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The preliminary discussion has shown that there is no immediately evident direct numerical relationship between the bird and the fish manu kake. There is an indirect such, though. The bird manu kake is placed at the beginning of a 300 glyph long sequence ending with Gb5-6:

296
Ga3-1 (61) Gb5-4 Gb5-5 Gb5-6 (360)
300

If we search for a similar structure for the fish manu kake we do not have to search for long:

258
Ga4-21 (105) Gb5-10 (364) Gb5-11 Gb5-12
260

104 glyphs before the fish manu kake should probably be thought of as 4 * 26 days. 260 is then equal to 10 * 26 days, together 14 * 26 days. The 364-day long year is not defined by the sun, but by the moonlit nights, because 364 = 13 * 28.

The 60 days arriving before Ga3-1, are probably to be regarded as a 'square' too (like 4 * 26), and 4 * 15 = 60. The 'coinage' being 15 days, we conclude that 360 = 24 * 15. With 24 * 15 corresponding to 14 * 26 it is probable that 20 * 18 corresponds to 13 * 28:

364 4 * 26 = 104 10 * 26 = 260 14 * 26 13 * 28
360 4 * 15 = 60 20 * 15 = 300 24 * 15 18 * 20

A confirmation that we have got the message right is the fact that there are 24 kiore - henua periods in Keiti. Also:

"... the first month of the Moriori year, was named Rongo (Lono). On the first of the new year the Moriori launched a small canoe to Rongo, although they built and used only rude craft for their fishing excursions. The canoe was manned by twelve figures symbolizing the personifications of the twelve months. Sometimes twenty-four figures were placed in the canoe, and Skinner interprets the additional twelve as representing the female counterparts of the months. As an old Maori once remarked. 'Everything has its female counterpart.'

... A curious diversion appears in the month list of the people of Porapora and Moorea in the Society Islands, which sheds light on the custom of the Moriori who sometimes placed 24 figures in the canoe which they dispatched seaward to the god Rongo on new years day. The names of the wives of the months are included, indicating that other Polynesians besides the Chatham Islanders personified the months ..." (Makemson)

Possibly we may have some future use for these 24 half-month names from the Society Islands, and I have listed them here.