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3. I'm sorry, I made a mistake, it is not easy to think straight when dealing with cyclical time. Sun is rising in the east and descending in the west. Likewise are the stars emerging in the east and disappearing in the west. This is the diurnal cycle at work.
 
Discussing dates involves the cycle of the year. I have seen, as winter advances, how Orion gradually is moving farther and farther towards the horizon in the west. It is the same direction as in the diurnal cycle, although much slower.
 
When I can see the stars in the night I know Sun has to be on the other side of the Earth, moving back from west to east. The same must be true for Orion and the other stars when they have descended in the west.
 
Therefore, when Orion is close to Sun, impossible to see because the constellation is rising heliacally, it will continue to be invisible for a long time afterwards - it will gradually advance across the sky roof from east to west during the daytime. After I have seen Orion early in the morning, before Sun makes observations impossible, Orion will during the following days - given observations at the same time - be gradually higher up in the sky, steadily advancing, not far from Sun, towards the horizon in the west.
 
My stumbling block was right ascension, which is not increasing towards the west but towards the east. Sun is advancing among the zodiacal constellations towards the east, not moving ahead towards the west but moving withershins. And the arrow of time is always moving in the same direction:
 
Menkar
culmination at midnight heliacal rising culmination at midnight
135 0 230
365
Alcyone
culmination at midnight heliacal rising culmination at midnight
137 0 228
365
Gb8-22 (464) Gb8-23 Gb8-24 Gb8-25
Atiks, Rana (55.1), Celaeno, Electra, Taygeta (55.3) Maia, Asterope, Merope (55.6), Alcyone (56.1), Pleione, Atlas (56.3)   Menkhib (57.6)
'May 15 '16 (136) '17 '18
14 Alrescha 15 (365) Sheratan 1 2

At my suggested precessional time for the rongorongo texts Menkar happened to culminate in the night of the northern winter solstice and Alcyone 10 days later in 'December 31:

  Allen's days of culmination   Days of heliacal rising  
Menkar 'December 21 (355) 134

'May 5 (125)

229
Alcyone 'December 31 (365) 136

'May 17 (137)

227
  365

My table was not so misleading after all.

When the Arabic manzil calendar has 136 days before its beginning in May 17 we could guess it was because the heliacal rising of Alcyone was thought to be a sign of the new year. But presumably it was because in May 17 the practically simultaneous Atlas would be rising the sky heliacally:

(Copied from Ian Ridpath's internet site.)