﻿124 
  

  

  THE 
  NATIONAL 
  GEOGRAPHIC 
  MAGAZINE 
  

  

  o 
  = 
  ■ 
  

  

  CX)CX) 
  

  

  1 
  1 
  

  

  OO 
  = 
  2 
  

   OOO 
  = 
  3 
  

  

  1 
  1 
  

  

  

  1 
  1 
  

  

  

  1 
  

  

  CXXO 
  = 
  4 
  

  

  

  

  

  = 
  5 
  

  

  

  o 
  

  

  o 
  

   1 
  

  

  1 
  1 
  i 
  ":.! 
  

  

  

  1 
  

  

  00 
  ~ 
  - 
  

  

  

  1 
  1 
  • 
  

  

  

  OOO 
  ;.. 
  

  

  OO 
  

  

  1 
  

  

  1 
  

  

  1 
  ' 
  

  

  i 
  

  

  OCXDO 
  „ 
  

  

  

  I 
  1 
  

  

  OOO 
  

  

  1 
  

  

  

  1 
  1 
  ,-, 
  ^ 
  

  

  1 
  I 
  - 
  1 
  : 
  I 
  

  

  o 
  

  

  

  1 
  1 
  „ 
  

  

  COX) 
  

  

  1 
  1 
  

  

  1 
  

  

  

  1 
  

  

  OO 
  

  

  1 
  

  

  

  1 
  3 
  = 
  » 
  

  

  

  1 
  I 
  

  

  

  OOO 
  

   1 
  l-»3 
  

  

  ^ 
  J 
  

  

  1 
  1 
  

  

  16 
  

  

  T 
  1 
  1 
  K 
  M 
  A 
  YA 
  ROM 
  A 
  N 
  NUM 
  gRAI,S 
  

  

  In 
  the 
  Maya 
  bar 
  and 
  dol 
  numerals, 
  the 
  dot 
  

   stands 
  for 
  i 
  and 
  the 
  bar 
  for 
  5- 
  These 
  ele- 
  

   ments, 
  when 
  added 
  together 
  in 
  the 
  proper 
  

   combinations, 
  give 
  the 
  numbers 
  from 
  6 
  to 
  19, 
  

   inclusive. 
  The 
  number 
  20 
  is 
  shown 
  at 
  the 
  bot- 
  

   tom 
  of 
  the 
  second 
  column. 
  It 
  is 
  also 
  the 
  hiero- 
  

   glyph 
  for 
  the 
  moon. 
  

  

  not 
  yet 
  been 
  determined, 
  though 
  doubt- 
  

   less 
  the 
  still 
  undeciphered 
  hieroglyphs 
  

   will 
  clear 
  up 
  this 
  point 
  when 
  their 
  mean- 
  

   ings 
  shall 
  have 
  been 
  worked 
  out. 
  

  

  It 
  is 
  evident 
  from 
  the 
  foregoing 
  that 
  

   the 
  element 
  of 
  time 
  was 
  of 
  primary 
  im- 
  

   portance 
  to 
  the 
  ancient 
  Maya, 
  and 
  that 
  

   its 
  record, 
  as 
  variously 
  manifested 
  by 
  the 
  

   sun, 
  moon, 
  and 
  planets, 
  fills 
  a 
  large 
  part 
  

   of 
  their 
  inscriptions. 
  

  

  MAYA 
  ARITHMETIC 
  

  

  Let 
  us 
  next 
  examine, 
  then, 
  some 
  of 
  the 
  

   features 
  of 
  Maya 
  arithmetic 
  and 
  see 
  how 
  

   these 
  chronological 
  and 
  astronomical 
  

   facts 
  were 
  expressed. 
  

  

  First, 
  the 
  Maya, 
  like 
  ourselves, 
  had 
  

   two 
  different 
  ways 
  of 
  writing 
  their 
  num- 
  

   bers, 
  one 
  by 
  bars 
  and 
  dots, 
  and 
  the 
  other 
  

   by 
  different 
  types 
  of 
  the 
  human 
  head. 
  

   The 
  former 
  may 
  be 
  likened 
  to 
  our 
  

   Roman 
  numerals, 
  and 
  the 
  latter 
  to 
  our 
  

   Arabic 
  numerals. 
  

  

  The 
  Maya 
  ''Roman 
  notation" 
  made 
  

   use 
  of 
  but 
  two 
  elements, 
  the 
  dot 
  standing 
  

   for 
  the 
  number 
  1 
  and 
  the 
  bar 
  standing 
  

   for 
  the 
  number 
  5. 
  In 
  this 
  respect, 
  at 
  

   least, 
  their 
  bar 
  and 
  dot 
  numerals 
  were 
  

   even 
  simpler 
  than 
  our 
  Roman 
  numbers, 
  

   since 
  we 
  have 
  to 
  use 
  seven 
  letters 
  — 
  I, 
  

   V, 
  X, 
  L, 
  C, 
  D, 
  and 
  M— 
  in 
  the 
  Roman 
  

   notation. 
  By 
  various 
  combinations 
  of 
  

   these 
  two 
  elements, 
  in 
  which 
  the 
  dot 
  had 
  

   the 
  value 
  of 
  1 
  and 
  the 
  bar 
  of 
  5, 
  the 
  Maya 
  

   wrote 
  the 
  numbers 
  from 
  1 
  to 
  19, 
  inclu- 
  

   sive 
  (see 
  the 
  examples 
  of 
  bar 
  and 
  dot 
  

   numerals 
  on 
  this 
  page). 
  

  

  The 
  Maya 
  "Arabic 
  notation" 
  made 
  

   use 
  of 
  13 
  different 
  types 
  of 
  human 
  heads 
  

   to 
  express 
  the 
  numbers 
  1 
  to 
  13, 
  inclu- 
  

   sive 
  ; 
  and 
  then, 
  by 
  applying 
  the 
  essential 
  

   characteristic 
  of 
  the 
  head 
  for 
  10, 
  a 
  flesh- 
  

   less 
  lower 
  jaw 
  to 
  the 
  heads 
  for 
  4, 
  5, 
  6, 
  

   7, 
  8, 
  and 
  9, 
  they 
  formed 
  the 
  numbers 
  14, 
  

   15, 
  16, 
  17, 
  18, 
  and 
  19, 
  respectively 
  (see 
  

   the 
  examples 
  of 
  head 
  numerals 
  on 
  the 
  

   opposite 
  page). 
  

  

  One 
  peculiar 
  feature 
  of 
  this 
  notation 
  

   was 
  the 
  use 
  of 
  two 
  kinds 
  of 
  heads 
  for 
  the 
  

   number 
  13 
  — 
  the 
  simple 
  form 
  shown 
  at 
  

   the 
  bottom 
  of 
  the 
  first 
  column 
  on 
  page 
  

   125, 
  and 
  the 
  compound 
  form, 
  3+10, 
  

   shown 
  at 
  the 
  top 
  of 
  the 
  second 
  column. 
  

   The 
  use 
  of 
  the 
  latter, 
  however, 
  was 
  very 
  

   rare, 
  there 
  not 
  being 
  more 
  than 
  two 
  or 
  

   three 
  examples 
  of 
  it 
  known. 
  

  

  The 
  higher 
  numbers 
  were 
  expressed 
  

  

  