742 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 
days are to be counted, and so his figures giving the number of days 
show. But this,as has been shown, will not suftice to correct the mis- 
take in our example. However, a very slight change, as 1 have shown, 
which Mr Goodman failed to find, which is simply adding 2 days to 
the time periods, will suffice to bring the series into harmony with the 
theory, and at the same time to verify his determination of the face 
numerals attached to the terminal date of the initial series—8 Ahau 
18 Tzee (year 2 Akbal). 
Although the initial series will be discussed farther on, it will per- 
haps be best to indicate here the probable processes by which Mr 
Goodman reached his conclusions in regard to the series now under 
consideration. 
According to the system which he has adopted and which he claims 
was the chronologic system of the inscriptions, 13 cycles, or units 
of the fifth order, make 1 great cycle, or 1 unit of the sixth order, 
and 73 great cycles complete what he terms the ‘‘grand era.” As 
this system will be more fully explained farther on, it is only neces- 
sary to state here that he concludes from his investigation that the 
dates found in the inscriptions all fall in the fifty-third, fifty-fourth, 
and fifty-fifth great cycles. As these are taken by him to be abso- 
lute time periods, each begins with its fixed and determinate day; 
in other words, there is no sliding of the scale. According to this 
scheme the fifty-third great cycle began with the day 4 Ahau 8 Zotz, 
the fifty-fourth with 4 Ahau 8 Cumhu, and the fifty-fifth with the day 
4 Ahau 3 Kankin, these dates following one another at the distance 
of one great cycle apart, which is correct on his assumption that 13 
cycles make one great cycle, a conclusion which I shall have occasion 
to question. 
Now, it is apparent that he assumes that 4 Ahau 8 Cumhu, the day 
following the first numeral series noted above, is the beginning day of 
his fifty-fourth great cycle. This being assumed, it follows that the 
preceding dates, 8 Ahau 18 Tzec and 1 Ahau 18 Zotz (which precedes 
the former in actual time by precisely one month), must fall in his 
fifty-third great cycle; and as the former (8 Ahau 18 Tzec) is the ter- 
minal date of the initial series, therefore this initial series goes back 
to 4 Ahau 8 Zotz, the beginning day of the fifty-third great cycle. 
As the time to be counted back from 4 Ahau 8 Cumhu to reach the 
closing date of the initial series is, according to the first numeral 
series, 8 ahaus, 5 chuens, 0 days, or 2,980 days, it must necessarily 
fall in the last katun ofthe fifty-third great cycle, which, according 
to his peculiar method of numbering periods, will be the 19th katun 
of the twelfth cycle. Counting back into this katun (using his tables), 
8 ahaus and the 5 months carries us into the ahau beginning with 1 
Ahau 8 Uo, as the only day Ahau of this period falling in the month 
