Now we must direct our attention to the seventeen hieroglyphs, which we find in the two columns on page 58, apart from the matter-of-course calendar date at the top, which is repeated at the bottom. One column contains 11 hieroglyphs and the other 6. I will here advance the following theory in regard to these hieroglyphs, which may serve until a better is found:-- Since, as a rule, the Tonalamatl is divided into 5 × 52 days, I believe that each group of three Tonalamatls treated of on page 59, is divided into 15 of these parts; that each hieroglyph, therefore, denotes 52 days and that the first three parts are separated from the others by the signs of beginning and end in the first and fifth places, so that three of these parts, which equal 156 days, always form a separate group. 156 is the 5th part of 780. With the omission of the first and fifth signs, the passage, I think, stands thus:-- 0 XIII Muluc 2 Kankin (13 Muluc). 1) 0-52 XIII Imix 14 Pax. 2) 53-104 XIII Ben 1 Pop (1 Ix). 3) 105-156 XIII Chicchan 13 Zip. -------------------------------------- 4) 157-208 XIII Caban 5 Xul. 5) 209-260 XIII Muluc 17 Mol. 6) 261-312 XIII Imix 9 Zac. -------------------------------------- 7) 313-364 XIII Ben 1 Kankin. 8) 365-416 XIII Chicchan 13 Pax. 9) 417-468 XIII Caban 25 Cumhu. -------------------------------------- 10) 469-520 XIII Muluc 12 Zip (2 Cauac). 11) 521-572 XIII Imix 4 Xul. 12) 573-624 XIII Ben 16 Mol. -------------------------------------- 13) 625-676 XIII Chicchan 8 Zac. 14) 677-728 XIII Caban 20 Mac. 15) 729-780 XIII Muluc 12 Pax. If we adopt this arrangement for the present we cannot fail to see that the author had an aim in view, when we consider the following:-- 1. The zero-point lies 15,609 days later than the normal date IV Ahau 8 Cumhu (9 Ix). This is equal to 20 × 780 or 60 × 260 increased by the interval between IV Ahau and XIII Muluc = 9. There are 86 days between 2 Kankin and 8 Cumhu _i.e._, 15,609 = 43 × 365 - 86, and from 9 Ix to 13 Muluc it is 43 years. 2. The same zero-point, 13 Muluc, lies in the year with the same name, that is, the very point where a Tonalamatl of the year ends. 3. In this arrangement the first as well as the last day of the year 1 Ix is exactly reached in the second and ninth groups. While the meaning of the second is as yet unintelligible to me, the end of the year is appropriately indicated by the ninth with its compound of Kin and the year-sign, above which there may be an Ix as a superfix, but misshapen for want of room. 4. Also the fact that it is the first of the two columns, which closes with this year-end, seems to show a purpose.