that 
  the 
  

   diagonal 
  line 
  19° 
  passes 
  through 
  this 
  point. 
  Therefore, 
  

   2F=38°. 
  

  

  (2) 
  Determine 
  the 
  refractive 
  index 
  of 
  a 
  prism 
  of 
  angle 
  58°, 
  

   which 
  shows 
  a 
  minimum 
  deviation 
  angle 
  of 
  42°. 
  

  

  The 
  refractive 
  index 
  formula 
  (2) 
  reads 
  

  

  . 
  58° 
  + 
  42° 
  

   Sm 
  2 
  _ 
  sin 
  50° 
  

  

  sin 
  ~ 
  " 
  sin 
  29 
  ° 
  

  

  To 
  find 
  n 
  from 
  this 
  formula 
  on 
  either 
  Plate 
  II 
  or 
  III 
  pass 
  

   along 
  the 
  horizontal 
  line, 
  cutting 
  the 
  ordinate 
  50, 
  to 
  its 
  inter- 
  

   section 
  with 
  the 
  diagonal 
  line 
  29 
  and 
  note 
  that 
  the 
  abscissa 
  at 
  

   this 
  point 
  is 
  1*580, 
  the 
  desired 
  refractive 
  index. 
  

  

  Birefringence 
  formulas 
  (Plate 
  Y). 
  — 
  The 
  standard 
  exact 
  

   equation 
  between 
  the 
  refractive 
  indices 
  of 
  a 
  section 
  whose 
  

   normal 
  includes 
  the 
  angles, 
  d- 
  and 
  #' 
  ', 
  with 
  the 
  two 
  optic 
  axes 
  is 
  

  

  4- 
  — 
  I 
  = 
  ( 
  4 
  — 
  -V) 
  sin 
  ■*> 
  sin 
  *• 
  (3) 
  

  

  a 
  y 
  \a 
  y 
  / 
  

  

  This 
  equation 
  contains 
  the 
  squares 
  of 
  the 
  reciprocals 
  of 
  the 
  

   refractive 
  indices, 
  the 
  computation 
  of 
  which 
  is 
  tedious 
  and 
  

   time-consuming. 
  To 
  obviate 
  this 
  part 
  of 
  the 
  computation, 
  I 
  

   have 
  computed 
  Table 
  2 
  (each 
  value 
  was 
  computed 
  to 
  eight 
  

   places, 
  only 
  six 
  of 
  which, 
  however, 
  are 
  listed), 
  in 
  which 
  the 
  

  

  value 
  of— 
  is 
  given 
  for 
  all 
  values 
  of 
  n 
  between 
  1-400 
  and 
  2*480 
  ; 
  

  

  within 
  these 
  limits 
  the 
  refractive 
  indices 
  of 
  practically 
  all 
  

   minerals 
  are 
  included. 
  The 
  table 
  is 
  also 
  intended 
  for 
  use 
  in 
  the 
  

   computation 
  of 
  the 
  optic 
  axial 
  angle 
  from 
  the 
  three 
  refractive 
  

   indices 
  (equation 
  5). 
  

  

  In 
  order 
  to 
  prepare 
  a 
  proper 
  graphical 
  plot 
  suitable 
  for 
  all 
  

   possible 
  values 
  it 
  has 
  been 
  found 
  expedient 
  to 
  express 
  the 
  

  

  1 
  1 
  

  

  

  /2 
  " 
  ~~ 
  ' 
  IH 
  

  

  , 
  a 
  y 
  

  

  fraction 
  

  

  1 
  1 
  

  

  as 
  a 
  percentage 
  

  

  2 
  2 
  

  

  a 
  y 
  

  

  

  what 
  percentage 
  —77- 
  

  

  1 
  . 
  . 
  1 
  

  

  TT 
  IS 
  Ot 
  — 
  — 
  

  

  y 
  a 
  2 
  

  

  to 
  ascertain, 
  in 
  short, 
  

  

  —j- 
  The 
  same 
  holds 
  

  

  y 
  ' 
  

  

  true 
  when 
  the 
  approximate 
  equation 
  4 
  is 
  used. 
  Having 
  given 
  

   the 
  differences 
  — 
  r 
  a 
  w 
  and 
  — 
  5 
  f- 
  or 
  y' 
  — 
  a 
  and 
  7 
  — 
  a, 
  

  

  ay 
  ay' 
  ' 
  ' 
  

  

  