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In Manuscript E Ira gave order to Makoi to make a cycle around the island in a single day, giving names as he went:

"Ira said the following to Makoi: 'You are the one who shall stay here. We, on the other hand, have to turn around.'

Makoi replied, 'All right with me!'

Then Ira continued to speak to Makoi: 'Tomorrow, when it grows light, set out and name the places beginning with Apina.'

Makoi replied, 'How shall I give the names?'

Again Ira spoke. 'In Hiva are the names that are to be taken to name (the places of the new land).' ..." (Manuscript E p. 37)

This order was given by Ira in day number 4 at Pu Pakakina A Ira, i.e. in day 5 if counting also day zero when the explorers arrived there:

Ahu Akapu A Hau Maka Te Pito O Te Kainga A Hau Maka   Pu Pakakina A Ira  ®
day zero day 1 day 2
Ga4-11 Ga4-12 Ga4-13 Ga4-14 Ga4-15 Ga4-16 (99)
Shir (158.9) p Carinae (159.3) φ Hydrae (160.3) no star listed (161) Vathorz Posterior (162.1), Peregrini, η Carinae (162.6) ν Hydrae (163.1)
Hora Iti 26 27 28 (240) Hora Iti 29 30 (242) 31 (*163)
ºAug 22 23 24 (236) ºAug 25 26 27 (*159)
'July 30 (*131) 31 'August 1 (213) 'August 2 3 (*135)  4 (216)
"July 16 17 (*118) 18 (199) "July 19 (200) 20 21 (*122)
α/91 Lac. (341.1), Homan, β Piscis Austrini (341.2), ν Tucanae (341.5), υ Aquarii (341.9) η Aquarii (342.1), Situla (342.7) ε Piscis Austrini (343.5), ο Pegasi (343.8) Matar (344.2) Leap night λ Pegasi (345.0), ξ Pegasi (345.1), τ Aquarii (345.7), μ Pegasi (345.9)
Tehetu'upú 25 26 (422) 27 (58 = 2 * 29) Tehetu'upú 28 29 (60) Tarahao 1 (*345)
426 - 366 = 60
ºFebr 21 22 (418) 23 (54 = 2 * 27) ºFebr 24 25 (56) ºFebruary 27 (*341)
422 - 365 = 57
'Jan 29 (*314) 30 31 (396) 'Febr 1 2 (33)  3 (399)
"Jan 15 (*300) 16 17 "Jan 18 (383) 19 (384) 20
¬ Pu Pakakina A Ira  ®
day 3 day 4 (order to Makoi) day 5 (cycle of Makoi)
Ga4-17 (100) Ga4-18 Ga4-19
no star listed (164)

Altair

Wings-27 ANA-TIPU
ALKES (165.6) Merak (166.2), DUBHE (166.7)
Hora Nui 1 (244) 2 (*165) 3
ºAugust 28 (240) 29 (*161) 30
'August 5 (*137) 6 (218) 7
"July 22 (22 / 7) 23 (204) 24 (*125)
ι Cephei (346.0), λ Aquarii, γ Piscis Austrini, σ Pegasi (346.5) Scheat Aquarii (347.0), ρ Pegasi (347.2), δ Piscis Austrini (347.4), Fomalhaut (347.8) Fum al Samakah (348.3), ο Andromedae (348.9)
 Tarahao 2 3 (428 = 62 + 366) 4 (429 = *348 + 81)
ºFebruary 28 29 (424 = 59 + 365) ºMarch 1 (425 = *344 + 81)
'February 4 (400) 5 (401 = *320 + 81) 6 (*321 = *348 - 27)
"January 21 (386) 22 (387 = *306 + 81) 23 (*307 = *348 - 41)
¬ Pu Pakakina A Ira  ®
day 6 day 7
Ga4-20 Ga4-21 (104)
11h (167.4)  Al Sharas (168.6)
χ¹ Hydrae (167.1), χ² Hydrae (167.3)
Hora Nui 4 (*167) 5 (248)
ºAugust 31 (*163) ºSeptember 1 (244)
'August 8 (220) 9 (*141)
"July 25 (206) 26 (*127)
Al Fargh al Mukdim-24 / Purva Bhādrapadā-26 / House-13 23h (350.0)
Scheat Pegasi, π Piscis Austrini (349.3), MARKAB PEGASI (349.5) π Cephei (350.6)
Tarahao 5 (64) 6 (*350)
ºMarch 2 (61 = 64 - 3) 3 (*346)
'February 7 (403) 8 (*323 = *350 - 27)
"January 24 (389) 25 (*309 = *350 - 41)

However, my description above does not fit with how the explorers went on from the Pakakina 'cave' - where Makoi got his instructions - to the yam plantation, which took place in Hora Nui 1.

From Hora Iti 29 (when the explorers arrived at Pu Pakakina A Ira) to Hora Nui 1 (when they left for the yam plantation) there are only 3 days - not a 'month'. Unless this 'month' was outside the ordinary calendar - as if invisible ('down in a cave').

