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We thus ascertain the position of the star in the time of Hesiod and in that of Ovid, to have been: for that of Hesiod, R.A. 12 h. 5 m. 42 s. N. Dec. 33° 29′ 25′′; for that of Ovid, R.A. 12 h. 40 m. 14 s. N. Dec. 29° 34′ 24′′.

The next step is to compute the hour angle of the star, first for its true rising in the Latitude of Boeotia, about 38 N., secondly for its true setting in the Latitude of Rome, about 42° N., and also the Local mean time at the same moment.

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The Sun rises at Rome on May 26 about 4.35 a.m., on June 6 about 4.30 a.m. According to Ovid, the star's morning setting was first visible on May 26, or, as he states later on, on June 6. If we consider him to have consulted two different authorities, one of which gave the true, the other the visible setting of the star, no reasonable exception can be taken to the value of his statements. The expressions the poet uses point to the time when the star's setting first occurred before sunrise; this for

theoretical astronomers would actually have taken place about May 26, and for practical observers about June 6, the star setting on the first-named day at 4.28 a.m., on the second at 3.45 a.m.

Again in the Fasti of Ovid, 1. 654, II. 76, we are told that Lyra, or Vega, was last visible when setting in the evening, about Feb. 1. "Ubi est hodie, quae Lyra fulsit heri?" Employing again the method of calculation indicated above, we find on that day at Rome the Sun would set about 5.10 p.m., and Lyra about 5.44. As the days at that time of the year are rapidly lengthening, while the star would set earlier every day, it is obvious that the date assigned for the last appearance of the latter is nearly exact.

Ovid makes however a remark about Capella which seems really erroneous. He says (Fasti v. 113) that she rises on May 1st, i.e. is then first visible in the morning. But at the time when he lived she would, according to the mode of computation used in the previous examples, have risen about 3.0 a.m., while the Sun would not have risen until after 5.0. We have a similar apparent mistake in Pliny and Columella, nearly contemporaries, who flourished in the latter half of the first century A.D. They fix Arcturus' rising for the 23rd or 21st of February; whereas on those days the Sun would set at Rome about 5.35 p.m., while the star would not pass the horizon in their time before 6.30 p.m. They seem to have copied from Hesiod without any thought.1

The late Mr. F. Baily, in his edition of Ancient Star Catalogues, published in Vol. XIII. of the Memoirs of the Royal Ast. Society, does not seem to have actually compared the positions there given to any of the principal stars with those which in the present day we must suppose them to have theņ occupied, though he refers to Delambre (Hist. Ast. Anc. Vol. II.), who gives tabulated results on this point from his own calculations. As however the present rate of change in the obliquity of the ecliptic would have made it in the time of Eratosthenes (250 B.C.) about 23° 43', whereas that astronomer fixed it roughly at 23° 51′, it is to be hoped that, making allowance

1 In the time of Ovid the position of Vega must have been about R. A. 17 h. 29 m., Dec. 38° 23′ N.; that of Capella, R.A. 2 h. 55 m., Dec. 40° 35′ N.

for inaccuracies in the MSS., such a process of verification may be attempted with sonie prospect of success; and possibly some explanation found of Ptolemy's idea, that in his time (A.D. 140) the amount of annual precession was only 36". It is curious that the error of 15' in the latitude of Alexandria, which Delambre imputes to the Greeks, answers nearly exactly to the obliquity of 23° 43', to which we are brought by its present known rate of change.

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APPENDIX B.

(COMMUNICATED.)

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On the size of the cart-wheel in Hesiod, Works and Days,' 1. 426.

THE as is the arc A C B.

10 PALMS=336

B

Measured along the rim ACB its length will be

36 inches x 3∙14 ÷ 4 = 28 inches. If we measure from end to end along A B we get for the length

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√2.182 inches 18/2 inches = 18 x 1.414 = 25 inches.

If we took the diameter a little less than 3 feet, say 32 inches instead of 36, the length A B from end to end will be

16 x 1.414 = 22 inches

the required length; since Tpισπílaμоv is about 22 inches. Hence probably the avis was measured straight from one end to the other, and not along the curved rim.

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