I go still further in my bold hypothesis. The time of the apparent revolution of Jupiter has been placed at 397 days. The Mayas, I think, computed it at 398 days. In the passage alluded to I regarded the following as the sign for Jupiter:—

We find these signs in pictures 4, 6, 7 and 9. The corresponding numbers reduced for the revolution of Saturn are

3986, 6762, 7972 and 10,748. I assume that the third picture, i.e., the number 2776, is another zero-point, in consequence of which the sign is here suppressed, and that still another is the tenth picture with the number 11,958, which has no relation to the revolution of Saturn.

If we compare these numbers with the 398, i.e., the apparent revolution of Jupiter, we have the following:—

3. 2776 = 7 × 398 - 10
4. 3986 = 10 × 398 + 6
6. 6762 = 17 × 398 - 4
7. 7972 = 20 × 398 + 12
9. 10748 = 27 × 398 + 2
10. 11958 = 30 × 398 + 18

The differences 10, 6, 4, 12, 2 and 18 are so small in comparison with 398, that the numbers 2776, etc., might very well have been regarded as approximate multiples of the revolution of Jupiter. And the remainders in the seventh and tenth pictures could be still further reduced. In the seventh picture, the first sign is very unusual and one which I do not remember having met with elsewhere. If it should be possible to regard it as the number of the thirteen week days, then it would follow (the Saturn sign being regarded as unimportant) that the contents of the rectangle meant:— 13 + a multiple of 398, by which this remainder would be reduced to -1.

The tenth picture has the cross b as the beginning of the rectangle. This is the sign for union, very often denoting especially the union of all the twenty days. Thus we have here (aside from the middle sign to be discussed later) the formula:— 20 + 30 × 398 - 2 = 11,958, or even 20 + 30 × 398 = 11,960.

The regular progression from the 7th multiple to the 10th, 17th, 20th, 27th, and 30th multiples in the above six equations is also somewhat in favor of my theory, while the four rectangles without the Jupiter sign are by no means multiples of the Jupiter revolution:—

1. 502 = 398 + 104
2. 1742 = 4 × 398 + 150
5. 5728 = 14 × 398 + 156
8. 9714 = 24 × 398 + 162 .