﻿E. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  529 
  

  

  Example. 
  — 
  To 
  illustrate 
  the 
  course 
  followed 
  in 
  solving 
  equa- 
  

   tions 
  21 
  and 
  22, 
  let 
  us 
  compute 
  the 
  correct 
  birefringence 
  of 
  

   the 
  section 
  of 
  aragonite 
  used 
  above 
  (page 
  527). 
  From 
  the 
  

   values 
  there 
  given 
  we 
  have 
  

  

  1 
  i 
  

   2 
  

  

  J 
  + 
  — 
  __) 
  _ 
  0-389489 
  

  

  and 
  & 
  + 
  &' 
  = 
  94 
  

  

  Equations 
  21 
  and 
  22 
  now 
  read 
  

   1 
  

  

  i-(^L_-L)= 
  0-037698 
  

   # 
  - 
  & 
  = 
  20° 
  

  

  = 
  0-389489 
  - 
  0-037698 
  . 
  cos 
  94° 
  

   = 
  0389489 
  - 
  0-037698 
  . 
  cos 
  20° 
  

  

  a 
  

   1 
  

   7 
  

   The 
  values, 
  0-037698 
  . 
  cos 
  20° 
  = 
  0-0355 
  and 
  

  

  0-037698 
  . 
  cos 
  94° 
  = 
  - 
  0-0027 
  

   can 
  be 
  read 
  off 
  directly 
  from 
  Plate 
  V. 
  Therefore 
  

  

  -4r 
  - 
  0-389489 
  + 
  0-0027 
  = 
  0-3921 
  

  

  a 
  

  

  -4- 
  = 
  0-389489 
  - 
  0-0355 
  = 
  03540 
  

   7 
  

  

  From 
  Table 
  II 
  we 
  now 
  find 
  that, 
  y 
  = 
  1*681, 
  and 
  a'= 
  1*597. 
  

   Accordingly, 
  y'— 
  a' 
  = 
  0-084, 
  a 
  value 
  0*005 
  higher 
  than 
  that 
  

   obtained 
  above 
  (page 
  527) 
  by 
  means 
  of 
  equation 
  3 
  and 
  Plate 
  Y. 
  

   In 
  this 
  particular 
  case 
  the 
  error 
  introduced 
  by 
  the 
  approximate 
  

   equation 
  is 
  over 
  5 
  per 
  cent. 
  

  

  A 
  check 
  on 
  the 
  above 
  values 
  of 
  — 
  jz- 
  and 
  — 
  — 
  can 
  be 
  had 
  by 
  

  

  a' 
  y 
  u 
  J 
  

  

  taking 
  their 
  difference 
  — 
  ^ 
  — 
  = 
  0-0381, 
  a 
  value 
  identical 
  

  

  a 
  y 
  

  

  with 
  that 
  obtained 
  above 
  by 
  use 
  of 
  equation 
  3. 
  

  

  Optic 
  axial 
  angle 
  formula 
  (Plates 
  VI 
  and 
  VII). 
  — 
  In 
  these 
  

   plates 
  the 
  variables 
  are, 
  abscissae 
  = 
  — 
  — 
  or 
  B 
  — 
  a, 
  ordi- 
  

  

  a 
  (3 
  ' 
  

  

  nates 
  — 
  or 
  y 
  — 
  /3 
  and 
  the 
  diagonal 
  lines 
  = 
  V. 
  The 
  

  

  p 
  y 
  & 
  

  

  drawings 
  are 
  made 
  on 
  the 
  assumption 
  that 
  —^- 
  *-<— 
  ~r* 
  

  

  