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Maori of Xew Zealand who likewise reckoned by decades, thirty- 

 six to the year,^*^ were doubtless obliged to count only nine days 

 in their third and last decade, when the alternating sequence of 

 29 and 30 day months gave them 29 days in their lunar month. 

 All this procedure is especially significant since it illustrates the 

 expedients which have been used by primitive peoples whose 

 months and weeks are both strictly lunar, to overcome the diffi- 

 culty presented by the fact that the length of a lunation is an odd 

 number, not yielding to subdivision into exactly equal parts. It 

 is a mark of late development w'hen the divisions of the month, as 

 the Roman nundinal period, and the Jewish seven-day week, run 

 continuously through the year. 



Bearing in mind this evidence yielded by contemporary or 

 almost contemporary races belonging to the lower culture, we 

 may approach the more difficult problem involved in the consid- 

 eration of the cycles used among historical peoples. We begin 

 with the division into decades employed by the ancient Peruvians, 

 the Greeks, and the Egyptians.^'^ It seems reasonable to regard 

 such lo-day cycles, like those of the primitive peoples just men- 

 tioned, as originating in the desire to find a convenient division 

 of the lunar month, a division perhaps suggested by the increase, 

 culmination, and decrease of the moon, as shown by the waxing 

 crescent, the more or less full disk, and the waning crescent. If 

 it be held that the arrangement by decades was rather suggested 

 by denary arithmetic, we may at least feel confident that it would 

 not have been chosen except for its close approximation to the 

 length of the lunar month. As a matter of fact such a sequence 

 represents the true course of the lunation in days more correctly 



^"Taylor, Te Ika a Maui, 177; cf. Waitz-Gerland, op. cit., vi. 72. In 

 some of the Caroline Islands we find, not decades, but a curious three-fold 

 division, evidently associated with the moon. Thus at Yap the 30-day 

 month is divided into pul = new moon (1-13 days), botrau = iu\\ moon 

 (14-23 days), /ir;no;-=: darkness (23-30 days). See Christian, op. c;7., 394. 



^' The Chinese have no formal division of the month, but it is a common 

 practice among them to speak of anything as happening in the first, middle, 

 or third (last) decade (Hastings, op. cit., iii. 83). A similar arrangement 

 prevailed in Japan (ibid., 115). 



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