An Introduction to the Study of the Maya Hieroglyphs

by Sylvanus Griswold Morley

The number 20 was expressed in two different ways: (1) By the sign shown in figure [45]; and (2) by the numeral 0 in the bottom place and the numeral 1 in the next place above it, as in figure [63], a. The first of these had only a very restricted use in connection with the tonalamatl, wherein numeration by position was impossible, and therefore a special character for 20 (see fig. [45]) was necessary. See Chapter VI.

The numbers from 21 to 359, inclusive, involved the use of two places—the kin place and the uinal place—which, according to Table [VIII], we saw had numerical values of 1 and 20, respectively. For example, the number 37 was expressed as shown in figure [63], b. The 17 in the kin place has a value of 17 (17 × 1) and the 1 in the uinal, or second, place a value of 20 (1 (the numeral) × 20 (the fixed numerical value of the second place)). The sum of these two products equals 37. Again, 300 was written as in figure [63], c. The 0 in the kin place has the value 0 (0 × 1), and the 15 in the second place has the value of 300 (15 × 20), and the sum of these products equals 300.

To express the numbers 360 to 7,199, inclusive, three places or terms were necessary—kins, uinals, and tuns—of which the last had a numerical value of 360. (See Table [VIII].) For example, the number 360 is shown in figure [63], d. The 0 in the lowest place indicates that 0 kins are involved, the 0 in the second place indicates that 0 uinals or 20's are involved, while the 1 in the third place shows that there is 1 tun, or 360, kins recorded (1 (the numeral) × 360 (the fixed numerical value of the third position)); the sum of these three products equals 360. Again, the number 7,113 is expressed as shown in figure [63], e.

The 13 in the lowest place equals 13 (13 × 1); the 13 in the second place, 260 (13 × 20); and the 19 in the third place, 6,840 (19 × 360). The sum of these three products equals 7,113 (13 + 260 + 6,840),

Fig. 63. Examples of the second method of numeration, used exclusively in the codices.

The numbers from 7,200 to 143,999, inclusive, involved the use of four places or terms—kins, uinals, tuns, and katuns—the last of which (the fourth place) had a numerical value of 7,200. (See Table [VIII].) For example, the number 7,202 is recorded in figure [63], f.

The 2 in the first place equals 2 (2×1); the 0 in the second place, 0 (0×20); the 0 in the third place, 0 (0×360); and the 1 in the fourth place, 7,200 (1×7,200). The sum of these four products equals 7,202 (2+0+0+7,200). Again, the number 100,932 is recorded in figure [63], g. Here the 12 in the first place equals 12 (12×1); the 6 in the second place, 120 (6×20); the 0 in the third place, 0 (0×360); and the 14 in the fourth place, 100,800 (14×7,200). The sum of these four products equals 100,932 (12+120+0+100,800).

The numbers from 144,000 to 2,879,999, inclusive, involved the use of five places or terms—kins, uinals, tuns, katuns, and cycles. The last of these (the fifth place) had a numerical value of 144,000. (See Table [VIII].) For example, the number 169,200 is recorded in figure [63], h. The 0 in the first place equals 0 (0×1); the 0 in the second place, 0 (0×20); the 10 in the third place, 3,600 (10×360); the 3 in the fourth place, 21,600 (3×7,200); and the 1 in the fifth place, 144,000 (1×144,000). The sum of these five products equals 169,200 (0+0+3,600+21,600+144,000). Again, the number 2,577,301 is recorded in figure [63], i. The 1 in the first place equals 1 (1×1); the 3 in the second place, 60 (3×20); the 19 in the third place, 6,840 (19×360); the 17 in the fourth place, 122,400 (17×7,200); and the 17 in the fifth place, 2,448,000 (17x144,000). The sum of these five products equals 2,577,301 (1+60+6,480+122,400+2,448,000).