SEYFFARTH— ON THE THEORY OF THE MOON S MOTIONS. 505 



to this class of opponents Scaliger, Dodrjuell, Des Vignoles, and 

 Freret, who put Ptolemy's newyears clays in the ist year of each 

 Babylonian king, are to be numbered. 



The real dates of the Eclipses in the Almagest. 



11, 12 & 13. Ptolemy (Aim. iv. 10, p. 279) says that in the 54th 

 and 55th years of the second Calippian period three lunar eclipses 

 happened, of which the latter two belonged to the same Calippian 

 year (zw auzw us irei). These eclipses the Almagest refers to 



— 200, Sept. 22d; to — 199, Mar. 19th, and to — 199, Sept. 12th. 

 Since, however, the Greek year commenced with the ist day of 

 HecatombaBon, June 2d (p. 40S), it is evident that Ptolemy's 

 eclipses in — 199, March 19th, and in — 199, Sept. 12th, refer to 

 two different Calippian years, and not to the same Greek year 

 (auzpv eroc) : for the eclipse in —199, March 19th, belonged to 

 the 53d year of the Calippian period, whilst the eclipse on Sept. 

 1 2th in —199 appertained to the 54th year of the same period. 

 Moreover, the first Calippian period was, as is well known, a 

 continuation of Meton's lunar cyclus of 19 years, which had com- 

 menced not in — 429, as Ptolemy imagined, but in — 428, with 

 May 15th (p. 40S), viz. during Apseudes' archonship ; and the 

 archons of the times of Calippus ruled, in consequence of the lost 

 year between Thucydides and Xenophon (p. 469), two years later 

 than Ptolemy calculated. Consequently, the aforesaid 3 eclipses 

 are to be postdated as follows : — The first of them happened in 



— 199, Sept. 12, 13I-1. 30m., 13 3 W., which year belonged to the 

 54th year of the Calippian period ; the 2d refers to — 197, July 

 23d, nh. 45m., a n°E. ; the 3d to— 196, Jan. 16th, 511.30m., 

 y 5°E. According to our Table (p. 429), the longitudes of the 

 Nodes were at that time nearly 4 31 ' shorter, and the oppositions 

 happened about 3 hours later. Indeed, the latter eclipses apper- 

 tained, as Ptolemy's ancient historiographer said, to the same 

 Greek year, because July 23d in — 197 and Jan. 16th in — 196 

 belonged to the very same Calippian year. Hence these three 

 eclipses alone demonstrate that Ptolemy's chronology of ancient 

 eclipses is wrong. 



15. Ptolemy (Aim. vi. 5, p. 390) mentions a lunar eclipse 

 observed in Rhodus during the 37th year of the third Calippian 

 period, which he referred to — 140, Tan. 27th, 9I1., 13 n°W., 



