INTEODUCTION TO STUDY OF MAYA HIEKOGLYPHS 



57 



B 



Pop in B, after which both wheels start to revolve in the directions 

 indicated by the arrows. 



The first day of the year whose beginning is shown at the point of 

 contact of the two wheels in figure 21 is 2 Ik Pop, that is, the day 

 2 Ik which occupies the first position in the month Pop. The next day 

 in succession will be 3 Akbal 1 Pop, the next 4 Kan 2 Pop, the next 

 5 Chicchan 3 Pop, the next 6 Cimi 4 Pop, and so on. As the wheels 

 revolve in the directions indicated, the days of the tonalamatl succes- 

 sively fall into their 

 appropriate p o s i- 

 tions in the divi- 

 sions of the year. 

 Since the number of 

 cogs in A is smaller 

 than the number in 

 B, it is clear that 

 the former will 

 have returned to 

 its starting point, 

 2 Ik (that is, made 

 one complete revo- 

 lution) , before the 

 latter will have 

 made one complete 

 revolution; and, 

 further, that when 

 the latter (B) has 

 returned to its 

 starting point, 

 Pop, the corre- 

 sponding cog in B 

 will not be 2 Ik, 

 but another day (3 Manik) , since by that time the smaller wheel will 

 have progressed 105 cogs, or days, farther, to the cog 3 Manik. 



The question now arises, how many revolutions will each wheel 

 have to make before the day 2 Ik will return to the position Pop. 

 The solution of this problem depends on the application of one 

 sequence to another, and the possibilities concerning the numbers or 

 names which stand at the head of the resulting sequence, a subject 

 already discussed on page 52. In the present case the numbers in 

 question, 260 and 365, contain a common factor, therefore our prob- 

 lem falls under the third contingency there presented. Consequently, 

 only certain of the 260 days can occupy the position Pop, or, in 

 other words, cog 2 Ik in A will return to the position Pop in B in 

 fewer than 260 revolutions of A. The actual solution of the problem 



Fig. 21. Diagram showing engagement of tonalamatl wheel of 260 days (A), 

 andhaab wheel of 365 positions (B); the combination of the two giving 

 the Calendar Round, or 52-year period. 



