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visible to the naked eye. These then ought always to have been, and for some time always were, excluded from Rural Calendars intended for the use of practical men. We find, however, from the fragments of Calippus, which have been preserved in the parapegma of Geminus, when verified by computation', that this astronomer had substituted the true risings and settings for the apparent ones which were marked in tables of Meton, Eudoxus, and Euctemon. Hence great caution would be indispensable. If the rising of a star was named, it would be necessary to state whether the true or apparent rising was indicated, and whether it was the morning or evening rising, and to proceed in like manner for the setting of a star. Some little attention is paid to these points by Columella 2 and Pliny, but in Virgil, and especially in Ovid, everything is vague and unsatisfactory, risings and settings of all descriptions are thrown together at random without a clue to guide us, and blunders of the grossest description are so thickly interspersed that it often becomes difficult to trace the error to its source, or to discover what the author could have intended. We shall substantiate these charges by a few examples.

There is a cluster of stars in the constellation Taurus, called 'Pleiades' by the Greeks, and 'Vergiliae' by the Latins. The appearance and disappearance of these served from a very remote age to mark the approach of summer and the beginning of winter. Let us first note down the exact period of their risings and settings calculated for the latitude of Rome and the year 44 B.C.

'Ortus Matutinus verus,' 16 April.
'Ortus Vespertinus verus,' 18 Oct.
'Occasus Matutinus verus,' 29 Oct.

'Occasus Vespertinus verus,' 26 April.

'Ortus Mat. apparens s. heliacus,' 28 May.

'Ortus Vesp. appar.

'Occasus Mat. appar.

25 Sept.

'9 Nov.

'Occasus Vesp. appar. s. heliacus,' 8 April.

Now look to Ovid. After describing a festival celebrated on the 1st of April, he continues, Fast. 4. 165

1 They are not distinguished from the others in the parapegma itself. 2 Thus we find in Columella such expressions as the following, which are to a certain extent guarded: 'VI. Non. Mai. Sucula cum sole exoritur.' 'XIII. XII. Kal. Nov. solis exortu Vergiliae incipiunt occidere,' &c.

'Nox ubi transierit, caelumque rubescere primo
Coeperit, et tactae rore querentur aves;
Semustamque facem vigilata nocte viator
Ponet, et ad solitum rusticus ibit opus:
Pleiades incipiunt humeros relevare paternos
Quae septem dici, sex tamen esse, solent.'

These lines refer to the setting of the Pleiades in the morning twilight. According to the legend the Pleiades were the daughters of Atlas, who supported the heavens on his shoulders, and hence, when they disappeared from the sky, might be said to remove a portion of their father's load, 'humeros relevare paternos.' The meaning in plain prose therefore is, 'The Pleiades set in the morning on the 2nd of April.' But it will be seen from the table given above that the Pleiades really set in the morning on the 9th of November. They set in the evening, however, on the 8th of April, which comes tolerably near to the date fixed, and is clearly the phenomenon the poet intended to record, but he blundered between the morning setting and the evening setting, which are six months apart.

Again, in Fast. 5. 599

'Pleiades adspicies omnes, totumque sororum
Agmen, ubi ante Idus nox erit una super.
Tum mihi non dubiis auctoribus incipit aestas:
Et tepidi finem tempora veris habent.'

The meaning here, although not very clearly expressed, is, 'The Pleiades rise in the morning (heliacally) on the 14th of May, marking the end of spring and the beginning of summer.'

But it will be seen by the table, that at the time when Ovid wrote, the Pleiades did not rise heliacally at Rome until the 28th of May, but they did rise heliacally at Athens on the 16th, in the age of Meton. Hence this notice was manifestly copied from a Grecian Calendar computed for the fifth century B. C.

We have already (p. 230) adverted to an error with regard to the rising of Sirius, which Ovid assigns to the last of April, the very day on which, according to Columella, who is here perfectly correct, it sets heliacally.

In the same passage (see Extracts, p. 42) we are told that the constellation 'Aries' sets on the 30th of April. Here again we have a mistake. The 'Occasus vespertinus apparens' must be indicated, but it is placed more than five

weeks too late, since it actually took place on the 20th of March, even the 'Occasus matutinus verus' was on the 5th of April.

We have seen, p. 229, that Ovid fixes upon V. Id. Feb. (9th of February) as the commencement of spring, and on VII. Kal. Mai. (25th of April) as the middle point.

He departs here from the arrangement of Caesar, who divided the year into eight portions, according to the follow

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The commencement of spring was marked by no celestial phenomenon, but announced by the soft breathings of Favonius; the beginning of summer was connected with the morning rising of the Pleiades, which however took place, the true on the 16th of April, the apparent on the 28th of May. The true evening setting of the Lyre was on the 14th of August, the apparent on the 24th. The true morning setting of the Pleiades was on the 29th of October, the apparent on the 9th of November.

It may be a matter of surprise that Julius Caesar did not begin his year with the winter solstice, which happened 46 B. C. at Rome, on the 24th of December, oh 9' A. M. He was probably induced to neglect this natural arrangement by a superstitious desire to make the beginning of the reformed calendar correspond with a New Moon. According to the calculation of Ideler, the mean New Moon fell upon the 1st of January, B. C. 45, at sixteen minutes past six in the evening, the true New Moon on the 2nd of January, at thirty-four minutes past one in the morning.

It seems highly probable that Macrobius alludes to this fact, when he observes,

'Annum civilem Caesar habitis ad lunam dimensionibus constitutum edicto palam posito publicavit ;'

for in no other way could the Julian Year be said to have any connection with the course of the Moon.

1 Cp. Varro R. R. 1. 28, Pliny H. N. 18. 25, Columella, R. R. 9. 14.

In this Appendix the excellent work of Ideler, entitled 'Handbuch der mathematischen und technischen Chronologie,' has been closely followed. The principal authorities with regard to the sidereal astronomy of the ancients are— Joannis F. Pfaff, 'Commentatio de Ortibus et Occasibus siderum apud auctores classicos commemoratos,' Gotting. 1786; a paper by Ideler, 'Ueber den astronomischen Theil der Fasti des Ovid,' in the Berlin Transactions for 1822, 1823; and Symbolae Observationum in Ovidii Fastos,' by F. H. Gesenius, printed at Altona in 1806.

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