1877.] history of Astronomy. 71 



star in tlie 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. RA. and 33" 30' North Dec. On Feb. 20 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 5.53 p.m., a relative position of the two luminaries 

 which fairly answers to the words of the poet. And while investi- 

 gating the position of the star, Mr 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 24, and would set June 1 at 3.30 a.m., July 1 at 1.32 

 a.m., Aug. 1 at 1 1.30 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 will 

 employ the same formulae will find that the results given are 

 approximately accurate. It is probable that theoretical astro- 

 nomers 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 formulae employed are those given in Loomis's Astronomy, 

 and are the following: 



(1) To reduce E.A. and Dec. to Long. {L) and Lat. {I). 



Let J. be a subsidiary angle : w the inclination of the ecliptic, 

 tan A = sin R.A. . cot Dec, 

 tan L = sin (A + o)) tan E,.A, cosec A, 

 tan Z —sinLcot (A + Q)). 



(2) To perform the reverse process: 



V being the new Long, due to change from precession, A^ the 

 subsiding angle, 



tan A' = sin D cot I, 



tan R. A. = sin (J.^ — &>) tan V cosec J.\ 



tan Dec. = sin R A. cot {A^ — co). 



