I now give the six numbers, first the two highest, then the other four from right to left, adding in each case the calendar date and the year in which they should be situated:-- 1,538,342; IV Ik 15 Zac (12 Muluc). 1,535,004; VII Kan 2 Chen (3 Kan). 1,268,540; IV Ahau 8 Mol (1 Ix). 1,234,220; IV Ahau 18 Kayab (11 Kan). 1,272,544; IV Kan 17 Yaxkin (12 Muluc). 1,272,921; IV Imix 9 Mol (13 Ix). The first, third and fifth numbers are already known from page 31a, and hence they need no further discussion here. As these three numbers depend on the day XIII Akbal, so the other three all proceed from the day III Chicchan in the following positions, which are again suppressed in the Manuscript:-- 1,483,585 = III Chicchan 8 Zac (5 Cauac). 1,233,985 = III Chicchan 8 Kankin (10 Cauac). 1,272,465 = III Chicchan 18 Zip (12 Muluc). The second date in the manuscript is 13 Kankin and the third is 13 Zip; hence there is one line too many in the former number and one too few in the latter. While on page 31a the origin of the numbers belonging to the day XIII Akbal seems to be quite clear, here their relation to one another is entirely concealed. I must, therefore, refrain from expressing any conjecture in regard to them. Now the numbers set down in the Manuscript are formed only by the addition of the encircled numbers also found there. The encircled number for the first expressed number is 51,419, which is the same number we found with the corresponding day XIII Akbal; the second has 235 and the third 456 = 260 + 196. The 51,419 was 197 × 260 + 199; but 199 is the interval from III Chicchan to VII Kan, just as it is from XIII Akbal to IV Ik. The 235 is the interval between III Chicchan and IV Ahau and the 196 that from III Chicchan and IV Imix. By the addition of these differences, the numbers written out in the Manuscript are obtained:-- 1,483,585 + 51,419 = 1,535,004 (VII Kan). 1,233,985 + 235 = 1,234,220 (IV Ahau). 1,272,465 + 456 = 1,272,921 (IV Imix). Keeping in mind what was said in reference to page 31a, let us now examine the six numbers and dates collectively. The fact that the days IV Ahau and XIII Akbal occur here and consequently also III Chicchan is not surprising. Nor is the choice of VII Kan and IV Ik an accident, for the interval between these days is exactly the same as that between III Chicchan and XIII Akbal, viz:--218 days. Hence the distance from III Chicchan to VII Kan is also exactly equal to that between XIII Akbal to IV Ik, viz:--199 days. Finally, the distance from VII Kan to III Chicchan is exactly equal to that between IV Ik and XIII Akbal, viz:--61 days. IV Imix and IV Kan are separated from the normal date IV Ahau by 3 × 13 = 39 and 8 × 13 = 104 days. Regarding the encircled numbers, so far as they are independent of 260, I would note the following:--