784 MAYAN CALENDAR SYSTEMS [ETH ANN.19 
it or its value in another way/” This, in the absence of proof, is 
but simple guesswork. However, before we examine it, uttention is 
called to the further assumption that what would, according to his 
system, be the beginning ahau of the series, which he would number 
20, is omitted because it is considered as already passed. He observes 
in a quotation which will be found on a previous page of this paper, 
that ahaus are numbered 20, 1, 2, 3, etc., up to 19, but the evidence to 
establish the correctness of this assertion is nowhere given in his paper. 
I presume, therefore, that it is based upon the chronologic system 
that he has constructed, of which further notice will be taken before 
closing this paper. But how does it happen they are found numbered 
1, 2, 3, ete., In an inscription when Mr Goodman tells us that in the 
katuns, taken in their order, they were numbered 9, 5, 1, 10, 6, 2, 11, 7, 
3, 12,8,4,13% That, in telling in a numeral series how many ahaus 
are to be added, the numbers must be given 1, 2, 3, etc, is very evident; 
but if ahaus were real periods in the Maya chronology, and not simply 
units of the third order, as we have stated, why are they not numbered 
in this inscription in the order in which they come in the katun? It 
may readily be seen that the succession 9, 5, 1, 10, 6, ete., arose from 
counting by the day numbers 1-13 by divisions of four, as in the series 
in the Cortesian codex, the count being backward; as, for example, 
counting upward from the bottom of one of the other columns in table 
3, or by the 360-day periods, as referred to elsewhere and as asserted 
by Mr Goodman. 
He quotes the following from Perez (page 12): 
There was another number which they called wa katun, and which served them as 
a key to find the katuns. According to the order of its march it falls on the days of 
the wayeb yaab and revolves to the end of certain years: katuns 13, 9,5, 1, 10, 6, 2, 11, 
W312) 8,4. 
On this he remarks as follows (loc. cit.): 
Poor Don Pio! To have the pearl in his grasp and be unaware of its priceless- 
ness—like so many others! But I must not exult too much yet. The succession of 
the katuns, reckoned according to this principle, is yet to be ascertained before my 
fancied discovery can be established by a crucial test. I score the ahaus off in the 
foregoing order, and, sure enough, the twentieths give the desired result: 11,9, 7,5, 
3, 1,12, 10,8,6,4,2,18. Eureka! The perturbed spirit of the Maya calendar, which 
has endeavored so long to impart its message to the world, may rest at last. 
As the *‘uayeb haab” signifies the five added days of the year and is 
so recognized by him, how is it possible to reconcile this count, which 
“falls on the days of the uayeb haab,” with the count of his ahaus 
which only cover 360 days each and recognize no 5 added days, which 
only come into notice when the year of 865 days is considered, which 
he says the Maya left behind when they entered on a chronologic 
count? It seems doubtful, therefore, whether this explanation will 
allay ‘*the perturbed spirit of the Maya calendar.” 
