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.
Dr. Förstemann, in 1886, was probably the first to mention these pages
specifically. At this time he corrected many of the errors in the
series, and related the rows of days to the number series.[6] He had
already recognized a close relation between the difference between the
1st and 9th pictures, i.e., 10,748, and the Saturn sidereal period of
10,753 days. Of course, in order to do this he had also identified the
various signs in the “constellation bands,” assigning them to various
planets.[7] These identifications are based on little more than the wish
he had that they might be those planets, and for that reason they are
seriously open to doubt.
[6] Förstemann, 1886, p. 34.
[7] Ibid., pp. 68-71.
Cyrus Thomas, two years later, also discussed this series at some
length, but confined his considerations entirely to the mathematical
side of the work. He also pointed out most of the errors, agreeing in
the main with Förstemann. He considered that the series contained 11,960
days. In his conclusion he said “the sum of the series as shown by the
numbers over the second column of Plate 58b is 33 years, 3 months, and
18 days. As this includes only the top day of this column (10 Cimi), we
must add two days to complete the series, which ends with 12 Lamat.”[8]
[8] Thomas, 1888, p, 325.
During the following years, Dr. Förstemann repeatedly referred to these
pages in his publications and, in 1898, published an article devoted to
these pages alone.[9] The most detailed as well as the final discussion
of these pages is that given in his book on the Dresden Codex.[10] In
pages 53-58, and 51b and 52b he recognizes the similarity to pages
46-50, and remarks that the Mayas not only combined the _tonalamatl_
and the Mercury year, but also attempted to bring the lunar revolution
into accord with these two. In other words, Förstemann seems to imply
that the primary purpose of the series was the counting of the Mercury
years, and that the lunar part of the problem was secondary.
[9] Förstemann, 1898.
[10] Ibid., 1901, pp. 118-133.
He explains the number 11,958 as the result of attempts to make the
lunar count agree with 11,960. “They [the Mayas] found that 405 lunar
revolutions amounted approximately to 11,958 days, which is, in fact,
the largest number on the second half page of page 58.”[11] This will
not stand at all as the reason for the 11,958 since 405 lunar
revolutions come to 11,959.889 days, and if the Mayas knew the
revolutions accurately enough to know when to intercalate a day, they
most certainly would not have intentionally formed the number 11,958,
when they were perfectly well aware of the fact that the time was more
than 11,959 days. He recognizes in the numbers 177, 148 and 178
multiples of lunar months of 29 and 30 days.
[11] Förstemann, 1901, p. 121.
Dr. Förstemann at this time divides the series into the three equal
divisions in which it has since been considered. These are of 3986 days,
thus causing the intercalated days to come at the same time in all
three.[12] He also divided each of these three divisions into three
unequal groups of 1742, 1034, and 1210 days each. He advances theories,
based on the positions of the pictures in the series, to show that the
series also referred to the siderial periods of Saturn and Jupiter, and
discusses the meaning of the glyphs found on these pages.
[12] Ibid., p. 123.
This detailed discussion by Dr. Förstemann of pages 51-58 of the Dresden
has been used as a foundation by many in further studies of these
pages. It is highly probable, however, that a careful study of his
interpretations will have to be made, in which the proved assumptions
must be clearly differentiated from those in which the “wish is father
to the thought.”
Mr. Bowditch, in 1910,[13] discussed these pages and their relation to
the astronomical knowledge of the Mayas. He divided the series into the
same groups as Dr. Förstemann, basing his division upon the pictures
which occur in every case immediately after the number 148.[14] Mr.
Bowditch brought out very clearly that this series is a lunar series,
by means of a table which compares the numbers recorded in the
manuscript and the multiples of true lunations.[15] There can be no
question on this point, for the difference between the recorded days and
the true lunations is never more than .9 of a day. He also pointed out a
way in which this series could be used over and over again in the form
of a cycle,[16] and then discussed the relation of this series to the
Saturn and Mercury periods, disagreeing with Förstemann on several
points.
[13] Bowditch, 1910, pp. 211-231.
[14] Ibid., p. 218.
[15] Bowditch, 1910, pp. 222, 223.
[16] Ibid., p. 224.
Mr. Bowditch also pointed out a peculiar coincidence between the
synodical revolutions of Jupiter and the numbers in the series, but
based his argument on quite different material from the similar theory
of Dr. Förstemann’s. The important fact brought out is that the three
parts of the series under discussion are almost exactly equal to 10
revolutions of Jupiter, for one revolution of Jupiter consumes 398.867
days.[17] “This would give a reason for the selection of 11,958 to
11,960 days or 405 revolutions, and for the division of this number into
three sections of 3986 days each.”[18]
[17] Ibid., pp. 229, 230.
[18] Ibid., p. 231.
Dr. Förstemann and Mr. Bowditch differ in regard to some of the
corrections which should be made in the manuscript, but on the whole the
two discussions of these pages supplement one another. The general
conclusion to be drawn from them is that these pages of the Dresden are
closely associated with the synodical lunar month, and possibly, with
the synodical revolution of Jupiter.
