THOMAS] NUMBER OF CYCLES IN GREAT CYCLE 235 



periods, they all begin with the day 4 Ahau. If tlie first day of the 

 ahaus is Ahau, then it is certain that the first day of each of the 

 higher periods will be Ahau, though we count 13 or 20 cycles to the 

 great cycle. As the days of the calendar are numbered 1, 2, 3, etc., 

 lip to 13, the count then beginning again with 1, and this numbering 

 is continued in regular order, and as Ahau will return only every 20th 

 day it is apparent that it will receive different numbers. If the days 

 are written out in regular succession and the series is made of suffi- 

 cient length, it will be found, if we select a 13 Ahau and begin our 

 count with it and count 360 daj's (1 ahau) to each step, that the num- 

 bers attached to the days (which will of cour.se be Ahaus) will come (the 

 count being forM'ard) in the following order: 13, 9, 5, 1, 10, 6, 2, 11, 7, 

 3, 12, 8, 4, 13, 9, 5, etc., this order being maintained wherever in the 

 series we may begin. , 



As it takes 20 ahaus or units of the ord order to make one of the 

 4th, it follows that if the day numbers are written out in succession 

 in the order above stated, the fii-st days of the katuns will be those of 

 the 20th ahaus, their numbers will therefore come in the following 

 order: 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, 13, 11, 9, 7, etc., the order 

 remaining the same regardless of the point at which the count begins. 

 As 20 katuns make 1 cycle, the numbers of the first da.ys of the 

 cycles will be the same as those of the 20tli katuns, and will be as fol- 

 lows: 13, 12, 11, 10, 9, 8, 7, G, 5, 4, 3, 2, 1, 13, 12, etc. The beginning 

 point in these series is arbitrary. 



It may also be shown by simple calculation that the order of the 

 day numbers of the first days of the higher periods or orders of units 

 will be as given above. As the numbers of the first days of the ahaus 

 vary successively by 4, if we multiply 4 by 20 (20 ahaus being required 

 to make a katun) and divide by 13, the remainder is 2; hence, if the 

 first day of a given katun is 9, the first day of the one which follows 

 will be 7 Ahau, the diflfereuce being subtracted if counting forward, 

 and added if counting backward. When the number of the day is 

 less than 3 we add 13, and then subtract in counting forward, and in 

 counting backward subtract 13 when the sum is greater than this 

 number. As it takes 400 ahaus to make 1 ej^cle, we multiply the 

 difference, 4, by this number, and divide the ijroduct by 13. This 

 leaves a remainder of 1, hence we subtract 1 from the number of the 

 first day of a given cycle to find the first of that which follows, or 

 add 1 to find the first of that which precedes. 



As, according to Goodman's theory, 13 cj^cles make a great cj'cle, 

 then it requires 20x20x13 ahaus to make 1 great cycle. We mul- 

 tiply 4 by 20x20x13 (or 5,200) and divide by 13. This leaves no 

 remainder, and hence, according to this scheme, the day numbers of 

 the first day of all the great cycles will be the same, and so Goodman 

 gives them in his "Perpetual Chronological Calendar." Here the 

 question of number arises. Is it 1 Ahau, 2 Ahau, or 3 Ahau, etc., to 



