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. TABLE III UPPER NUMBERS OF 148-DAY GROUPS Number Difference Group (0) 502 502 1742 \ 2244 | 1034 | 3986 3278 | 1210 / 4488 1742 \ 6230 | 1034 | 3986 7264 | 1210 / 8474 1565 \ 10039 | 1211 | 11250 | 3986 708 | (11958) | (502) / TABLE IV UPPER NUMBERS OF 178-DAY GROUPS Number Difference Group (1564) \ (0) | 1211 | 3986 1211 | 1211 / 2422 2598 \ 5020 | 3986 1388 / 6408 2598 \ 9006 | 3986 1388 / 10394 1564 (11958)