282 MAYAN CALENDAR SYSTEMS [eth. ann. Tz 



repeat it here. The writer claims to have been a descendant (grand- 

 son) of the rnling chief of the Cakehiqnels at the time of the arrival 

 of the Spaniards, and was then a j'outh of probably some IG or 18 

 years. Jndging by his method of giving dates, he seems to have been 

 familiar with a calendar then in use. Moreover his station would 

 indicate that he had been trained in the study of the chronologj" of 

 his tribe. I am, therefore, inclined to accept as substantially coi-- 

 rect his statements so far as they bear on the calendar system, though 

 the traditional portion maybe of very little or no historical value. If 

 this view be accepted, it may throw some light on one troublesome 

 feature of the Maya calendai- — the introduction of the multiple 18 in 

 counting the months. Why the change from the lunar period to a 

 period of twenty days to the month was made, is not easilj^ accounted 

 for, except on the supposition that, having decided for ceremonial or 

 other reason to abandon the lunar count, it was natural to follow the 

 vigesimal system, hence the 20 days to the month, 20 months to the 

 year, and 20 years to the cycle or ahau. The necessity, however, for 

 some adjustment between the ceremonial and true year brought about 

 at length the adoption of 18 months and 5 added days, and the sub- 

 stitution of 18 in place of 20 in time numeration. It seems possible, 

 if the annalist be correct in his time count, that the peculiar native 

 calendar may have come into use somewhat in this way. 



I can find no grounds whatever for Goodman's assertion that the 

 calendar year of the Cakchiquels consisted of 366 days. They may be 

 in a historical mention which I have failed to find, but l\y no possible 

 means can this year be made to agree with the calendar of the Annals 

 without assuming an ai'bitrary break in the succession of the days at 

 the end of each year. 



MAYA METHOD OF CALCULATION 



As I have, in my paper on the "Mexican and Central American 

 Numeral Systems,"" brought up the question. How did the Maja 

 priests actually perform their calculations relating to time series, some 

 of them reaching into millions? I propose to discuss the subject 

 somewhat nujre at length here. As was stated in that paper, these 

 calculations sometimes required changing series of days, chnens, 

 ahaus, katuns, cycles, and even great cycles (or more correctly units of 

 the 1st, 2d, lid, 4th, 5th, aiid even the 6th order in the vigesimal sys- 

 tem), to years, months, and days, reaching from one given date to 

 another. As such calculations could not i>ossibly have been made 

 mentally, the authors of the inscriptions and codices must have had 

 some method of "ciphering," to use a school-boy term, or of making 

 the calculation bj' marking on some object. As was stated in the 

 paper referred to, the ouly allusion to the subject by an early author- 

 it}', so far as is known, is the statement by Landa that they i)erformed 

 them " on the ground or some flat thing." 



" Nineteenth Annual Report of the Bureau of American Ethnology. 



