﻿Determination 
  of 
  the 
  Plagioclase 
  Feldspars. 
  511 
  

  

  m 
  

  

  y 
  = 
  

  

  m. 
  + 
  mjc 
  m„ 
  

  

  1 
  + 
  — 
  aj 
  

  

  m 
  l 
  

  

  which 
  is 
  again 
  a 
  parabola. 
  For 
  convenience 
  in 
  plotting 
  it 
  is 
  

   an 
  advantage 
  to 
  have 
  x 
  always 
  greater 
  than 
  unity. 
  In 
  case 
  it 
  

   is 
  less 
  than 
  unity 
  the 
  relation 
  Ab^Ai^ 
  may 
  be 
  written 
  Ab 
  x 
  An 
  s 
  

   wherein 
  3> 
  1 
  and 
  a 
  second 
  parabola 
  drawn 
  for 
  which 
  Ab 
  is 
  

   always 
  unity. 
  Thus 
  Ab 
  3 
  An 
  2 
  may 
  be 
  written 
  Ab 
  3/2 
  An 
  1 
  and 
  the 
  

   curve 
  An 
  x 
  used, 
  while 
  Ab 
  3 
  An 
  4 
  may 
  be 
  written 
  Ab 
  1 
  An 
  4/3 
  , 
  to 
  

   which 
  the 
  curve 
  Ah 
  1 
  is 
  applicable. 
  

  

  In 
  the 
  first 
  plot 
  of 
  1901, 
  the 
  plagioclases 
  were 
  plotted 
  

   according 
  to 
  weight 
  percentages 
  (the 
  variations 
  in 
  the 
  chemical 
  

   constituents 
  being 
  then 
  represented 
  by 
  straight 
  lines) 
  and 
  the 
  

   molecular 
  proportion 
  curves 
  were 
  plotted 
  for 
  this 
  case. 
  In 
  the 
  

   present 
  plot 
  the 
  plagioclases 
  are 
  plotted 
  in 
  molecular 
  percent- 
  

   ages 
  and 
  the 
  molecular 
  proportion 
  curves 
  have 
  been 
  modified 
  

   accordingly. 
  

  

  Curves 
  3. 
  Refractive 
  indices 
  a, 
  j3, 
  7, 
  compared 
  with 
  to 
  and 
  e 
  

   of 
  quartz. 
  

  

  Curve 
  J±. 
  Optic 
  axial 
  angles. 
  

  

  Curve 
  5. 
  Extinction 
  angles 
  on 
  001 
  (cleavage 
  flake 
  method). 
  

  

  Curve 
  6. 
  Extinction 
  angles 
  on 
  010 
  (cleavage 
  flake 
  method). 
  

  

  Curve 
  7. 
  Maximum 
  extinction 
  angles 
  in 
  symmetrical 
  zone 
  

   (sections 
  normal 
  to 
  010, 
  the 
  plane 
  of 
  albite 
  twinning 
  lamellae). 
  

   Statistical 
  method 
  of 
  Michel- 
  Levy. 
  

  

  Curve 
  8. 
  Extinction 
  angles 
  on 
  sections 
  normal 
  to 
  a. 
  Fouque 
  

   method. 
  

  

  Curves 
  9. 
  Extinction 
  angles 
  on 
  section 
  normal 
  to 
  7 
  ; 
  referred 
  

   in 
  curve 
  9a 
  to 
  plagioclase 
  lamellae 
  (010) 
  and 
  in 
  curve 
  9b 
  to 
  

   cleavage 
  lines 
  after 
  001. 
  Fouque 
  method. 
  

  

  Curve 
  10. 
  Extinction 
  angles, 
  on 
  section 
  normal 
  to 
  /3, 
  the 
  

   optic 
  normal, 
  referred 
  to 
  cleavage 
  after 
  (010) 
  and 
  plagioclase 
  

   lamellae. 
  

  

  Curves 
  11. 
  Curves 
  for 
  combined 
  Carlsbad 
  and 
  albite 
  twin- 
  

   ning 
  lamellae 
  showing 
  symmetrical 
  extinction 
  angles. 
  Michel- 
  

   Levy's 
  original 
  chart 
  of 
  these 
  values 
  was 
  based 
  on 
  a 
  formula 
  

   deduced 
  by 
  Mallard, 
  the 
  values 
  of 
  observation 
  used 
  in 
  the 
  

   formula 
  having 
  been 
  supplied 
  largely 
  by 
  Michel 
  -Levy. 
  It 
  

   has 
  long 
  been 
  known 
  that 
  this 
  chart 
  is 
  seriously 
  in 
  error 
  in 
  

   certain 
  particulars, 
  errors 
  of 
  20 
  per 
  cent 
  in 
  the 
  molecular 
  

   composition 
  of 
  the 
  plagioclase 
  being 
  possible 
  with 
  certain 
  sets 
  

   of 
  angles. 
  In 
  view 
  of 
  this 
  fact, 
  the 
  writer 
  has 
  taken 
  the 
  meas- 
  

   urements 
  of 
  Becke, 
  Tertsch 
  and 
  one 
  or 
  two 
  by 
  himself 
  on 
  

   plagioclases 
  of 
  known 
  composition, 
  and 
  calculated 
  the 
  extinc- 
  

   tion 
  angles 
  for 
  sections 
  in 
  the 
  symmetrical 
  zone, 
  such 
  sections 
  

   being 
  10° 
  apart. 
  For 
  each 
  feldspar 
  a 
  set 
  of 
  18 
  extinction 
  

   angles 
  was 
  thus 
  obtained 
  for 
  the 
  poles 
  —90° 
  to 
  +90°. 
  These 
  

  

  Am. 
  Jour. 
  Sci.— 
  Fourth 
  Series, 
  Vol. 
  XXXVI, 
  No. 
  215.— 
  November, 
  1913. 
  

   36 
  

  

  