In general, then, the apparent irregularities in the manuscript fall into two great classes, those which are corrected in the next column or are easily detected because of their disagreement with the record in the other two series, and those which are not obviously due to carelessness. The latter will be considered under the solutions. The former may be dismissed as clerical errors not affecting the solution. In this group are two of the irregularities in the lower numbers (columns 26 and 50), and all eight in the upper numbers, seven of which occur in the first third of the manuscript. The six errors in the day series, and the transposition of columns 6 and 7, also belong in this class.
By referring to Table II it will be noticed that the pictures occur after the 148-day groups in each case. The upper numbers immediately preceding the pictures are given in Table III (p. 11), together with the differences between them. By grouping these differences, it becomes apparent that the pictures may be divided into three large groups of 3986 days; two out of the three containing the same difference numbers, 1742, 1034, and 1210. If, in the last group, the number 10,039 were changed to 10,216 by adding 177, the differences for this group would also read as the others, when the end of the series and the beginning of the series are added together (708 + 502 = 1210), for the 10th picture is, in a sense, out of the grouping since it occurs after the last number in the series. The 148-day groups are arranged in the same order for they occur in the same columns as the numbers used above.
By applying the same process to the 178-day groups, it is found that they also can be divided into groups which contain 3986 days. In this case the second and third groups contain the same numbers, 2598 and 1388 (Table IV). If the number 1211 in the first group is changed to 1034 by subtracting 177, the last number of this group would be 1388; and the first number 2598 could be formed by adding the remainder at both ends of the series (1564 + 1034 = 2598).
It should be remembered at this point that the only column in which the lower numbers contained 178 is column 23, of which the upper number is 3986. This gives further grounds for dividing the series as it stands into three parts of 3986 days, each containing 23 columns.
| Number | Difference | Group | |
|---|---|---|---|
| (0) | 502 | ||
| 502 | 1742 |  | |
| 2244 | 1034 | 3986 | |
| 3278 | 1210 | ||
| 4488 | 1742 | | |
| 6230 | 1034 | 3986 | |
| 7264 | 1210 | ||
| 8474 | 1565 |  | |
| 10039 | 1211 | ||
| 11250 | 708 | 3986 | |
| (11958) | (502) |
| Number | Difference | Group | |
|---|---|---|---|
| (0) | (1564) | | |
| 1211 | 1211 | 3986 | |
| 2422 | 1211 | ||
| 5020 | 2598 |  | 3986 |
| 6408 | 1388 | ||
| 9006 | 2598 | | 3986 |
| 10394 | 1388 | ||
| (11958) | 1564 |
The three parts are not exactly alike, however, as has already been pointed out in considering the probable errors. If the upper numbers and day numbers in column 6 should be altered, so that the difference 178 might occur in that column instead of column 7, and if, by the same process, the difference of 148 could occur in column 59 instead of 58, then the three parts of the series would be entirely alike. The three facts mentioned are, however, very strong evidence for supposing that the people who used this table considered it as consisting of three equal parts.
This series in the Dresden is very similar to other pages of the Dresden and other manuscripts, two examples of which are given as illustrations. One of the most interesting parallels is the series on pages 46-50 of this same manuscript. This series covers a period of 2920 days which is divided into 20 unequal subdivisions. On page 24, which just precedes page 46, this number is used as a unit in multiplication, that is, the numbers occurring on page 24 are separated from each other by 2920 or multiples of this number. On pages 44b and 45b the number 78 is divided into four unequal parts, and on pages 43b and 44b it is used as a unit in a series which finally reaches the number 1940 × 78.
SOLUTIONS
The first references to these pages in the manuscript were concerned chiefly with the reading of the numbers without any theories in regard to the probable meaning of the series.