MORLEY] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 81 



553 of them, there is a remamder of 11. This the rule says is to be 

 added (or counted forward) from the known coefficient (in this case 

 2) in order to reacli the resulting coefficient. 2 + 11 = 13. Since 

 this number is not above 13, 13 is not to be deducted from it; there- 

 fore the coefficient of the ending day of the second katmi is 13, as 

 shown in Table IX. Similarly we can prove that the coefficient of 

 the ending day of the third katun in Table IX will be 11. Again, we 

 have 7,200 to count forward from the known coefficient, in this case 

 13 (the coefficient of the ending day of the second katim) . But we have 

 seen above that if we deduct all the 13s possible from 7,200 there will 

 be a remainder of 1 1 ; consequently this remainder 1 1 must be added 

 to 13, the known coefficient. 13 + 11=24; but since this number is 

 above 13, we must deduct 13 from it in order to ffiid out the resulting 

 coefficient. 24 — 13 = 11, and 11 is the coefficient of the ending day 

 of the third katun in Table IX. By applying the above rule, all of 

 the coefficients of the ending days of the katuns could be shown to 

 follow the sequence indicated in Table IX. And since the ending 

 days of the katuns determined their names, this same sequence is also 

 that of the katims themselves. 



The above table enables us to establish a constant by means of 

 which we can always find the name of the next katun. Since 7,200 

 is always the number of days in any katun, after deducting all the 

 13s possible the remainder will always be 11, which has to be added 

 to the known coefficient to find the unknown. But since 13 has to 

 be deducted from the resulting number when it is above 13, sub- 

 tracting 2 will always give us exactly the same coefficient as adding 

 11; consequently we may formulate for determining the numerical 

 coefficients of the ending days of katuns the following simple rule: 

 Subtract 2 from the coefficient of the ending day of the preceding 

 katun in every case. A glance at Table IX will demonstrate the 

 truth of this rule. 



In the names of the katuns given in Table IX it is noteworthy that 

 the positions which the ending days occupied in the divisions of the 

 haab, or 365-day year, are not mentioned. For example, the first 

 katun was not called Katun 2 Ahau 8 Zac, but simply Katun 2 Ahau, 

 the month part of the day, that is, its position in the year, was omitted. 

 This omission of the month parts of the ending days of the katuns in 

 the u kahlay katunob has rendered tliis method of datmg far less 

 accurate than any of the others previously described except Calendar- 

 round Dating. For example, when a date was recorded as falling 

 within a certain katun, as Katun 2 Ahau, it might occur anywhere 

 within a period of 7,200 days, or nearly 20 years, and yet fulffil the 

 given conditions. In other words, no matter how acciu-ately this 

 Katun 2 Ahau itself might be fixed in a long stretch of time, there 

 was always the possibility of a maximum error of about 20 years in 

 43508°— Bull. 57—15 6 



