whose name the numeral five enters as a component part), the katun by a similar bird-face with a normal jaw, the tun by the normal glyph which it bears on its head, or its fleshless jaw, the uinal by its frog-like appearance and the curl at the corner of its mouth, and the kin by the glyph on the forehead or the filed teeth. In many of the more elaborate carvings the significance of the sign is shown more by its position in the series than by anything else. Now a great number of the stelæ bear inscriptions which start with a high number expressed in this manner (Fig. 56); at the top is the great cycle glyph, which is an elaborate affair and really means little more than that a count of days is to follow, since there could hardly be any mistake regarding this period which represents over fifty-one centuries. Below, usually in two columns of glyphs, is a number of days, expressed in cycles, katuns, tuns, uinals and kins, and this is followed by a day-and-month date. In the transliteration of Mayan dates, the numerals alone are given as a rule; thus the date shown in Fig. 56, _b_, transliterated as 9. 16. 10. 0. 0. 1 _ahau_, 3 _zip_, means the day 1 ahau, after 3 days of the month _zip_ have passed, being 9 cycles, 16 katuns, 10 tuns, 0 uinals, and 0 kins from the chronological starting-point of the present “Great Cycle.” Now the astonishing fact is this, that throughout the whole of the Maya country, i.e. the area over which ruins in the Maya style are scattered, including Chiapas, Guatemala, Yucatan and northern Honduras, if the long count of days (expressed in cycles, katuns, etc.) be reckoned back from the final day-and-month date, the same day is always reached, viz. 4. ahau, 8. cumhu. Thus all Maya reckoning dates from one definite day in the past, and this day must almost certainly be an artificial date in the sense that it must have been obtained by calculation at a far later time, since it is practically four thousand years from the earliest date which can in any sense be claimed as historical.[5] The starting date itself is found at Quirigua (on a stela which also bears a date in the ninth cycle), and here it is shown to be the concluding date of a cycle thirteen, which must be the last cycle of the preceding “grand cycle.” Many, if not most, of the inscriptions seem to be devoted to the calculation of dates; in the course of the glyphs, most as yet unreadable, one continually comes upon a “distance-number” expressed as above, and then the day-and-month sign to which this leads, reckoning from the date last given. In the longer inscriptions, notably that in the “temple of inscriptions” at Palenque, which contains over six hundred consecutive glyphs, these calculations extend over considerable periods of time. The great probability is that such calculations are not historical, but of a ritual nature. The Maya had no system of intercalary days by which the year of 365 days could be squared with