96 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 



Head-variant Numerals 



Let us next turn to tlie consideration of the Maya "Arabic nota- 

 tion," that is, the head-variant numerals, wliich, hke all other known 

 head variants, are practically restricted to the inscriptions.^ It 

 should be noted here before proceeding further that the full-figure 

 numerals found in connection with full-figure period, day, and month 

 glyplis in a few inscriptions, have been classified with the head- 

 variant numerals. As explained on page 67, the body-parts of such 

 glyphs have no function in determining their meanings, and it is only 

 the head-parts which present in each case the (U^termining character- 

 istics of the form intended. 



In the "head" notation each of the numerals, 0, 1, 2, 3, 4, 5, 6, 7, 8, 

 9, 10, 11, 12, 13 2 is expressed by a distinctive type of head; each 

 type has its own essential characteristic, by means of which it can 

 be distinguished from all of the others. Above 13 and up to but not 

 including 20, the head numerals are expressed by the application of 

 the essential characteristic of the head for 10 to the heads for 3 to 9, 

 inclusive. No head forms for the numeral 20 have yet been dis- 

 covered. 



The identification of these head-variant numerals in some cases is 

 not an easy matter, since their determining characteristics are not 

 always presented clearly. Moreover, in the case of a few numerals, 

 notably the heads for 2, 11, and 12, the essential elements have not 

 yet been determined. Head forms for these numerals occur so rarely 

 in the inscriptions that the comj)arative data are insufficient to 

 enable us to fix on any particular element as the essential one. 

 Another difficulty encountered in the identification of head-variant 

 numerals is the apparent irregularity of the forms in the earher 

 inscriptions. The essential elements of these early head numerals 

 in some cases seem to dift'er widely from those of the later forms, 

 and consequently it is sometimes difficult, indeed even impossible, to 

 determine their corresponding numerical values. 



1 The following possible exceptions, however, should be noted: In the Codex Peresianus the 

 normal form of the tun sign sometimes occurs attached to varying heads, as (*). ^^ hether these 

 heads denote numerals is unknown, but the construction of this gl)-ph in such eases (a head 

 attached to the sign of a time period) absolutely parallels the use of head-variant numerals with 

 time-period glyphs in the inscriptions. A much stronger example of the possible use of head numerals with 

 period glyphs in the codices, however, is found in the Dresden Codex. Hero the accompanying 

 head (f) is almost surely that for the number 16, the hatchet eye denoting 6 and the fleshless lower 

 jaw 10. Compare (f) with fig. 53, f-i, where the head for 16 is shown. The glyph (J) here ^,_^_ 



t shown is the normal form for the kin sign. Compare fig. 34, 6. The meaning of these two WS^ 

 forms would thus seem to be 16 kins. In the passage in which these glj-phs occur Ihe glji^h l"-'^^' 

 next preceding the head for 16 is "8 tuns," the numerical coelTicicnt S being expressed by one -f 

 bar and three dots. It seems reasonably clear here, therefore, that the form in question is a head 

 numeral. However, these cases are so very rare and the context where they occur is so little understood, 

 that they have been excluded in the general consideration of head-variant numerals presented above. 



» It will appear presently that the number 13 could be expressed in two different ways: (1) by a 

 special head moaning 13, and (2) by the essential characteristic of the head for 10 applied to the head 

 for3(i. e., 10-t-3=13), 



