MORLEY] INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 53 



that the third year, beginning with the 11th name, would necessarily 

 end with the 15th name; and the fourth year, beginning with the 16th 

 name (the 1096th from the beginning) would necessarily end with 

 the 20th, or last name, in the sequence. It results, therefore, from 

 the foregoing progression that the ffth year will have to begin with 

 the 1st name (the 1461st from the beginning), or the same name with 

 wliich the^rs^ year also began. 



Tliis is capable of mathematical proof, since the 1st day of the 

 fifth year has the 1461st name from the beginning of the sequence, for 

 1461 = 4x365+1 = 73x20+1. The 1 in the second term of this 

 equation indicates that the beginning day of the fifth year has been 

 reached; and the 1 in the third term indicates that the name-part 

 of this day is the 1st name in the sequence of twenty. In other 

 words, every fifth year began with a day, the name part of which 

 was the same, and consequently only four of the names in Table I 

 could stand at the beginnings of the Maya years. 



The four names which successively occupied this, the most impor- 

 tant position of the year, were: Ik, Manik, Eb, and Caban (see Table V, 

 in which these four names are shown in their relation to the sequence 

 of twenty). Beginning with any one of these, Ik for example, the 

 next in order, Manik, is 5 days distant, the next, Eb, another five 

 days, the next, Caban, another 5 days, and the next, Ik, the name 

 with which the Table started, another 5 days. 



Table V. RELATIVE POSITIONS OF DAYS BEGINNING MAYA YEARS 

 IK EB 



Since one of the four names just given invariably began the Maya 

 year, it follows that in any given year, all of its nineteen divisions, the 

 18 uinals and the xma kaba kin, also began with the same name, 

 which was the name of the first day of the first uinal. This is neces- 

 sarily true because these 1 9 divisions of the year, with the exception of 

 the last, each contained 20 days, and consequently the name of the 

 first day of the first division determined the names of the first days 

 of all the succeeding divisions of that particular year. Furthermore, 

 since the xma kaba kin, the closing division of the year, contained 

 but 5 days, the name of the first day of the following year, as well as 



