morley] IKTEODUCTION TO STUDY OF MAYA HIEEOGLYPHS 



103 



have head-variant numerals; but that the earliest of these latter 

 antedate the earliest bar and dot Initial Series may well be doubted. 



Table X. CHARACTERISTICS OF HEAD-VARIANT NUMERALS TO 19, 

 INCLUSIVE 



Characteristics 



Head for 



Head for 1 



Head for 2 



Head for 3 



Head for 4 



Head for 5 



Head for 6 



Head for 7 



Head for 8 



Head for 9 



Head for 10 



Head for U 

 Head for 12 

 Head for 13 



Head for 14 

 Head for 15 

 Head for 16 

 Head for 17 

 Head for 18 

 Head for 19 



Clasped hand across lower part of face. 

 Forehead ornament composed of more than one -part. 

 Oval in upper part of head. (?) 

 Banded headdress or fillet. 



Bulgmg eye with square irid, snagliie front tooth, ciu-ling fang from back of mouth. 

 Normal form of tim sign as headdress. 

 "Hatchet eye." 



Large scroll passing imder eye and curling up in front of forehead. 

 Forehead ornament composed of one part. 

 Dots on lower cheek or around mouth and in some cases beard. 

 Fleshless lower jaw and in some cases other death's-head characteristics, trun- 

 cated nose, etc. 

 Undetermined. 



Undetermined; type of head known, however. 



(a) Long pendulous nose, bulging eye, and curling fang from back of mouth. 

 (6) Head for 3 with fleshless lower jaw of head for 10. 



Head for 4 with fleshless lower jaw of head for 10. 



Head for 5 with fleshless lower jaw of head for 10. 



Head for 6 with fleshless lower jaw of head for 10. 



Head for 7 with fleshless lower jaw of head for 10. 



Head for 8 with fleshless lower jaw of head for 10. 



Head for 9 with fleshless lower jaw of head for 10. 



Mention should be made here of a numerical form wliich can not 

 be classified either as a bar and dot numeral or a head variant. 

 This is the thumb (*), which has a numerical value of one. 

 ' We have seen in the foregoing pages the different characters which 

 stood for the numerals to 19, inclusive. The next point claiming 

 our attention is, how were the higher numbers written, numbers 

 which in the codices are in excess of 12,000,000, and in the inscrip- 

 tions, in excess of 1,400,000? In short, how were numbers so large 

 expressed by the foregoing twenty (0 to 19, inclusive) characters? 



The Maya expressed their higher numbers in two ways, in both of 

 which the numbers rise by successive terms of the same vigesimal 

 system : 



1. By using the numbers to 19, inclusive, as multiphers mth the 

 several periods of Table VIII (reduced in eacli case to units of the 

 lowest order) as the multiplicands, and — 



2. By using the same numbers^ in certain relative positions, each of 

 which had a fixed numerical value of its own, hke the positions to the 

 right and left of the decimal point in our own numerical notation. 



1 As previously explained, the number 20 is used only in the codices and there only in connection with 

 tonalamatls. 



