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The time structure for the explorers in Manuscript E appears to be 5 weeks at sea followed by a quarter up on land before the last pair of months and their return voyage. 35 + 90 = 125 = 5 * 5 * 5 followed by 59 + 5 = 64 = 8 * 8, and 125 + 64 = 189 = 3 * 3 * 3 weeks.

Other interpretations could be complementary, e.g. how the distance to Te Pou could be 35 + 40 = 75 days. Sirius rose heliacally in June 30 (181) and 181 - 75 = 106. Or if He Maro 1 is counted only once: 181 - 74 (= 1 / 10 of the number of glyphs on the tablet) = 107:

Almuqaddam 10 11 (700) 12 (336)
April 15 16 (471) 17 (107)
Ca1-25 Ca1-26 Ca2-1 (27)
kiore ki te huaga kua moe ki te tai. Te heke
Achernar (23.3)   Benetnash (208.5)
Polaris, Baten Kaitos (26.6), Metallah (26.9), Segin, Mesarthim (27.2), Sheratan (27.4)

March 30 is Gregorian day 89 (= 189 - 100). After adding also 8 weeks we will reach 145 = May 25 (5-25) - a π glyph:

Sheratan 9 10 11
May 25 (145) 26 27
Ca3-14 Ca3-15 Ca3-16
tapamea - tagata hoi hatu ki te ariki kiore i te henua

Counting He Maro 1 twice or not could be comparable to counting day 193 or not.

Ana-muri (the star at the end, Aldebaran) could perhaps correspond to Hiva. From May 28 (148) to November 25 (329) there are 181 days:

Syrma 10 (193) 11 12 13 Az Zubana 1 2
Nov. 25 26 27 28 29 (333) 30
Ca9-21 Ca9-22 Ca9-23 Ca9-24 Ca9-25 Ca9-26
ka mau - i te inoino ka iri ka hua i te inoino te hau tea te inoino kua iri kua puo te inoino
She Low (248.7), Antares (249.1), Marfik, φ Ophiuchi (249.5)  ω Ophiuchi (249.8), σ Herculis (250.3) τ Scorpii (250.7), Han (251.0) ζ Herculis (252.1), η Herculis (252.5) no star listed Wei (254.3)
May 27 28 29 30 (150) 31 June 1
Sheratan 11 12 13 14 Pleione 1 2
no star listed Aldebaran (68.2), Theemin (68.5) no stars listed

Ana-mua (Antares, the front star) would then have a position similar to the time of the arrival of Hotu Matua. The explorers left the island 5 days later, which according to my arguments above could be June 1.

Ka

Ka. Particle of the affirmative imperative, of cardinal numerals, of independent ordinal numerals, and of emphatic exclamation, e.g. ka-maitaki! how nice! Vanaga.

. 1. To light a fire in order to cook in the earth oven (see umu): he-ká i te umu, he-ká i te kai. 2. Figuratively: to fire up the soul. To put oneself in a fury (with manava): ku-ká-á toona manava he has become furious. Vanaga.

1. Of T. 2. Imperative sign; ka oho, ka tere, ka ea, begone!; ka ko iha, a greeting T; ka mou, hush; ka oho, goodbye. 3. Infinitive sign; mea meitaki ka rava, a thing good to take; ka harai kia mea, to accompany. 4. A prefix which forms ordinals from cardinals. 5. The dawning of the day. 6. Different (? ke). Churchill.

Iri

1. To go up; to go in a boat on the sea (the surface of which gives the impression of going up from the coast): he-eke te tagata ki ruga ki te vaka, he-iri ki te Hakakaiga, the men boarded the boat and went up to Hakakainga. 2. Ka-iri ki puku toiri ka toiri. Obscure expression of an ancient curse. Vanaga.

Iri-are, a seaweed. Vanaga.

The half-year from May 28 to November 25 is a comparably dark season on Easter Island when it is easier to observe the stars than in the next half-year. The night sky of November 26 could have Aldebaran as a sign of the end of star-gazing. However, my table does not support such an idea:

Date Heliacal star RA distance Nakshatra star
March 26 (85) Ankaa (5.0) 181.3 Chang Sha (186.3)
April 1 (91) η Andromedae (11.4) 181.5 Mimosa (192.9)
April 17 (107) Polaris (26.6) 181.9 Benetnash (208.5)
April 24 (114) Mira (33.7) 181.1 κ Virginis (214.8)
May 26 (146) Ain (65.7) 181.3 Heart (247.0)
May 28 (148) Aldebaran (68.2) 180.9 Antares (249.1)
July 6 (187) Wezen (107.1) 181.3 Nunki (288.4)
July 26 (206) Avior (126.4) 180.8 Gredi (307.2)
August 21 (233) Regulus (152.7) 181.9 Sadalmelik (334.6)
September 4 (247) Dubhe (166.7) 181.1 Fomalhaut (347.8)

According to Manuscript E the explorers returned to Hiva when their calendar had the date Tangaroa uri 20. Barthel translated Tangaroa uri as October. From October 20 (293) to November 30 (334) there are 41 days.

