﻿F. 
  E. 
  Wright 
  — 
  Methods 
  in 
  Microscopical 
  Petrography. 
  515 
  

  

  has 
  been 
  greatly 
  decreased 
  while 
  above 
  80° 
  the 
  distortion 
  has 
  

   been 
  materially 
  decreased. 
  In 
  Plate 
  IV 
  the 
  abscissae 
  are 
  the 
  

   angles 
  *, 
  the 
  ordinates, 
  the 
  angles 
  r, 
  and 
  the 
  diagonal 
  lines, 
  the 
  

   refractive 
  indices. 
  This 
  plate 
  has 
  the 
  advantage 
  over 
  Plates 
  

   II 
  and 
  III 
  in 
  that 
  it 
  covers 
  all 
  possible 
  values 
  of 
  the 
  three 
  vari- 
  

   ables 
  i, 
  r, 
  and 
  n, 
  but 
  for 
  ordinary 
  work 
  it 
  is 
  less 
  accurate 
  than 
  

   Plates 
  II 
  and 
  III. 
  

  

  In 
  the 
  preparation 
  of 
  Plates 
  III 
  and 
  IY, 
  Table 
  I 
  of 
  sin 
  2 
  a? 
  has 
  

   been 
  found 
  convenient: 
  The 
  values 
  in 
  this 
  table 
  are 
  given 
  to 
  

   five 
  places 
  ; 
  they 
  were 
  computed, 
  however, 
  to 
  eight 
  places. 
  

  

  Fig. 
  4. 
  

  

  It 
  has 
  been 
  suggested* 
  that 
  instead 
  of 
  the 
  sine 
  or 
  sine 
  2 
  values 
  

   the 
  log 
  sine 
  values 
  be 
  plotted. 
  As 
  noted 
  above, 
  however, 
  the 
  

   logarithmic 
  trigonometric 
  functions 
  show 
  so 
  great 
  distortion 
  

   that 
  the 
  degrees 
  from 
  50° 
  to 
  90° 
  are 
  crowded 
  together 
  and 
  

   cannot 
  be 
  properly 
  treated 
  graphically 
  except 
  on 
  a 
  very 
  large 
  

   plot. 
  For 
  graphical 
  purposes, 
  therefore, 
  the 
  direct 
  values 
  of 
  

   the 
  trigonometric 
  functions 
  are 
  superior 
  to 
  their 
  logarithms. 
  

  

  To 
  use 
  Plate 
  II 
  when 
  i 
  and 
  n 
  are 
  given 
  run 
  the 
  eye 
  along 
  

   the 
  abscissa 
  until 
  the 
  proper 
  n 
  is 
  reached 
  and 
  then 
  pass 
  up 
  the 
  

   n 
  ordinate 
  to 
  the 
  required 
  angle 
  i 
  and 
  thence 
  along 
  the 
  diago- 
  

   nal 
  r 
  line 
  to 
  the 
  margin 
  where 
  the 
  r 
  degrees 
  are 
  marked 
  (as 
  

   indicated 
  on 
  small 
  figure 
  a 
  of 
  Plate 
  II). 
  The 
  use 
  of 
  Plates 
  II, 
  

   III, 
  and 
  IY 
  is 
  illustrated 
  in 
  fig. 
  4 
  and 
  is 
  so 
  simple 
  in 
  principle 
  

   and 
  practice 
  that 
  further 
  explanation 
  is 
  unnecessary. 
  

  

  Plates 
  II 
  and 
  III 
  may 
  also 
  serve 
  in 
  the 
  solution 
  of 
  the 
  mini- 
  

   mum 
  deviation 
  prism 
  equation 
  2 
  above. 
  The 
  equation 
  is 
  

  

  reduced 
  to 
  the 
  proper 
  form 
  by 
  noting 
  that 
  — 
  half 
  the 
  prism 
  

  

  angle, 
  corresponds 
  to 
  the 
  angle 
  r 
  of 
  equation 
  1,. 
  while 
  

  

  A 
  + 
  B 
  

  

  half 
  the 
  sum 
  of 
  the 
  prism 
  angle 
  and 
  minimum 
  deviation 
  angle, 
  

   corresponds 
  to 
  i 
  of 
  equation 
  1. 
  Having 
  given 
  r 
  and 
  i 
  find 
  the 
  

   intersection 
  of 
  the 
  diagonal 
  line 
  r 
  with 
  the 
  horizontal 
  i 
  line, 
  

   the 
  abscissa 
  of 
  this 
  point 
  being 
  then 
  the 
  desired 
  n 
  value. 
  

  

  * 
  Centralblatt 
  f. 
  Min., 
  1913, 
  p. 
  126. 
  

  

  