Three years after Mr. Bowditch’s discussion, Mr. Meinshausen published
an article in which the relation of this series to eclipses was first
brought out.[19] He compared, by means of two tables, recorded eclipses
of the 18th and 19th centuries with the numbers in the Dresden Codex.
Out of the 69 dates in the manuscript all but 15 dates agreed with the
first case, and, in the second, all but 13, due to the fact that all the
eclipses are not visible at one place on the earth’s surface. “Another
indication that the numbers in the codex have arisen from the
observation of eclipses lies in the fact that the exact grouping of the
numbers which is induced by the insertion of pictures in the number
periods is also possible in lunar eclipses which are visible at one
particular point.”[20] In the table given to uphold this statement, the
numbers, to be sure, can be grouped in the manner which he suggests; but
they can also be grouped in other series. In his opinion the reason for
the grouping “lies in the close proximity of a solar eclipse to a lunar
eclipse,”[21] that is, that at the date at which the pictures are
inserted a solar eclipse occurred 15 days either before or after a lunar
eclipse. There are two facts which tend to uphold this theory. One is
the occurrence of the sun and the moon in shields over nearly all
pictures, which he interprets as “signs of solar and lunar eclipses”;
the other is the series of dates on pages 51a and 52a, which are 15 days
apart. In a table of recorded eclipses proof is given that such double
eclipses can occur at the intervals which separate the pictures in the
manuscript. Since these intervals vary a great deal, Meinshausen
believes that they will form the means of identifying the specific
eclipses recorded in the manuscript.
[19] Meinshausen, 1913, pp. 221-227.
[20] Ibid., p. 225.
[21] Meinshausen, 1913, p. 225.
His general conclusion is that “the material advanced will prove
sufficiently that these numbers are associated in some way with solar
and lunar eclipses, and this explanation must remain standing at least
until other numbers, corresponding equally remarkably, are found.”[22]
[22] Ibid., pp. 226, 227.
Professor R. W. Willson of the Astronomical Department of Harvard
University, working on a similar theory at about the same time, had
found, however, that no series of solar eclipses corresponding to the
intervals of the pictures in the text was visible in Yucatan between the
Christian era and the time of the Spanish conquest.[23] This apparently
invalidates Meinshausen’s theory.
[23] Professor Willson’s work on the Dresden manuscript has not yet
been published. It is referred to here only through his kind
permission.
Professor Willson believes that the table in the manuscript indicates
the days of ecliptic conjunction (that is, New Moon occurring so near
the moon’s node that eclipses _may_ occur) and, as Mr. Bowditch has
shown, with a high degree of accuracy. Sufficient proof of this, in
Professor Willson’s opinion, is the close correspondence of the
intervals of the codex with the intervals of Schram’s lunar table.[24]
[24] Schram, 1908, pp. 358, 359.
The similarity between the numbers in the Dresden and Schram’s table is
so remarkable that it seems advisable to point out some of the most
outstanding features. In addition to giving the days of multiples of the
lunar synodic months, this table also gives the time of possible
occurrences of both solar and lunar eclipses. Eclipses occur in cycles,
the best known of which is the Saros, although there are also smaller
cycles which are not so accurate. Table V (p. 17) gives the occurrences
of central solar eclipses according to Schram. It should be noticed that
they occur in groups of threes and fours, each set being separated from
the preceding one by 29 synodical months. The numbers in each group are
only six months apart. Table VI (p. 17) is a corresponding series of
lunar eclipses, which also occur in a grouping similar to that of the
solar eclipses. It should be noticed in passing that the first numbers
of these groups, in both the solar and lunar eclipses are separated by
47 and 41 lunations, the latter occurring after every third group in
Table V.
Table VII (p. 17) contains the numbers which are in the same columns as
the 178-day groups in the Dresden. By comparing Table V and Table VII,
it will be found that the numbers in the Dresden are the same as the
first numbers in groups 1, 2, 4, 5, 7 and 8 of the solar eclipses. In
the last two numbers there is a difference of one day, which is
explained by recalling the addition of an extra day in the day series
but not in the upper numbers of the Dresden. If 679 days are added to
each number in Table VII, which amounts to the same thing as advancing
the Dresden table 679 days with respect to Schram’s table, it will be
found that these numbers will also agree with the first numbers in
groups 2, 3, 5, 6 and 8 and with the second number in group 9 of the
lunar eclipses, in Table VI. A similar agreement may be observed for the
148-day groups (see Table III).
This remarkable agreement between the 178-day groups in the Dresden and
the occurrences of eclipses may have several meanings. (1) One
possibility, and one which should always be kept in mind, is that this
agreement is simply another coincidence, of which there are always many
in chronological work. (2) It may be that the numbers refer to dates of
prophesied eclipses which the Mayas had learned occurred at more or less
regular intervals. (3) Since this table has a place in the calendar of
the Mayas (for a date probably occurs on page 52a), it may be that these
numbers refer to definite historical eclipses. If they do, they will
afford a means by which an absolute correlation between the Maya and
the Julian calendars may be obtained. Professor Willson is at present
working on this problem.