March io, 1893.] 



SCIENCE. 



1 29 



last day of the month — or these days considered as the first of 

 the monlh, as Dr. Seler concludes As Caban, counting in this 

 way, is the 5th day of the month in Ben (Ix) years, we take it as 



16 

 our starting point. As the figures in this column ( 5) show that 

 16 months and 5 days, or 325 days, have been counted up to this 

 point, our 4 Caban must be the oth day of the 17th month. It 

 follows from this that the starting-point of the series is 5 Ben 

 and that the year is 5 Ben (or 5 Ix, counting from the last day of 

 the preceding month). If there are 365 days in a year there will 

 be 40 days (out of the 65) to count in this year and 25 in the next. 

 As the year (including the 5 added days) will end on 5 Caban, the 

 next will begin with 6Ezanab (a Cauac year). Counting forward 

 25 days in this year, we reach 4 Ik, which is the day under the 

 6th column, but it is the 5th and not the lOlh day of the month. 

 This is not an accidental hit, but has been found true in all these 

 series so far as I have tested them, except that in some the months 

 begin with the usual days as the series on pp. 63-64. 



But this is not all, the same result will be obtained in the series 

 we are examining If we start with 4 Caban of either of the other 

 three years, except that 4 Ik in the Kan (Akbal) years will fall 

 on the 20th day of the month, in Muluc (Lamat) years on the 15th, 

 and in Ix (Ben) years on the 10th. 



It follows, therefore, that these series can be traced and ex- 

 plained as well upon the theory of 365 days to the year as 360. 

 That the series on pp. 46-50 can only be followed out on the usual 

 calendar system is admitted by Dr. FOrstemann, and it was through 

 a suggestion he kindly gave me a year or two ago that I was in- 

 duced to examine it on this theory. 



Is it therefore legitimate, in view of these conflicting results 

 based upon the Codex and Calendar, to say that Dr. Forstemann's 

 discussion " amounts to a demonstration ?" Does not what has 

 been shown do away with his conclusions so far as they are based 

 upon the supposed year of 360 days? If all the series susceptible 

 of being tested can be explained satisfactorily in conformity with 

 the usual Calendar, is there any necessity of resorting to any 

 other theory ? 



It is somewhat strange that Dr. Forstemann should consider 

 the series we have been referring to, the sum total of wliich is 

 5 



1 or 1820 days, as based on the year of 360 days; and yet refer 

 (0 



that on pp. 68-64, which has precisely the same sum total, to the 

 year of 364 days. Both are divisible by 364 and neither by 360, 

 and the numerals in both are gi^en on the same plan, the only 

 difference being that in one case the intervals are 65 and in the 

 other 91. Is this a sufficient basis upon which to found the 

 theory of such a radical change in the calendar system ? Yet it 

 seems to be the only foundation for this conclusion. That there 

 must have been steps of improvement in the calendar to bring it 

 nearer and nearer the true year is admitted, but is it likely that 

 these various stages of progress showing years of different length 

 will be found in one and the same Codex ? It is only necessary to 

 state that this series can also be counted by the usual calendar. 

 In speaking of the divisors of 364, Dr. Forstemann says : ''The 

 number 364 is, however, not merely equal to 4 x 91i but also 

 28 X 13, and this seems to have been the cause of the year being 

 divided into periods of 13 days, as the period of 20 days was a 

 natural divisor of 360 days." As the steps in the formation of the 

 calendar indicate periods of usage of the different years, we must 

 conclude, if this supposition be correct, that the division of the 

 year into periods of 13 days was not in vogue during the time the 

 year of 360 days was in use. Nevertheless, we see by the red 

 numerals attached to the days that it is used in connection with 

 the series on pp. 71-73, which he thinks is based on the year of 

 360 days. In this we have another illustration of the objections 

 which present themselves to the supposition that years of different 

 length were used in the same calendar. 



There is another consideration which, according to the opinion 

 accepted by most archffiologists, stands opposed to the idea that 

 the year of 360 days should be found in the Dresden Codex. It 

 is that the time-system used on the Palenque "Tablet of the 

 Cross" is that of the usual calendar except that the count is from 



S' 



the days usually given as the last of the month. This is sus- 

 ceptible of proof beyond any reasonable doubt. If, as is generally 

 supposed, this tablet is one of the oldest records remaining in which 

 calendar dates are used, and antidates the Dresden Codex, is it 

 isrobable we shall find an older year in the latter? 



