Thus a day VIII Ahau hitherto unmentioned is introduced into the computations. This day has no doubt been chosen, because it divides the Tonalamatl beginning with IV Ahau into two parts of 160 and 100 days, which are in the proportion of 8 to 5, _i.e._, the same proportion as the Venus year to the solar year. This day VIII Ahau may also figure in the large numbers of the first two columns on page 70, for 1,394,120 and 1,201,200 are both divisible by 14, the interval between VIII Ahau and IX Ix. Now I believe that the large numbers were constructed in the following twofold manner (I add the corresponding dates):-- 160 1,408,940 = 5419 × 260 --------- 1,409,100 = VIII Ahau 3 Yax (9 Cauac). 111,554 --------- 1,520,654 = IX Ix 7 Zip (3 Muluc). 160 1,437,020 = 5527 × 260 --------- 1,437,180 = VIII Ahau 18 Mol (8 Kan). 83,474 --------- 1,520,654 = IX Ix 7 Zip (3 Muluc). 160 1,465,360 = 5636 × 260 --------- 1,465,520 = VIII Ahau 8 Uo (8 Ix). 101,812 --------- 1,567,332 = IV Eb 5 Pop (1 Muluc). 160 1,532,440 = 5894 × 260 --------- 1,532,600 = VIII Ahau 13 Pax (9 Muluc). 34,732 --------- 1,567,332 = IV Eb 5 Pop (1 Muluc). The last record of the date of VIII Ahau seems to throw light on the date 13 Pax (page 70, column 3), which is directly above the date VIII Ahau, and which I have already mentioned in the discussion of the groups of hieroglyphs. Indeed, it seems as if a day VIII Ahau occurred a fifth time in that passage, for in consequence of the correction made by the scribe we read here VIII Ahau 13 Yaxkin. This would point to a year 7 Muluc, the position of which between the other four is, of course, undetermined. If the two large numbers in the Manuscript were treated in the same way as the other large numbers, they would not be recorded at all, but instead of them there would have been two numbers belonging to the day IV Ahau and under them would have been the encircled numbers 208 and 86, or these numbers increased by a multiple of 260. This passage would then read about as follows:-- 1,567,540 (IV Ahau) 1,520,740 (IV Ahau) 208 (IV Eb) 86 (IX Ix). These two numbers for IV Ahau are equal to 6029 and 5849 Tonalamatls. If 5549 × 260 be subtracted from these, the remainders are 480 and 300 Tonalamatls respectively, _i.e._, 124,800 and 78,000, and these are in the proportion of 8 to 5. Now the two large numbers have the difference 46,678 = 179 × 260 + 138; the latter is the interval from IX Ix to IV Eb. The four numbers of the days VIII Ahau seem to stand in very irregular relation to one another and yet they show the following striking results, if the first and third and also the second and fourth numbers be combined (as I combined them under page 24):-- In the first case we see the following:--