From I Ahau 3 Xul (4 Cauac) to I Ahau 18 Kayab (3 Kan) there is a lapse of 9360 days or 12 apparent Mars years of 780 days, such as we shall find as the principal subject of page 59. 9360, however, equals 25 × 365 + 235 days. We shall meet with this 235 again as a difference on page 63. But from I Ahau 18 Kayab (3 Kan) to I Ahau 13 Mac (10 Muluc) there are 11,960 days, _i.e._, the 104 Mercury years, which we found on page 24, and which we shall find again as the principal period on pages 51-58. But this is equal to 32 years + 280 or 33 years - 85 days. Now if 113,880, 9360, 11,960 are added together, we have for the entire period under discussion here, 135,200 days, and this is equal to 2 × 260 × 260 days. Thus the Mayas seem actually to have had an idea of a second power. Finally I would call attention to a singular double connection between the numbers occurring here:-- 37,960 - 11,960 = 26,000 = 100 Tonalamatls, 11,960 - 9,360 = 2600 = 10 Tonalamatls. But if we subtract 2 × 11,960 = 23,920 from 37,960, the remainder is 14,040, _i.e._, an extraordinary number which often occurs and is equal to 54 × 260, 39 × 360 and 18 × 780. In short, a Mars and a Mercury-lunar period are inserted in the two spaces between the three solar-Venus periods. Now, let us try to gain a clearer understanding of this subject by approaching from another side. As we have seen, the beginning of the middle one of the three equal periods of 37,960 days, is the date I Ahau 18 Kayab (3 Kan). Now, however, page 24 furnished us with a day number for this date, 1,364,360, and from this the beginnings of the other two periods may be computed in the following way:-- I Ahau 3 Xul (4 Cauac) = 1,317,040, I Ahau 18 Kayab (3 Kan) = 1,364,360, I Ahau 13 Mac (10 Muluc) = 1,414,280. Between the first number and the second there are 47,320 days = 2^3 × 5 × 7 × 13^2, and between the second and third 49,920 days = 2^8 × 3 × 5 × 13 days. But, according to what has been stated above, 47,320 = 37,960 + 9360, and 49,920 = 37,960 + 11,960. The whole period is therefore divided as follows:-- It begins with a Venus-solar-Tonalamatl-period followed by 12 Mars years, then the great period again followed by 8 × 13 = 104 Mercury years, and lastly, apparently about the present time, comes the third great period, which, as already stated, ends 135,200 days after the first date. The case assumes a different aspect, if we insert between the three dates the other two from page 24:-- 1,317,040 = I Ahau, 1,352,400 = I Ahau, 1,364,360 = I Ahau, 1,366,560 = IV Ahau, 1,414,280 = I Ahau. Here we have again, as examination of page 24 showed, the difference 11,960 between the second and third numbers, while there is no longer any connection with the periods of 37,960 days.