S60 NUMERAL SYSTEMS (ETH. ANN. 19 
the units used by the Mayan tribes were as follow, the day being the 
primary unit: 
unit of the 5th order = 20 units, of the 4th order = 144,000 days. 
unit of the 6th order = 20 units of the 5th order = 2,880,000 days. 
1 unit of the Ist order = 1 day. 
1 unit of the 2d order = 20 units of the Ist order = 20 days. 
1 unit of the 8d order = 18 units of the 2d order = 360 days. 
1 unit of the 4th order = 20 units of the 8d order = 7,200 days. 
i 
1 
As this notation has been fully explained and discussed in the pre- 
ceding paper, I pass at once to an examination of the general 
numeral system of the Mayan tribes. The notation given above dif- 
fered from that of general application in the change of the second step 
from 20, as it should be according to the regular yigesimal system, to 
18, probably to facilitate counting with the month factor. ; 
As 20 is the basis of the higher counts, attention will be directed first 
to the steps leading up to this number. The oldest records to which 
we can appeal for knowledge of the system in use among the Mayan 
tribes are the inscriptions and codices. From these we can, however, 
learn only the method of wrztiéng numbers, not the number names; 
yet the method of writing will indicate to some extent the process in 
oral counts. Although the symbols commonly used for this purpose 
are now well known from the frequent notices of them which have 
been published, it is necessary for our present purpose that they be 
presented here. 
1 5 Chy ae e ———— ——— 
Dye abe i ees [pe ees _——— 
yd ONC Sipecniome ———— b= 
Aree caate Gi mensions im Sees o> 
5 0 — 




From these it is seen that the count as expressed in symbols is 
from 1 to 4 by sing dots, or the unit repeated; but that to indicate 5 
the method is changed, and a single short line is used instead of five 
dots. Though frequently horizontal, it is not necessarily so, but is 
found both in the codices and inscriptions in a vertical position; 
oftener, even, in the latter than in the former. The next four num- 
bers, 6, 7, 8, and 9, are formed by adding to the single line one, two, 
three, and four dots or units, but 10 is represented by two parallel 
lines. That these lines must be parallel, or substantially so, whether 
horizontal or vertical, seems to be requisite in the Mayan hiero- 
glyphic writing. Dots are added to the two lines to indicate the num- 
bers 11, 12, 13, and 14; three parallel lines are used to represent 15, 