Dr. Forstemann's suggestion that the series on p. 24 and pp. 

 46-50, especially those on the latter plates, refer to the revolutions 

 of the planet Venus, appears to rest upon a surer foundation than 

 his theory in regard to the year of 360 days. It is a singular fact 



8^ 

 that the series on p. 24 is divided into periods of 2 >■ or 3920 days, 



0) 

 which is an exact multiple of 584; and that the series on pp 46-50 

 is not only divided into periods of 2920 days, but these are subdi- 

 vided into periods of 584 days. As will be seen by referring to the 

 plates of the Codex 46-50 or to my "Aids" (p. 298), the red 



U 4 12 

 counters at the bottom of each of the five plates are 16 10 10 8 

 or 286, 90, 250, and 8, the sum of which is 584, the length of the 

 apparent revolution of the planet Venus. As the numeral series 

 (the word "numeral" is used specially here) runs through five 

 pages, the period 584 being repeated in each, we have a total of 



8 



2 or 2920 days. But the " numeral series" is only one-thirteenth 

 



part of the entire series, for when one horizontal tine of the day 

 columns at the top has been traced through the five pages to its 

 end on p. 50, we return to p. 46 and trace the second line through, 

 for they connect according to the red counters, and so continue 

 until we have traced the thirteen lines ending with 1 Ahau, the 

 lower right-hand day-symbol on p. 50. Thus we see that the en- 

 tire series embraces a period of 37960 days; or exactly 104 years 

 of 365 days, a fact noticed by Dr. Forstemann. Yet this is not 

 all that we find in this respect on these five plates. They con- 

 tain two other precisely similar series. The one which has been 

 referred to is based on and relates only to the month symbols 

 which form the upper line of the text in the middle division; the 

 next, using the same series of days and numerals, is connected 

 with the month symbols forming the upper line of the text in the 

 lower division, and the third with the month symbols in the lower 

 line of the lower division. Dr. Forstemann also alludes to these 

 three series. As each series embraces 104 years, we might sup- 

 pose the three together to form one great cycle, or Ahau-Katun, 

 of 312 years, but, unfortunately, there seems to be no other con- 

 nection between them than that they are divided into the same 

 intervals and same days. This is evident from the fact that the 

 upper series (not counting back the 11 months and 16 days with 

 which it begins) commences with 3 Cib, the 4th day of the month 

 Yaxkin in the year 11 Ben (or 11 Ix, counting from the last day 

 of the month); the second or middle series from 3 Cib, the 8ih 

 day of the month Zac in the year 4 Muluo (or Lamat);' the last 

 or lower series with 8 Cib, the 19th day of the year 4 Ezanab (or 

 4 Cauac, counting from the last day of the month). 



If we count back 11 months 16 days from the first date given 

 in each series, thus reaching the initial day, the following singular 

 result is obtained : the first is found to commence with 3 Yimx, 

 the 13th day of the month Mao in the year 10 Muluc (or 14th day, 

 counting from Lamat); the second, on 2 Yimx, the 18th day of 

 the month Kayab in the year 3 Kan (19th day, counting from 

 Akbal); the third, on 2 Ymix, the third day of the month Xul in 

 the year 4 Cauac (4tb day, counting from Ezanab). Therefore, 

 if we arrange them to follow one another in time, we shall find 

 an interval between the first and second of 19 years, and between 

 the second and third of 27 years. It is therefore probable that 

 these three series cover substantially the same period, the dates 

 of the different series falling, in most cases, in different months 

 of the same years; or, in other words, that the periods embraced 

 overlap one another. The great length of the series, and their 

 failure to connect, present the chief reasons for doubting Dr. 

 Forstemann's suggestion in regard to their meaning. On the 

 other hand, there is an oft-repeated glyph in the text which seems 



I It is strange that tbe author of the Codex has, In this single instance In 

 all these long series, counted from the 1st day of the month. 



