464 BUREAU OF AMERICAN ETHNOLOGY [bull. 28 



to have seen that the period of 11,1)00 days could not be made to 

 coincide with a multiple of lunar revolutions. With 405 lunar revo- 

 lutions they obtained only 11,958 days, and this number is actually- 

 the highest of the series on the second half of page 58. 



In order to make the series of 11,958 days applicable to one of 

 11,960 days, they employed a most ingenious device. As the starting 

 point for each term of the series they took not a single day, but 

 three consecutive daj^s: For the first term, XI 4, XII 5, XIII 6; 

 for the last, IX 2, X 3, XI 4. So the first day of the first (erm was 

 actually 11,958 days distant from the first day of the last term, but 

 the first day of the first term was distant 11,960 days from the third 

 day of the last term. 



At all events, the whole period of 11,958 days was first divided into 

 three equal periods of 3,980 days each. In order to divide these 

 smaller periods still further the term of 177 days was used, as far as 

 this was practicable ; but 177 is the half of a lunar j^ear of 854 days, 

 which is composed of months of 30 days and months of 29 days; 

 that is, to each month, in round numbers, are allowed 29.5 days. 



177 is, therefore, equal to 3X29+3X30; but the average of 29.5 

 days for the duration of a lunar revolution is a little too small. In 

 order to raise it to the most exact value possible, in certain places of 

 the series of two other numbers were introduced, viz: 148=2X29-1- 

 3X30 and 178=2X29+4X30; 148 is equivalent to 5 months of 

 29.6 days and 178 to 6 months of 29.060+ days. Now, we must see 

 in what proportion these 148 and 178 days were distributed among 

 the periods of 177. 



First we see that the term of 3,980 days, that is, a third of the whole 

 period, Avas divided into three sections of 1,742, 1,034, and 1,210 days 

 in the following manner : 



1,742=8X1774- 148+ 178 

 1,034= 4X177+ 148+ 178 

 1,210= 6X177+ 148 



3,986=18X177+3. 148+2. 178 



This equals 135 months of 29.520 days each. How did the Maya 

 express this fraction ? Perhaps it will be shown in the future that in 

 accordance with their vigesimal system, they approximately denoted 



it thus: 29 + ^+4^-0 + 8^. 



The whole period of 11,958 days was therefore divided in the fol- 

 lowing way: 



3X 1,742=24X 177+3 X 148+3X 178 

 3X1,034=12X177+3X148+3X178 

 3X1,210=18X177+3X148 



3X3,986=54X177+9X148+6X178 



