﻿536 
  P. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  

  

  pole 
  C 
  ; 
  we 
  accomplish 
  this 
  by 
  subtracting 
  50° 
  from 
  X 
  lA 
  and 
  X 
  lB 
  

   and 
  have 
  the 
  equations 
  to 
  solve 
  

  

  cot 
  cj> 
  A 
  = 
  sin 
  17° 
  cot 
  ( 
  — 
  46°) 
  

   cot 
  cf> 
  B 
  = 
  sin 
  35° 
  -5 
  cot 
  4 
  1° 
  h 
  

  

  From 
  Plate 
  VII 
  we 
  read 
  off 
  directly 
  

  

  cf> 
  A 
  = 
  180° 
  — 
  15°-7 
  

   <t> 
  B 
  = 
  28°-l 
  

  

  Therefore, 
  -^— 
  — 
  - 
  = 
  96°*2, 
  and 
  the 
  desired 
  extinction 
  angle, 
  

  

  90°-96°-2=-- 
  -6°-2. 
  

  

  These 
  values 
  might 
  also 
  have 
  been 
  obtained 
  directly 
  by 
  use 
  

   of 
  the 
  projection 
  plots, 
  but 
  the 
  above 
  method 
  is 
  more 
  accurate 
  

   and 
  takes 
  less 
  time. 
  

  

  Plate 
  IX 
  is 
  a 
  graphical 
  solution 
  of 
  the 
  general 
  equation 
  

  

  sin 
  A 
  — 
  sin 
  B 
  sin 
  C 
  (24) 
  

  

  The 
  equations 
  8, 
  10, 
  12, 
  14, 
  16, 
  18 
  can 
  all 
  be 
  expressed 
  in 
  

   this 
  form 
  and 
  can 
  therefore 
  all 
  be 
  solved 
  by 
  Plate 
  IX. 
  Thus 
  

   equation 
  16 
  may 
  be 
  written 
  

  

  sin 
  /x 
  2 
  = 
  sin 
  (90° 
  — 
  /xj 
  sin 
  X 
  1? 
  or 
  

   sin 
  /x 
  2 
  sin 
  (90° 
  — 
  /xj 
  

  

  sin 
  X 
  l 
  1 
  

  

  and 
  solved 
  graphically 
  by 
  Plate 
  IX, 
  as 
  indicated 
  in 
  figure 
  9 
  

  

  (16a) 
  

  

  Fig. 
  9. 
  

  

  Example. 
  — 
  Let 
  the 
  normal 
  to 
  a 
  given 
  section 
  be 
  located 
  by 
  

   the 
  two 
  angles 
  \ 
  t 
  = 
  37°, 
  and 
  /x 
  J 
  = 
  41° 
  ; 
  express 
  its 
  position 
  by 
  

   the 
  two 
  angles 
  X 
  2 
  and 
  /* 
  2 
  (see 
  figure 
  6). 
  Equations 
  15 
  and 
  16 
  

   apply 
  to 
  this 
  case. 
  

  

  