128 



SCIENCE 



[Vol. XXI. No. 527 



toria de Tlascala, the Codex Chimalpopoca, the Anales de CuauJi- 

 titlan, manuscripts of Ixtlilxochitl, Leon y Gauia, Father Pich- 

 ardo, and others. Very curious are the catechisms of the early 

 missionaries written in the Mexican hieroglyphic characters, the 

 maps, charts, plans, "Titulos de Tierra," legal documents, and 

 royal ordinances, throwing light on the early history and settle- 

 ment of the territory of Mexico. 



M. Boban concludes his long and arduous task by adding a 

 comprehensive and well-arranged index to his volumes; and I 

 should not omit to mention that he increases the practical value 

 of his work by inserting a series of biographical notices and many 

 quotations and references to contemporary Mexican archaeological 

 literature. 



I have reserved the best piece of news to the last. I learn 

 from good authority that it is the intention of the enlightened 

 M. Goupil finally to concede to scholars the access to this marvel- 

 lous storehouse of American antiquity by placing it in the posses- 

 sion of the Manuscript Deijartment of the Bibliotheque Nationale. 

 Certainly no one in this generation will more deservedly receive 

 the thanks of all genuine Americanists than the donor of such a 

 treasure to public use. 



TIME-PERIODS OF THE MAYAS. 



BY PROFESSOR CYRnS TBOMAS, WASHINGTON, D.C. 



In "Current Notes on Anthropology,'' Science, Feb. 10, refer- 

 ence is made by Dr. Brinton to the article on "Time-Periods of 

 the Mayas." by Dr. Forstemann, in Globus (Bd. 63. No. 3). In 

 closing this notice, he remarks that "Dr. Forstemann's discussion 

 of the subject amounts to a demonstration," — an asserton I think 

 he will find it difficult to maintain. I presume, however, it was 

 based on Dr. Forstemann's well-known ability as an investigator 

 in this line, his long and faithful study of the time-symbols of the 

 Maya Codices, and his great caution in presenting conclusions, 

 rather than on a thorough examination of the data. 



I am indebted to Dr. Forstemann for several valuable sugges- 

 tions in my work in this line; it was through one of these, given 

 in a private communication, that I was led to the evidence on 

 which I base some of the objections offered here to his conclu- 

 sions. 



He believes that the different steps by which the Mayas reached 

 their final calendar with the year of 365 days, consisting of 18 

 months of 20 days each, were as follows: First, the period of 20 

 days, next the period of 18 months, giving the year of 360 days ; 

 next, the year of 364 days, formed by adding four days at the end 

 of the eighteenth month, at which time the division into periods 

 of 13 days was introduced; and, finally, the year of 365 days, by 

 adding another day at the end of the eighteenth month. The 

 evidence on which this is based he believes he finds in the Codices, 

 chiefly in the Dresden Codex. He believes he finds evidence of 

 the use of all these years, as also of the Tonalamatl or Sacred year 

 of 360 days in the latter Codex. 



We take first his basal or cvclical period : — 



11 

 19 ' 

 f. [-or 14040 days, found in the right column of Dres., p. 73. 



oj 



There is no doubt that this denotes, as he contends, 14040 days, 

 or 39 years, if we count 360 days to the year. " From this,"' he 

 adds, " proceed two series, of which one has the difference 65, 

 . . . while the other increases by 54" He alludes to the series 

 running through the upper division of pp. 71-73, where the dif- 

 ference is 54; and that running through the middle and lower 

 divisions of the same plates, where the difference is 65 (see our 

 "Aids to the Study of the Maya Codices," pp. 38^-387). It is to 

 be noticed, however, that there is no connection between his 

 typical number and these series, and why he has thus referred to 

 them is not aiDparent. On the contrary, it appears from the 9 Ix 

 below it to belong to the right-hand series of the upper division. 

 I also made the mistake in my " Aids" (p. 337, note) of connect- 

 ing this 9 Ix with one of the series mentioned. 



