﻿F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  511 
  

  

  A 
  + 
  B 
  

  

  sin 
  — 
  - 
  — 
  

  

  n= 
  ^— 
  (2) 
  

  

  sin 
  - 
  

  

  where 
  A 
  is 
  the 
  minimum 
  deviation 
  angle, 
  JB, 
  the 
  prism 
  angle, 
  

   and 
  n, 
  the 
  refractive 
  index 
  (Plates 
  II 
  and 
  III). 
  

  

  3. 
  Birefringence 
  formula 
  

  

  -i--^=(I-l)sinS.sinS' 
  (3) 
  

  

  a 
  y 
  \a 
  y/ 
  

  

  wherein 
  # 
  and 
  #' 
  are 
  the 
  angles 
  included 
  between 
  the 
  normal 
  

   to 
  a 
  given 
  birefracting 
  plate 
  and 
  its 
  two 
  optic 
  axes, 
  a 
  and 
  7 
  

   the 
  highest 
  and 
  lowest 
  principal 
  refractive 
  indices 
  of 
  the 
  min- 
  

   eral, 
  a' 
  and 
  y' 
  the 
  two 
  refractive 
  indices 
  of 
  the 
  given 
  crystal 
  

   section 
  (Plate 
  Y). 
  

  

  4. 
  Approximate 
  birefringence 
  formula 
  (Plate 
  V). 
  

  

  2 
  = 
  sin 
  $ 
  . 
  sin 
  S'. 
  (4) 
  

  

  y 
  — 
  a 
  

  

  5. 
  Optic 
  axial 
  angle 
  formula 
  

  

  1 
  _ 
  1 
  

   tan 
  2 
  Va 
  = 
  f— 
  £ 
  (5) 
  

  

  wherein 
  2 
  F 
  is 
  the 
  optic 
  axial 
  angle 
  and 
  a, 
  /3, 
  7, 
  the 
  three 
  

   principal 
  refractive 
  indices 
  of 
  the 
  mineral 
  (Plates 
  YI 
  and 
  YII). 
  

  

  6. 
  Approximate 
  optic 
  axial 
  angle 
  formula 
  (Plates 
  YI 
  and 
  

   YII) 
  

  

  -P 
  

  

  tan 
  2 
  Fa 
  

  

  7. 
  The 
  transformation 
  equations 
  between 
  the 
  angles 
  ^> 
  (azi- 
  

   muth) 
  and 
  p 
  (polar 
  distance), 
  and 
  the 
  latitude 
  and 
  longitude 
  

   angles, 
  \ 
  and 
  /i 
  19 
  and 
  \ 
  and 
  />c 
  2 
  , 
  as 
  indicated 
  in 
  figure 
  1, 
  in 
  

   which 
  (j> 
  is 
  the 
  angular 
  azimuth 
  of 
  point 
  P, 
  /o, 
  its 
  polar 
  dis- 
  

   tance, 
  \ 
  15 
  its 
  longitude, 
  and 
  fi„ 
  its 
  latitude 
  when 
  OE 
  is 
  the 
  

   pole, 
  and 
  X 
  2 
  , 
  its 
  longitude, 
  and 
  /ot 
  2 
  , 
  its 
  latitude 
  when 
  ON 
  is 
  the 
  

   pole. 
  The 
  transformation 
  equations 
  which 
  connect 
  these 
  three 
  

   sets 
  of 
  angles 
  are 
  : 
  

  

  