716 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 
fifth order or the 144,000-day period. Férstemann, as has been already 
stated, applies the name *‘old year” to the 360-day period, apparently 
under the idea that it at some previous time constituted the full year; 
“old ahau” to the 7,200-day period (a fourth application of this 
term); and *‘old katun” to a period of 18,720 days or 52 ‘* old years” 
(52 X 360 = 72 260). To express 9 cycles, 12 katuns, 18 ahaus, 5 
chuens, 16 days, Mr Goodman uses this abbreviation: 9-12-18-5 x 16, 
the < indicating that the two numbers between which it stands are 
usually attached to one symbol. Dr Férstemann, as an abbreviation 
to express the same orders of units, uses the same method, omitting 
only the x, thus: 10, 19, 6, 0, 8 (Zur Entzitferung der Mayahand- 
schriften, 1887, p. 6). 
It will perhaps be as well to insert here what I have to say in refer- 
ence to Mr Goodman’s expressions in regard to, and use of, the term 
ahau as applied to atime period. The names applied to time periods 
as a means by which to refer to them are comparatively unimportant, 
unless such application involves other questions. We quote first the 
following passage from his work (p. 21): 
I now come to what has been a stumbling-block to every one who has hitherto 
attempted to deal with the Mayarecords. It has been known that the Mayas reckoned 
time by ahaus, katuns, cycles, and great cycles, but what was the precise length of any 
of these periods has been a debatable question. Some have contended, with the best 
of proof apparently, that the katun is a period of twenty years, while others have 
maintained, with proof equally as good, that it is a period of twenty-four years. 
The truth is, it is neither. 
The contention arose from a misapprehension, or total ignorance rather, of the 
Maya chronological scheme. It was taken for granted that a year of 365 days must 
necessarily enter into the reckoning; whereas the moment the Mayas departed from 
specitic dates and embarked upon an extended time reckoning, they left their annual 
calendar behind and made use of a separate chronological one. 
The use of the term ahau-katun is avoided everywhere in these pages. Such a 
period never existed, except as a delusion of Don Pio Perez and his misguided fol- 
lowers. The error originated from a misconception of the Yucatec method of dis- 
tinguishing the katuns. The ahau was numbered according to its position in the 
katun, as the eighth, tenth, or the sixth from the close; but the katun was desig- 
nated by the particular number of the day Ahau with which it ended. Thus, for 
instance, it might sometimes be spoken of as the katun 10 Ahau; and at other times 
by a mere reversal of the phrase, as the 10 Ahau katun. More frequently, however, 
the term katun was not used at all, its existence and number being implied by 
simple mention of the ahau date. But there was no ahau-katun. 
On page 23, in speaking of the ahau, he adds: 
This period is the real basis of the Maya chronological system. Everything 
proceeds by ahaus, till in succession the katuns, cycles, great cycles, and grand era 
are formed from them. 
The ahau is a period of 360 days—the sum of the days in the eighteen regular 
months—and derives its name undoubtedly from the fact that it always begins with 
the day Ahau. It is the period, not between two Ahaus with the same numeral, but 
between the second two with a differentiation of four in their day numbering. Movy- 
ing forward with this progression of four it results that the ahaus follow each other 
