number is again reached, and the calculation is (by hypothesis) repeated, starting again at the left with a new day-sign below the first. Such a column is seen in the lower part of page 17, where we find 6 Oc, Ik, Ix; these are to be completed by restoring below an erased Cimi and Ezanab, completing the 260 days and bringing us around again to 6 Oc. The total of all the black “counters” in any series must always be some multiple of 13, usually 52 or 65, as stated. And since each “counter” is the interval between its adjoining red numbers, wherever a red and a black number are given, the other red number, whether before or after, can always be filled in.

No traces of this initial column appear for the series in the middle division, and several of the numerals are also erased. Two obscurities must be cleared up before trying to fill out the series. On page 16 right is a partly erased black numeral, which from the traces may be either 10 or 11. Taking it as 10, we have 13 plus 10 equals an erased red 10; plus 5 (on page 17) equals the red 2 below the 5. This verifies so far. But we next find—plus 5 equals 8, which is of course incorrect. An inspection of the MS. and the photographs reveals a reddish spot (or perhaps even three such spots) in the extreme upper right corner of the picture space, 17-a, and also a dark spot under the black 5 in 17-b. It is possible that the separated red dots (one doubtful) are to be read together as 3; or that the red dots under the 5 are to be disregarded in the count (just as is the red 8 on the next page, 18-a), and the red number for 17-a found in the upper right, above the seated figure. If the red number in 17-a is 3, the two numbers in 16-c must be 11. Or it may be assumed that the spot under the 5 in 17-b belongs to it, making 6 instead of 5, which figures out. The final result is the same, as we have either 10 and 6, or 11 and 5, in these two places, and either reaches properly the clear red 8 in 17-b.

In 18-a we find black 26, with a small red 8 below, and a large red 13 in the usual place at the side. The red 8 will have to be disregarded, as not part of the series, which requires 13, and nothing else.

We may now possibly set down the series as follows, using small figures above the the line for the black counters, and putting in parentheses all numbers restored:

(6)³9⁽⁶⁾(2)⁵7⁶13¹¹(11)⁵3⁵8⁵(13)²⁶13¹⁰10, or else
(6)³9⁽⁶⁾(2)⁵7⁶13¹⁰(10)⁵2⁶8⁵(13)²⁶13¹⁰10

This leaves us the black number at the beginning, in 15-a, and both numbers at the end, 18-c, still not filled in. Adding together all the counters we get 82, plus at least the two missing black numbers, one at each end. If the total were 104, we might expect it to have been comprised within the four subsections 15-a to 18-a. But 104 is not a tonalamatl fraction. 130 days, although a tonalamatl half, is an unknown division, and would hardly get into the space. If we begin the series in the upper division of the page (as occurs in Dres.) and come around to the middle division, the probabilities would require that it displayed a full series of 260 days, and again also that it began to the left of page 15. The probabilities of this series as it is, therefore, indicate at least a page 14 to the left, arranged like the other four, and forming one chapter with them.

We have now to deal with the puzzling numeral columns, in alternating colors, found to the left of each subsection of the upper and middle divisions—24 columns in all. These have been referred to at some length in the preliminary discussion of the colors, and there is little more that can be said. As there said, the entire reason for alternating the colors can not be certainly assumed. Alternation of color occurs not only where it is needed to distinguish bars, but also where we have only lines of dots, which are of course self-separating. And to say that it is only for artistic purposes is a mere begging of the question. Only four or five of these columns are complete, and a footing of the numbers in each gives us varying amounts from 113 to 153, and tells us nothing. On the parts that are left we six times have a Chuen with a black number apparently belonging to it (perhaps a multiplier), and also once a double Chuen, as in Tro.-Cort. The use of the red kal-sign, or 20, is frequent.

The lower division of these pages was also subdivided, into four sections on each, which we may refer to as d, e, f, g. Each contains a picture, with black and red numerals as above, surmounted by four glyphs only. The pictures are all quite incomplete; neither is there anything to add to what has been already said of the glyphs.

In the middle of page 17 one tonalamatl ends, with a red 6, and another begins, also with 6. The second starts with the day 6 Oc, is divided into fifths, and the initial column must have been in full: 6 Oc, Ik, Ix, Cimi, Ezanab. The restoration of the series gives: 6²²2^{(15 in two stages)}(4)¹⁰1⁴6. This however only gives a total of 51 for the black counters. There is space to the right for another section, but whatever may have been written there has entirely disappeared. The last three numbers 1⁴6 seem unmistakable, the especially so. If we regard the last 6 as an error for 5, and then restore ¹6 in section 18-g, it would give the necessary 52. This is the one passage in the Codex where I can see no way but to assume a mistake in the writing; for 1 plus 4 does not equal 6, and unless for some entirely unknown reason the error is clear.

The preceding tonalamatl may have been divided either into 52- or 65-day periods. If the period was 52, it must have begun with an initial column on page 15, right side. In this event it would be restored as follows:

(initial 6)^{(19 in two stages)}(12)⁶5⁷12^{(12 in two stages)}(11)⁸6,

giving 52. In this case a third tonalamatl must have begun somewhere to the left, and ended on the erased right side of page 15.

A different restoration would carry the initial column back to the extreme edge of page 15, when we would have this:

(initial 6)⁽²⁾(8)⁸3¹¹(1)^{(11 in two stages)}(12)⁶5⁷12^{(12 two stages)}(11)⁸6

giving 65.

To choose between these two would be mere guessing.

The well-known pages 19 and 20 come next. Together they make four compartments, up and down the full length of the pages, two with red and two with black backgrounds. Each is, or rather was, preceded by a column of 13 “year-bearers.” The left column on each page I have restored, although no traces of it are left. But apart from its manifest necessity, as part of the series, if the width of the red ground on page 20 (see the photographs) is measured, it will be found to be just the correct proportion, and part of the straight left edge of the red can still be seen, just left of the rod in the hand of the mummy-figure, and leaving just room for the Ezanab column. In the colored plates I