﻿238 
  J. 
  M. 
  Blake 
  — 
  Plotting 
  Crystal 
  Zones 
  on 
  the 
  Sphere. 
  

  

  rests 
  in 
  a 
  shallow 
  leather-lined 
  cup 
  which 
  turns 
  on 
  a 
  central 
  

   adjustable 
  screw 
  point. 
  

  

  The 
  main 
  value 
  of 
  the 
  sphere 
  when 
  used 
  in 
  connection 
  with 
  

   crystal 
  work 
  is 
  dependent 
  upon 
  its 
  adaptability 
  for 
  the 
  reten- 
  

   tion 
  of 
  data 
  relating 
  to 
  plane 
  positions. 
  It 
  is 
  obvious 
  that 
  

   plotting 
  on 
  the 
  sphere 
  cannot 
  be 
  performed 
  with 
  as 
  great 
  accu- 
  

   racy 
  as 
  upon 
  paper 
  ; 
  but 
  if 
  we 
  refer 
  to 
  the 
  measurements 
  that 
  

   have 
  already 
  been 
  made 
  with 
  the 
  goniometer, 
  and 
  keep 
  the 
  

   plotting 
  work 
  corrected, 
  we 
  can 
  attain 
  sufficient 
  exactness 
  to 
  

   enable 
  us 
  to 
  perform 
  valuable 
  work 
  having 
  crystal 
  description 
  

   for 
  its 
  object. 
  This 
  work 
  can 
  be 
  done 
  by 
  such 
  aid 
  with 
  econ- 
  

   omy 
  of 
  time 
  and 
  labor. 
  In 
  fact, 
  we 
  can 
  perform 
  work 
  that 
  

   would 
  hardly 
  be 
  attempted 
  if 
  dependent 
  on 
  the 
  methods 
  that 
  

   have 
  so 
  long 
  been 
  in 
  most 
  frequent 
  use. 
  

  

  In 
  order 
  to 
  secure 
  the 
  greatest 
  degree 
  of 
  accuracy 
  that 
  a 
  

   given 
  crystal 
  will 
  yield, 
  we 
  make 
  use 
  of 
  the 
  best 
  average 
  zone 
  

   tangent 
  spaces 
  that 
  can 
  be 
  obtained 
  from 
  a 
  measurement 
  of 
  the 
  

   whole 
  crystal. 
  It 
  will 
  follow 
  from 
  this 
  that 
  the 
  greatest 
  num- 
  

   ber 
  of 
  planes 
  we 
  can 
  develop 
  on 
  a 
  salt, 
  or 
  the 
  greater 
  number 
  

   of 
  trustworthy 
  reflections 
  we 
  can 
  obtain 
  from 
  a 
  mineral, 
  will 
  

   tend 
  to 
  a 
  more 
  accurate 
  determination 
  of 
  the 
  length 
  of 
  the 
  

   crystal 
  axes. 
  

  

  With 
  these 
  few 
  hints 
  relating 
  to 
  the 
  hoped-for, 
  eventual, 
  

   exact 
  determination 
  of 
  crystal 
  laws 
  and 
  constants, 
  we 
  will 
  turn 
  

   our 
  attention 
  to 
  some 
  practical 
  methods 
  of 
  collecting 
  and 
  pre- 
  

   senting 
  data 
  in 
  available 
  form 
  for 
  future 
  generalization 
  and 
  

   mathematical 
  treatment. 
  In 
  so 
  doing 
  we 
  will 
  endeavor 
  to 
  make 
  

   it 
  apparent, 
  that 
  graphic 
  and 
  mechanical 
  methods 
  can, 
  with 
  

   advantage, 
  be 
  substituted 
  for 
  a 
  great 
  mass 
  of 
  the 
  work 
  com- 
  

   monly 
  undertaken 
  by 
  algebraic 
  and 
  analytical 
  methods. 
  These 
  

   algebraic 
  attempts 
  are 
  many 
  times 
  founded 
  on 
  uncertain 
  meas- 
  

   urements, 
  and 
  mathematical 
  precision 
  cannot, 
  therefore, 
  be 
  

   expected 
  on 
  such 
  a 
  basis. 
  By 
  the 
  methods 
  here 
  advocated, 
  

   the 
  matter 
  of 
  collecting 
  useful 
  data 
  is 
  much 
  facilitated, 
  and 
  the 
  

   work 
  can 
  be 
  undertaken 
  by 
  a 
  larger 
  number 
  of 
  observers. 
  

  

  If 
  we 
  examine 
  a 
  tangent-plane 
  projection 
  of 
  the 
  normals 
  

   made 
  from 
  a 
  suitable 
  view-point, 
  we 
  will 
  have 
  a 
  series 
  of 
  points 
  

   arranged 
  in 
  parallel 
  rows. 
  Another 
  set 
  of 
  rows 
  having 
  a 
  

   different 
  spacing 
  length 
  may 
  cross 
  the 
  first 
  set 
  through 
  the 
  

   center 
  at 
  right 
  angles, 
  as 
  in 
  the 
  orthorhombic 
  forms, 
  or 
  they 
  

   may 
  pass 
  obliquely 
  at 
  one 
  side 
  of 
  the 
  center, 
  as 
  we 
  find 
  with 
  

   the 
  oblique 
  systems. 
  

  

  In 
  addition 
  to 
  these 
  rows 
  of 
  points, 
  which 
  are 
  the 
  intersec- 
  

   tions 
  of 
  the 
  normals 
  with 
  the 
  projection 
  plane, 
  there 
  are 
  planes 
  

   whose 
  normals 
  do 
  not 
  pierce 
  this 
  plane, 
  but 
  lie 
  parallel 
  to 
  it. 
  

   These 
  may 
  be 
  called 
  the 
  prismatic 
  planes. 
  These 
  latter 
  have 
  

   their 
  part 
  in 
  the 
  growth 
  and 
  shaping 
  of 
  the 
  crystal, 
  and 
  they 
  

  

  