When the difference groups[25] are divided into months it is found that it is an easy matter to arrange the months in an alternating series. The group of 177 days is composed of three 30-and three 29-day months, either of which when alternated can begin the group, which then ends with the other, i.e., 29, 30, 29, 30, 29, 30, or 30, 29, 30, 29, 30, 29. The group of 148 days consists of three 30-and two 29-day months, necessitating that it begin and end with a 30-day month when alternated, thus, 30, 29, 30, 29, 30. In the 178-day group one of the 29-day months is replaced by a 30-day month, otherwise the group is exactly like that of 177 days, which it exceeds by one day. It is evident that there will always be three 30-day months in succession in the 178-day group, and that care must be taken in choosing the right sequence of the 177-day groups which fall near those of 148 days in order to avoid having two 30-day months in succession. [25] That is, the 177-day, 148-day and 178-day groups. There remains simply the substitution of the six or five months, as the case may be, in place of the difference groups in the manuscript. However, if the Mayas considered each third of the table as a unit, it is reasonable to assume that the sequence of the months in each third is identical. Therefore it is necessary to arrange a sequence for only one-third, that is, 135 months, and then, if the assumption is correct, this sequence will fit the other two-thirds of the series. Each third of the table consists of 135 months covering three more days than would be covered by a simple alternation of 30-and 29-day months. These three intercalary days were inserted at definite intervals. A clue to the position of two of them is given by the 178-day groups. One was inserted between the 30th and 35th months, another 47 months later, between the 77th and 82d months. Theoretically the extra day should be inserted in the 34th month after the beginning of a series of alternating 29-and 30-day months, for then the error between the synodical revolution of the moon and the calendrical months becomes more than one day. In the 29-day month preceding the 34th, namely the 32d month, the error at the end is also practically one day, i.e., .98 days. The 29-day month most nearly the centre of the first 178-day group is the 32d month of the series, the third in the group. The Mayas may have chosen this month because of its position in the 178-day group, making the sequence of the months 29, 30, 30, 30, 29, 30, if the 30th month was a 29-day month as it would be by simple alternation.