1034 35
2422 82
5020 170
6408 217
9006 305
10394 352
In order to determine the exact extent to which the eclipse seasons
affect these pages in the Dresden Codex it is necessary to work out in
as great detail as possible the calendar represented.
Modern astronomy shows that the synodical revolution of the moon
consumes 29.53059 days, about .03 days more than 29-1/2 days. Since a
calendar must be based on whole days the natural method of combining the
months would be to alternate one of 29 days with one of 30 days. At the
end of two months or 59 days the true synodical month would be in
advance of the calendrical month by .06118 days. Every two months this
error is doubled so that at the end of 34 months the calendar would have
completed 1003 days and the synodical month 1004.04 days. (See Table
VIII, p. 19.) One method of correcting this would be to make the last
month a 30-day month instead of one of 29 days as it would be by simple
alternation. This 34-month period could then be repeated as a cycle with
an accumulating error of .04 days at every repetition.
Such a series utterly disregards, however, all other phenomena such as
eclipses, seasons, etc. As soon as eclipses are considered the
arrangement of the months must be altered in order to use the
periodicity of eclipses in the calendar. Eclipses occur at regular
seasons, approximately six months apart. The average interval between
eclipse seasons is 173.310 days, 3.874 days less than six synodical
lunar months. In Table IX (p. 20) the eclipse season is compared with
the nearest synodical lunar month. It will be noticed that the
difference increases between the two series until it is necessary to use
five synodical months for one interval instead of six to keep the
difference less than half a month. It is necessary to do this three
times in 135 synodical months, or 3986.630 days, which exceed 23 eclipse
seasons, or 3986.131 days, by practically one half-day. It would be most
logical to drop these extra months out of the set of six, during that
group in which the difference tends to become most nearly half a month.
That would be just before the 23d, 70th, and 117th month, that is, 47
months apart, requiring 41 months to complete the 135-month period.