or CALIPPUS (Κάλλιππος or Κάλιππος), an astronomer of Cyzicus. He was a disciple of one of Eudoxus' friends, and followed him to Athens, where he became acquainted
575
with Aristotle (who mentions him Metaph. 11.8), and assisted that philosopher in rectifying and completing the discoveries of Eudoxus. (Simplic. in lib. II. de Coel p. 120a.) His observations are frequently referred to by Geminus and Ptolemy in their meteorological calendars (see Geminus, Elem. Astron. cap. 16, in Petav. Uranolog. p. 64, &c. and Ptol φάσεις ἀπλανῶν ἀστέρων καὶ συναγωγὴ ἐπισημασιῶν, ibid. p. 71, &c.), and were probably made at Cyzicus, since Ptolemy (ad fin.) says, that Callippus observed at the Hellespont. Such calendars were fixed in public places, for common use, and hence called παραπήγματα: they record the times of the different risings and settings of the fixed stars, with the ἐπισημασίαι, or principal changes in the weather supposed to be connected with them, as deduced from the observations of various astronomers. Callippus invented the period or cycle of 76 years, called after him the Callippic. Several attempts had been previously made to discover intervals of time of moderate length, which should be expressible in whole numbers by means of each of the three natural units of time--the solar year, the lunar month, and the solar day: and, in particular, Meton, about a century before, had observed the remarkable approximation to equality between 19 years and 235 months, and had introduced the celebrated cycle of 19 years, which he also assumed to contain 6940 days. This would make the year = 365 5/19 days; and, therefore, Callippus, observing that the difference between this and the more correct value 365 1/4 was 5/19 - 5/20 = 1/4 x 19 = 1/76, proposed to quadruple the Metonic period, and then subtract one day. He supposed, that 76 years = 940 months = 27759 days; both of which suppositions are considerably nearer the truth than Meton's. (Geminus, El. Ast. cap. 6, Uranolog. p. 37.) If we take the mean values of the year and month, in days, to be 365.2422414 and 29.5305887215 respectively, then 76 years =27758d 9h 50m 54s, and 940 months = 27758d 18h 4m 54s nearly; but these numbers would not be strictly accurate in the time of Callippus.
The Callippic period seems to have been generally adopted by astronomers in assigning the dates of their observations; and the frequent use which Ptolemy makes of it enables us to fix the epoch of the beginning of the first period with considerable certainty. It must have begun near the time of the summer solstice, since Ptolemy refers to an observation of that solstice made at the end of the 50th year (τῷν́ ἕτελ λήγοντι) of the first period (μεγ. σύνταξ. 3.2, vol. i. p. 163, ed. Halma); and out of a number of other observations recorded by the same writer, all but two, according to Ideler, indicate the year B. C. 330, whilst four of them require the evening of June 28 for the epoch in question. It is not certain at what time the period came into civil use; it would naturally be employed not to supersede, but to correct from time to time, the Metonic reckoning. The inaccuracy of the latter must have become quite sensible in B. C. 330; and it is evident, from the praise which Diodorus (12.36) bestows upon it, that it could not have remained uncorrected down to his time. (Ideler, Hist. Untersuch. über die Astron. Beobachtungen der Alten, Berlin, 1806, p. 214, &c., Handbuch der Technischen Chronologie, Berlin, 1825, vol. i. p. 344, &c.; Petavius, Doctrin. Temp. 2.16; Scaliger, De Emend. Temp. lib. ii.; Delambre, Hist. de l'Astron. Ancienne, vol. i. p. 200.)
[W.F.D]