29() MAYAN CALENDAR SYSTEMS [eth. ann. 22 



lapse of time from the begiuniug' date of one anil the ending date of 

 the other 7,070 years. Is it at all i)rol)able that the one -t Aliau 8 

 Ciinihu is the same in actual time as the other? That the count is 

 necessarily forward iu the codex series may be proved thus: The 

 last column (that in the lower left-hand portion) reaches back to the 

 initial date, wliich is found to be 1 Ahau is Kayab, the same as the 

 terminal date which stands below the column. Xow if the supposi- 

 tion be correct that, as is usual in this code.x, this column is the sum 

 of the series, and there is no mistake on the part of the aboriginal 

 artist, the first number column, that in the extreme lower right-hand 

 corner of the plate, 8-2-0, 9 Ahau (the sj-mbol appears to be 8, but 

 the fourth dot is hid by the red bonier line, as can easily be shown by 

 the steps fi'om date to date toward the left) should give the exact lapse 

 of time from 1 Ahau 18 Kayab. Counting forward 8-2-0, or 2,920 

 days, from 1 Ahau IS Kayab, 3'ear 2 Akbal, we reach 9 Ahau 18 Kayab, 

 year 10 Akbal, the date under this first column. Counting forward 

 2,920 days (the difference between the first column and the next one 

 to the left) from the last date (9 Ahau 18 Kayab), we reach 4 xVhau 18 

 Kayali, year o Akbal, the date under the second column. Counting 

 back the sum (>£ this second column — 5,840 days — we reach, as we 

 should, 1 Ahau 18 Kayab, the initial date. 



As further proof that the series is continuous and the count for- 

 ward, let us select at random the third column, counting from the 

 right, of the third section from the bottom, to wit, 1^8— 1—0, 11 Ahau. 

 Counting forward 32,12ti days, the sum of this column, from 1 Ahau 

 IS Kayab, we reach 11 Ahau 18 Kayab, year 12 Akbal — the day under 

 this column. If we take the column immediately above (third from 

 the right in the fourth division from the bottom of the page) which 

 reads 9-11-7-0, 1 Ahau, equal to 08,900 days, and count forward from 

 the initial date 1 Ahau 18 Kayab, we reach 1 Ahau 13 Mac, year 9 

 Lamat. Subtracting this column from that to the left of it — 



1-5-14- -1-0 

 9-11- 7-0 



16- 2-15-0 



we find the remainder to be 10-2-15-0, or 110,220 days. Counting for- 

 ward this number of days from 1 Ahau 13 Mac, the date under the 

 third column from the right, we reach 1 Ahau 18 Uo, year 3 Akbal, 

 the date under the last or fourth column from the right, which proves 

 the steps thus far taken to be correct. 



Although the upper division is too nearly obliterated for any of its 

 columns to be used to calculate forward to the final column, we can 

 do this as correctly by subtracting the last column of the fourth 

 division from the terminal column of the entire series, thus — 



9-9- 16- 0-0 

 1-5-14- 4-0 



8-4- 1-U-O 



