have head-variant numerals; but that the earliest of these latter antedate the earnest bar and dot Initial Series may well be doubted.
Table X. CHARACTERISTICS OF HEAD-VARIANT NUMERALS 0 TO 19, INCLUSIVE
| Forms | Characteristics |
| Head for 0 | Clasped hand across lower part of face. |
| Head for 1 | Forehead ornament composed of more than one part. |
| Head for 2 | Oval in upper part of head. (?) |
| Head for 3 | Banded headdress or fillet. |
| Head for 4 | Bulging eye with square irid, snaglike front tooth, curling fang from back of mouth. |
| Head for 5 | Normal form of tun sign as headdress. |
| Head for 6 | "Hatchet eye." |
| Head for 7 | Large scroll passing under eye and curling up in front of forehead. |
| Head for 8 | Forehead ornament composed of one part. |
| Head for 9 | Dots on lower cheek or around mouth and in some cases beard. |
| Head for 10 | Fleshless lower jaw and in some cases other death's-head characteristics, truncated nose, etc. |
| Head for 11 | Undetermined. |
| Head for 12 | Undetermined; type of head known, however. |
| Head for 13 | (a) Long pendulous nose, bulging eye, and curling fang from back of mouth. |
| (b) Head for 3 with fleshless lower jaw of head for 10. | |
| Head for 14 | (b)Head for 4 with fleshless lower jaw of head for 10. |
| Head for 15 | (b)Head for 5 with fleshless lower jaw of head for 10. |
| Head for 16 | (b)Head for 6 with fleshless lower jaw of head for 10. |
| Head for 17 | (b)Head for 7 with fleshless lower jaw of head for 10. |
| Head for 18 | (b)Head for 8 with fleshless lower jaw of head for 10. |
| Head for 19 | (b)Head for 9 with fleshless lower jaw of head for 10. |
Mention should be made here of a numerical form which 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 0 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 inscriptions, 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 0 to 19, inclusive, as multipliers with the several periods of Table [VIII] (reduced in each case to units of the lowest order) as the multiplicands, and—