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88 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 



elements alone the Maya expressed all the numerals from 1 to 19, in- 

 clusive. The normal forms of the numerals in the codices are shown 

 in figure 39, in which one dot stands for 1, two dots for 2, three dots 

 for 3, four dots for 4, one bar for 5, one bar and one dot for 6, one bar 

 and two dots for 7, one bar and three dots for 8, one bar and four dots 

 for 9, two bars for 10, and so on up to three bars and four dots for 19. 

 The normal forms of the numerals in the inscriptions (see fig. 40) are 

 identical with those in the codices, excepting that they are more elabo- 

 rate, the dots and bars both taking on various decorations. Some of 

 the former contain a concentric circle (*) or cross-hatch- 

 Q ® "^» (**) ' ^*^^^® appear as crescents (f ) or © (a) O) 

 ** tt t curls (If), more rarely as (J) or (J J). The bars * ''' " 

 show even a greater variety of treatment (see fig. 41) . All these deco- 

 rations, however, in 

 no way affect the 

 numerical value of 

 the bar and the 

 dot, which remain 5 

 and 1, respectively, 

 throughout the 

 Maya writing. Such 

 embellishments as 

 those just described 

 are found only in 



Fig. 39. Normal forms of numerals 1 to 19, inclusive, in the codices. the inscriptions, and 



their use was proba- 

 bly due to the desire to make the bar and dot serve a decorative 

 as well as a numerical function. 



An important exception to this statement should be noted here in 

 connection with the normal forms for the numbers 1, 2, 6, 7, 11, 12, 

 16, and 17, that is, all which involve the use of one or two dots in their 

 composition.^ In the inscriptions, as we have seen in 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 ^ side of the bar, or bars, as the case may be, and consequently 



onn 1 In one case, on the west side of Stela E at Quirigua, the number 14 is also shown with an orna- 

 ff mental element (*). This is very unusual and, so far as the writer knows, is the only example of 

 " its kind. The four dots in the numbers 4, 9, 14, and 19 never appear thus separated in any other 



* te.xt known. 



2 In the examples given the numerical coefficients are attached as prefixes to the katun sign. Fre- 

 quently, however, they occur as superfixes. In such cases, however, the above observations apply equally 

 well. 



