THOMAS] Goodman's archaic calendars '251 



not perfected, lie had probably oiUliued the tables of his "Archaic 

 Chronological Calendar," but instead of numbering them as we find 

 thein now given in his work, the cycles were numbered 1, -2, 3, etc., up 

 to lo; the katiins, 1, 2, ;>, etc., to 20, etc. Conceiving tlie idea that 

 the numbers in the series (as the lo-O-'.i) should express the numbers 

 in his scheme — that is to say, sliould be read the 13th ahau, the 9th 

 chuen, and 0th day — he found that it would not give the correct result. 

 Here indeed was a diflticulty, a difficulty of fitting facts to a theory, but 

 not one in reality, foi' the series taken as it stands works out correctly. 

 In order to overcome this difficulty and at the same time save his 

 theory he seemingly hit upon the ingenious device of a supposed 

 May.in method of numberiug periods somewhat as the surveyor num- 

 bers his stations, beginning with (nauglit), or what gives the same 

 result and avoids the u.se of the cypher, which he contends was not 

 used by the Mayas, of bringing forward the last number of the 

 l^receding period to be the first of the one following. Thus in his 

 "Archaic Annual Calendar" he has pushed down one step the true 

 dominical days, Akbal, Lamat, Ben, Ezanab, although retaining 

 their proper numbers, and has brought forward, Avitli the number 20 

 attached, the preceding days, Ik, Manik, Eb, Caban, and begins the 

 numbering of the chuens with 18, of the ahaus and katuns witli 20, 

 etc. This, of course, overcomes the difficulty, as wliat is numbered 

 the first ahau, etc., is, in fact, tlie second, and in the example given 

 the loth ahau is, in fact, the 14tli, and the 0th chuen the lOtli, and 

 hence, by his method of numbering, tlie 13th ahau, Otli chuen, 0th 

 day is equivalent to 13 complete ahaus, plus complete chuens, plus 

 days. Tliis plan will undoubtedly preserve tlie proper order of 

 succession. The only real eri'ors it introduces, if considered merely a 

 method of numbering, is in making the wrong days dominicals and 

 in carrying tlie la.st day of one month forward to become the first 

 day of the next, one or two examples of which are pointed out in my 

 previous paper. These examples have since been more fully dis- 

 cu.ssed by Mr. Bowditcli, with the result of strongly inclining liini to 

 accept Goodman's theory in this respect. They are noted in my 

 Maya Year (figure 20), though not discussed there as to the point 

 here raised. 



As further evidence bearing on this question, I add the following: 

 There is no such method of numbering found in the inscriptions, or 

 in the codices, Mayan or Mexican, unless in the examples above 

 referred to, and there is no such method mentioned l\v any of the 

 early writers. Perhaps, however, the most important j)oint to be 

 decided in this connection is the query. Did the Mayas in fact 

 numljer these so-called periods? How many were to be taken was 

 indicated by symbols, but there is no evidence, so far as I am 

 aware, that tliey were numbered, except in a single instance found 



