724 MAYAN CALENDAR SYSTEMS (ETH. ANN. 19 
days on this year, we reach 9 Ix, the 17th day of Mac, the 13th month 
of the year 13 Ezanab, which corresponds with the day under the red 
column. 
As the columns and totals are precisely as given by Dr Férstemann 
(Zur Entzifferung der Mayahandschriften, 1891, p. 17), we have proof 
here of the correctness of his system and of the value assigned the 
several orders of units or time periods which, in one of the series, 
involves very high numbers, and also proof that they are precisely 
the same as the time periods used by Mr Goodman in his work, which 
appeared six years later, with the one exception noted below. 
In calculating these series, Dr Férstemann has assumed that 20 units 
of the fifth order make one of the sixth order; or, to use Mr Goodman’s 
nomenclature, that 20 cycles make one great cycle. Although the 
latter author counts but 13 cycles to the great cycle, according to 
the chronological system he believes was used by the authors of the 
inscriptions, he admits that in the Dresden codex the count was 20, 
which is evident from plate 31, where the place of the fifth order of 
units (cycles) has the number 19. 
As the opportunity is afforded here of testing on a higher unit Mr 
Goodman’s theory that the red oval indicates full count (20 where this 
is the proper number, or 18 where that is the number), I shall use 
it. As will be seen by reference to page 723 where the series are 
given, the ahaus of the red: series are counted as 0 (naught), when 
according to Mr Goodman’s theory they should be 20, Let us try 
the calculation with this number. Subtracting the black from the red 
as before, the result is as follows: 

Great Cycles Cycles Katuns Ahaus Chuens Days 
4 6 | 20 13 10 
4 5 19 13 12 8 
Difference... --- 2 7 ] 2 
This difference reduced to days gives 16,942 instead of 9,742, as by 
the former method. Assuming 4 Eb under the black column, as 
before, to be the 5th day of the month Pop in the year 13 Lamat, we 
subtract 360, the remaining days of the year 13 Lamat, from 16,942, 
and, dividing the remainder by 365, obtain 45 years and an overplus of 
157 days—7 months 17 days. By table 3 we find that counting 45 
years from 13 Lamat brings us to 6 Ben, the next year being 7 Ezanab. 
By table 1 we ascertain that the 17th day of the Sth month of this 
year is 7 Ix. This is wrong, as it should be 9 Ix, the day number 
being the test in this case, as the addition of even months will nee- 
essarily bring us back to the same day. ‘This shows Mr Goodman’s 
theory on this point to be incorrect so far as the Dresden codex is 
concerned, where this particular symbol is chiefly, if not exclusively, 
used. 
Our next example is from plate 62, is, like the preceding, in the 
