﻿F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  535 
  

  

  Determine 
  the 
  extinction 
  angles 
  for 
  several 
  sections 
  which 
  are 
  

   twinned 
  both 
  after 
  the 
  Carlsbad 
  and 
  albite 
  law 
  and 
  show 
  sym- 
  

   metrical 
  extinction 
  angles. 
  From 
  Plate 
  Till, 
  the 
  required 
  

   angles 
  can 
  be 
  ascertained 
  without 
  difficulty. 
  

  

  In 
  fig. 
  8 
  let 
  A 
  and 
  B 
  be 
  the 
  positions 
  of 
  the 
  two 
  optic 
  axes 
  

   and 
  A, 
  A 
  , 
  /* 
  A 
  and 
  \ 
  B 
  , 
  /jl 
  b 
  , 
  their 
  spherical 
  coordinates. 
  The 
  ex- 
  

   tinction 
  direction 
  for 
  the 
  direction 
  OC, 
  pole 
  of 
  the 
  projection, 
  can 
  

   be 
  found 
  by 
  the 
  rule 
  of 
  Fresnel-Biot, 
  which 
  states 
  that 
  the 
  vibra- 
  

   tion 
  directions 
  of 
  any 
  section 
  bisect 
  the 
  angles 
  between 
  the 
  pro- 
  

   jections 
  of 
  the 
  optic 
  axes 
  on 
  that 
  section. 
  Thus 
  in 
  fig. 
  8, 
  the 
  ex- 
  

   tinction 
  direction 
  bisects 
  the 
  angle 
  BCA. 
  If, 
  therefore, 
  the 
  

   angles 
  <£ 
  A 
  and 
  <p 
  B 
  be 
  computed, 
  then 
  half 
  their 
  sum 
  determines 
  

   the 
  position 
  of 
  the 
  extinction 
  direction 
  and 
  the 
  angle 
  which 
  this 
  

   direction 
  includes 
  with 
  the 
  vertical 
  axis 
  ON 
  is 
  the 
  extinction 
  

   angle. 
  If 
  A, 
  lA 
  and 
  /x 
  lA 
  of 
  the 
  point 
  A 
  be 
  given, 
  the 
  angle 
  <£ 
  A 
  is 
  

   readily 
  calculated 
  by 
  equation 
  7. 
  Thus, 
  for 
  the 
  axis 
  A, 
  the 
  

   equation 
  becomes 
  

  

  cot 
  <£ 
  A 
  = 
  sin 
  85°'5 
  cot 
  47°'o. 
  

  

  In 
  this 
  case 
  /* 
  19 
  >45°; 
  fig. 
  7b, 
  therefore, 
  should 
  be 
  used. 
  

   On 
  Plate 
  VIII 
  we 
  find 
  the 
  intersection 
  of 
  the 
  diagonal 
  line 
  

   47°*5 
  with 
  the 
  ordinate 
  through 
  the 
  abscissa 
  85*5, 
  to 
  be 
  at 
  

   <f> 
  A 
  = 
  180° 
  - 
  41-6. 
  Similarly 
  B 
  = 
  42*4. 
  Accordingly, 
  

  

  $£±^? 
  = 
  9o°-4 
  and 
  the 
  desired 
  extinction 
  angle 
  is 
  90°-90°'4 
  

  

  = 
  - 
  0°-4. 
  

  

  To 
  find 
  now 
  the 
  extinction 
  angle 
  for 
  the 
  section 
  whose 
  

   normal 
  is 
  in 
  the 
  albite 
  twinning 
  plane 
  (shows 
  symmetrical 
  

   twinning) 
  and 
  includes 
  an 
  angle 
  of 
  50° 
  with 
  the 
  pole 
  C 
  (fig. 
  8), 
  

   we 
  rotate 
  the 
  projection 
  until 
  this 
  direction 
  coincides 
  with 
  the 
  

  

  