111,554 = 429 × 260 + 14.
83,474 = 321 × 260 + 14.
101,812 = 391 × 260 + 152.
34,732 = 133 × 260 + 152.
A day VIII Ahau is 14 days back of the day IX Ix, and another VIII Ahau is
152 days back of IV Eb.
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):--