MORLEY— MAYA SUPPLEMENTARY SERIES 



higher lunar period. If so, it is probable that those in the first column, 

 i.e., those having no coefficients, represent the first positions in such 

 periods, that in effect they are coefficients of i. Algebra affords a 

 parallel case in its coefficient of unity, ia and a representing the same 

 quantity. 



In explaining the function of these bar-and-dot coefficients we 

 are not without some aid from the manuscripts. Indeed in a passage 

 from the Dresden Codex presenting a lunar count, we find a close 

 analogy which probably explains why these coefficients never rise 

 above 6. On pages 51-58 of this manuscript there are recorded 405 

 successive lunations which are arranged in a series of groups, some 

 groups containing 6 lunations and others 5. The individual lunations 

 vary from 29 to 30 days in length and are so cleverly arranged within 

 the groups that at no group ending in the entire period — nearly 33 

 years — is the cumulative error as much as a day out with the actual 

 number of lunar revolutions. 



One striking characteristic of this series at once claims our atten- 

 tion. The number of lunations in a group, and there are sixty-nine 

 groups in all, never rises above 6, precisely the highest bar-and-dot 

 numeral ever appearing in Glyph C. It seems highly improbable that 

 such an unusual coincidence is accidental, particularly in view of the 

 fact that we know, on other grounds, that the Supplementary Series 

 deals with a lunar count. On the contrary it strongly suggests that 

 the bar-and-dot coefficients in Glyph C denote the positions of specific 

 lunations in groups, the units of which never rise above 6, just as in 

 the lunar count of the Dresden Codex. 1 



These pages of the Dresden Codex prove clearly that the Maya 

 had the practice of grouping their lunar months of 29 and 30 days 

 each into groups of 5 and 6 lunations each, and if this is true of the 

 Dresden Codex, it would seem as though it should be equally true of 

 the inscriptions, another work of the same priestly class. 



Of the sixty-nine groups in the Dresden Codex only nine are com- 

 posed of five lunar months, all the others having six. In other words 

 a sixth lunar month occurred less often than any of the other five, in 

 the proportion of 60 to 69. 2 In the bar-and-dot coefficients of Glyph 

 C, 6 occurs less often than any other numeral, it is true, but much 

 less than in the ratio of the Dresden Codex. Perhaps this indicates 

 that groups of six lunar months were of much less frequency in the 

 Supplementary Series than in the lunar series of the Dresden raanu- 



1 Dr R. K. Morley, of the Worcester Polytechnic Institute, was the first to note this impor- 

 tant coincidence, and to explain the bar-and-dot coefficient of Glyph C on positional grounds. 



2 That is to say, in nine groups there was no sixth month. 



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