944 NUMERAL SYSTEMS [ETH. ANN. 19 
in regular succession from left to right throughout; the lower, where 
the numbers are unaccompanied by day symbols, from right to left, 
beginning on plate 90 with the number 2, to plate 81, where the number 
is 26. The upper line issimple and easily followed, and, counting the 
days, embraces four twenties. To what the numbers in the lower 
line—which follow in regular succession, 2, 3, 4, etc.—refer is as yet 
unknown, though it seems they have some relation to 13; and why 
they begin with 2 is also without satisfactory explanation. 
Plates 91 to 96 are to be taken from left to right, according to the 
paging. The counters in the middle express the intervals between 
the left-hand day of the lower line of one plate and the left-hand day 
of the lower line of the next plate, etc. The same is true also of 
plates 72 to 75. 
Borgian codec—As the only object in view at present is to illus- 
trate the use of numbers in the Mexican codices, and not to introduce 
attempted explanations of the figures, I give a few illustrations from 
the Borgian codex, which is probably the oldest of the existing Na- 
huatl manuscripts. Neither in this nor in the two last codices to 
which I have referred does there appear to be any indication of a 
tendency to arrange the counters in groups of 5. Where it is practi- 
‘able—that is, where the number is not too great—they are placed in 
a single straight row, but the arrangement is governed by the space. 
We turn to plates 18 to 21. Here the pages are arranged in two 
divisions, an upper and lower, each having a row of day symbols run- 
ning along its lower edge; in the upper division the large red counters 
are placed in a column at the right of each page, and in the lower at 
the left. With two exceptions (upper divisions of plates 20 and 21) 
there are six counters in each column; in the exceptions there are 4 in 
acolumn. Starting with Cipactli, right of lower division plate 21, 
passing over six days we reach Tochtli, at the right of the lower divi- 
sion of plate 20, and so on to Ehecatl, at the right of the lower division 
of plate 18. Counting six more takes us to Atl, at the left of the upper 
division of plate 18; six more to Cozcaquauhtli, left of the upper divi- 
sion, plate 19; six more to Calli, plate 20, and four more to Tochtli, 
left of the upper division of plate 21. Counting four days from Coz- 
caquaubtli to the last day of the upper division of this plate brings us 
back to Cipactli, the beginning, the sum of the days being 52, or 
4X13. 
The 12 large red counters in the upper division of plate 17 express 
the number of intervening days between a day of the right section and 
a corresponding day of the left section, the counting being always for- 
ward in the calendar. The red counters on plate 58 indicate the interval 
between the corresponding days of the different sections in the order 
in which they follow one another. Commencing with the right section 

