GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND NORMAL-FORM PERIOD GLYPHS
Texts Recording Initial Series
Because of the fundamental importance of Initial Series in the Maya system of chronology, the first class of texts represented will illustrate this method of dating. Moreover, since the normal forms for the numerals and the period glyphs will be more easily recognised by the beginner than the corresponding head variants, the first Initial Series given will be found to have all the numerals and period glyphs expressed by normal forms.[[112]]
In plate [6] is figured the drawing of the Initial Series[[113]] from Zoömorph P at Quirigua, a monument which is said to be the finest piece of aboriginal sculpture in the western hemisphere. Our text opens with one large glyph, which occupies the space of four glyph-blocks, A1-B2.[[114]] Analysis of this form shows that it possesses all the elements mentioned on page [65] as belonging to the so-called Initial-series introducing glyph, without which Initial Series never seem to have been recorded in the inscriptions. These elements are: (1) the trinal
superfix, (2) the pair of comblike lateral appendages, (3) the normal form of the tun sign, (4) the trinal subfix, and (5) the variable central element. As stated above, all these appear in the large glyph A1-B2. Moreover, a comparison of A1-B2 with the introducing glyphs given in figure [24] shows that these forms are variants of one and the same sign. Consequently, in A1-B2 we have recorded an Initial-series introducing glyph. The use of this sign is so highly specialized that, on the basis of its occurrence alone in a text, the student is perfectly justified in assuming that an Initial Series will immediately follow.[[115]] Exceptions to this rule are so very rare (see p. [67]) that the beginner will do well to disregard them altogether.
The next glyph after the introducing glyph in an Initial Series is the cycle sign, the highest period ever found in this kind of count[[116]]. The cycle sign in the present example appears in A3 with the coefficient 9 (1 bar and 4 dots). Although the period glyph is partially effaced in the original enough remains to trace its resemblance to the normal form of the cycle sign shown in figure [25], a-c. The outline of the repeated Cauac sign appears in both places. We have then, in this glyph, the record of 9 cycles[[117]]. The glyph following the cycle sign in an Initial Series is always the katun sign, and this should appear in B3, the glyph next in order. This glyph is quite clearly the normal form of the katun sign, as a comparison of it with figure [27], a, b, the normal form for the katun, will show. It has the normal-form numeral 18 (3 bars and 3 dots) prefixed to it, and this whole glyph therefore signifies 18 katuns. The next glyph should record the tuns, and a comparison of the glyph in A4 with the normal form of the tun sign in figure [29], a, b, shows this to be the case. The numeral 5 (1 bar prefixed to the tun sign) shows that this period is to be used 5 times; that is, multiplied by 5. The next glyph (B4) should be the uinal sign, and a comparison of B4 with figure [31], a-c, the normal form of the uinal sign, shows the identity of these two glyphs. The coefficient of the uinal sign contains as its most conspicuous element the clasped hand, which suggests that we may have 0 uinals recorded in B4. A comparison of this coefficient with the sign for zero in figure [54] proves this to be the case. The next glyph (A5) should be the kin sign, the lowest period involved in recording Initial Series. A comparison of A5 with the normal form of the kin sign in figure [34], a, shows that these two forms are identical. The coefficient of A5 is, moreover, exactly like the coefficient of B4, which, we have seen, meant zero, hence glyph A5 stands for 0 kins. Summarizing the above, we may say that glyphs A3-A5 record an Initial-series number consisting of 6 cycles, 18 katuns, 5 tuns, 0 uinals, and 0 kins, which we may write thus: 9.18.5.0.0 (see p. [138], footnote 1).
Now let us turn to Chapter IV and apply the several steps there given, by means of which Maya numbers may be solved. The first step on page [134] was to reduce the given number, in this case 9.18.5.0.0, to units of the first order; this may be done by multiplying the recorded coefficients by the numerical values of the periods to which they are respectively attached. These values are given in Table [XIII], and the sum of the products arising from their multiplication by the coefficients recorded in the Initial Series in plate [6], A are given below: