270 MAYAN CALENDAR SYSTEMS [eth. ann. 22 



This will meet eveiy requirement, including the liraitation.s above 

 mentioned, as fully ;m(l as coiupleteh' as the series given l)y Goodman, 

 even if we hold to his theory of 13 cycles to tlie great cycle and 

 73 great cycles to his grand era, and follow his own method of 

 counting. Tlie same thing is true if we select, as the first great cycle, 

 an J' other of the 40 which j)recede that with which we began tlie count. 



There is another fact which appears to conflict with Goodman's 

 theorj' and, indeed, to be irreconcilable with it. According to this 

 theory, the grand era, consisting of 130,650,000 days, is the least 

 common multiple of all the different factors of the regular calendar 

 as well as of his chronological calendar, at the beginning of which 

 all the periods start anew on their grand round. That this number 

 is the common multiple of all tliese periods or factors is true. But 

 how are we to reconcile the theory with the fact that he begins this 

 great era with the day 4 Ahau 13 Yax, which is certainlj' not the 

 beginning day of a year or of a month? It is true the 136,050,000 

 days is an exact multiple of 365, but, starting the count of 305 with 

 the day 4 Ahau 13 Yax makes the latter number a mere numeral 

 factor; no regular Maj^an year could begin with the day 4 Ahau or 

 with the 13th da}^ of the month Yax. From February 1, 1899, to the 

 following January 31, in our time system, is a year's time, but the 

 period is composed of parts of two calendar years. 



Goodman's theory, in order to be correct and keep the time periods 

 In proper order, if his grand era is a true and absolute rounding-out 

 period of all the minor periods, absolutely requires that this great 

 period shall begin with the 1st day (or 20th if he prefers this number- 

 ing) of the month Pop, and the first year of the 52-year cycle or calen- 

 dar round. Otherwise, when the era ends, it will be in the middle 

 of a year, as it will if it begins on 4 Ahau 13 Yax, and closes with 

 3 Cauac 12 Yax. 



The question next in importance is, are his tables correct, though 

 based on an erroneous theory? Those of the first series, termed the 

 "Archaic Annual Calendar," ai'e nothing more than the ordinary cal- 

 endars of the 52 years of what has hereto foi-e been termed a "cycle," 

 but to which he applies the name "calendar round," each year being 

 given separately. The}' are all contained in u\y condensed calendar. 

 This is nothing new, as the method had been in use for a number of 

 years before Goodman commenced his investigations. As his "Archaic 

 Chronological Calendar" is nothing more than a continuous series of 

 ahaus, or 300-day jjeriods, using Ahau as the " initial da.v " through 39 

 of the 5th order of Tinits, following one another in regular succession, 

 it is correct — with certain exceptions to l)e noted — where Ahau is used 

 as the initial day in the count, but will not apply when any other day 

 is selected as the initial date. It is erroneous in counting 13 of the 

 cycles or the 5th order of units to the next higher order, and in begin- 

 ning the numbering of the so-called periods with 73, 13, and 20. His 

 tables of years are also erroneous in the latter respect. 



