﻿502 
  Lane 
  and 
  Keller— 
  Notes 
  on 
  Michigan 
  Minerals. 
  

  

  The 
  arm 
  corresponding 
  to 
  the 
  plane 
  yft 
  lies 
  nearest 
  the 
  center. 
  

   The 
  real 
  obliquity 
  of 
  y 
  appears 
  to 
  be 
  about 
  17°. 
  The 
  direc- 
  

   tion 
  of 
  y 
  from 
  the 
  center 
  of 
  the 
  field 
  of 
  view, 
  i. 
  e. 
  the 
  normal 
  

   to 
  p, 
  makes 
  an 
  angle 
  of 
  about 
  150° 
  with 
  the 
  direction 
  of 
  /3 
  ; 
  i. 
  e. 
  

   y 
  p 
  j(3= 
  150° 
  circa. 
  The 
  optical 
  angle 
  does 
  not 
  appear 
  large. 
  

   [According 
  to 
  Lacroix 
  it 
  is 
  45°.j 
  

  

  From 
  the 
  double 
  obliquity 
  of 
  the 
  axial 
  image 
  it 
  follows 
  that 
  

   the 
  position 
  of 
  formation 
  of 
  a 
  cross 
  by 
  closing 
  in 
  of 
  the 
  hyper- 
  

   bolas, 
  which 
  occurs 
  approximately 
  when 
  /3 
  is 
  in 
  the 
  direction 
  of 
  

   one 
  of 
  the 
  principal 
  planes 
  of 
  the 
  nicols, 
  will 
  not 
  be 
  a 
  position 
  

   of 
  extinction. 
  The 
  angle 
  to 
  be 
  turned 
  varies 
  but 
  is 
  always 
  

   noticeable. 
  The 
  formation 
  of 
  the 
  cross 
  is 
  almost 
  exactly 
  paral- 
  

   lel 
  to 
  the 
  trace 
  of 
  t, 
  and 
  makes 
  an 
  angle 
  against 
  the 
  direction 
  

   of 
  extinction 
  of 
  from 
  8° 
  to 
  11°. 
  The 
  axial 
  image 
  is 
  of 
  course 
  

   liable 
  to 
  disturbance 
  from 
  the 
  twinning. 
  

  

  The 
  direction 
  of 
  y 
  from 
  the 
  normal 
  to 
  p 
  also 
  seems 
  to 
  make 
  

   an 
  angle 
  of 
  about 
  80° 
  with 
  the 
  trace 
  of 
  b, 
  (in 
  the 
  sense 
  opposite 
  

   to 
  that 
  of 
  the 
  angle 
  bt 
  ?). 
  

  

  These 
  data 
  harmonize 
  fairly, 
  but 
  not 
  absolutely, 
  and 
  it 
  must 
  

   be 
  remembered 
  that 
  the 
  directions 
  of 
  extinction 
  do 
  not 
  pass 
  

   exactly 
  through 
  y. 
  By 
  every 
  indication, 
  however, 
  y 
  lies 
  within 
  

   the 
  small 
  circle 
  marking 
  its 
  position. 
  

  

  The 
  pleochroism 
  is 
  as 
  usual: 
  — 
  f, 
  yellow; 
  /?, 
  blue, 
  (not 
  so 
  

   far 
  as 
  I 
  have 
  noticed 
  reddish) 
  ; 
  a, 
  green. 
  .This 
  so 
  far 
  as 
  color 
  is 
  

   concerned 
  is 
  precisely 
  that 
  of 
  certain 
  hornblende, 
  approaching 
  

   glaucophane, 
  which 
  occurs 
  in 
  the 
  crystalline 
  schists 
  and 
  has 
  a 
  

   cellular 
  structure 
  [e. 
  g. 
  specimen 
  No. 
  11270 
  of 
  the 
  Mich. 
  Geol. 
  

   Survey.] 
  The 
  pleochroism 
  of 
  such 
  hornblende 
  has 
  also 
  been 
  

   noted 
  by 
  Lacroix. 
  Moreover, 
  such 
  hornblendes 
  like 
  chloritoid 
  

   contain 
  alkali 
  as 
  well 
  as 
  Fe, 
  Mg, 
  Al 
  a 
  , 
  Fe 
  2 
  and 
  Si. 
  

  

  Transverse 
  sections 
  of 
  the 
  plates 
  of 
  chloritoid 
  frequently 
  

   show 
  twinned 
  lamellae 
  parallel 
  to 
  the 
  basis, 
  though 
  this 
  Cham- 
  

   pion 
  chloritoid 
  has 
  sometimes 
  thick 
  un 
  twinned 
  plates. 
  In 
  

   such 
  cases, 
  as 
  might 
  be 
  expected 
  if 
  the 
  twinning 
  was 
  accord- 
  

   ing 
  to 
  Tschermak's 
  law 
  xor 
  the 
  micas, 
  there 
  are 
  three 
  sets 
  of 
  

   lamellae, 
  with 
  different 
  extinction 
  angles. 
  The 
  larger 
  extinc- 
  

   tion 
  angles 
  are 
  in 
  those 
  lamellae 
  where 
  the 
  pleochroism 
  is 
  most 
  

   purely 
  blue 
  in 
  one 
  direction, 
  — 
  that 
  near 
  to 
  ft. 
  The 
  other 
  

   lamellae 
  where 
  the 
  change 
  of 
  color 
  is 
  from 
  green 
  to 
  yellow 
  

   have 
  far 
  smaller 
  extinction 
  angles. 
  When 
  one 
  set 
  of 
  lamellae 
  

   have 
  a 
  very 
  large 
  extinction 
  angle, 
  the 
  other 
  two 
  sets 
  have 
  

   generally 
  quite 
  small 
  angles. 
  

  

  § 
  4. 
  The 
  analysis 
  of 
  the 
  carefully 
  selected 
  material 
  gave 
  the 
  

   following 
  results 
  : 
  — 
  

  

  