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Comment: In Euktemon’s time, on May 7 when η Tau (mag. 2.86) was rising, the sun was
9° 29′ below the horizon. This is technically not ‘visible’—with a flat horizon first visibility
would occur about May 23, with the sun 16° below the horizon. If we allow an extinction
angle of ‘Thom’s Rule + 1’, as suggested by Mann (Mann, 2011: 252–253, for Thom’s
Rule, see Thom, 1967: 15; see also Ruggles, 1999: 52), then we would have η Tau (mag.
2.86) at an altitude of about +4° and the sun at –16° below the horizon, and this occurred
around May 29. However, given the mountainous nature of much of the Greek landscape, I
do not think that we need worry too much about allowing for an extinction angle, as the
high hills tend to obviate the need (cf. Ruggles, 1999: 230 n. 23). So the actual date of heliacal rising was considerably later than the date provided by the parapegma. But the parapegma’s date of May 7 puts the sun 52 (equinoctial) minutes short of rising, which
practically suits Pliny’s criterion.
Day 31 (= May 25), according to Euktemon Eagle rises in the evening.
Comment: This refers to the evening rising of Aquila. On May 25 when α Aql was rising,
the sun was 7°10′ below the horizon. This is ‘visible’—with a flat horizon last visibility
would occur on May 25, with the sun 7° below the horizon, so long as we do not include an
extinction angle. Adding the extinction angle, in this case of about 2°, shifts the date to
around May 27. As it is, the date of May 25 and α Aql on the horizon would have the sun
41 (equinoctial) minutes after setting, which also suits Pliny’s criterion.
Day 32 (= May 26), according to Euktemon Arktouros sets at dawn; there is sign of
weather …. Hyades rise at dawn; there is sign of weather.
Comment: This refers to the morning setting of Arcturus, and the morning rising of
the Hyades.
(a) On May 26 when α Boo (Arcturus) was setting, the sun was 2°08′ below the horizon.
This is technically not ‘visible’—with a flat horizon first visibility would occur about 4
June, with the sun 7° below the horizon and no extinction angle allowed for. Adding an
extinction angle of about 2° would shift the date to around May 30. A date of 26 May puts
the sun only 12 (equinoctial) minutes short of rising, which does not suit Pliny’s criterion.
Technically, then, this counts as a true and therefore invisible morning setting. Morning
settings are characteristically not this parapegma’s forte in terms of accuracy, whereas
morning risings and evenings settings are better. I am not sure what this tells us, except that
a star phase nearer the sun seems easier to plot than one at the opposite horizon.
(b) At dawn on May 26 when α Tau (the prime star in the Hyades) was on the horizon, the
sun was 6°38′ below the horizon. This is technically not ‘visible’—with a flat horizon first
visibility would occur about June 4, with the sun 11° below the horizon. Including an
extinction angle of about 2° delays the first rising even further to about June 7. But a date
of May 26 puts the sun 38 (equinoctial) minutes short of rising, which practically suits
Pliny’s criterion.
The short analysis of a very small data set here might suggest that the star risings
and settings were not physically observed, but calculated (see Hannah, 2020b, for
an analysis of another part of the parapegma producing similar results).
The Stars in Ancient Greece
Comment: In Euktemon’s time, on May 7 when η Tau (mag. 2.86) was rising, the sun was
9° 29′ below the horizon. This is technically not ‘visible’—with a flat horizon first visibility
would occur about May 23, with the sun 16° below the horizon. If we allow an extinction
angle of ‘Thom’s Rule + 1’, as suggested by Mann (Mann, 2011: 252–253, for Thom’s
Rule, see Thom, 1967: 15; see also Ruggles, 1999: 52), then we would have η Tau (mag.
2.86) at an altitude of about +4° and the sun at –16° below the horizon, and this occurred
around May 29. However, given the mountainous nature of much of the Greek landscape, I
do not think that we need worry too much about allowing for an extinction angle, as the
high hills tend to obviate the need (cf. Ruggles, 1999: 230 n. 23). So the actual date of heliacal rising was considerably later than the date provided by the parapegma. But the parapegma’s date of May 7 puts the sun 52 (equinoctial) minutes short of rising, which
practically suits Pliny’s criterion.
Day 31 (= May 25), according to Euktemon Eagle rises in the evening.
Comment: This refers to the evening rising of Aquila. On May 25 when α Aql was rising,
the sun was 7°10′ below the horizon. This is ‘visible’—with a flat horizon last visibility
would occur on May 25, with the sun 7° below the horizon, so long as we do not include an
extinction angle. Adding the extinction angle, in this case of about 2°, shifts the date to
around May 27. As it is, the date of May 25 and α Aql on the horizon would have the sun
41 (equinoctial) minutes after setting, which also suits Pliny’s criterion.
Day 32 (= May 26), according to Euktemon Arktouros sets at dawn; there is sign of
weather …. Hyades rise at dawn; there is sign of weather.
Comment: This refers to the morning setting of Arcturus, and the morning rising of
the Hyades.
(a) On May 26 when α Boo (Arcturus) was setting, the sun was 2°08′ below the horizon.
This is technically not ‘visible’—with a flat horizon first visibility would occur about 4
June, with the sun 7° below the horizon and no extinction angle allowed for. Adding an
extinction angle of about 2° would shift the date to around May 30. A date of 26 May puts
the sun only 12 (equinoctial) minutes short of rising, which does not suit Pliny’s criterion.
Technically, then, this counts as a true and therefore invisible morning setting. Morning
settings are characteristically not this parapegma’s forte in terms of accuracy, whereas
morning risings and evenings settings are better. I am not sure what this tells us, except that
a star phase nearer the sun seems easier to plot than one at the opposite horizon.
(b) At dawn on May 26 when α Tau (the prime star in the Hyades) was on the horizon, the
sun was 6°38′ below the horizon. This is technically not ‘visible’—with a flat horizon first
visibility would occur about June 4, with the sun 11° below the horizon. Including an
extinction angle of about 2° delays the first rising even further to about June 7. But a date
of May 26 puts the sun 38 (equinoctial) minutes short of rising, which practically suits
Pliny’s criterion.
The short analysis of a very small data set here might suggest that the star risings
and settings were not physically observed, but calculated (see Hannah, 2020b, for
an analysis of another part of the parapegma producing similar results).
The Stars in Ancient Greece