1. The beginning day in each case is the day Kan, which thereby indicates its position as the first. 2. The last three starting-points are the same; the first three end dates, at least, are the same in the Tonalamatl, though not in the year. 3. The two numbers 2b and 4b are exactly the same. 4. The first three numbers are each divisible without a remainder by 17, the interval from XIII Akbal to IV Ahau, which was true also of the 1,268,540 in the second column on page 63, although only this last number has anything to do with these important days, of which the other three numbers are independent. On the other hand, a notable difference between the first serpent and the other three is, that the day XI Kan is the starting-point of the first and IX Kan of the others. There are, however, 80 days between IX Kan and XI Kan. Hence the numbers 2a and 1b are separated from each other by 66,640 = 256 × 260 + 80, although they have the same end III Chicchan. Further it is to be noted that the largest of the eight numbers, 12,489,781, is separated from the lowest, 12,388,121, _i.e._, the black number from the red one of the first serpent, by only 101,660, _i.e._, by not a full one per cent of the entire magnitude. 101,660 = 5 × 18,980 + 26 × 260 or 391 × 260 or 7820 × 13. It is to be noted also that the differences between the black and red numbers in the second and third serpents (60,021 and 28,132) are divisible by 13 (4617 × 13 and 2164 × 13). They _must_ be, since all six numbers refer to the day III. Finally the question naturally arises, how did the computer obtain these values, _i.e._, how was the whole structure built up? On page 63 we found a 136,864 (not 136,884) set down in strikingly small characters and crowded between the other numbers, which would remain a mystery unless one assumed that it was reserved there for this structure; it is 91 × 1504. At first I thought it possible that this 136,864 had been again multiplied by 91, the real basal number of this section; for we had found a second power once before (on pages 46-50) by computation, viz:--2 × 260 × 260. The result of multiplication in this case would be 12,454,624, and the differences between the eight numbers in the serpents would be as follows:--1a + 35,157, 1b - 66,503, 2a + 137, 2b and 4b - 60,884, 3a - 17,814, 3b + 12,318, 4a - 165. But these differences are doubtful, inasmuch as they bear no relation to the dates beginning and ending the serpent numbers. On the other hand, another number contains the desired properties. I refer to the 12,412,920, _i.e._, it is 109 times the so-called Ahau-Katun of 113,880 days, and I believe I have found that the Ahau-Katun and its multiples were mostly used in the formation of the large numbers. In the following table I have placed this number beside each of the serpent numbers, have then found the difference between the two and have added to it the interval between the first and last day of each serpent number:--