fOrstemann] the large NUMBERS 399 



numbers designates a particular day in the course of history. For the 

 Mayas seem to have known no other way of designating a day with 

 perfect exactness. That is to say, if tliey designated the day only by 

 its number in the week of 13 days and by its position in the series of 

 twenty day signs, this designation Avould apply to a multitude of 

 days recurring at intervals of 260; but this designation would be 

 satisfactor}^ only in certain cases. 



It was possible, indeed, to proceed with more precision by adding 

 to the number of the w^eek day and to the day sign also the month 

 and the position of the day in this month. This mode was frequently 

 employed, as we shall see below ; but even this was not always quite 

 free from error, for these four designations would apply to any day 

 recurring at an interval of exactly 52 years. I do not find the least 

 indication of a custom to increase the degree of certainty by a state- 

 ment of the corresponding Ahau katun of 312 years. 



A perfectly exact computation was attained only by deciding on 

 some fixed day (the creation of the world, perhaps, or the birth of a 

 principal god) as a point of departure, and by counting the days from 

 this zero jDoint. But unless I am quite mistaken a fourth day of the 

 week must have been used for tiiis zero point, occupying the seven- 

 teenth place in the day series (according to the notation now intro- 

 duced, a day IV 17 or 4 Ahau), and one which also possessed the 

 peculiarity of being the seventh day " of the eighteenth month, which 

 can only be the case in a year 9 Ix. Hence this important day is a 

 4 Ahau 8 Cumku. 



It is not difficult to understand that in proceeding from this zero 

 point every number must designate a particular day. If the number 

 is divisible by 260 without a remainder, a day IV 17 is, of course, 

 intended; if, on the contrary, there is a remainder, it is only neces- 

 sary to count forward in the Maya calendar from the day IV 17 a 

 number of daj^s equal to this remainder in order to find the day sought. 

 Thus thtj remainders 1, 2, 3, 4, etc., lead to the days V 18, VI 19, 

 VII 20, VIII 1, etc.; the remainders 256, 257, 258, 259 lead to the 

 days XIII 13, I 14, II 15, III 16. Consequently, the day 1,201,114, 

 for instance, is a IX 11; 1,202,032 is a IV 9; 1,233,985 is a III 2, etc. 



In the same wa}^ the day sought can be found, if, instead of 

 counting foi-ward from the day IV 17 as many days as are equal to 

 the remainder left after division by 260, we count backward from 

 IV 17 a number of days equal to 260 less that remainder. The result 

 is the same whether one counts 174 forward or 86 backward, 52, 25. 

 or 243 forward or 208, 235, or 17 backward. Tliese numbers counted 



" Doctor FOrstemann is proceedini;; upon the theory that the first days of the years were 

 Kan, Miiliie, Ix. Caiiac. instead of Akbal, Lamat, Ben, ICzanab, now conceded to be the 

 system of the Dresden codes. Hence it would be properly the eighth day. C. T. 



