THOMAS] GOODMA N’S SYSTEM 7938 
again with the same date from which they started. Such a result in the case of the 
former requires 949 cycles, and in that of the latter 73 great cycles, each of which 
reckonings constitutes a period of 374,400 years. 
It is also apparent in the following expression (p. 26): 
The grand era is composed of seventy-three great cycles and comprises 374,400 
years, or 136,656,000 days. It is the period in which the Maya chronological calen- 
dar completes itself, just as their annual calendar does in a period of 52 years. 
This number of days is the product of the factors 20 18x 20 x 20x 
13x73. Now let us examine his reason for introducing the 13 and 
73 iustead of carrying on the count according to the usual Maya 
vigesimal notation, as Dr Férstemann has done. This is easily seen. 
Having conceived the idea that all the factors of the calendar system 
are time periods and must come into harmony in the highest period, 
it was absolutely necessary to bring these prime numbers into the 
count. The 13 is necessary to the day numbering and to the 52-year 
period (413), and the 73 to the 365-day period (5x73), and as 4 and 
5 are factors of the lower periods (as 20) the prime numbers only were 
necessary to complete the scheme. As the attempt to introduce both 
these into one period would have required the use of the very large 
multiplier 949 (see his use of it, p. 27), the 13 was introduced into the 
grand cycle. We might ask, and seemingly with good reason, why 
not in one of the lower orders? The answer is apparent—the records 
show beyond question that, up to the cycle, the multiplier, except in 
the case of the chuen, was 20. But in passing from the cycle to the 
grand cycle, but a single example has been found in the inscriptions 
showing a higher number than 13, and this, as has already been stated, 
Mr Goodman decides must be erroneous. 
As the introduction of the 13 somewhere is absolutely necessary to 
round out his grand multiple, how, we may ask, was the system com- 
pleted in accordance with the Dresden codex which he admits (page 3) 
‘““pertains to the archaic system in the main, though reckoning 20 
cycles to the great cycle”? Unless 949 is introduced as a multiplier 
in the next step, which can not be supposed possible, the entire scheme 
is destroved and the several steps reduced merely to those of notation, 
which in fact they are. The idea that the Mayan tribes of Chiapas, 
Guatemala, and Honduras had such a magnificent rounding-out system, 
while the Yucatec tribes, though having a system similar in other 
respects, failed to introduce the rounding-out factors, is, to say the least. 
very strange. In order to include the 365 days of the year in the great 
multiple, it was also necessary to introduce the prime number 73, 
which is not a divisor of any of the lower periods. This explains Mr 
Goodman’s theory of a great cycle composed of 13 cycles and a grand 
era composed of 73 great cycles, as he could not otherwise have a 
general rounding-out period. These are of course necessary to this 
scheme, but the crucial question is, did the Maya have any such scheme, 
