498 BUREAU OF AMERICAN ETHNOLOGY [bull. 28 



Not until long after all 1 have thus far explained became clear to 

 me did I recognize that the Mayas had also very naturally turned 

 their attention to the period of the moon's revolution. The wonder- 

 ful series on pages 51 to 58 of the Dresden codex, already mentioned, 

 only arrives at the number 11,960; or, when we take into consideration 

 that there are three day signs with every number, the highest number 

 there is in reality only 11,958. This number, however, is arrived at 

 because periods of 177, 148, and 178 days follow each other strangely 

 mixed ; indeed, the 177 occurs fifty-four times, the 148 nine times, the 

 178 six times. But now 



177=3x29-f3x30 

 148=2X29+3X30 

 178=3x29+3x30+1 



The entire series, therefore, is constructed thus : 



.54X177=162X29+102X30 = 9,5.58 

 9X148= 18X29+ 27X30 = 1,332 

 0X178= 18X29+ 18x30+6= 1,008 



198 X 29 + 207 X 30 + 6 = 1 1 .9.58 



There is, I think, nothing more natural here than to see alternate 

 months of 29 and 30 days, just as they alternated with the Greeks. 



The 198 months of the one kind and the 207 of the other together 

 make 405 months. But if we divide 11,958 by this 405, we find the 

 length of the moon's revolution as observed by the Mayas to be 29.526 

 days. 



But the actual synodical revolution of the moon is 29.53 days. The 

 Mayas, therefore, made it too short by only four-thousandths of a 

 day; surely an amazing achievement. If they had employed merely 

 the period of 177 clays, the month would only have amounted to 29.5 

 days; by the addition of the nine periods of 148 days, only to 29.512. 

 The six j^eriods of 178 days, containing the intercalary days, were 

 thus quite essential in order to reach this singularly accurate result. 



Thus we see combined on pages 46 to 50 of the Dresden codex the 

 revolutions of the sun and Venus and on pages 51 to 58 those of the 

 moon and mercury, that is, the revolutions of the four heavenly bodies 

 most conspicuous in their movements combined in pairs; on the one 

 hand, the two slower ones, on the other, the two of swifter motion, but 

 of comparatively less brilliancy. Page 59 may refer to the revolution 

 of Mars alone, while page 60, the final page of this front side of Codex 

 Vaticanus B, seems lastly, but in a way as yet unexplained, to con- 

 dense, as it Avere, the entire contents of this section. Perhaps above 

 we here see the contest between these heavenly bodies, and below the 

 victorv of the one over the other. 



