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. Let us now try to interpret the meaning of the remaining rectangles (always omitting the Saturn sign as a matter of course.) In pictures 2 and 8 the rectangle also contains the sign of the moon or of the twenty days. Beside it in picture 2 is the sign, which in my "Erläuterungen," page 16, I regarded as the sign for Mercury. Hence we have here 20 + 15 × 115 = 1745, _i.e._, only 3 units more than the required 1742. The rectangle with the eighth picture contains in addition to the moon a sign which looks as if it were intended for a whole divided into four parts. Until something better (perhaps the the sign of Venus) is proposed, I will assume that it is the quarter of the Tonalamatl, _i.e._, 65, and I take the required number to be 9714 in the form of 20 + 149 × 65 + 9. Above the third picture I see a Mercury and a Venus sign and I read 584 + 19 × 115 = 2769, which is only 7 units less than the required 2776.