But if we subtract 2 × 11,960 = 23,920 from 37,960, the remainder is 14,040, i.e., an extraordinary number which often occurs and is equal to 54 × 260, 39 × 360 and 18 × 780.
In short, a Mars and a Mercury-lunar period are inserted in the two spaces between the three solar-Venus periods.
Now, let us try to gain a clearer understanding of this subject by approaching from another side.
As we have seen, the beginning of the middle one of the three equal periods of 37,960 days, is the date I Ahau 18 Kayab (3 Kan). Now, however, page 24 furnished us with a day number for this date, 1,364,360, and from this the beginnings of the other two periods may be computed in the following way:—
| I Ahau 03 Xul (4 Cauac) | = 1,317,040, |
| I Ahau 18 Kayab (3 Kan) | = 1,364,360, |
| I Ahau 13 Mac (10 Muluc) | = 1,414,280. |
Between the first number and the second there are 47,320 days = 23 × 5 × 7 × 132, and between the second and third 49,920 days = 28 × 3 × 5 × 13 days.
But, according to what has been stated above, 47,320 = 37,960 + 9360, and 49,920 = 37,960 + 11,960.
The whole period is therefore divided as follows:—
It begins with a Venus-solar-Tonalamatl-period followed by 12 Mars years, then the great period again followed by 8 × 13 = 104 Mercury years, and lastly, apparently about the present time, comes the third great period, which, as already stated, ends 135,200 days after the first date.
The case assumes a different aspect, if we insert between the three dates the other two from page 24:—