Yam plantation ®
Ga4-17 (100) Ga4-18 Ga4-19
no star listed (164)

Altair

Wings-27 ANA-TIPU
ALKES (165.6) Merak (166.2), DUBHE (166.7)
Hora Nui 1 (244) 2 (*165) 3
ºAugust 28 (240) 29 (*161) 30
'August 5 (*137) 6 (218) 7
"July 22 (22 / 7) 23 (204) 24 (*125)
ι Cephei (346.0), λ Aquarii, γ Piscis Austrini, σ Pegasi (346.5) Scheat Aquarii (347.0), ρ Pegasi (347.2), δ Piscis Austrini (347.4), Fomalhaut (347.8) Fum al Samakah (348.3), ο Andromedae (348.9)
 Tarahao 2 3 (428 = 62 + 366) 4 (429 = *348 + 81)
ºFebruary 28 29 (424 = 59 + 365) ºMarch 1 (425 = *344 + 81)
'February 4 (400) 5 (401 = *320 + 81) 6 (*321 = *348 - 27)
"January 21 (386) 22 (387 = *306 + 81) 23 (*307 = *348 - 41)
¬ Yam plantation ®
Ga4-20 Ga4-21 (104)
11h (167.4)  Al Sharas (168.6)
χ¹ Hydrae (167.1), χ² Hydrae (167.3)
Hora Nui 4 (*167) 5 (248)
ºAugust 31 (*163) ºSeptember 1 (244)
'August 8 (220) 9 (*141)
"July 25 (206) 26 (*127)
Al Fargh al Mukdim-24 / Purva Bhādrapadā-26 / House-13 23h (350.0)
Scheat Pegasi, π Piscis Austrini (349.3), MARKAB PEGASI (349.5) π Cephei (350.6)
Tarahao 5 (64) 6 (*350)
ºMarch 2 (61 = 64 - 3) 3 (*346)
'February 7 (403) 8 (*323 = *350 - 27)
"January 24 (389) 25 (*309 = *350 - 41)

They stayed 'one month' also at the yam plantation, before their king arrived in Tagaroa Uri 15, i.e. they were there for a duration longer than an ordinary month:

He Anakena Hora iti Hora nui Tagaroa uri  Ko Ruti Ko Koró
'July' 'August' 'September' 'October' 'November' 'December'
Tua haro  Tehetu'upú Tarahao Vaitu nui Vaitu potu He Maro
'January' 'February' 'March' 'April' 'May' 'June'

September has 30 days and 'one month' here becomes 30 + 15 = 45 days. Together with 3 calendar days at Pu Pakakina it means 48 (twice 24) days beyond Te Pito O Te Kainga A Hau Maka.

Kaiga

1. Action of eating; meal; nourishment (katiga was the ancient word). 2. Ground; country; island. 3. Womb, uterus (also matakao). Vanaga.

Land, country, place, region, estate, soil; noho kaiga, indigenous, a native of; mau kaiga, proprietor; hooa te kaiga, to buy land. T Pau.: kaiga, the soil. Mgv.: kaiga, land, country, property, the earth, the world. Mq.: kaina, kaika, residence, property, patrimony. Ta.: aiá, place of residence. Churchill.

Pu Pakakina 3 48
Yam plantation 45
Paka

1. Dry; to become dry (of things); pakapaka, to dry out. Te paka is also the name of the moss-covered areas, between the small lakes of volcano Rano Kau, through which one can pass without getting one's feet wet. 2. To go, to depart; he-paka-mai, to come; he-oho, he-paka, they go away. 3. To become calm (of the sea): ku-paka-á te tai. Pakahera, skull, shell, cranium; pakahera puoko tagata, human skull; pakahera pikea, shell of crab or crayfish. Gutu pakapaka, scabbed lips. Hau paka, fibres of the hauhau tree, which were first soaked in water, then dried to produce a strong thread. Moa gao verapaka, chicken with bald neck. Ariki Paka, certain collateral descendents of Hotu Matu'a, who exercised religious functions. Vanaga.

1. Crust, scab, scurf; paka rerere, cancer; pakapaka, crust, scabby. 2. Calm, still. 3. Intensive; vera paka, scorching hot; marego paka, bald; nunu paka, thin. 4. To arrive, to come. 5. To be eager. 6. To absorb. 7. Shin T. Pakahera, calabash, shell, jug. Pakahia, to clot, curdle, coagulate. Pakapaka, dry, arid, scorching hot, cooked too much, a desert, to fade away, to roast, a cake, active; toto pakapaka, coagulated blood; hakapakapaka, to dry, to broil, to toast. Pakahera pikea, shell of crab or crayfish. Churchill.

Poko

1. Fragrant; to smell, to give off a smell: he-poko te eo, it gives off a pleasant smell. 2. To hunt, to catch with a trap, to snare. He-kî e Tori: maaku-á e-ea ki te manu, e-poko i te po i ruga i te opata. Tori said: I shall go and catch birds at night, up on the cliff. 3. Thunder (also hatutiri). 4. (Also: pokopoko.) Hollow, hole, depression, any deep, concave object; to leave in a hole, in a depression. Pokoga, chasm; summit. Pokohata, female rat: kio'e pokohata. Pokopoko, woman bent under the weight of her years: vî'e pokopoko. Vanaga.

1. Sound of the sea; tai poko, breakers. Pokopoko, to slap water. Mgv.: pokokina, resonant, clear-toned. Mq.: poko, to slap the water in imitation of drumming; pokokina, sound of water. 2. Rut, beaten path. P Pau.: poko, hollow; pokopoko, concave, to excavate. Mgv.: poko, to dig, to excavate, to hollow out. Mq.: pokoko, to crack open; pokona, to hollow out, to excavate. Ta.: poópoó, hollow, deep. 3. Infernal; pokoga, hell, infernal cave; topa ki te pokoga, to damn (lit: to go down to hell.) Mq.: pokona, cavity, hole. Churchill.

Pokopoko: 1. Womb. PS Sa.: po'opo'o, clitoris. Mq.: pokopoko, pudendum muliebre. 2. Pokopoko vae, footprints. 3. Concave, deep, ditch, mysterious; pokopoko ihu, nostril (Ta.: poópoó ihu); pokopoko ke, fathomless; pokopoko taheta, concave. Hakapokopoko, to deepen. Chuchill.

Pu Pakakina A Ira could to refer to the dry (paka) 'crater' down into which the thirsty Raven looked in vain. But he could hear its sound (poko kina).