The point he makes is, that this number is divisible by 360. and 

 that the two series referred to can be explained on this theory, 



hence it is presumable a year of this length was used in con- 

 structing them. Now it must be conceded that if these series 

 can be explained and traced out in accordance with the usual 

 calendar of 365 days to the year, and the four year-series, Dr. 

 Forstemann's argument loses its force, and falls short of a " de- 

 monstration." 



Let us see if this can be done. For this purpose we present 

 here a part of the series in the middle division of the plates al- 

 luded to. 



1 



4 19 16 13 9 6 3 



15 10 5 15 10 5 



4 Manik 4 Ik 4 Caban 4 Eb 4 Manik 4 Ik 4 Caban. 



This series, which begins with the number and day at the 

 right, ascends, and is to be read from right to left, the difference 

 being 65 days, or 3 months and 5 days, if the numbers are intended 

 to denote days, months, and years. The 19 in the 6th, or next to 

 the left-hand column, is evidently the same as 1 unit of the third 

 order and one of the second, or 1 year, 1 month (counting 360 

 days to the year). If the year contained only 360 days, it must 

 have commenced year after year with the same day unless there 

 was an arbitrary change. On this theory the numbers in the 

 lower line of numerals (with one exception) might denote the day 

 of the month. For example, Caban would be the 5th day of the 

 month if the year began with Ben, or with Ix counting from the 

 last day of the month ; Ik the 10th, Manik the 15th, and so on 

 through the entire series, and also in numerous other series. This 

 would seem to be a sufficient " demonstration " of the theory, and 

 was considered so by me in my "Aids," but the numeral system 

 in the Maya calendar is exceedingly deceptive. Before this is 

 conceded, it is necessary to overcome the following objections : 

 The figures in the middle row do not give the months correctly 

 nor those in the upper the years. The 3, 5, in the first column, 

 really denote the 5th day of the 4th month. While the 1 in the 

 left-hand column, if taken in this way, would refer to the second 

 year. Moreover, if the numbers in the "month" and "day 

 lines" were intended to denote the numbers of the months and 

 days of the months there could be no blanks, such as we see in 



13 

 the 4th column above ( 0). That the symbol represented by the 

 cipher signifies "nothing," is admitted by Dr. Forstemann, and 

 is jDroven by the number in the month line. As upon the theory 

 of 360 days to the year, all the years should begin with the same 

 day, while this method of counting time remained in vogue, the 

 different series based upon this method should be referred to 

 years commencing with the same day. This, however, is not the 

 case, as the series now under consideration pertains to a year 

 commencing with Ben ; while the long series on pp. 52-58 can be 

 reckoned only in years beginning with Lamat. Nor is it possible 

 to bring these series into harmony in this respect upon the theory 

 of a year of 360 days unless we assume there were arbitrary 

 changes, which amounts to begging the question. It is also in- 

 consistent with this theory that the series on pp. 63-64, which 

 Dr. Forstemann believes to be founded on the year of 864 days, 

 gives precisely the same results in the respect mentioned as the 

 other series referred to. In truth, it is impossible that the "day" 

 and " month lines" of numerals should indicate the days of the 

 month and numbers of the months throughout a series extending 

 over several years, except upon the theory of 360 days to the 

 year. We are forced, therefore, to the conclusion, even on Dr. 

 Forstemann's theory, that these series are only successions of in- 

 tervals in which the columns of numerals simply denote the sum 

 of these intervals at the various steps. 



We will now proceed in our attempt to explain the series on 

 pp. 71-73, of which a portion is given above, by the usual calen- 

 dar system of 365 days' to the year and the four year-series. No 

 difference between the two systems will appear until we reach 

 the end of the first year of the series. As this is reached in pass- 



(16 (19 



ing from the 5th to the 6tli column, ^ 5 and J 10 we 



/ 4 Caban ( 4 Ik, 



start with 4 Caban of the 5th column. As before stated, this 

 series proceeds from right to left and is to be counted from the 



