108 MEXICO AND CENTRAL AMERICA 
to have been arbitrarily changed to a notational one of 
twenty days. Now the exact duration of a lunar revo- 
lution is 29 days, 12 hours, 44 minutes, 2.87 seconds. If 
the customary period of 29.5 days is taken for con- 
venience there is an error of about two full days in five 
years. Such an error was too great to pass the Mayan 
calendar makers. On pages 51 to 58 of the Dresden 
Fig. 43. Representations of the Moon: a, sun and moon 
hieroglyphs; 6, moon from a ‘‘celestial band’; c, moon hiero- 
glyph used for 20 in codices. 
Codex their solution is recorded unmistakably. A sue- 
cession of 405 lunar revolutions, or nearly 33 years is 
calculated by the addition of groups of five and six revo- 
lutions, the former given as 148 days and the latter as 
either 177 or 178 days. This method of calculation 
may have been a device to carry fractions or it may have 
been based upon ecliptic data. ‘The steps of the calcu- 
lations are put down in a sort of double entry, first by 
numbers, second by named days. ‘The numbers add up 
to 11,958 while the total difference between the named 
days is 11,959. The purpose appears to have been to 
approximate 11,960. This last number of days con- 
tains the tonalamatl an even number of times and 
would thus form a re-entering series since it would al- 
ways begin with the same day. Now it is a remarkable 
fact that the total obtained by modern astronomers for 
405 lunar revolutions is 11,959.888 days or only 0.112 of 
a day less than 11,960. Therefore, this re-entering series 
of the Mayan astronomers can be used nine times be- 
