MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 129 



lowest period, so long as its several periods always stand in the same 

 relation to each other. For example, in figure 56, g, 6 cycles, 17 katuns, 

 2 tuns, 10 uinals, and kins represent exactly the same number as 

 kins, 10 uinals, 2 tuns, 17 katuns, and 6 cycles; that is, with the 

 lowest term first. 



It was explained on page 23 that the order in which the glyphs are 

 to be read is from top to bottom and from left to right. Applying 

 this rule to the inscriptions, the student will find that all Initial Series 

 are descending series; that in reading from top to bottom and left 

 to right, the cycles will be encountered first, the katuns next, the 

 tuns next, the uinals, and the kins last. Moreover, it will be found 

 also that the great majority of Secondary Series are ascending series, 

 that is, in reading from top to bottom and left to right, the kins will 

 be encountered first, the uinals next, the tuns next, the katuns next, 

 and the cycles last. The reason why Initial Series always should be 

 presented as descending series, and Secondary Series usually as 

 ascending series is unknown; though as stated above, the order in 

 either case might have been reversed without affecting in any way 

 the numerical value of either series. 



This concludes the discussion of the first method of expressing the 

 higher numbers, the only method which has been found in the 

 inscriptions. 



Second Method of Numeration 



The other method by means of which the Maya expressed their 

 higher numbers (the second method given on p. 103) may be called 

 "numeration by position," since in this method the numerical value 

 of the symbols depended solely on position, just as in our own deci- 

 mal system, in which the value of a figure depends on its distance 

 from the decimal point, whole numbers being written to the left and 

 fractions to the right. The ratio of increase, as the word "decimal" 

 implies, is 10 throughout, and the numerical values of the consecutive 

 positions increase as they recede from the decimal point in each 

 direction, according to the terms of a geometrical progression. For 

 example, in the number 8888.0, the second 8 from the decimal point, 

 counting from right to left, has a value ten times greater than tlie first 

 8, since it stands for 8 tens (80); the third 8 from the decimal point 

 similarly has a value ten times greater than the second 8, since it 

 stands for 8 hundreds (800); finally, the fourth 8 has a value ten 

 times greater than the third 8, since it stands for 8 thousands 

 (8,000). Hence, although the figures used are the same in each case, 

 each has a different numerical value, depending solely upon its posi- 

 tion with reference to the decimal point. 



In the second method of writing their numbers the Maya had 

 devised a somewhat similar notation. Their ratio of increase was 20 in 

 all positions except the third. The value of these positions increased 

 43508°— Bull. 57—15 9 



