﻿A. 
  IT. 
  Phillips 
  — 
  Symmetry 
  of 
  Crystals. 
  31 
  

  

  stand 
  and 
  holes 
  in 
  the 
  disks, 
  large 
  enough 
  to 
  allow 
  easy 
  motion 
  

   to 
  a 
  lead 
  ball, 
  of 
  an 
  inch 
  and 
  a 
  half 
  in 
  diameter, 
  which 
  forms 
  

   a 
  universal 
  joint 
  ; 
  into 
  this 
  lead 
  sphere 
  a 
  knitting 
  needle 
  of 
  

   proper 
  size 
  is 
  set 
  in 
  the 
  direction 
  of 
  the 
  radius 
  and 
  upon 
  the 
  

   end 
  a 
  small 
  card,P, 
  is 
  placed 
  which 
  represents 
  the 
  position 
  and 
  

   inclination 
  of 
  the 
  crystal 
  face 
  under 
  consideration. 
  The 
  lead 
  

   ball 
  being 
  so 
  much 
  heavier 
  than 
  the 
  needle, 
  the 
  pole 
  may 
  be 
  

   placed 
  in 
  any 
  position 
  whatever 
  within 
  the 
  quadrant 
  and 
  

   remain 
  stationary. 
  

  

  At 
  b, 
  the 
  vertical 
  disk 
  is 
  not 
  soldered 
  to 
  the 
  equatorial 
  disk, 
  

   but 
  a 
  slot 
  is 
  cut 
  wide 
  enough 
  to 
  allow 
  the 
  pole 
  to 
  pass 
  to 
  the 
  

   right 
  back 
  quadrant. 
  The 
  pole 
  thus, 
  in 
  the 
  prism 
  zone, 
  has 
  a 
  

   range 
  of 
  180 
  degrees 
  and 
  any 
  face 
  in 
  this 
  zone 
  may 
  be 
  repre- 
  

   sented 
  by 
  the 
  pole. 
  There 
  is 
  a 
  similar 
  slot 
  at 
  c, 
  which 
  allows 
  

   the 
  pole 
  to 
  pass 
  from 
  the 
  right 
  to 
  the 
  left 
  front 
  quadrants, 
  

   allowing 
  a 
  range 
  of 
  180 
  degrees 
  in 
  each 
  dome 
  zone. 
  The 
  only 
  

   quadrant 
  not 
  accessible 
  to 
  the 
  pole 
  is 
  the 
  back 
  left. 
  The 
  right 
  

   front 
  quadrant 
  is 
  lined 
  with 
  mirrors, 
  which 
  represent 
  planes 
  of 
  

   symmetry 
  ; 
  by 
  placing 
  the 
  pole 
  in 
  the 
  required 
  position 
  any 
  

   crystal 
  face 
  is 
  represented, 
  and 
  if 
  wished, 
  a 
  card 
  may 
  be 
  cut 
  

   and 
  placed 
  in 
  the 
  mirrors, 
  when 
  the 
  exact 
  shape 
  of 
  the 
  form 
  

   will 
  be 
  reflected. 
  The 
  model 
  in 
  the 
  figure 
  represents 
  the 
  holo- 
  

   hedral 
  orthorhombic 
  class 
  ; 
  with 
  the 
  pole 
  in 
  any 
  position 
  within 
  

   the 
  quadrant, 
  not 
  in 
  contact 
  with 
  a 
  mirror, 
  will 
  represent 
  a 
  

   pyramid, 
  as 
  the 
  eight 
  reflected 
  poles 
  may 
  be 
  counted, 
  represent- 
  

   ing 
  the 
  eight 
  possible 
  faces 
  of 
  the 
  form. 
  When 
  the 
  pole 
  is 
  

   moved 
  in 
  contact 
  with 
  one 
  of 
  the 
  mirrors 
  (the 
  lead 
  ball 
  should 
  

   be 
  placed 
  a 
  little 
  eccentric 
  in 
  favor 
  of 
  the 
  octant 
  in 
  which 
  the 
  

   mirrors 
  are 
  placed 
  to 
  permit 
  of 
  this), 
  it 
  will 
  be 
  seen 
  that 
  

   two 
  poles 
  will 
  be 
  in 
  contact, 
  indicating 
  that 
  two 
  faces 
  of 
  the 
  

   most 
  general 
  form, 
  the 
  pyramid, 
  will 
  coincide, 
  yielding 
  a 
  form 
  

   of 
  four 
  faces, 
  a 
  dome 
  or 
  prism, 
  according 
  to 
  the 
  position 
  of 
  the 
  

   pole. 
  

  

  When 
  the 
  pole 
  is 
  placed 
  in 
  any 
  one 
  of 
  the 
  three 
  angles 
  of 
  

   the 
  octant, 
  it 
  will 
  be 
  seen 
  that 
  four 
  of 
  the 
  eight 
  poles 
  of 
  the 
  

   pyramid 
  coincide 
  forming 
  the 
  pinacoids 
  of 
  two 
  faces, 
  which 
  

   are 
  also 
  shown 
  as 
  fixed 
  in 
  forms, 
  as 
  there 
  is 
  but 
  one 
  position 
  

   for 
  the 
  pole 
  in 
  the 
  angle. 
  

  

  For 
  the 
  tetragonal 
  system 
  an 
  intermediate 
  mirror 
  may 
  be 
  

   placed 
  at 
  45 
  degrees 
  to 
  the 
  one 
  containing 
  the 
  crystallograph- 
  

   ical 
  axes 
  ; 
  the 
  ditetragonal 
  pyramid 
  will 
  be 
  reflected 
  by 
  

   the 
  mirrors, 
  when 
  a 
  card 
  is 
  placed 
  between 
  them, 
  as 
  in 
  the 
  

   figure, 
  and 
  16 
  poles 
  may 
  be 
  counted. 
  For 
  the 
  hexagonal 
  sys- 
  

   tem 
  the 
  intermediate 
  mirror 
  is 
  placed 
  at 
  30 
  degrees, 
  when 
  24 
  

   reflections 
  may 
  be 
  counted. 
  For 
  the 
  isometric 
  system 
  three 
  

   pieces 
  of 
  tin 
  are 
  cut 
  and 
  soldered 
  at 
  their 
  intersection, 
  the 
  tri- 
  

   gonal 
  axis 
  of 
  the 
  system, 
  so 
  as 
  to 
  divide 
  the 
  octant 
  symmetri- 
  

  

  