Chapter II

, every glyph was a balanced picture, exactly fitting its allotted space, even at the cost of occasionally losing some of its elements. To have expressed the numbers 1, 2, 6, 7, 11, 12, 16, and 17 as in the codices, with just the proper number of bars and dots in each case, would have left unsightly gaps in the outlines of the glyph blocks (see fig. 42, _a-h_, where these numbers are shown as the coefficients of the katun sign). In _a_, _c_, _e_, and _g_ of the same figure (the numbers 1, 6, 11, and 16, respectively) the single dot does not fill the space on the left-hand[60] side of the bar, or bars, as the case may be, and consequently {89} the left-hand edge of the glyph block in each case is ragged. Similarly in _b_, _d_, _f_, and _h_, the numbers 2, 7, 12, and 17, respectively, the two dots at the left of the bar or bars are too far apart to fill in the left-hand edge of the glyph blocks neatly, and consequently in these cases also the left edge is ragged. The Maya were quick to note this discordant note in glyph design, and in the great majority of the places where these numbers (1, 2, 6, 7, 11, 12, 16, and 17) had to be recorded, other elements of a purely ornamental character were introduced to fill the empty spaces. In figure 43, _a_, _c_, _e_, _g_, the spaces on each side of the single dot have been filled with ornamental {90} crescents about the size of the dot, and these give the glyph in each case a final touch of balance and harmony, which is lacking without them. In _b_, _d_, _f_, and _h_ of the same figure a single crescent stands between the two numerical dots, and this again harmoniously fills in the glyph block. While the crescent () is the usual form taken by this purely decorative element, crossed lines (**) are found in places, as in (); or, again, a pair of dotted elements (++), as in (++). These variants, however, are of rare occurrence, the common form being the crescent shown in figure 43.

[Illustration: FIG. 42. Examples showing the way in which the numerals 1, 2, 6, 7, 11, 12, 16, and 17 are _not_ used with period, day, or month signs.]

[Illustration: FIG. 43. Examples showing the way in which the numerals 1, 2, 6, 7, 11, 12, 16, and 17 _are_ used with period, day, or month signs. Note the filling of the otherwise vacant spaces with ornamental elements.]

[Illustration: FIG. 44. Normal forms of numerals 1 to 13, inclusive, in the Books of Chilan Balam.]

The use of these purely ornamental elements, to fill the empty spaces in the normal forms of the numerals 1, 2, 6, 7, 11, 12, 16, and 17, is a fruitful source of error to the student of the inscriptions. Slight weathering of an inscription is often sufficient to make ornamental crescents look exactly like numerical dots, and consequently the numerals 1, 2, 3 are frequently mistaken for one another, as are also 6, 7, and 8; 11, 12, and 13; and 16, 17, and 18. The student must exercise the greatest caution at all times in identifying these {91} numerals in the inscriptions, or otherwise he will quickly find himself involved in a tangle from which there seems to be no egress. Probably more errors in reading the inscriptions have been made through the incorrect identification of these numerals than through any other one cause, and the student is urged to be continually on his guard if he would avoid making this capital blunder.

Although the early Spanish authorities make no mention of the fact that the Maya expressed their numbers by bars and dots, native testimony is not lacking on this point. Doctor Brinton (1882 b: p. 48) gives this extract, accompanied by the drawing shown in figure 44, from a native writer of the eighteenth century who clearly describes this system of writing numbers:

They [our ancestors] used [for numerals in their calendars] dots and lines [i. e., bars] back of them; one dot for one year, two dots for two years, three dots for three years, four dots for four, and so on; in addition to these they used a line; one line meant five years, two lines meant ten years; if one line and above it one dot, six years; if two dots above the line, seven years; if three dots above, eight years; if four dots above the line, nine; a dot above two lines, eleven; if two dots, twelve; if three dots, thirteen.

This description is so clear, and the values therein assigned to the several combinations of bars and dots have been verified so extensively throughout both the inscriptions and the codices, that we are justified in identifying the bar and dot as the signs for five and one, respectively, wherever they occur, whether they are found by themselves or in varying combinations.

In the codices, as will appear in