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whether five or seven days were to be reckoned from the Calends 

 to the day of the first quarter.-^ In Babylonia, where the 

 month began in theory on the day when the new moon was 

 visible, and where the lunar movements were also followed with 

 great attention for astrological purposes, the royal astronomers 

 sent regular reports to the king as to the appearance or non- 

 appearance of the new moon.-* 



13. LUNAR WEEKS 



The lunar month which in rude communities provides a satis- 

 factory chronological unit does not meet the needs of an ad- 

 vancing society. Shorter periods become desirable, both for the 

 regulation of religious festivals and for the ordering of markets 

 and business engagements. In some instances brief cycles of 

 3 and 4 days may have been arbitrarily determined without ref- 

 erence to the moon. In west Africa, however, we frequently 

 find the month divided into seven weeks of four days each 

 (supra), a circumstance indicating that the week is now regarded 

 as a division of the lunation. An ii-day period which, indeed, 

 would make an unsatisfactory division of the lunation, appears 

 to be unknown. A vulgar cycle of 12 days is still used in China, 

 the number twelve having been suggested, probably, by the num- 

 ber of months in the year."^ A sim.ilar explanation may hold 

 good for the 13-day period of the Mexicans, who appear to have 



^Macrobius, Saturnalia, i. IS, 9', Varro, De lingua Latina, 6, 27; 

 Mommsen, Romische Chronologie, 16 sq. 



"R. C. Thompson, Reports of the Magicians and Astronomers of 

 Nineveh and Babylon, London, igoo, ii. p. xviii sq. Cf. Ginzel, in Klio, 

 1901, i. 193, who refers to the observations made of the length of time 

 during which the new moon was visible in the evening on the first of the 

 month. 



^' The cycle has some connection with astrology and is doubtless of late 

 development. See Hastings, Encyclopaedia of Religion and Ethics, iii. 84. 

 counted thirteen months to the lunar year.^® Since new moon 



-* J. de Acosta, Natural and Moral History of the Indies, edited by C. R. 

 Markham, London, 1880, ii. 393, 396; H. H. Bancroft, Native Races of the 

 Pacific Coast, ii. 515; Payne, op. cit., ii. 310, 323 sqq. Mr. Payne however, 

 suggests as a factor leading to the choice of the number 13, the recognition 



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