274 MAYAN CALENDAR SYSTEMS [eth. ann. 22 



not Siiy the "numbers" whieli so return are katuus, but that they 

 "served as a key to find the katuns," clearly distinguishing between 

 the "katuns" and "certain years." There is nothing, therefore, in 

 the quotation which implies that the numbers in the series 13, 9, 5, etc., 

 were tlie numbers of the katuns, nor is there any mention therein of 

 the numbers of the katuns or of the number of years constituting a 

 katun. It is to Landa that we must go for information on the latter 

 point. According to his statement, which has been oft repeated, the 

 Mayas counted their ages by 20 years," but he says nothing in reference 

 to tiie oi-der of numbering.* 



As the periods referred to are unquestionably years, the katuns 

 must be periods of years; and writers who have so contended ai'e cor- 

 rect in this respect, and 20 years is the number assigned to a katun by 

 all the early authorities, whether right or wrong. 



The direction of counting, it is true, is backward, but, as Good- 

 man states, the reference among the Mayas is generally to past time, 

 and the example Landa gives of counting time, in connection with 

 the passage referred to, relates to what had passed. He .says an 

 elderly man of whom he had spoken could easily count back 300 years 

 by means of the katuns or ages. This author, if I rightly understand 

 his language, indicates that they had a still higher count of 13 x 20 

 years. His language is as follows : 



No solo tenian los indios cuenta en el aiio y meses, como qiteda diclio. y sena- 

 lado atras pero tenian cierto modo de contar los tiempos y sus cosas por edades, 

 las quales hazian de veynte en veynte anos, contando xni veyntes con tina de las 

 XX letras de los meses que llaman Ahan, sin orden sino retruecanados como 

 pareceran en la siguiente raya redonda; llaman les a estos en su lengua Katunes." 



Thirteen times 20 is 260, or five cycles of 52 years each, the same num- 

 ber of years that there are days in their so-called sacred year. Possi- 

 bly, however, he may refer here to the 260-day period. 



When we free our minds entirely from any thought that ahaus, 

 katuns, etc. , represent or have anj' relation to time j)eriods, and look 

 upon them merely as numbers, just as we think of tens, hundreds, etc., 

 the difficulties raised by Goodman's theory of a Maya " chronological 

 calendar" vanish. The Mayas of one section, for some historical, tradi- 

 tional, or mythological reason, selected a particular initial date for 

 their era, and, as a usual thing, counted long periods from it, and in 

 doing so used numbers in accordance with their numeral system, and 

 represented these in their inscriptions by certain symbols. This is 

 all of Goodman's supposed wonderful chronological system— this and 

 nothing more. 



It would have been much better if he had used the real Mayan 

 numeral terms as they stand (as Dr Brinton has suggested), or in a 



« Landa, De Las Cosas, p. 312. 



(lit will doubtless be recalled that in the "Study of the Manuscript Troano" I contended that 

 the ahaus or katuns consisted of 24 yeara, basing my conclusion on the order given above: but 

 a more oaretul study of the passage quoted above from Perez does not necessarily indicate that 

 these periods were numbered according to the order given. 



