500 TRANS. ST. LOUIS ACAD. SCIENCE. 



the day of his predecessor's death, and the planetary configura- 

 tions, the Apis periods, the Triacontaeteris, mentioned in the 

 premises (p. 405), place beyond question that the Canicular peri- 

 ods commenced in -2780, — 1320, + 140, and not, as Ptolemy, 

 Petavius, and Ideler imagined, one year earlier. 



2. Ptolemy counts from Caligula to Titus two years too much, 

 because he knew not that the consuls a.d. 47 and 78 were Extra- 

 ordinarii, as the inscriptions and coins have demonstrated (p. 422). 



S. In consequence of this gross blunder, Ptolemy referred the 

 death of Augustus to a.d. 14 instead of 16, for the latter year is 

 confirmed by many infallible arguments, both historical and as- 

 tronomical (p. 455). Hence the battle near Actium, fought 

 during the 14th year of Augustus, happened in _28, and not, as 

 Ptolemy stated, in -30, which result is confirmed by Josephus 

 (An. XV. 5, 2) ; for he refers this battle to the 7th year of Herod, 

 who reigned from Sept. nth in —35, as we have seen (p. 454), 

 accordingly to _ 28. Moreover, since the reign of Augustus com- 

 menced with Caisar's death, three months prior to the Olympian 

 games, i.e., as a multitude of historical and mathematical develop- 

 ments have brought to light (p. 448), in -41, and not in -43, it is 

 evident that Ptolemy must have likewise antedated by two years 

 all events of Greek history connected with the Olympiads ; for 

 the Olympian games were celebrated, and the archons, closely 

 connected with the Olympiads, ruled two years later than Ptole- 

 my conjectured. Hence Ptolemy's eclipses, referred to the 

 archons Phanostratus and Evander, and to the Calippian periods, 

 must of necessity be postdated by two years. 



4. According to the Olympian games, the Apis periods, and 

 several eclipses, Alexander the Great died in -320, and yet Ptol- 

 emy's Historical Canon refers this event to -323, three years too 

 early. On this occasion even Ideler, the boldest advocate of 

 Ptolemy's chronology, concedes Ptolemy's statements to be some- 

 times wrong. Alexander's death in -320 is, in the first place, 

 confirmed by the renewal of an Apis period in -320; for Diodor 

 (i. 76, 84. p. 25 B.) and the Almagest itself (Ideler Chron. i. 182) 

 report that one year after Alexander's death, i.e. in the first year 

 of Ptolemaius Lagi (Soter I.) the Apis period was renewed, which 

 was also the case in -320 (p. 405). Further, Diodor (xviii. S) 

 and Dinarch (D^m. 81, p. 108, 28) bear witness that Alexander 



