APPENDIX VI. 
THE. SUPPLEMENTARY SERIES. 
The Supplementary Series is a group of glyphs, usually 8 in number, which 
never occurs independently, but which, if present at all, always accompanies an 
Initial Series. Goodman was the first to call attention to this group, which he 
believed fixed the position of the accompanying Initial Series in some other method 
employed by the Maya in counting time.!' Later he modified this view somewhat, 
coming to the conclusion that the Supplementary Series showed the relation of the 
regular chronology (7. ¢., the Long Count) to a special chronology in each city, 
dating 1 in each case from its foundation; in short, that the Supplementary Series 
were in the nature of ab urbe condita reckonings, starting from a different date in 
each city.” 
In 1901 Bowditch suggested the name Supplementary Series for this count, 
on the ground that the glyphs of which it is composed always stand close to the 
Initial Series terminal date, the meaning of which he believed they “supplemented” 
in some way, and hence the name Supplementary Series by which they have since 
been known.’ 
The writer’s own investigation of the Supplementary Series dates from 1907, 
but it was not until 1915 chat he announced the meaning of the group as presenting 
a lunar count of some sort,’ and it was not until 1916, in a special paper on the sub- 
ject for the Holmes Anniversary volume, that he was able to prove this by adequate 
mathematical evidence.® 
It is not his purpose to attempt to cover the ground of that longer and more 
detailed study here, but rather to state, as briefly as may be, the principal con- 
clusions which it brought out as to the nature of this group of glyphs, and to indi- 
cate the results of subsequent investigations along the same line, not only by him- 
self, but also by Guthe, R. K. Morley, and Willson, which are as yet unpublished.® 
The Supplementary Series occupies one of three positions with reference to the 
Initial Series: (1) immediately preceding the Initial Series terminal date; (2) im- 
mediately following the Initial Series terminal date; and (3) standing eee the 
two parts (7. ¢., the day and month-signs) of the ate Series terminal date. Of the 
80 Initial Series examined in 1916, 6 were found to fall in Class 1 above; 11 in Class 
2, and 63 or more than 78 per cent. in Class 3, which we may therefore conclude was 
the normal position, particularly during the Great Period, since most of the aber- 
rant examples in Classes 1 and 2 date from the Early or Middle Period. Thus, by 
their proximate position thereto, the Maya priests sought to indicate that this 
count was to be interpreted with and by the aid of the accompanying Initial Series 
in each case. 
The normal Supplementary Series (best exemplified at Quirigua and Piedras 
Negras) is composed of 8 glyphs, though this number is not constant and may rise 
as high as 9 (some of the Yaxchilan texts for example) or fall as low as 4 (Stela 3, 
Uaxactun). The earliest example known, Stela 20 at Copan [9.1.10.0.0 (?)], has 
7 glyphs, however, the only one missing being the non-numerical Glyph B. 
The sequence of these 8 characters, i. é., their relative positions in the series, 
no matter which are present, is extremely Cane. the only irregular feature being 
that in many texts, some of them, notably Glyphs D and E, are wanting. The 
ce Srey an ad ats ER SS SO a Es ee 2 eee 
1Goodman, 1897, p. 118. —*Lbid., 1905, p. 647. 3Bowditch, 1g01¢, pp. 5, 9, 15, 17, 19, and 24; and 1910, p. 244. 
4Morley, 1915, p. 152, note I. 5Tbid., 1916. 
6Guthe’s studies on the lunar series in the Dresden Colex are now in course of publication. See Guthe, 1920. 
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