328 BUREAU OF AMEEICAN ETHNOLOGY \mnA.. 28 



l^eriod of revolution of these bodies with the solar year of 365 

 days and Avith the period of 20X13 days, the true basis of the 

 system. The apparent period of revolution of Venus may be set 

 down with tolerable accuracy as 584 days. Five such revolutions 

 give us the figures 2,920, or 8 solar years of 365 days. This precise 

 number is jDlainly the basis of the computations on certain pages 

 of the Dresden manuscript. But 65 such periods give us the number 

 37,960, that is, double the period of 52 years, wdiich, as T said, is the 

 direct result of the application of the designation of days in accord- 

 ance Avith the system of the 20 characters and the 13 digits to the 

 solar year of 365 days. In like manner, as Forstemann has also 

 proved, the apparent revolution of Mercury around the sun, which 

 is completed in 115 days, seems to be brought into connection-with the 

 period of 20X13 days; for 104 of these revolutions produce the 

 number 11,960, which is as well forty-six times the period of 20X13 

 days. And this number clearly forms the basis of other pages in the 

 Dresden manuscript." 



Now, while this elaboration of the system is shown with tolerable 

 clearness by the extensive computations continued throughout entire 

 series of pages, we are still in doubt in regard to the cardinal ques- 

 tion, whether the Mayas and jNlexicans were capable of harmoniz- 

 ing this system, in which none but entire days are reckoned, with the 

 actual duration of the year, Avhich includes a fraction of a day; in 

 other words, Avhether they were acquainted Avith intercalation, and 

 how they managed it. It is evident that the solar year of 365 days 

 necess'arily caused a displacement of the beginning of the year, Avhich 

 must needs become very apparent Avithin a comparative!}^ short space 

 of time.' That this circumstance Avas not taken into account by the 

 Mexicans, at least, Avithin short periods of time, is proA^ed by the 

 displacement of the beginning of the year, Avhich, as I haA"e shown, 

 actually occurred in the space from the conquest of the city of Mexico 

 to the time AA'hen Father Sahagun Avrote his history.'' The Mayas 

 were more S3'stematic than the Mexicans in regard to chronologic 

 dates, since they had in the first place longer periods, somewhat over 

 256 years, AA'ithin Avhich they could mark off 13 divisions Avith more 

 precision. And furthermore, it seems to folloAV from botli manu- 

 scripts and stone monuments that the Mayas possessed a normal date 

 to Avhich all present, past, and future events Avere referred, the days 

 being simply reckoned from or up to this. This normal date, Avhich 

 Forstemann has also taught us to recognize, is 4 Ahau 8 Cumku, 

 that is, the day designated by the figure 4 and the character Ahau, 

 which was the eighth day of the month Cumku. Wherever in the 

 manuscripts the dates of day and month are accurately indicated, the 



" Forstemann, Dii? Zeitpei'iodea der Mayas, Globus, v. (53, n. 2. 



"Die Bilderlinndscliriften Alex, von TTnmboldt. in der Koni^e Bibliothek zii Berlin. 



