MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 107 



remaining. Consequently, the sum of these products equals 7,100 

 (6,840 + 260 + 0). 



The numbers 7,200 to 143,999 were expressed by multiplying the 

 kin, uinal, tun, and katun signs by the numerals to 19, inclusive, 

 and adding together the resulting products. For example, figure 

 56, j, shows the number 7,204. We have seen in Table VIII that 1 

 katun = 20 tuns, and we have seen that 20 tuns = 7,200 kins (20 X 360) ; 

 therefore 1 katun = 7,200 kins. This number falls short of the num- 

 ber recorded by exactly 4 kins, or in other words, no tuns or uinals 

 are involved in its composition, a fact shown by the tuns and 

 uinals between the 1 katun and the 4 kins. The sum of these four 

 products = 7,204 (7,200 + + + 4) . The number 75,550 is shown in 

 figure 56, Jc. The 10 katuns = 72,000; the 9 tuns, 3,240; the 15 

 uinals, 300; and the 10 kins, 10. The sum of these four products = 

 75,550 (72,000+3,240 + 300 + 10). Again, the number 143,567 is 

 shown in figure 56, Z. The 19 katuns= 136,800; the 18 "tuns, 6,480; 

 the 14 uinals, 280; and the 7 kins, 7. The sum of these four prod- 

 ucts =143,567 (136,800 + 6,480 + 280 + 7). 



The numbers 144,000 to 1,872,000 (the highest number, according 

 to some authorities, which has been found ^ in the inscriptions) were 

 expressed by multiplying the kin, uinal, tun, katun, and cycle signs by 

 the numerals to 19, inclusive, and adding together th^ resulting 

 products. For example, the number 987,322 is shown in figure 56, m. 

 We have seen in Table VIII that 1 cycle = 20 katuns, but 20 ka- 

 tuns = 144,000 kins; therefore 6 cycles = 864,000 kins; and 17 

 katuns = 122,400 kins; and 2 tuns, 720 kins; and 10 uinals, 200 kins; 

 and the 2 kins, 2 kins. The sum of these five products equals the 

 number recorded, 987,322 (864,000 + 122,400 + 720 + 200 + 2). The 

 highest number in the inscriptions upon which all are agreed is 

 1,872,000, as shown in figure 56, n. It equals 13 cycles (13 x 144,000), 

 and consequently all the periods below^ — the katun, tun, uinal, and 

 kin — are indicated as being used times. 



Number of Cycles in a Great Cycle 



This brings us to the consideration of an extremely important point 

 concernmg which Maya students entertain two widely different opin- 

 ions; and although its presentation will entail a somewhat lengthy 

 digression from the subject under consideration it is so pertinent to 

 the general question of the higher nimabers and their formation, that 

 the writer has thought best to discuss it at this point. 



In a vigesimal system of numeration the unit of increase is 20, and 

 so far as the codices are concerned, as we shall presently see, this 



1 There may be three other numbers in the inscriptions which are considerably higher (see pp. 114-127). 



