No doubt in the numerical notation there were special signs for each of these higher unities; but neither Bishop Landa nor the native writers who composed the singular “Books of Chilan Balam” have handed them down. Modern sagacity, however, has repaired ancient negligence, and we can, almost to a certainty, restore the numerical notation of the aboriginal arithmeticians.
The scholar who has worked most successfully in this field is Dr. Förstemann, the editor of the Codex of Dresden, and I shall introduce a condensed statement of his results, referring the student to his own writings for their demonstration.
3. Numerical and Allied Signs.
The first important discovery of Dr. Förstemann in this direction was that of the sign for the naught or cipher, 0. It is given in Fig. [2].[[16]] It has a number of variants, some ornamental in design. Next, he discovered the system of notation of high numbers. This is not like ours, but resembles that in use in the arithmetic of ancient Babylonia and some parts of China. The numerals are arranged in columns, to be read from below upward, the value of each unit of a given number being that power of 20 which corresponds to the line on which it stands counted from the bottom. This will be readily understood from the following example:—
| Maya numerals. | Simple values. | Composite values. | ||||||
|---|---|---|---|---|---|---|---|---|
 | 8 | (1 = 204, | = | 160,000; | hence, | 8 × | 160,000) = | 1,280,000 |
 | 11 | (1 = 203, | = | 8,000; | hence, | 11 × | 8,000) = | 88,000 |
 | 8 | (1 = 202, | = | 400; | hence, | 8 × | 400) = | 3,200 |
 | 7 | (1 = 20, | = | 20; | hence, | 7 × | 20) = | 140 |
 | 0 | (1 = 1, | = | 1; | hence, | 0 × | 1) = | 0 |
| Total | 1,377,340 | |||||||
Fig. 2.—Maya Notation.
This would be according to the regular system of the Maya numeration as given above; but in applying it to the calculations of the native astronomer who wrote the Dresden Manuscript, Dr. Förstemann discovered a notable peculiarity which may extend over all that class of literature. In the third line from the bottom, where in accordance with the above rule the unit is valued at 20 × 20 = 400, its actual value is 20 × 18 = 360.
It immediately suggested itself to him that in time-counts this irregular value was assigned in order that the series might be brought into relation to the old solar year of 360 days, composed of 18 months of 20 days each, in the native calendar.
This correction being made, the above table would read:—
| 8 | (1 = | 7200 | × 20 = | 144,000) | = | 1,152,000 |
| 11 | (1 = | 360 | × 20 = | 7,200) | = | 79,200 |
| 8 | (1 = | 20 | × 18 = | 360) | = | 2,880 |
| 7 | (1 = | 20) | = | 140 | ||
| 0 | (1 = | 1) | = | 0 | ||
| 1,234,220 |