934 NUMERAL SYSTEMS [FTH. ANN. 19 
they had a specific symbol, though not of the ordinary form, The 
sum (18,980) could be expressed thus: 
- - =14,400 

——= 4,320 
suche) — 260 
S= 0 
18, 980 
By using this form and subtracting until the given sum should be 
reduced below 18,980 the number of subtractions would indicate the 
number of 52-year periods. The years could be obtained in the same 
way by repeated subtractions from the overplus with the ordinary 
symbols, thus: 
7) 360 
Q= 
—_ >= oO 

365 
Whether this was the method followed I can not say, but it is cer- 
tain that the desired result could be obtained in this way. Nevyerthe- 
less, this method of changing high series, reaching into millions of 
years, must have been very tedious, unless there was some way of 
shortening the process. I may, however, have more to say on this 
subject in a subsequent paper, in which I propose to discuss the 
Quirigua inscriptions. 
NUMBERS IN THE MEXICAN CODICES 
The data relating to the use of numbers in the Mexican codices, so 
far as we are as yet able to interpret the symbols, are meager com- 
pared with those relating tonumbers in the Mayan codices and inscrip- 
tions. We lack also in this investigation the means of demonstration 
in regard to the higher numbers, being limited in this respect to the 
statements of historians and the interpreters of the Mendoza and 
Vatican codices. However before proceeding with the examination 
of the codices, it is necessary to refer briefly to certain facts in regard 
to the Mexican time system. 
This system is, as is well known and as I have shown in a previous 
paper,’ like that of the Maya, except in the names of the days and 
months and in the symbols used to represent them. As there will be 
occasion to refer to these in discussing the numbers in the Mexican 
codices they are for the convenience of the reader given here. A 
condensed calendar like that used in discussing Mayan dates in our 
previous paper is also given. 

1 Notes on certain Mayan and Mexican Manuscripts, in Third Ann. Rep. Bur. Eth. 
