111,554 - 101,812 is 9742, the very same number which we shall afterward find as the difference of the serpent numbers on page 69.
83,474 - 34,732 = 48,742. If 9472 be subtracted from this, the remainder is exactly 39,000 = 150 Tonalamatls = 50 revolutions of Mars. I have already found this number on page 31a, and also the double of it, 78,000, on page 24, and this I found by using 68,900 + 9100 for my computation.
111,554 - 83,474 = 28,080, i.e., exactly the double of the important 14,040, which is recorded on page 73.
101,812 - 34,732 = 67,080, i.e., = 258 Tonalamatls or 86 revolutions of Mars.
111,554 - 34,732 = 76,822; if 122, the interval from IV Eb to IX Ix be subtracted from this, the remainder is 76,700 = 295 Tonalamatls.
101,812 - 83,474 = 18,338; if 138, the interval from IX Ix to IV Eb, be subtracted from 18,338, the remainder is 18,200 = 70 Tonalamatls = 50 ritual years of 364 days each, i.e., exactly the double of the 9100 specified on page 24.
Now we also have the following equations for the four numbers:—
| 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.