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7. To find the Nilometer's k star we have to go back in time to the end of the 21st hour, to the region of stars defined by the left (female) hand (of the male Aquarius), to μ and the preceding ε, which determin the 10th Chinese mansion, the Girl:

... ε, 3.4, was Al Bali, the brightest one of the 21st manzil, Al Sa'd al Bula', the Good Fortune of the Swallower, which included μ and ν; these last also known as Al Buläān in the dual. Kazwini said that this strange title came from the fact that the two outside stars were more open than α and β of Capricorn, so that they seemed to swallow, or absorb, the light of the other!

These 'open' stars presumably allude to the idea of the open hand of Mother Earth at the horizon in the west, waiting to receive the head of descending Sun, see at Albali:

... The horizon in the west is where Sun disappears in late afternoon. In the morning when Sun reappears in the east he is like a newborn baby, at noon he is standing tall, and in the afternoon he shrinks - he is growing old. His disappearance in the west was called 'the biting of the sun' (Chikin) by the Maya:

  

23
Ga8-23 (*290) Gb1-21 (*314) Gb1-22
ι Lyrae (289.5), Al Baldah (290.1) 24.2 Yue (314.3) Albali (314.8)
'January 5 (370) 23 'January 29 (394) '30
Shaula 3 (234) Al Baldaah 1 (258) 2
Swallowing the Eye:
Gb1-23 Gb1-24 Gb1-25 Gb1-26 (256) Gb2-1 (*320)
Baten Algiedi (315.8), μ Aquarii (316.0)      Armus (319.0), Dorsum (319.3)  χ Capricorni (320.0), ν Aquarii (320.3)
'January 31 'February 1 '2 '3 '21h (319.6)
Al Baldaah 3 4 5 6 7 (264)
21
Gb2-23 Gb2-24 (280) Gb2-25 Gb2-26
21.6 υ Aquarii (341.9), η Aquarii (342.1) Situla (342.7)    
21 'February 26 (422) 27 '28 'March 1
21 Saad Balaa 1 2 3 (288) 4
Gb2-27 (*346) Gb2-28 Gb2-29 Gb2-30
τ Aquarii (345.7) λ Aquarii (346.5), Scheat (347.0)    
'March 2 '3 '4 (63) '5
5 (*426) 6 7 (292) 8

The stars determining the 'Swallowing' (corresponding to the Chinese lunar mansion Girl) are evidently positioned immediately beyond 314, where the Ox is 'decapitated' (yue means battle-axe):

Mansion number Name Star
8 (Southern) Dipper φ Sagittarii
9 Ox β Capricorni
10 Girl ε Aquarii
11 Emptiness β Aquarii
12 Rooftop α Aquarii
13 Encampment α Pegasi
14 Wall γ Pegasi

The Ox mansion refers to β Capricorni (Dabíh) at the base of the left horn of the Goat:

Gb1-13 Gb1-14 (*307) Gb1-15 Gb1-16 Gb1-17
ξ Capricorni (305.8) Gredi (307.2) σ Capricorni (307.5), Alshat (307.9), Dabih (308.0)   Okul (309.6), Bos (309.9), ο Capricorni (310.2)
'January 21 '22 '23 (388) '24 '25
Al Naam 6 (250) 7 8 9 10
Gb1-18 (248) Gb1-19 Gb1-20
    τ Capricorni (312.6), υ Capricorni (312.8)
'Janurary 26 '27 (392) '28
11 12 Al Naam 13

"Dabih ... comes from the Arabic al-dhābi, meaning 'the butcher'." (Wikipedia)