﻿534: 
  F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  

  

  these 
  conditions 
  Plate 
  VIII 
  has 
  been 
  so 
  drawn 
  that 
  equation 
  

   15a 
  can 
  only 
  be 
  solved 
  graphically 
  for 
  angles 
  fi 
  1 
  _<45°. 
  For 
  

   larger 
  angles, 
  equation 
  15 
  can 
  be 
  written 
  

  

  tan 
  (90°- 
  f 
  t 
  1 
  ) 
  = 
  tan 
  (90° 
  - 
  A 
  2 
  ) 
  b) 
  

  

  1 
  sin 
  (90° 
  - 
  AJ 
  V 
  ) 
  

  

  This 
  equation 
  can 
  be 
  solved 
  equally 
  well 
  by 
  Plate 
  YIII 
  but 
  

   only 
  for 
  angles, 
  /i 
  x 
  , 
  > 
  45°. 
  The 
  two 
  different 
  methods 
  of 
  

   solutions 
  are 
  illustrated 
  in 
  figures 
  7a, 
  7b. 
  

  

  Fig. 
  7. 
  

  

  This 
  principle 
  of 
  reciprocation 
  is 
  useful 
  in 
  any 
  equation 
  

   which 
  is 
  to 
  be 
  solved 
  graphically, 
  and 
  in 
  which 
  the 
  values 
  range 
  

   from 
  to 
  1 
  and 
  beyond, 
  thus 
  causing 
  the 
  plot 
  to 
  extend 
  beyond 
  

   the 
  bounds 
  of 
  the 
  diagram. 
  

   The 
  equation 
  

  

  AC 
  

   B~ 
  1 
  

  

  can 
  alwavs 
  be 
  written 
  in 
  the 
  form 
  

  

  1 
  

  

  1 
  

  

  A 
  

  

  C 
  

  

  1 
  

  

  B 
  

  

  In 
  case 
  A 
  and 
  C 
  are 
  tangent 
  functions 
  as 
  in 
  the 
  present 
  

   instance, 
  the 
  form 
  of 
  the 
  plate 
  is 
  simple 
  and 
  yet 
  it 
  is 
  competent 
  

   to 
  solve 
  equation 
  15 
  for 
  all 
  values 
  of 
  A 
  x 
  and 
  fi 
  im 
  

  

  The 
  actual 
  modus 
  operandi 
  is 
  best 
  illustrated 
  by 
  an 
  

   example 
  : 
  

  

  The 
  positions 
  of 
  the 
  two 
  optic 
  axes 
  in 
  oligoclase 
  (Ab 
  87 
  An 
  13 
  ) 
  

   as 
  determined 
  by 
  Becke 
  are 
  : 
  for 
  optic 
  axis 
  A, 
  A 
  lA 
  = 
  67° 
  and 
  

   /x 
  lA 
  *=-46°; 
  for 
  axis 
  B, 
  X 
  lB 
  = 
  85°-5, 
  and 
  p 
  lB 
  =+ 
  47°"5. 
  

  

  *This 
  angle 
  is 
  sometimes 
  designated 
  $, 
  but 
  in 
  view 
  of 
  the 
  fact 
  that 
  <p 
  is 
  

   used 
  to 
  denote 
  the 
  azimuth 
  angle 
  in 
  crystallography 
  it 
  would 
  seem 
  better 
  to 
  

   give 
  it 
  the 
  same 
  significance 
  in 
  optical 
  work 
  and 
  to 
  use 
  the 
  letter 
  fi, 
  as 
  

   above, 
  to 
  designate 
  the 
  latitude 
  angle. 
  

  

  