Lastly, the upper right-hand square, reading the same way as the last.

Ollin, 4, 11, 5, 12, 6, 13, 7, 1, 8, 2, 9, 3, 10.

We have only to turn to our abridged calendar ([Table III]) to find this explained. If we take the Ix column and select every fourth day, to wit, Ix, Ezanab, Ik, Cimi, and Oc, and read the line of numbers opposite each, we shall find them corresponding precisely with those mentioned here. For instance, those opposite Ix the same as those opposite Cipactli, &c.

We further notice that these five names, Cipactli, Coatl, Atl, Acatl, and Ollin, or, to use the English names, Dragon, Snake, Water, Cane, and Movement, are precisely those of column 1 of the arrangement of the Mexican days as heretofore given ([Table XI]).

On plates 13-17 of the Vatican Codex, B, Kingsborough, Vol. III, we find precisely the same arrangement as that just described, and where the numerals are so distinct that there can be no doubt in regard to any of them. The days are exactly the same—Cipactli, Coatl, Atl, Acatl, and Ollin—and in the same order, but the plates are to be taken in the reverse, order, commencing with 17, and the columns and lines are to be read thus: Commencing at the bottom at the right hand, upward to the top, and then along the line toward the left.

On Plate 58 of the Borgian Codex we find six lines of days with five in each line. Five out of these six lines are composed of the five days just named, simply varied as to the respective positions they occupy in the line, but maintaining the same order.

On Plate 17, same Codex, we see two lines corresponding with the first and second columns of the arrangement of the days heretofore given.

But without further reference to these smaller or isolated groups, we have conclusive proof of this method of arranging the days among the Mexicans, in three extended series—one found on Plates 49-56 of the Vatican Codex B; one on Plates 31-38 of the Borgian Codex, and another on Plates 1-8 of the Bologna Codex.

I give here the arrangement found in the first, which is precisely the same as that of the Borgian Codex, except that this is to be read from the left to the right, and that of the Borgian Codex from the right to the left, both commencing with the bottom line (numbered 5 in the following list):

A photo-engraved copy of one plate of the former is also given in [Fig. 5], as it furnishes proof that the days and the order in which they follow each other are the same as I have given them.