246 BUREAU OF AMERICAN ETHNOLOGY [Bn.i.. ." 



uniiiistakably records 19 iiinals, a niiinl)er which had no existence in 

 the Maya system of numeration, since 19 iiinals are always recorded 

 as 1 tun and 1 uinal.^ Therefore the coefficient in Cl is incorrect on 

 its face, a fact we have been able to determine before proceeding with 

 the calculation indicated. If not 19, what then was the coefficient 

 the ancient scribe should have engraved in its place? Fortunately 

 the rest of this text is unusually clear, the Initial-series number 

 9.15.6. ?.l appearing in Bl-Dl, and the terminal date which it 

 reaches, 7 Imix 19 Zip, appearing in C2 D2. Compare C2 with figure 

 16, a, h, and D2 with figure 19, d. We know to begin with that the 

 uinal coefficient must be one of the eighteen numerals to 17, inclu- 

 sive. -Trying first, the number will be 9.15.6.0.1, which tlie student 

 will find leads to the date 7 Imix 4 Chen. Our first trial, therefore, 

 has proved unsuccessful, since the date recorded is 7 Imix 19 Zip. 

 The day parts agree, but the month parts are not the same. This 

 month part 4 Chen is useful, however, for one thing, it shows us how 

 far distant we are from the month part 19 Zip, which is recorded. 

 It appears from Table XV that in counting forw^ard from position 

 4 Chen just 260 days are required to reach position 19 Zip. Conse- 

 quently, our first trial number 9.15.6.0.1 falls shortof the numberneces- 

 sary by just 260 days. But 260 days are equal to 13 uinals; therefore 

 we must increase 9.15.6.0.1 by 13 uinals. This gives us the number 

 9.15.6.13.1. Reducing this to units of the first order and solving for 

 the terminal date, the date reached w^ill be 7 Imix 19 Zip, wliich agrees 

 with the date recorded in C2 D2. We may conchule, therefore, that 

 the uinal coefficient inCl should have been 13, instead of 19 as recorded. 

 Another error of the same kind — that is, one which may be detected 

 by inspection — is shown in figure 84, B. Passing over glyphs 1, 2, 

 and 3, we reach in glyph 4 the date 5 Kan 13 Uo. Compare the 

 upper half of 4 with figure 16,/, and the lower half with figure 19, h, c. 

 The coefficient of the month sign is very clearly 13, which represents 

 an impossible condition when used to indicate the position of a day 

 whose name is Kan; for, according to Table VII, the only positions 

 which the day Kan can ever occupy in any division of the year 

 are 2, 7, 12, and 17. Hence, it is evident that we have detected an 

 error in this text before proceeding with the calculations indicated. 

 Let us endeavor to ascertain the coefficient which should have been 

 used with the month sign in glyph 4 instead of the 13 actually recorded. 

 These glyphs present seemingly a regular Secondary Series, tlie stall- 

 ing point being given in 1 and 2, the number in 3, and the terminal 

 date in 4. Counting this number 3.4 forward from the starting 

 point, 6 Ahau 13 Kayab, the terminal date reached will be 5 Kan 

 12 Uo. Comparing this with the terminal date actually recortled, 

 we find that the two agree except for the month coefficient. But 

 since the date recorded represents an impossible condition, as we 



1 For a seeming exception to this statement, in the codices, see p. 110, footnote 1. 



