Ga2-4	Ga2-5 (*99)	Ga2-6	Ga2-7
	ν Puppis (99.2), ψ3 Aurigae (99.4)	ψ2 Aurigae (99.5)	ψ4 Aurigae (100.5), Mebsuta (100.7),  Sirius (101.2), ψ5 Aurigae (101.4), Cor Serpentis
'June 27	'28	'29 (180)	'30

Ga2-8	Ga2-9	Ga2-10	Ga2-11
ψ6 Aurigae (101.7),  τ Puppis (102.2), ψ7 Aurigae (102.4)	ψ8 Aurigae (103.2)	Alhena (103.8), ψ9 Aurigae (103.9)	Adara (104.8), ω Gemini (105.4)
'July 1 (182)	'2	'3	'4 (185)

Ca 180 * (181 - 172) = 1620 years earlier (than ca 1870) - or around 250 A.D. - Sirius would have risen heliacally at winter solstice. The proper motion of Sirius resists the precession and we therefore have to count with 180 years for each day (instead of the normal 72 years). North of the equator this event would have occurred at the summer solstice, possibly to be interpreted as a sign that the year now was turning around into the 'back side'.

Around 250 A.D. the midnight culmination of Cor Serpentis would presumably  have occurred at a different date than the heliacal rising of Sirius, but I have not searched for data regarding its proper motion.

I decide to see what more information Allen has regarding culmination dates. After flipping through his book and accumulating most of the facts this is the result:

The table supports my suggestion that Allen has the wrong date for the culmination of Cor Serpentis. Possibly he took the culmination date for Ras Alhague by mistake.

It is possible to perceive a contrast in length between the day differences on one hand for the stars which are rising heliacally early in the 1st half of the year (January - April) and on the other hand for the stars which are rising early in the 2nd half of the year (June - July). Presumably the explanation is that Earth moves quicker in its orbit close to perihelion (in January 4) than close to aphelion (in July 4). This has to be kept in mind when we speculate about the culmination dates for other stars than those listed in my table above.