THOMAS] SIGNIFICATION OF THE NUMERAL SERIES 295 



nized calendar the 1,025 years, etc., may be pushed backward or for- 

 ward at will. Hence a Mayan scribe may write 9-15-0-0-0 from 4 

 Ahau 8 Ciimhu to -1 Ahaii 13 Yax (as in number 20) ; and 52 j'ears later 

 another ma3' write the same series, as in number 27, and both will 

 be strictly correct, but the -4 Ahaii 8 Cumhu of the first will be 52 

 years earlier than that of the second. The mere fact, therefore, that 

 4 Ahau 8 Cumhu is reached by counting back the different numeral 

 series is not evidence that in each case identically the same 4 Ahau 

 8 Cumhu is reached. Other evidence having some bearing on the 

 question must be introduced to establish this identity. The only fact 

 apparent in the series themselves which seems to favor the theory of 

 identity is that each runs back 9 cycles plus the minor numbers. 

 This undoubtedly favors the theory of identical date. 



Let us turn now to the Dresden codex, and give attention to what 

 I have termed siibsidiary series; that is to say, short series ap- 

 parently, as was suggested in the theoretical series given above, 

 intended to connect with 4 Ahau 8 Cumhu. As I have expressed 

 doubts as to the correctness of Seler's suggestion about that on plate 

 LXIX, attention is called to the long compound series on plate XXIV 

 (see our plate Lxxxii). This series begins at the right-hand edge of 

 the bottom section .md runs leftward to the middle; it then passes to 

 the next section above, and so on to the top of the page, the conclud- 

 ing column being that in the lower division of the left-hand portion. 

 No months are given except at the bottom of the long number col- 

 umns and the one short column in the lower left-hand portion of the 

 plate. The last date standing in the lower left-hand corner is 4 Ahau 

 8 Cumhu, and over it is the number series 6-2-0 (the symbol in a 

 red loop). The next date to the right is 1 Ahau 18 Kayab; this 

 stands under the niimeral series 9-9-16-0-0. Counting back from 

 4 Ahau 8 Cumhu, the short series, 6 ahaus, 2 chuens, days, or 2,200 

 days, we are brought to 1 Ahau 18 Kaj'ab, while if we count forward 

 from the same date it brings us to 7 Ahau 18 Cumhu, which shows 

 the backward count to be the correct one, if the design of the artist 

 was to connect the two series; moreover, the count of the long sei'ies, 

 if made toward the right, is backward. 



We know that in all the series given in the above list, where 4 

 Ahau 8 Cumhu is the principal date, it is the initial day and the 

 numeral series follows it; in other words, the count must be backward 

 to reach it. Taking number 15 of the list — Stela K of Quirigua — 

 54-9-18-15-0-0 — we find that the terminal date lies .3,920 j'ears subse- 

 quent to 4 Ahau 8 Cumhu. Turning to the last column of the series 

 on plate xxiv of the Dresden codex, which is 9-9-16-0-0, we find that 

 the count, when the .short series of 2,200 days is added, reaches back- 

 ward from 4 Ahau 8 Cumhu 3,750 j-ears. In other words, we count 

 forward in the codex 3,750 years to 4 Ahau 8 Cumhu, and in the 

 inserixjtion series forward from this date 3,920 years, making the total 



