Number of Number of Elapsed days Elapsed days
month days in month calendar month synodical month Error
1 30 30 29.53 -.47
2 29 59 59.06 .06
3 30 89 88.59 -.41
4 29 118 118.12 .12
5 30 148 147.65 -.35
6 29 177 177.18 .18
7 30 207 206.71 -.29
8 29 236 236.24 .24
9 30 266 265.78 -.22
10 29 295 295.31 .31
11 30 325 324.84 -.16
12 29 354 354.37 .37
13 30 384 383.90 -.10
14 29 413 413.43 .43
15 30 443 442.96 -.04
16 29 472 472.49 .49
17 30 502 502.02 .02
18 29 531 531.55 .55
19 30 561 561.08 .08
20 29 590 590.61 .61
21 30 620 620.14 .14
22 29 649 649.67 .67
23 30 679 679.20 .20
24 29 708 708.73 .73
25 30 738 738.26 .26
26 29 767 767.80 .80
27 30 797 797.33 .33
28 29 826 826.86 .86
29 30 856 856.39 .39
30 29 885 885.92 .92
31 30 915 915.45 .45
32 29 944 944.98 .98
33 30 974 974.51 .51
34 29 1003 1004.04 1.04
This series of 135 lunar months, or 23 eclipse seasons, can be repeated
almost indefinitely, alternating 3986 and 3987 days to the series and
still keep the synodical month in accord with the eclipse season. But
another factor must also be considered. Months of 29 and 30 days cannot
be simply alternated and either conform with the true synodical month or
complete the ecliptic series mentioned, for 3986 contains three more
days than sixty-eight 30-day months, and sixty-seven 29-day months.
Therefore in the 3986 series three of the 29-day months must be changed
to 30-day months, and in the 3987 series four must be changed. The
position of these changes is arbitrary. They can, for example, be the
34th, 68th, and 102d months, and when necessary, the 134th.