Our next step is to determine the respective numbers of the Ahaues as located in the grand cycle.
We start as a matter of course with the understanding that the numbers were as heretofore stated—13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2—and that they always followed each other in the order here given; that is to say, 1 always followed 3, 12 always followed 1, and so on.
On folios 71, 72, and 73 of the Dresden Codex 
Fig. 7. we find the following figures placed in one continuous line (Fig. 7); (a sufficient number for illustration only are given):
Commencing with the left-hand figure and reading to the right, the numbers given in them are 11, 13, 2, 4, 6, 8, 10, 12, 1, 3, 5, 7; in the lower right-hand corner of page 73 we find the missing 9. The fact that the order is here reversed, if read from left to right, is no evidence that this is the order in which the Ahaues (if these figures refer to these periods) followed each other, as it is possible they should be read from right to left. But the fact that we here find thirteen peculiar figures, with the knot denoting the tying of years or period of years, with numbers following each other in the order, whether direct or reversed, of those used in numbering the Ahaues, is sufficient to justify us in believing that they refer to these periods. The only reason I see for any doubt as to the correctness of this conclusion is that on pages 62 and 63 we find similar figures containing numeral characters for 16, 15, 17, and 19, numbers that cannot refer to the Ahaues. Possibly they may be used to designate the years of the Ahaues, but 'be this as it may, a close inspection of the knots will show that they are different from those on pages 71, 72, and 73.
Knowing the order in which they follow each other, it is evident that if we can determine the number of any one in the series it is a very simple matter to number all the rest.
As the possibility of our being able to compare dates of the Maya system with those of the Christian era depends on the correct determination of this point, I will give not only my own conclusion, illustrating it by means of a table (XVII), but will also show the result of following out
