SEYFFAKTH— ON THE THEORY OF THE MOON S MOTIONS. 4O9 



As the ancient Romans commenced the months with the ap- 

 pearance of the crescent subsequent to the astronomical new- 

 moon, and, accordingly, each day with sunset, 6 hours prior to 

 the Julian day. beginning at midnight ; it is natural that our Me- 

 nologium commences, e.g. Pyanepsion with Sept. i, and so in all 

 other cases. In order to harmonize the Greek days, likewise 

 beginning with sunset, with our civil days, we have the Julian 

 dates in the preceding table diminished by a unit. The Spartan 

 months began, as we learn from Thucydides (v. 19, iv. 11S ; Plut. 

 Nic. 28). two days later. 



The leap-years of the Greeks were, as Cenborin (De d. n. iS) 

 reports, the same in which the Olympian games were celebrated. 

 In such years, the first three months of the Greek year com- 

 menced with the following day of the Julian months, as specified 

 in the Table. 



By means of this Solar Calendar of the Greeks, e.g. the follow- 

 ing events of Greek history are incontrovertibly fixed ; first, the 

 years in which Archon Apseudes ruled. Diodor (xii. 36) reports 

 that, during the archonship of Apseudes, Meton commenced his 

 Lunar year and Lunar cyclus of 19 years with the 13th day of Sci- 

 rophorion, that is, as our Table shows, with the 15th day of May. 

 Julian stvle. In — 42S the new moon happened on May 13th 

 about 7 o'clock after noon, and consequently the crescent became 

 visible on May 15th after sunset. Since then no new moon coin- 

 cides twice with May 13th during a period of 19 years; the 

 archonship of Apseudes, extending from July in — 429 to July in 

 — 42S, is mathematically fixed. Petavius ard his adherents put 

 Apseudes earlier by one year, but erroneously. By the way, this 

 fact demonstrates that ldeler's exposition of Meton's Lunar Cal- 

 endar is wrong, because he referred Apseudes to a wrong year. 

 This result, moreover, is confirmed by Ptolemy (Aim. iii. 2, p. 

 162, 163. II.), who reports that, during the same year of Apseu- 

 des, Meton and Euctemon found the summer solstice coinciding 

 with sunrise on June 27 (Phamenoth 21st), because the summer 

 solstice happened, according to our Solar Tables, on the same 

 day at 5 o'clock a.m , during the year — 42S 



These two facts involve a result of great importance. The Pelo- 

 ponnesian war commenced, on the part of the Athenians, with 

 their naval expedition against Sparta, which took place in the 



