THOMAS] METHOD OF COMPUTATION 933 
That they had time tables by which they could compute intervals of 
moderate length, as the day series in the Codex Cortesianus, which 
could be used as the Mexican Tonalamatl, is well known; we can use 
them to-day for that purpose. It would seem also from the four 
plates in the Dresden codex, and four in the Troano codex, showing 
the four year series, that they also had tables by which to count year 
intervals, but there are no indications of tables to aid in the reduction 
of the higher orders of units—cycles, katuns, etc. In the Mexican 
manuscripts, as will be seen in the following chapter, the number of 
tzontli (400 each) and aiguipillé (8,000 each)—the highest counts dis- 
covered therein—were indicated simply by repeating the symbols, 
but the Maya had reached the art of numbering their symbols. Now, 
it is apparent that the latter must have had some method of computa- 
tion where such high numbers as those indicated were involved. This 
was necessary even to ascertain the number of days in a cycle or katur, 
and when several of these and of each of the lower units were to be 
reduced to primary units, or days, and these to be changed into years, 
months, and days, and the commencing and ending dates determined, 
the count would seem to transcend the power of simple mental compu- 
tation. How then was this accomplished? It would seem, therefore, 
that they must have had some way of making these lengthy calcula- 
tions other than counting ‘‘in the head;” but what it was we have no 
means of determining. 
There would seem to be no doubt that they had a way of *‘cipher- 
ing”—to use a schoolboy term—and this appears to be confirmed by 
Landa, who, speaking of their method of counting, says: 

Que su cuenta es de vy en v, hasta xx, y de xx en xx, hasta c, y de c en c hasta 
400, y de cece en ccce hasta yiir mil. Y desta cuenta se servian mucho para la con- 
tratacion de cacao. Tienen otras cuentas muy largas, y que las protienden in infinitum, 
contandolas yt mil xx yezes que son c y Lx mil, y tornando a xx duplican estas 
ciento y Lx mil, y despues yrlo assi xx duplicando hasta que hazen un incontable 
numero: cuentan en el suelo o cosa Ilana. 
‘ 
The last phrase, ‘‘cuentan en el suelo o cosa Ilana,” indicates the 
manner in which they made their calculations, to wit, on the ground or 
on some flat or smooth thing. Brassuer translates the sentence thus: 
‘*Leurs comptes se font sur le sol, ou une chose plane.” This certainly 
indicates ‘‘figuring” or performing calculations by marking on a 
smooth surface. Although multiplication and division seem impos- 
sible with their symbols, it is possible, as Professor McGee suggests 
to me, that they reached the desired result by repeated additions and 
subtractions. These operations may be readily performed with the 
ordinary number symbols (dots and short lines), the orders of units 
being indicated by position, as in the Dresden codex. The chief dif- 
ficulty would be to change the sum of units into years. This, when 
the number was large, must have been accomplished by means of what 
Goodman calls the ‘‘calendar round” or 52-year period, for which 
