DR. PEARSON ON SOME POINTS IN THE HISTORY OF ASTRONOMY. Dr. PEARSON read a paper on some passages from the classics, one from Hesiod, and three from Ovid, which he considered might be fairly tested by Modern Astronomy. Admitting, as is often averred, that many allusions of this nature in the classics are either inaccurate or wrong, some he thought might still be found to have the stamp of truth about them. On the one hand, it is certain that in Greece the phenomena of the heavens had from the earliest times many thoughtful and attentive observers. In the time of Hesiod, which may be perhaps best assumed to have been about the middle of the eighth century B.C., the rising or setting of the stars seems to have been the recognised guide in distinguishing the successive seasons of the year: the Metonic cycle, now known under the title of the Golden Numbers, was discovered as early as the time of Socrates; and the ordinary authorities, such as the article Astronomia in the Dictionary of Antiquities, show how much interest the subject attracted down to the period of Ptolemy and Hipparchus. On the other hand, it must be allowed that the references we can actually find in classical authors are often vague or rhetorical; and that, probably excepting Hesiod, those whose writings we refer to wrote on second-hand authority. It may be therefore fully admitted that the question requires to be investigated with much caution. The first reference was to Hesiod (Op. et Di. 564-7), as being the most distinct passage in that author's writing, although there are others which deserve consideration as data in Practical Astronomy: these lines, Dr. Pearson said, he thought deserved the best attention, as the whole character of the work in which they occur is most genuine and natural, nor is it easy to study it without the impression that the author was himself dependent, as a practical agriculturist, on the facts that he recites. The passage itself runs thus: Εἶτ ̓ ἂν δ ̓ ἑξήκοντα μετὰ τροπὰς ήελίοιο Πρῶτον παμφαίνων ἐπιτέλλεται ἀκροκνέφαιος. From this we learn that, sixty days after the winter solstice, Arcturus rose during twilight in the evening. Arcturus' position for Jan. 1, 1875, is given in the Nautical Almanac as R.A. 14 h. 9 m. 55 s., Dec. 19° 50' 22" N. If we convert these data into Latitude and Longitude, reduce the star's longitude by about 36° 10′, which at the annual rate of 50′′ 1 for precession will bring us to about 730 B.C., and reconvert the star's new longitude and latitude into R.A. and Dec., we shall find that the position of the star in the early part of the eighth century B.C., which may be fairly taken to represent the era of Hesiod, was something about 12 h. 6 m. R.A. and 33° 30' North Dec. On Feb. 19 at that time, in Lat. 38° N., about the situation of Ascra and Helicon, the Sun would set about 5.40 p.m., while Arcturus would rise above the horizon about 5.57 p.m., a relative position of the two luminaries which fairly answers to the words of the poet. And while investigating the position of the star, Dr. Pearson said he found he had unintentionally explained, as he believed, the epithet "late-setting," applied to Arcturus in Hom. Od. E' 272. Arcturus at that epoch would first have been visible at the time of its morning setting about May 15, and would set June 1 at 3.30 a.m., July 1 at 1.32 a.m., Aug. 1 at 11.30 p.m.* During the early summer therefore, when the Greek seaman or agriculturist was often spending the nights out of doors, the late time at which this brilliant star would set must have been quite unmistakeable, and Ulysses is naturally described as keeping his eye fixed on it, as carefully as he kept the Bear on his left, to determine his voyage eastwards. In order to satisfy criticism, the series of computations by which this result is obtained are given the computations will be omitted in two of the subsequent examples, but any one who * A star's rising or setting is about 4 m. earlier each successive day. will employ the same formula will find that the results given are approximately accurate. It is probable that theoretical astronomers may be able to suggest better or more precise methods of obtaining the required results, but those employed have the advantage of being quite simple, and are anyhow approximately correct. The calculation of Arcturus' place for the era of Ovid is also given, as it naturally accompanies that for the time of Hesiod. The formulæ employed are those given in Loomis's Astronomy, and are the following: (1) To reduce R.A. and Dec. to Long. (L) and Lat. (1). Let A be a subsidiary angle: w the inclination of the ecliptic, tan Asin R.A..cot Dec., tan L = sin (A + w) tan R.A. cosec A, tan sin L cot (A + w). (2) To perform the reverse process : L' being the new Long. due to change from precession, A' the subsidiary angle, We apply these formulæ to find the place of Arcturus about the era of Hesiod. Taking the mean position of the star as given above: then 10.1726987.(-) =tan 303° 53′ 49′′ tan A, 9.6161790 (+) = tan 202° 27′ 5′′ = tan L. 9.7760393 (+) = tan 30° 50′ 28" tan l. The next step is, taking the amount of annual precession, it is owned somewhat boldly, at 50" 1, to estimate its amount first for 1900 years to bring it to 27 B.C., about the era of Ovid, and again for 700 years, to bring it to that of Hesiod. The first amount is about 26° 26' 30", and the second about 9° 44′ 30′′, which will bring us to 176° 0' 35" as the Long. in the time of Ovid, and 166° 16' 5" in that of Hesiod. As it is certain that the inclination of the ecliptic has not changed more than 20' to 30', within the periods in question, we may safely deal with the Latitude of the star as stationary in the interval. Consequently, L, L' being the Longitude of the star in the time of Hesiod and of Ovid: its latitude in both: L 166° 16' 5", L' = 176° 0′ 35′′, l = 30° 50′ 28′′, and on these data we proceed to compute its R.A. and Dec., and from these the times of the star's rising and setting at these two epochs. = 8.8422274(+) .10·2239607 (+) tan a' ......... 9.0661881 (+) 186° 38′ 341" 23 45 0 (a' - w) 162 53 34 ... sin (a'-w) tan L' 9∙4685814(+) 8.8435834(-) cosec a'....10.9367372 (-) tan R.A. ...... 9.2489020 (+) R.A. 12 h. 40 m. 14 s. sin R.A. ...... cot (aw)...10·5117660 (−) tan Dec. ...... N. Dec. 9.2421704(-) 9.7539364(+) 29° 34′ 24′′. |