The real aim of the computation on these pages is to find a number in which the following periods of time are united with the Tonalamatl of 260 days:--1. The ritual year of 364 days, and consequently also a quarter of it, the Bacab period of 91 days. 2. The period of 104 days, being the number of days which remain after a Tonalamatl has been deducted from a ritual year. The hypothesis advanced by Mrs. Zelia Nuttall ("Note on the Ancient Mexican Calendar System," Stockholm, 1894) and also the entirely different opinion held by Mr. Charles P. Bowditch ("The Lords of the Night and the Tonalamatl of the Codex Borbonicus" in the American Anthropologist, N. S., Vol. II, New York, 1900) prove the existence not only of merely arbitrary Tonalamatls for the purpose of prediction, as those in our Manuscript, but also of Tonalamatls having a fixed position in certain years. But after the manner peculiar to priestcraft, the number sought is found only by an indirect and mysterious process. In the first place we find on page 32a all the days set down in the following manner:-- XIII XIII XIII XIII Manik Cib Chicchan Ix Chuen Ahau Muluc Ezanab Men Kan Ben Ik Cauac Lamat Caban Cimi Akbal Eb Imix Oc. That is to say, a series counting from the day XIII Akbal, the New Year's day of the year I Kan, recurring every 52 years, furthermore a series which shows the same difference of 91 from the day XIII Akbal to XIII Ix, XIII Chicchan, etc., and finally ends with XIII Akbal again, after it has run through a period of 20 × 91, _i.e._, 1820 days = 7 Tonalamatls, like a similar representation of 7 Tonalamatls on page 51. Above these 20 days, and to the left of them, numbers are set down rather irregularly, which begin with 91 and are multiples of that number. The signs of the days corresponding to these numbers are joined to them; but they are omitted with the numbers of lowest value. Hence we have:--91, 182, 273, 364 (4), 455 (5), 546 (6), 637 (7), 728 (8), 819 (9), 910 (10). Then with a bound follow 1456 and 1820; with the last number Akbal is reached in the natural way, which day the scribe had erroneously set down again with 1456 in place of Cauac. The number 728 already united the numbers 91, 104 and 364, but did not include the number 260. This inclusion is accomplished by the number 3640 on page 32, quite on the left where we find the numbers 10 and 2, under which only a 0 has been omitted. With the usual hiatuses this series seems to end on page 31, where I think the numbers 4, 0, 16 and 0 ought to stand, but they are almost wholly effaced; this would then be 320 × 91, 280 × 104, 112 × 260, 80 × 364 = 29,120.