'J62 MAYAN CALENDAR SYSTEMS [eth. ann.22 



It is also cqTially apparout that liis theory of a Maj'a chronological 

 system, distinci, from the Maj^a calendar system — the Maj'aii method 

 of niimeration in counting time — and his method of counting 13 

 so-called cj'cles onlj- to the so-called great cycle and 73 great cycles 

 to his so-called grand era are not justified by the facts, nor is his 

 method of numbering the cycles, katuns, etc., beginning with 73, 13, 

 and 20, satisfactorily proved; and also that his selection of Ik, Manik, 

 Eb, and Caban as the dominical days is erroneous, the true dominical 

 daj'S being Akbal, Lamat, Ben, and Ezanab, both in the inscriptions 

 and Dresden codex. 



TjCt us turn next to liis method of numbering the so-called great 

 cycles. According to his theory, as we have seen, 73 great cycles are 

 counted to what he calls the grand era, the common multiple of aU 

 the factors of the calendar sj'stem and supposed "chronological 

 system." The reason why he adopted this theory is explained in my 

 previous paper, and the explanation need not be repeated here, except 

 so far as merely to state that in order to find a common multijile of 

 the various time periods, one must include the Tiumber 30.5, which 

 contains the i:)rime number 73. 



That there was in the Maya system a number or order of units 

 corresponding with Goodman's great cycle is certainly true, but this 

 pertained to their numeral, and not their time, system. It is also 

 admitted that the large quadruple glyph that usually heads the initial 

 series is the symbol used to rejiresent this number or order of units. 

 But, as has been shown, there is no reason whatever for believing that 

 they were numbered otherwise than in accordance with the vigesimal 

 system ; that is to say, 20 cycles to the great cycle, and 20 great cj^cles 

 to the next higher unit. It is necessary, therefore, for Goodman, before 

 his theory can be accepted, to show bj' satisfactorj' evidence that, on 

 reaching the cycles and great cycles, the ordinary method of proceed- 

 ing by the vigesimal system was abandoned and other multiples were 

 introduced. That there was a change from this rule in passing from 

 the 2nd order of units, or chuens, to the 3rd oi-der, or ahaus, where 18 

 was made the multiple, is jiroved by incontrovertible evidence and 

 hence must be admitted, even though we maj' not be able to show by 

 absolute demonstration why the cliange was made. Nevertheless, we 

 are justified in believing that, in this instance, the method of numera- 

 tion was made to correspontl with the number of months in the year. 

 But no such reason appears for Goodman's proposed change in the 

 higher orders of units; we are, therefore, justified in rejecting the 

 idea until other proof, besides its necessity to support a theory, is 

 shown. It must be made evident by proof that the series can not be 

 otherwise explained, which we have shown is not the case, or it must 

 be shown that the great cycle symbols present, by their forms, the 

 nuntbers assigned them. 



