﻿Notations 
  employed 
  in 
  Theories 
  of 
  Crystal-structure. 
  205 
  

  

  and 
  that 
  Schoenflies 
  did 
  the 
  same 
  in 
  Ky 
  stalls 
  ysteme 
  und 
  

   Krystallstruetur, 
  p. 
  622. 
  

  

  In 
  some 
  cases 
  Schoenflies 
  (in 
  his 
  paper 
  in 
  the 
  Math. 
  

   Annalen, 
  xxxiv.) 
  gave 
  the 
  same 
  symbol 
  to 
  two 
  groups. 
  

   Where 
  one 
  of 
  these 
  groups 
  is 
  derived 
  from 
  the 
  other 
  by 
  the 
  

   substitution 
  of 
  the 
  operation 
  S(t) 
  for 
  S, 
  or 
  S(£ 
  + 
  t) 
  for 
  S(£), 
  I 
  

   have 
  underlined 
  the 
  symbol 
  in 
  the 
  case 
  of 
  the 
  latter 
  group. 
  

   Similarly 
  he 
  gives 
  the 
  symbol 
  Y 
  3 
  as 
  representing 
  3 
  distinct 
  

   groups. 
  

  

  For 
  convenience 
  of 
  printing, 
  English 
  capitals 
  are 
  substituted 
  

   for 
  German 
  in 
  the 
  symbols 
  of 
  Schoenflies, 
  as 
  no 
  error 
  can 
  

   thereby 
  arise. 
  

  

  An 
  asterisk 
  against 
  a 
  symbol 
  means 
  that 
  a 
  reference 
  is 
  

   made 
  to 
  it 
  in 
  the 
  notes 
  following 
  the 
  tables. 
  

  

  Table 
  I. 
  

  

  A. 
  Schoenflies. 
  

  

  A. 
  Schoenflies. 
  

  

  C. 
  Jordan. 
  

  

  L. 
  Sohncke. 
  

  

  W. 
  Barlow. 
  

  

  E. 
  v. 
  Fedorow. 
  

  

  Krystallsyst. 
  

  

  Mat 
  hem. 
  An- 
  

  

  Annali 
  di 
  

  

  Entwickel- 
  

  

  Zeitschr. 
  f. 
  

  

  Zeitschr. 
  

  

  u. 
  Krystall- 
  

  

  nalen, 
  xxviii. 
  

  

  Matema- 
  

  

  ung 
  einer 
  

  

  Krystall. 
  u. 
  

  

  f. 
  Kryst. 
  u. 
  

  

  structur, 
  

  

  p. 
  319 
  ; 
  xxix. 
  

  

  tica 
  pura 
  

  

  Theorie 
  der 
  

  

  Min. 
  xxiii. 
  

  

  Min. 
  xxiv. 
  

  

  1891. 
  

  

  p. 
  50 
  (1887) 
  ; 
  

  

  ed 
  appl. 
  

  

  Krystall- 
  

  

  pp. 
  1-63 
  

  

  pp. 
  232-237 
  

  

  

  & 
  xxxiv. 
  p. 
  172 
  

   (1889). 
  

  

  Baud 
  ii 
  

  

  struktur, 
  

  

  (1894). 
  

  

  (1895). 
  

  

  

  1869. 
  

  

  1879. 
  

  

  

  

  o, 
  

  

  no 
  symbol 
  

   given. 
  

  

  3 
  

  

  1 
  

  

  65 
  

  

  Is 
  

  

  Co 
  1 
  

  

  0,(2) 
  

  

  29 
  

  

  2 
  

  

  63 
  

  

  3s 
  

  

  c 
  2 
  2 
  

  

  C 
  2 
  (2) 
  

  

  31 
  

  

  3 
  

  

  62 
  

  

  la 
  

  

  c, 
  3 
  

  

  C 
  3 
  (2) 
  

  

  33 
  

  

  4 
  

  

  64 
  

  

  4s 
  

  

  V 
  1 
  

  

  v 
  4 
  

  

  91 
  

  

  5 
  

  

  56 
  

  

  9s 
  

  

  V 
  2 
  

  

  v 
  7 
  

  

  abs. 
  

  

  6 
  

  

  53 
  

  

  4a 
  

  

  V 
  3 
  

  

  v 
  8 
  

  

  93 
  

  

  12 
  

  

  55 
  

  

  7 
  a 
  

  

  V 
  4 
  

  

  v 
  9 
  

  

  abs. 
  

  

  14 
  

  

  54 
  

  

  Sa 
  

  

  V 
  5 
  

  

  V 
  6 
  

  

  abs. 
  

  

  * 
  9,13 
  

  

  57 
  

  

  oa 
  

  

  V 
  6 
  

  

  v 
  3 
  

  

  92 
  

  

  7 
  

  

  59 
  

  

  10s 
  

  

  V 
  7 
  

  

  V 
  2 
  

  

  99 
  

  

  8 
  

  

  61 
  

  

  12s 
  

  

  V 
  8 
  

  

  V~ 
  

  

  100 
  

  

  10 
  

  

  60 
  

  

  lis 
  

  

  V 
  9 
  

  

  V\ 
  

  

  101 
  

  

  11 
  

  

  58 
  

  

  6 
  a 
  

  

  <v 
  

  

  C 
  x 
  (3) 
  

  

  61 
  

  

  17 
  

  

  48 
  

  

  38 
  s 
  

  

  c 
  3 
  2 
  

  

  C 
  2 
  (3) 
  

  

  63 
  

  

  15 
  

  

  42 
  

  

  68 
  a 
  

  

  3 
  3 
  

  

  C 
  2 
  '(3) 
  

  

  64 
  

  

  16 
  

  

  43 
  

  

  69 
  a 
  

  

  C3 
  4 
  

  

  C 
  3 
  (3) 
  

  

  62 
  

  

  18 
  

  

  51 
  

  

  39 
  s 
  

  

  D3 
  1 
  

  

  D,(3) 
  

  

  130 
  

  

  21 
  

  

  49 
  

  

  * 
  45 
  s 
  

  

  D3 
  2 
  

  

  D 
  3 
  (3) 
  

  

  abs. 
  

  

  25 
  

  

  50 
  

  

  * 
  44 
  s 
  

  

  D3 
  3 
  

  

  D 
  2 
  (3) 
  

  

  132 
  

  

  19 
  

  

  44 
  

  

  * 
  72 
  a 
  

  

  3V 
  

  

  D 
  4 
  (3j 
  

  

  abs. 
  

  

  23 
  

  

  46 
  

  

  * 
  70 
  a 
  

  

  D3 
  5 
  

  

  D 
  2 
  '(3) 
  

  

  133 
  

  

  20 
  

  

  45 
  

  

  * 
  73 
  a 
  

  

  W 
  

  

  D/<8) 
  

  

  abs. 
  

  

  24 
  

  

  47 
  

  

  * 
  71 
  a 
  

  

  D3 
  7 
  

  

  D. 
  5 
  (3) 
  

  

  131 
  

  

  22 
  

  

  52 
  

  

  46 
  s 
  

  

  