2. They are all counted from a day, Ahau, that is, 4 Ahau 8 Cumhu. Consequently, all the periods of the Long Count, except the kin or primary unit, end with days the name parts of which are the sign Ahau. This method of recording dates always involves the use of at least two factors, and usually three: 1. A particular period of the Long Count, as Cycle 9, or Katun 14, etc. 2. The date which ends the particular period recorded, as 8 Ahau 13 Ceh, or 6 Ahau 13 Muan, the closing dates respectively of Cycle 9 and Katun 14 of Cycle 9; and 3. A glyph or element which means "ending" or "is ended," or which indicates at least that the period to which it is attached has come to its close. The first two of these factors are absolutely essential to this method of dating, while the third, the so-called "ending sign," is usually, though not invariably, present. The order in which these factors are usually found is first the date composed of the day glyph and month glyph, next the "ending sign," and last the glyph of the period whose closing day has just been recorded. Very rarely the period glyph and its ending sign precede the date. The ending glyph has three distinct variants: (1) the element shown as the prefix or superfix in figure 37, _a-h_, _t_, all of which are forms of the same variant; (2) the flattened grotesque head appearing either as the prefix or superfix in _i_, _r_, _u_, _v_ of the same figure; and (3) the hand, which appears as the main element in the forms shown in figure 37, _j-q_. The two first of these never stand by themselves but always modify some other sign. The first (fig. 37, _a-h_, _t_) is always attached to the sign of the period whose end is recorded either as a {78} superfix (see fig. 37, _a_, whereby the end of Cycle 10 is indicated[53]), or as a prefix (see _t_, whereby the end of Katun 14 is recorded). The second form is seen as a prefix in _u_, whereby the end of Katun 12 is recorded, and in _i_, whereby the end of Katun 11 is shown. This latter sign is found also as a superfix in _r_. [Illustration: FIG. 37. Ending signs and elements.] The hand-ending sign rarely appears as modifying period glyphs, although a few examples of such use have been found (see fig. 37, _j_, _k_). This ending sign usually appears as the main element in a separate glyph, which precedes the sign of the period whose end is recorded (see fig. 37, _l-q_). In these cases the subordinate elements differ somewhat, although the element () appears as the suffix in _l_, _m_, _n_, _q_, and the element (+) as a postfix therein, also in _o_ and _p_. In a few cases the hand is combined with the other ending signs, sometimes with one and sometimes with the other. {79}