From 780 onward this number is itself always the difference of the higher terms of the present series. At the same time 780 days are the duration of the apparent revolution of Mars, which is here supplementary, as it were, since page 24 treated of the revolutions of the sun and of Venus, and also of those of the moon and of Mercury. Hence in the present passage we find the numbers 1560, 2340, 3120 and 3900, always accompanied by the day III Lamat. The larger numbers require a few corrections; I read them 13,260 (17 × 780), 15,600 (20 × 780), 31,200 (40 × 780), 62,400 (80 × 780) and 72,540 (93 × 780). The very largest again are correctly set down; first 109,200 equal to 140 × 780, but here also equal to 1050 × 104 and 300 × 364, so that in this series the goal aimed at is not reached until later than it is in the two preceding series. Then follows 131,040 = 168 × 780, 1260 × 104, 360 × 364, but finally 151,320, which number = 1455 × 104 and 194 × 780, but is not divisible by 364. Detached in the usual way from this series on the left of page 43 is the number 1,435,980. Above and below it is the day III Lamat, further down IV Ahau, and between them is 352 in a red circle. This number seems to have been obtained in the following way:--The writer began with the distance between III Lamat and IV Ahau, which is 92, added to it 172 × 260 = 44,720, and subtracted the result 44,812 from 13 Ahau-Katuns = 1,480,440. The remainder was 1,435,628, which number would correspond to the date III Lamat 6 Zotz (4 Kan), which, however, is suppressed in the Manuscript. The 352 = 260 + 92 was added to this sum, and the result was the 1,435,980 written out in the Manuscript, _i.e._, a day IV Ahau 13 Zip (5 Muluc). Now this number is the one sought; it is 5523 × 260 = 1841 × 780 = 3945 × 364, and hence must also be equal to 263 × 5460, since the 780 and 364 are united in 5460. According to our present knowledge, it would seem to lie in the future, but not far from the present; the solar and Mars revolutions are united in it. There is but a single hieroglyph here, the hieroglyph of the animal which is the chief subject of the next section; from which it appears that the two sections are closely connected. Pages 44b--45b. This section supplements the pictures and hieroglyphs belonging to the series just examined. Therefore it likewise extends over 78 days and divides them as follows:-- III 19 IX 19 II 19 VIII 21 III. These five days are plainly intended to be the days III Lamat, IX Manik, II Cimi, VIII Chicchan, III Cimi. With regard to the real purport of this section, it is my opinion that it has reference to the time of the shortest day and also to the four winds and that this section therefore forms, in a measure, a contrast to pages 38-41, where attention was called to the rainy season, the longest day and the thunderstorms.