Here the starting-point is the number 52, which belongs to day IV Eb and this is separated from IV Ahau by 208 days _i.e._, it divides the Tonalamatl in the proportion of 1 to 4. To the number 52 then, for unknown reasons was added 4623 × 260 = 1,201,980, and thus the number 1,202,032, suppressed in the Manuscript, was obtained for the day IV Eb. To this sum the encircled number 208 was then added and the result was 1,202,240, the number in the Manuscript. The number = 23,120 × 52 = 4624 × 260, which is self-evident, but it also = 5780 × 208, _i.e._, it is a multiple of the encircled number. It consequently also = 11,560 × 104, and thus it is related to the first and third numbers just now discussed. The position of this number is IV Ahau 18 Kankin (1 Kan) and the position of the suppressed number is IV Eb 10 Zotz (also 1 Kan). We ought now to discuss the last two numbers of this section amounting to millions:--1,567,332 and 1,520,654, which are in the third and fourth columns at the top of page 70. But before going further, we must examine four other numbers, two of which, 111,554 and (with my correction) 101,812, are in column 4 on the lower part of page 70, and the other two, 83,474 and 34,732, are on the top of page 73. Although these four numbers are not ornamented with circles, they all have the significance of the numbers enclosed in circles and are designations of differences between suppressed and specified numbers. Let us first of all examine their curious relation to one another:-- The Manuscript should have set down under these numbers the day IX Ix twice and IV Eb twice, from which days the numbers in question must be computed; but here the two errors already mentioned were made. 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.