204 MAYAN CALENDAR SYSTEMS [eth. an-n. 22 



follows: Fifty-fourth great cycle, 9 cycles, 14 katuns, 13 ahaus, 4 

 chuens, and 17 days, to 12 Caban 5 Kayab, countlnjj forwai-d from 4 

 Ahati 8 Cuinhu, the first daj' of the fifty-fourth great cycle, as Good- 

 man has numbered these supposed time periods. 



It is proper, however, to mention at the outset that the terms "great 

 cycle," "cycle," "katun," "ahau," and "chuen" are used merely for 

 convenience in comparisons with Goodman's renderings, and that I do 

 not accept them as appropriate, or in any way adopt his theory that 

 they denote real time periods, because I believe them to be nothing 

 more than the orders of units in Mayan numeration; nor must it be 

 tinderstood that I accept his theory of a separate Mayan chronologic 

 system. As the application of these terms has been fully explained 

 in my previous paper, it is only necessary to restate here their numer- 

 ical vahie: 



1 chtien - 30 days (1x20) 



1 ahau _ 360 days (18x20) 



1 katun 7,200 days (18X20X20) 



1 cycle 144,000 days (18X20X20X20) 



The great cycle as given by Goodman equals 1,872,000 days or 18 x 

 20x20x20x13, but should, as I shall endeavor to show, be counted 

 as equal to 2,888,000 days, or 18x20x20x20x20. The number 54 

 standing in the great-cycle place in the above series (54^0-14—13-4—17) 

 is to be considered as having no numerical value; it is not to l)e read 

 "54 great cycles," but "the fifty-fourth great cj'cle" (according 

 to Goodman's method of numbering these supposed time periods), 

 while the other numerals, 9, 14, etc., ai'e to be used as true numbers — 

 that is, 9 cycles, 14 katuns, 13 ahaus, 4 chuens, 17 days — the 54 being 

 entirely omitted from the calculation. The sum of the series will 

 therefore be as follows, the day being the unit: 



9 cycles (each 144, 000) 1,296,000 days (9X30X20X20X18) 



14 katuns (each 7. 300) 100, 800 days (14x20X20X18) 



13 ahaus (each 360) 4,680 days (13X20X18) 



4 chuens (each 30) 80 days (4 X 30) 



17 days 17 days 



Sum of the series 1 , 401 , 577 days 



After the initial series the next number-series (reversed), 13-9-9, or 

 13 ahaus, 9 chuens, and 9 days, is found in the compound glyph num- 

 bered 1(> in Maudslay's drawing, the numbering of which has been 

 retained in our plate LXXI. The date which follows — 6 Cimi 4 Tzec — 

 is found in the right-hand portion of glyph 18 and the left-hand 

 portion of glyph 19. 



As all the numbers of the initial series, including that attached to 

 the month and day forming the terminal date, are face characters, 

 and are considerably worn and dim, the question arises. How did 

 Goodman ascertain their number value? 



Although some of these characters are so dim and imperfect that 



