It has been explained (see pp. [74]-[76]) that in addition to Initial-series dating the Maya had another method of expressing their dates, known as Secondary Series, which was used when more than one date had to be recorded on the same monument. It was stated, further, that the accuracy of Secondary-series dating depended solely on the question whether or not the Secondary Series was referred to some date whose position in the Long Count was fixed either by the record of its Initial Series or in some other way. The next class of texts to be presented will be those showing the use of Secondary Series in connection with an Initial Series, by means of which the Initial-series values of the Secondary-series dates, that is, their proper positions in the Long Count, may be worked out even though they are not recorded in the text.
The first example presented will be the inscription on Lintel 21 at Yaxchilan, which is figured in plate [16].[[182]] As usual, when an Initial Series is recorded, the introducing glyph opens the text and this sign appears in A1, being followed by the Initial-series number itself in B1-B3. This the student will readily decipher as 9.0.19.2.4, recording apparently a very early date in Maya history, within 20 years of 9.0.0.0.0 8 Ahau 13 Ceh, the date arbitrarily fixed by the writer as the opening of the first great period.
Reducing this number by means of Table [XIII] to units of the first order[[183]] and deducting all the Calendar Rounds possible, 68 (see Table [XVI]), and applying rules 1, 2, and 3 (pp. [139], [140], and [141], respectively) to the remainder, the terminal date reached will be 2 Kan 2 Yax. This date the student will find recorded in A4 and A7a, glyph B6b being the month-sign "indicator," or the closing glyph of the
Supplementary Series, here shown with the coefficient 9. Compare the day sign in A4a with the sign for Kan in figure [16], f, and the month sign in A7a with the sign for Yax in figure [19], q, r. We have then recorded in A1-A4[[184]], and A7a the Initial-series date 9.0.19.2.4 2 Kan 2 Yax. At first sight it would appear that this early date indicates the time at or near which this lintel was inscribed, but a closer examination reveals a different condition. Following along through the glyphs of this text, there is reached in C3-C4 still another number in which the normal forms of the katun, tun, and uinal signs clearly appear in connection with bar and dot coefficients. The question at once arises, Has the number recorded here anything to do with the Initial Series, which precedes it at the beginning of this text?
Let us first examine this number before attempting to answer the above question. It is apparent at the outset that it differs from the Initial-series numbers previously encountered in several respects:
1. There is no introducing glyph, a fact which at once eliminates the possibility that it might be an Initial Series.
2. There is no kin period glyph, the uinal sign in C3 having two coefficients instead of one.
3. The order of the period glyphs is reversed, the highest period, here the katun, closing the series instead of commencing it as heretofore.
It has been explained (see p. [129]) that in Secondary Series the order of the period glyphs is almost invariably the reverse of that shown by the period glyphs in Initial Series; and further, that the former are usually presented as ascending series, that is, with the lowest units first, and the latter invariably as descending series, with the highest units first. It has been explained also (see p. [128]) that in Secondary Series the kin period glyph is usually omitted, the kin coefficient being attached to the left of the uinal sign. Since both of these points (see 2 and 3, above) are characteristic of the number in C3-C4, it is probable that a Secondary Series is recorded here, and that it expresses 5 kins, 16 uinals, 1 tun, and 15 katuns. Reversing this, and writing it according to the notation followed by most Maya students (see p. [138], footnote 1), we have as the number recorded by C3-C4, 15.1.16.5.
Reducing this number to units of the first order by means of Table [XIII], we have: