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The page in my 'preliminary reading' continues as follows directly after Worthen's description:

The nakshatra method - by which it was possible to determine where the Sun was by looking in the night at the right ascension stars determined by the face of the Full Moon - could easily have been used by people on Easter Island. In my supporting dates I have added 183 in order to move from a nakshatra day number to its corresponding heliacal day number (or the other way around).

For instance was the heliacal star position of St John's Eve (June 24) exactly half way around the year compared to the night sky of Christmas Eve, when Tejat Posterior was vertically aligned with the Full Moon. 175 (June 24) + 183 = 358 (Christmas Eve). 358 + 183 - 366 = 175. To make my method work properly we have to subtract 366 (= 2 * 183) instead of 365¼. Though had I not found evidence in the rongorongo texts for a cycle measuring 366 I would not have dared to suggest this simple and practical method.

In the night sky of June 24 the stars in Sagittarius (the Archer) were close to the Full Moon, i.e. they would rise with the Sun around Christmas. The bow and quiver (cfr at Castor and Pollux) is precisely what an Archer needs, but he was absent and instead present at the opposite side of the year:

GEMINI:
7 Punarvasu α and β Gemini Bow and quiver  113 = 88 + 25
the two restorers of goods Castor and Pollux July 12 (193)
SAGITTARIUS:
20 Purva Ashadha δ and ε Sagittarii Elephant tusk, fan, winnowing basket 278 = 260 + 18
first of the ashādhā (the invincible one, the name of a constellation) Kaus Dec 24 (358)

Kaus Medius is δ Sagittarii at the hand of the Archer and Kaus Australis is ε further south on his serpentine bow:

When using the nakshatra method it is useful to have associations across the sky roof. Lucia, for instance, is celebrated in the darkest of times and opposite to the season when the Sun is very high up (in the northern sky). In December 13 and close to the Full Moon were the bright and easy recognizable 3 stars in the Belt of Orion - Mintaka (δ), Alnilam (ε), and Alnitak (ζ):

Ga1-17 Ga1-18 Ga1-19 Ga1-20 Ga1-21
ψ Orionis (81.1), Nihal (81.7) MINTAKA, υ Orionis (82.4), χ Aurigae (82.5), ε Columbae (82.6) Al Hak'ah-3 / Mrigashīrsha-5 / Turtle-20 Three Stars-21 / ANA-IVA (7) ο Aurigae (85.8), γ Leporis (85.9)

Yang Mun

Arneb, Crab Nebula (83.0, φ¹ Orionis (83.1), HEKA, Orion Nebula (83.2), φ² Orionis (83.6), ALNILAM (83.7) Heavenly Gate, ν Columbae (84.0), ω Orionis (84.2),  ALNITAK, PHAKT (Phaet) (84.7)
June 10 11 12 13 14 (165)
ºJune 6 (*77) 7 8 9 (160) 10 (*81)
'May 14 (*54) 15 16 17 (137) 18 (*58)
'Vaitu Potu 14 15 16 (136) 17 18
"April 30 (*40) "May 1 2 (122 = 366 / 3) 3 (*43) 4 (124 + 366 = 490)
Lesath, δ Arae (264.7), Choo (264.9)  Alwaid, Maasym (265.1), Shaula (265.3), Kuma (265.6), σ Arae (265.9)

Hamal

Ras Alhague (266.1), Sargas (266.3), μ Ophiuchi, π Arae (266.5), Nan Hae (266.6),  ι Herculis (266.7) λ Arae (267.1), Girtab, ο Serpentis (267.6) Kelb Alrai, μ Arae (268.1), Kew Ho (268.6), η Pavonis (268.7), Apollyon (268.9)
December 10 11 (*265 = *82 + 183) 12 LUCIA 14 (348)
ºDec 6 (*260) 7 8 9 10 (344)
'November 13 14 (318) 15 16 17 (321)
 'Ko Ruti 13 14 15 16 (*240) 17
"October 30 31 "Nov 1 (*225) 2 3 (307)

Though the Chinese appear to have referred only to Alnitak in their 21st station Three Stars. More to the point, however: counting 5 days forward from Alnitak was the vertical line which at 6h (in our time) would be easy to find by looking from δ Aurigae (Praja-pāti), down to Menkalinan (β) and Mahashim (θ):

The blue descending 'river valley' of the Milky Way is today overcrossed at 6h by the blue ecliptic 'road' of the Sun (and the rest of the planets). In rongorongo times it would not have been very much different. Praja-pāti at the top of the 6h (midsummer) line means 'The Lord of Created Beings'.

Ga1-22 Ga1-23 Ga1-24 Ga1-25 Ga1-26
 μ Columbae, Saiph (86.5), τ Aurigae, ζ Leporis (86.6) υ Aurigae (87.1), ν Aurigae (87.2), Wezn, δ Leporis (87.7), Tze (87.9) Ardra-6 / ANA-VARU (8) η Leporis (89.0), PRAJA-PĀTI, MENKALINAN, MAHASTHIM, and γ Columbae (89.3), π Aurigae (89.4), η Columbae (89.7) μ Orionis (90.3), χ² Orionis (90.5)
χ¹ Orionis, ξ Aurigae (88.1), BETELGEUZE (88.3), ξ Columbae (88.5), σ Columbae (88.7)

Zuben Elgenubi

June 15 16 17 (168) 18 19
ºJune 11 12 13 (164) 14 15
'May 19 20 21 22 23 (*63)
'Vaitu Potu 19 20 (140) 21 22 23
"May 5 6 (126) 7 8 9 (*49)
Muliphen (269.0), Basanismus (269.5), Pherkard (269.9) Ptolemy Cluster (270.5) Rukbalgethi Genubi (271.1), ξ Herculis (271.5), Etamin, ν Herculis (271.7), ν Ophiuchi (271.8) ζ Serpentis (272.4), τ Ophiuchi (272.9) Winnowing Basket-7
18h (273.4)
NASH (273.7), θ Arae (273.8)
December 15 16 (350) 17 18 19 (*273)
ºDecember 11 12 (*266) LUCIA 14 (348) 15
'November 18 19 20 21 22 (*246)
 'Ko Ruti 18 19 20 (324) 21 22
"November 4 5 (*229) 6 (310) 7 8

There were thus 3 stars more or less horizontally oriented in the Belt of Orion and 3 stars precisely vertically oriented in Auriga, which made it possible to allude to the fact that once upon a time the 'horizontal' ecliptic road must have gone right through the 3 stars in the center of Orion at the sky equator (0º).