Number 334 for the last day of November is the only possible explanation I have discovered so far of why the Tahua tablet has 46 * 29 = 1334 glyphs - it could mean 1000 plus the time from January 1 to December 1.

Adjusting with these 41 days we could then look for the departure of the explorers from Hiva 181 days earlier than November 30, i.e. in day 334 - 181 = 153 (June 2). This date corresponds to Ca3-22, when Wei ('the Tail', ε Scorpii) was visible in the night sky:

Pleione 2 3 4 (383) 5 6 (20)
June 1 2 3 4 5 (156)
Ca3-21 Ca3-22 (73) Ca3-23 Ca3-24 (75) Ca3-25
tagata tuu rima ki ruga te maitaki te henua Rei hata ia tagata rogo
  Wei (254.3) Denebakrab (254.7), Grafias (255.4)    

But in Manuscript E the first day of He Maro was when the explorer's canoe touched land again:

... On the twenty-fifth day of the first month ('Vaitu Nui'), Ira and Makoi set sail; on the first day of the month of June ('Maro'), the bow of Ira's canoe touched land again ...

Possibly the beginning of June in the C text (up to and including Gregorian day 156) is describing the time when Sun (and the explorers) were still in Hiva (= north of the equator):

Almuqaddam 10 11 (700) 12 49
April 15 16 (471) 17 (107)
Ca1-25 Ca1-26 Ca2-1 (27)
kiore ki te huaga kua moe ki te tai. Te heke
    Benetnash (208.5)
Achernar (23.3)   Polaris, Baten Kaitos (26.6), Metallah (26.9), Segin, Mesarthim (27.2), Sheratan (27.4)
Pleione 7 (21) 8 9
June 6 (157) 7 8
Ca4-1 (77) Ca4-2 Ca4-3
kua tupu te rakau kua tupu - te kihikihi te hau tea
 λ Eridani (76.7)   Rigel (78.1), Capella (78.4) η Scorpii (259.9)

Possibly the C text has no sea-voyage, which could explain the growth of the 'Tree' from June 6 and forward. The adjustment with 41 days (= October 20 to November 30) would then increase to 35 + 41 = 76 days - which is close to the number of days in the Moon calendar (75 nights if Ca9-3 is included):

An Nathra 9 (101) 10 11 12 64
August 25 (237) 26 27 28
Ca6-17 (157) Ca6-18 Ca6-19 Ca6-20
tagata oho rima - ki te marama koia kua oho ki te marama kua moe
μ Hydrae (157.1) no star listed Shir (158.9) φ Hydrae (160.3)
12 Auva 13 Simak 1 2 3 4 (174)
November 1 2 3 4 5 6 (310)
Ca8-26 (225) Ca8-27 Ca8-28 Ca8-29 Ca9-1 Ca9-2 (230)
- - - - Ohiro Oata
te ahi ki te rima aueue - te ika tupu te ure o te henua erua kiore Te marama erua
Kochab (225.0) Ke Kwan (226.3), Ke Kwan (226.4) Zuben Elakribi (226.8), Nekkar (227.3) 15h (228.3) λ Lupi (228.9) κ Lupi (229.7), ζ Lupi (229.8)
π Lupi (227.9), Zuben Hakrabim (228.3)
3 May 4 5 (125) 6 7 8
2 Alrescha 3 4 (354) 5 6 7
no star listed Acamar (43.6) Menkar (44.7) 3h (45.7) no star listed Botein (46.9)
Algol (45.9), Misam (46.2)
Simak 5 (175) 11 Syrma 4 (187) 11 Az Zubana 3 (199)
November 7 November 19 December 1
Ca9-3 (231) Ca9-15 (243) Ca9-27 (255)
koia kua oho i te mauga pu hia etoru gagata hakaariki kia raua
Princeps (230.6), Zuben Elschemali (230.8), μ Lupi (231.3) 16h (243.5) Denebakrab (254.7), ι Ophiuchi (255.3), Grafias (255.4)
ι Cor. Borealis (242.5), ξ Scorpii (242.7), Acrab, Jabhat al Akrab (243.3), θ Lupi, Rutilicus (243.5)
May 9 (129) May 21 (141) June 2 (153)
Alresha 8 (358) Sheratan 5 Pleione 3 (17)
no star listed 4h (60.9) no star listed
no star listed